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cause of the observed effect. ## 2 Crustal Superfluid: An Overview The spin-down rate \(\dot{\Omega}_{\rm c}\) of the crust of a neutron star, with a moment of inertia \(I_{\rm c}\), obeys (Baym et al. 1969b) \[I_{\rm c}\dot{\Omega}_{\rm c}=N_{\rm em}-\Sigma I_{\rm i}\dot{ \Omega}_{\rm i}\] (1) where \(N_{\rm em}\) is the negative electromagnetic torque on the star, and \(\dot{\Omega}_{\rm i}\) and \(I_{\rm i}\) denote the rate of change of rotation frequency and the moment of inertia of each of the separate components, respectively, which are summed over. Steady state implies \(\dot{\Omega}_{\rm i}=\dot{\Omega}_{\rm c}=\dot{\Omega}\equiv{N_{\rm em}\over I}\), for all \(i\), where \(I=I_{\rm c}+\Sigma I_{\rm i}\) is the total moment of inertia of the star. Different models for the post-glitch recovery, and in particular the model of vortex-creep, invoke a decoupling-recoupling of a superfluid component in the _crust_ of neutron stars (Alpar et al. 1984; Jones 1991a; Epstein, Link & Baym 1992). The rest of the star including the core (superfluid) is assumed in these models to be rotationally coupled to the non-superfluid constituents of the crust, on timescales much shorter than that resolved in a glitch. The role of any superfluid component of a neutron star in its post-glitch behavior is understood as follows. Spinning down (up) of a superfluid at a given rate is associated with a corresponding rate of outward (inward) radial motion of its vortices. If vortices are subject to pinning, as is assumed for the superfluid in the crust of a neutron star, a spin-down (up) would require unpinning of the vortices. This may be achieved under the influence of a Magnus force \(\vec{F}_{\rm M}\) acting on the vortices, which is given, per unit length, as \[\vec{F}_{\rm M} = -\rho_{\rm s}\vec{\kappa}\times(\vec{v}_{\rm s}-\vec{v}_{\rm L})\] (2) where \(\rho_{\rm s}\) is the superfluid density, \(\vec{\kappa}\) is the vorticity of the vortex line directed along the rotation axis (its magnitude \(\kappa={h\over 2m_{\rm n}}\) for the neutron superfluid, where \(m_{\rm n}\) is the mass of a neutron), and \(\vec{v_{\rm s}}\) and \(\vec{v_{\rm L}}\) are the local superfluid and vortex-line velocities. Thus, if a lag \(\omega\equiv\Omega_{\rm s}-\Omega_{\rm c}\) exist between the rotation frequency \(\Omega_{\rm s}\) of the superfluid and that of the vortices (pinned and co-rotating with the crust) a radially directed Magnus force \((F_{\rm M})_{r}=\rho_{\rm s}\kappa r\omega\) would act on the vortices, where \(r\) is the distance from the rotation axis, and \(\omega>0\) corresponds to an outward directed \((F_{\rm M})_{r}\), vice-versa. The crust-superfluid may therefore follow the steady-state spin-down of the star by maintaining a critical lag \(\omega_{\rm crit}\) which will enables the vortices to overcome the pinning barriers. The critical lag is accordingly defined through the balancing \((F_{\rm M})_{r}\) with the pinning forces. At a glitch a sudden increase in \(\Omega_{\rm c}\) would result in \(\omega<\omega_{\rm crit}\), hence the superfluid becomes decoupled and could no longer follow the spinning down of the star (ie. its container). If, as is suggested , the glitch is due to a sudden outward release of some of the pinned vortices the associated decrease in \(\Omega_{\rm s}\) would also add to the decrease in \(\omega\), in the same regions. Therefore a fractional increase \({\Delta\dot{\Omega}_{\rm c}\over\dot{\Omega}_{\rm c}}\) same as the fractional moment of inertia of the decoupled superfluid would be expected. This situation will however persist only till \(\omega=\omega_{\rm crit}\) is restored again (due to the spinning down of the crust) and the superfluid re-couples, as illustrated by \(\Omega_{\rm s}\) and \(\Omega_{\rm c}\) curves in Fig. 1. The vortex creep model suggests (Alpar et al 1984) further that a superfluid spin-down may be achieved even while \(\omega<\omega_{\rm crit}\), due to the creeping of the vortices via their thermally activated and/or quantum tunnelling movements. A superfluid spin-down with a steady-state value of \(\omega<\omega_{\rm crit}\), and also a post-glitch smooth gradual turn over to the complete re-coupling for each superfluid layer is thus predicted in this model. It may be however noticed that the predicted gradual (exponential) recovery of the crustal spin frequency is not an effect peculiar to the creep process. It is mainly caused due to the assumed varying amplitude of the glitch-induced jump in \(\Omega_{\rm s}\) in the different layers of the superfluid (corresponding to their assumed varying critical lag values), which are thus re-coupled at various times. A similar behavior should be also expected even in the absence of any creeping, given the same series of the superfluid layers. The induced \(\Delta\dot{\Omega}_{\rm c}\over\dot{\Omega}_{\rm c}\) during a superfluid decoupling phase according to the creep model would be indeed the same as (or slightly smaller than) otherwise. ## 3 Observational Constraint The more recent glitches observed in Vela, and one in PSR 0355+54, have shown values of \[{\Delta\dot{\Omega}_{\rm c}\over\dot{\Omega}_{\rm c}}>10\%\] (3)

for such cases when the value of the lag \(\omega>>\omega_{\rm crit}\) \[v_{r}=v_{0}\exp{[-\frac{E_{\rm p}}{{\rm k}T}\left(\frac{\omega_{ \rm crit}-\omega}{\omega_{\rm crit}}\right)]/\left\{\exp[-\frac{E_{\rm p}}{{ \rm k}T}\left(\frac{\omega_{\rm crit}-\omega}{\omega_{\rm crit}}\right)]+1 \right\}},\] (9) which amounts to \[v_{r}\sim v_{0},\] (10) where \(v_{r}\) is the vortex radial velocity, and \(v_{0}\sim 10^{7}\ {\rm cm}/{\rm s}\) corresponds to a spin-up (down) time scale \(\sim 0.1\) s. Indeed, laboratory experiments on superfluid Helium have also showed (Tsakadze & Tsakadze 1975; Alpar 1987; Tsakadze & Tsakadze 1980) that a pinned superfluid either spins up _along_ with its vessel, or it never does so during the subsequent spinning down of the vessel (for conditions corresponding to \(|\Omega_{\rm sp}-\Omega_{\rm L}|<\omega_{\rm sp}\)). The case **(b)**, on the other hand, is not in accord with the general pinning conditions assumed in the vortex creep model, and is not likely to be invoked in that context. Nevertheless, the superfluid spin-up in the crust of a neutron star, for such a case of free unpinned vortices, is again expected to occur over very short timescales. The longest timescale for the spin-up of the crust by freely moving vortices, due to nuclear scattering alone, has been estimated (Epstein et al. 1992) to be only \(\lesssim 5\) s, for the Vela pulsar. It is only natural that the conclusions of the above two cases are the same, as the pinned vortices should behave like the free ones, once the critical lag is exceeded. Therefore, and in either cases (**a** or **b**), the superfluid would be spun up within a period of _only few seconds_ to (at least) a frequency such that \(\Omega_{\rm sp}-\Omega_{\rm c}=-\omega_{\rm sp}\), while the observable jump in \(\Omega_{\rm c}\) takes place at the glitch (see Fig. 1b). It is noted that the steady-state lag \(\omega_{\rm sp}\) according to the vortex creep model, in the so-called non-linear regime, would be slightly smaller than the critical lag (though slightly larger in the absence of any creeping). The difference is however a tiny fraction of the critical lag (Alpar et al. 1984), and may therefore be neglected in the present discussion if a non-linear regime is assumed. In contrast, a "linear" regime is also invoked in the vortex creep model for which \(\omega_{\rm sp}<<\omega_{\rm cr}\). However, the above conclusion remains the same, even for this case, and a "rapid" superfluid spin-up is again expected until \(|\omega|\lesssim\omega_{\rm sp}\) is achieved! This is because, according to the creep model the spin-down (up) rate depends "exponentially" on the difference \((\omega-\omega_{\rm sp})\); see Eq. 28 in Alpar et al. (1984). Hence, a relaxation of the superfluid under the assumed conditions with \(\omega_{\rm cr}>|\omega|>\omega_{\rm sp}\) should again take place on a time scale much shorter than the observed effect over \(\tau_{\rm sp}\), even for the case of a linear regime. ## 5 Superfluid Spin-up Moreover, the suggested spin-up scenario of APC should be dismissed at once since the required torque on the superfluid, during \(\tau_{\rm sp}\), may not be realized at all, under the assumed conditions of (creeping of the) pinned vortices (see Fig. 1a). That is the pinned superfluid could not be spun _up_ by the crust (ie. its container) while the latter is spinning _down_. This is simply because a spinning down vessel (or even one with a stationary constant rotation rate) albeit rotating faster than its contained superfluid could not result in any further _spin up_ of the vortex lattice which is, by virtue of the assumed pinning, already _co-rotating_ with it! As is well-known, an inward radial motion of the vortices, associated with a spin-up of the superfluid, requires the presence of a corresponding forward azimuthal external force acting on the vortices. This is indeed a trivial fact, considering that any torque on the bulk superfluid has to be applied primarily on the vortices. However, no _forward_ azimuthal force (via scattering processes between the constituents particles of the vortex-cores and the crust) may be exerted by the spinning _down_ crust on the vortex lattice which is already co-rotating with it. The azimuthal external force \(F_{\rm ext}\), being the viscous drag of the permeating electron (and phonon) gas co-rotating with the crust, depends on the relative azimuthal velocity \(v_{\rm rel}\) between the _crust_ and the _vortices_, as well as the associated velocity-relaxation timescale \(\tau_{v}\) of the vortices. The external drag force, per unit length, is given as \[n_{\rm v}F_{\rm ext} = \rho_{\rm c}{v_{\rm rel}\over\tau_{v}},\] (11) where \(n_{\rm v}\) is the number density of the vortices per unit area, and \(\rho_{\rm c}\) is the effective density of the "crust". Hence, for a spin-up of the superfluid to be achieved, the crust may impart the corresponding torque on the vortices only if it (tends to) rotates faster than the vortices, so that

\(v_{\rm rel}\) points to the proper forward direction. Accordingly, a superfluid spin-up requires the crust to be itself spinning up, or else if the crust is spinning down, the vortices must be already rotating slower than the crust; a requirement which is against the pinning condition. It should be trivially clear that the Magnus force could not be responsible for the required external torque, as it is an internal force exerted by the superfluid itself. Therefore, _no further superfluid spin-up_ might be expected to occur during the interval \(\tau_{\rm sp}\), namely after the initial fast spinning up of the crust, as well as the superfluid and its _vortices_, has been accomplished during the glitch rise time (compare Fig. 1a with Fig. 1b). The suggested long-term (over time \(\tau_{\rm sp}\)) superfluid spin-up in APC is a generalization of the vortex creep model to the case of a _negative_ lag, in contrast to the usual applications of the model to spin-downs driven by a positive lag. However, according to the existing formulation of the vortex creep model, a spinning up of the superfluid would require a _positive_ accelerating torque \(N_{\rm em}\) acting on the whole star (see, eg., Eqs. 28, and 38 in Alpar et al. 1984). Application of the same formalism (as is attempted in Eq. 5 of APC) to the suggested case of an spin-up in presence of the given _negative_\(N_{\rm em}\) is not, a priori, justified; it is indeed contradictory. The vortex creep model suggests that a radial Magnus force, due to a superfluid rotational lag, results in a radial bias in the otherwise randomly directed creeping of the vortices (Alpar et al. 1984; see Jahan-Miri 2005 for a critical discussion of the vortex creep model on this, and other, grounds). This might be, mistakenly, interpreted to imply that given a negative lag the inward creeping motion of the vortices, hence a superfluid spin-up, should necessarily follow, irrespective of the presence or absence of the needed torque on the superfluid. As already noted, the role of driving the vortices inward, ie. spinning up of the superfluid, may not be assigned to the Magnus force. The Magnus force associated with the rotational lag is a _radial_ force and is also an internal force exerted by the superfluid _itself_; both properties disqualifying it from being the source of a torque on the superfluid. Accordingly, the point to be emphasized is that the obvious requirement for a spin-up process, namely the realization of the needed torque, is indeed missing in the suggested mechanism of APC. Moreover, the inability of the superfluid to be spun up, in this case, is _not_ a direct consequence of the fact that pinned vortices may not respond freely to an applied external torque. Rather, the vortices under the assumed conditions do not have any "tendency" for an inward radial motion, in spite of the presence of an inward radial Magnus force which is balanced by the pinning forces. Thus creeping motion of the vortices may not be invoked as a resolution; radial creep should be prohibited accordingly. A change in the spin frequency of a superfluid involves not only a radial motion of the vortices but also a corresponding azimuthal one, as may be also verified from the solution of equation of motion of vortices during a superfluid rotational relaxation (see Eq. 9 in Alpar & Sauls 1988, and Eq. 4 in Jahan-Miri 1998). The torque may be transmitted only during such an azimuthal motion and would nevertheless require and initiate a radial motion as well. Therefore, purely _radial_ creeping of the vortices, which is implied by the existing formulation of the vortex creep model, may not be invoked as a spinning-up mechanism during the transition from \(\Omega_{\rm sp}-\Omega_{\rm L}=-\omega_{\rm sp}\) to \(\Omega_{\rm sp}\gtrsim\Omega_{\rm L}\). That is to say, no radial (creeping) motion of the vortices is permitted, for the assumed case, because the spinning down crust could not impart any _forward_ azimuthal force on the pinned vortices. The superfluid would rather remain decoupled at a constant value of \(\Omega_{\rm sp}\) (if not spinning down) during this transition which is achieved due only to the spinning down of the crust, as depicted in Fig. 1b. ## 6 Concluding Decoupling of (a part of) the moment of inertia of the crust of a neutron star at a glitch, from the rest of the co-rotating star, could readily account for the excess post-glitch spin-down rates comparable to the fractional moment of inertia of the decoupled part. The same preliminary fact applies to a (partial) decoupling of a (pinned) superfluid component in the crust, or elsewhere in the star, as well. A decoupled component (say, in the crust) could, in principle, result in an even larger excess spin-down rate of the star if it is further assumed to be spinning up while the rest of the star is spinning down; ie. a _negative_ coupling instead of a mere decoupling. Nevertheless, here we have shown that the only suggested mechanism for such

a _negative_ coupling of a pinned superfluid part in the crust not only fails quantitatively to account for the observed effect in pulsars, it is also ruled out conceptually since the required torque on the superfluid could not be realized at all. Given the standard picture of the interior of a neutron star(Sauls 1989; Pines & Alpar 1992), one is thus left to speculate on the possible role of the stellar core to induce the observed effect. That is, the observed large spin-down rates, over timescales of a day and more, should be caused by a decoupling of (a part of) the stellar core. The large moment of inertia \(I_{\rm core}\) of the core, with \({I_{\rm core}\over I}\sim 90~{}\%\), may easily account for the observations. Nevertheless, a non-superfluid component in the core would couple to the crust on very short timescales (\(<10^{-11}\) s) (Baym et al. 1969a), and could not have any footprint left in the observed post-glitch relaxation. Also, a core-superfluid with free (unpinned) vortices would be again expected to have very short coupling timescales of the order of less than one or two minutes (Alpar & Sauls 1988; Pines & Alpar 1992; Jahan-Miri 1998). However, the pinning of the superfluid vortices to the superconductor fluxoids in the core of neutron stars, might offer a way out of the dilemma. The effect has been originally suggested on theoretical grounds (Muslimov & Tsygan 1985; Sauls 1989; Jones 1991b), while its observable consequences for the rotational dynamics of a neutron star as well as its magnetic evolution have been investigated by various authors (Srinivasan 1990; Jones 1991b; Chau, Cheng & Ding 1992; Jahan-Miri 1996; Ruderman, Zhu & Chen 1998; Jahan-Miri 2000; 2002). Very briefly, the peculiar feature of the assumed pinning in the core, that is the _moving_ nature of the _pinning sites_, has to be highlighted, in this regard. The fluxoids are indeed predicted to undergo a steady outward radial motion throughout the active lifetime of a pulsar (Chau, Cheng & Ding 1992; Jahan-Miri 2000). At a glitch, a departure in the lag from its earlier critical value, causes a (dynamically partial) decoupling of the core, which may explain the observed initial large spin-down rates soon after a glitch (that could not be possibly caused by the crust, as discussed above). Nevertheless the core superfluid does spin down even before the critical lag value is restored, simply because the pinning barriers (the fluxoids), hence the superfluid vortices pinned to them, are moving radially, at all times. Otherwise, for the core superfluid to remain completely decoupled (the vortices being stationary) the superfluid rotation lag should amount to its critical value! since a crossing-through of the vortices and fluxoids, ie. unpinning events, would be inevitable. For the core superfluid, a _decoupling_ accompanies and implies _unpinning!_, contrary to the usual case of stationary pinning sites, as for the crust. Hence, during a post-glitch recovery phase (while the lag is still far from its critical value) the vortices move out along with the fluxoids, keeping the superfluid in a spinning down state, albeit at a slower rate than before the glitch. A quantitative modelling of the effects of a pinned superfluid component in the core on the post-glitch response, as well as its role in a (free) precession of the star, remains to be further studied in details. This work was supported by a grant from the Research Committee of Shiraz University. ## References * [1] Adams P. W., Cieplak M., and Glaberson W. I., _Phys Rev_, **32**, B171 (1985) * [2] Alpar M. A., Anderson P. W., Pines D., Shaham J., _Ap J_, **276**, 325 (1984) * [3] Alpar M. A., _J. Low Temp Phys_, **31**, 803 (1987) * [4] Alpar M. A., Sauls J. A., _Ap J_, **327**, 723 (1988) * [5] Alpar M. A., Pines D., Cheng K. S., _Nature_, **348**, 707 (1990) * [6] Alpar M. A., Chau H. F., Cheng K. S., Pines D., _Ap J_, **409**, 345 (1993) * [7] Anderson P. W., Itoh N., _Nature_, **256**, 25 (1975) * [8] Baym G., Pethick C., Pines D., _Nature_, **224**, 673 (1969a) * [9] Baym G., Pethick C., Pines D., Ruderman M., _Nature_, **224**, 872 (1969b) * [10] Buckley K. B., MetlitskiM. A. , Zhitnitsky A. R., _Phys. Rev._, **C69** , 055803 (2004). * [11] Chau H. F., Cheng K. S., Ding K. Y., _Ap J_, **399**, 213 (1992) * [12] Cheng K. S., Alpar M. A., Pines D., Shaham J., _Ap J_, **330**, 835 (1988) * [13] Epstein R. I., Link B. K., Baym G., in Pines D., Tamagaki R., Tsuruta S., eds, Proc. US-Japan

SENS '90, _The Structure and Evolution of Neutron Stars_. Addison-Wesley Pub., p. 156 (1992) * [14] Flanagan C. S., in Alpar M. A., Kiziloglu U., van Paradijs J., eds, Proc. NATO ASI C450, _The Lives of the Neutron Stars_. Kluwer, Dordrecht, p. 181 (1995) * [15] Jahan-Miri M., _MNRAS_, **283**, 1214 (1996) * [16] Jahan-Miri M., _Ap J_, **501**, L185 (1998) * [17] Jahan-Miri M., _Ap J_, **532**, 514 (2000) * [18] Jahan-Miri M., _MNRAS_, **330**, 279 (2002) * [19] Jahan-Miri M., _J. Low Temp. Phys._, **139**, 371 (2005) * [20] Jones D. I. , Anderson N., _MNRAS_**324**, 811 (2001) * [21] Jones P. B., _ApJ_, **373**, 208 (1991a) * [22] Jones P. B., _MNRAS_, **253**, 279 (1991b) * [23] Krawczyk, A., Lyne A. G. , Gil, J. A., Joshi, B. C., _MNRAS_, **???**, ??? (2003) * [24] Link B. K. , _Phys. Rev. Lett._, **91**, 101101 * [25] Lyne A. G. , _Nature_, **326**, 569 (1987) * [26] Lyne A., Graham-Smith F., _Pulsar Astronomy_, Cambridge University Press (1998) * [27] Muslimov A. G. & Tsygan A. I., _Ap. Sp. Sci._, **115**, 43 (1985) * [28] Pines D., Alpar M. A., in Pines D., Tamagaki R., Tsuruta S., eds, Proc. US-Japan SENS '90, _The Structure and Evolution of Neutron Stars_. Addison-Wesley Pub., p. 7 (1992) * [29] Ruderman M., Zhu T., Chen K., _Ap J_, **492**, 267 (1998). * [30] Sauls J. A., in Ogelman H., van den Heuvel E. P. J., eds, Proc. NATO ASI 262, _Timing Neutron Stars_. Kluwer, Dordrecht, p. 457 (1989) * [31] G. Srinivasan, D. Bhattacharya, A. G. Muslimov A. G., and A. I. Tsygan, _Curr. Sci._, **59**, 31 (1990) * [32] Tsakadze J. S., Tsakadze S. J., _Sov Phys Usp_, **18**, 242 (1975) * [33] Tsakadze J. S., Tsakadze S. J., _J. Low Temp Phys_, **39**, 649 (1980) Figure 1: As is shown, schematically, by the _thin_ and the _dotted_ lines, a superfluid, as in the crust of a neutron star, whose vortices are pinned and co-rotating, at a rate \(\Omega_{\rm c}\), with its spinning down vessel, may spin-down at the same rate as the vessel provided a certain lag between its rotation frequency \(\Omega_{\rm s}\) and \(\Omega_{\rm c}\) is maintained. A decrease in the lag, say at a glitch, results in a decoupling of the superfluid and hence a larger spin-down rate for the vessel. The superfluid starts spinning down again once the lag is increased to its steady-state value. The _thick_ line represents the superimposed behavior of a second superfluid component, \(\Omega_{\rm sp}\), which supports a much smaller steady-state lag. Its behavior as implied in APC90 is shown in the panel **(a)**, in contrast to that suggested here, shown in **(b)**. The unresolved rising time of \(\Omega_{\rm c}\) at the glitch instant \(t=t_{\rm g}\) should be reckoned as a measure of the expected coupling time of the superfluid due to free motion of vortices, in contrast to the suggested spin-up period \(\tau_{\rm sp}\) in **(a)**.

# The effect of grain size distribution on H\({}_{2}\) formation rate in the interstellar medium Azi Lipshtat\({}^{1}\) and Ofer Biham\({}^{1}\) \({}^{1}\)Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel ###### Abstract The formation of molecular hydrogen in the interstellar medium takes place on the surfaces of dust grains. Hydrogen molecules play a role in gas-phase reactions that produce other molecules, some of which serve as coolants during gravitational collapse and star formation. Thus, the evaluation of the production rate of hydrogen molecules and its dependence on the physical conditions in the cloud are of great importance. Interstellar dust grains exhibit a broad size distribution in which the small grains capture most of the surface area. Recent studies have shown that the production efficiency strongly depends on the grain composition and temperature as well as on its size. In this paper we present a formula which provides the total production rate of H\({}_{2}\) per unit volume in the cloud, taking into account the grain composition and temperature as well as the grain size distribution. The formula agrees very well with the master equation results. It shows that for a physically relevant range of grain temperatures, the production rate of H\({}_{2}\) is significantly enhanced due to their broad size distribution. keywords: ISM: molecules - molecular processes ## 1 Introduction The chemistry of interstellar clouds consists of reactions taking place in the gas phase as well as on the surfaces of dust grains (Hartquist and Williams, 1995). In particular, the formation of H\({}_{2}\) takes place on grain surfaces while all competing gas phase processes are orders of

magnitude less efficient (Gould & Salpeter, 1963). Hydrogen molecules are necessary for the initiation of gas-phase reaction networks that give rise to the chemical complexity observed in interstellar clouds. Molecules serve as coolants during gravitational collapse, enabling the formation of stars. In diffuse clouds the H\({}_{2}\) formation process takes place on bare grains that consist of amorphous silicates and carbon. In dense molecular clouds the grains are coated by ice mantles. Upon collision with a grain, an H atom has a probability \(\xi\) to become adsorbed on the surface. The adsorbed H atom (adatom) resides on the surface for an average time \(t_{\rm H}\) (residence time) before it desorbs. In the Langmuir-Hinshelwood mechanism, the adsorbed H atoms diffuse on the surface of the grain either by thermal hopping or by tunneling. When two H atoms encounter each other on the surface, an H\({}_{2}\) molecule may form (Williams, 1968; Hollenbach & Salpeter, 1970, 1971; Hollenbach et al., 1971; Smoluchowski, 1981, 1983; , 1985; Duley & Williams, 1986; Pirronello & Avera, 1988; Sandford & Allamandola, 1993). The formation rate \(R_{\rm total}\) (cm\({}^{-3}\)s\({}^{-1}\)) of molecular hydrogen on dust-grain surfaces is commonly evaluated using the Hollenbach-Werner-Salpeter formula \[R_{\rm total}={1\over 2}n_{\rm H}\langle v_{\rm H}\rangle n_{\rm grain}\langle \sigma_{g}\rangle\gamma,\] (1) where \(n_{\rm H}\) (cm\({}^{-3}\)) is the number density of hydrogen atoms in the gas, \(\langle v_{\rm H}\rangle\) (cm s\({}^{-1}\)) is the average velocity of hydrogen atoms, \(n_{\rm grain}\) (cm\({}^{-3}\)) is the number density of dust grains and \(\langle\sigma_{g}\rangle\) (cm\({}^{2}\)) is the average grain cross section (Hollenbach et al., 1971). Assuming spherical grains, \(\langle\sigma_{g}\rangle=\pi\langle r^{2}\rangle\) where \(r\) (cm) is the grain radius. The parameter \(0\leq\gamma\leq 1\) is the recombination efficiency, namely, the fraction of atoms hitting the grain which come out in molecular form. The total grain mass amounts to about \(1\%\) of the hydrogen mass in the cloud. The number density of dust grains is about \(10^{-13}-10^{-12}\) smaller than the total number density of hydrogen atoms. In previous studies, a typical grain radius of \(0.17\mu\)m was used, assuming a mass density of \(\rho_{g}=2\) (gram cm\({}^{-3}\)) (Hollenbach et al., 1971). Under these assumptions, for gas temperature of 100 K and \(\gamma=0.3\), Eq. (1) can be simplified to \[R_{\rm total}=R\cdot n_{\rm H}n,\] (2) where \(R\simeq 10^{-17}\) (cm\({}^{3}\) s\({}^{-1}\)) is the rate coefficient and \(n=n_{\rm H}+2n_{\rm H_{2}}\) (cm\({}^{-3}\)) is the total density of hydrogen atoms in both atomic and molecular (\(n_{\rm H_{2}}\)) form (Hollenbach et al., 1971). Eq. (2) is commonly used for the evaluation of the hydrogen recombination rate in models

of interstellar chemistry. In this paper we present a direct calculation of \(R_{\rm total}\), without using rate coefficients. The grain size distribution \(n_{g}(r)\) (cm\({}^{-4}\)) in interstellar clouds is broad with many small grains and few large grains. The surface area is dominated by the small grains. This distribution can be approximated by a power law of the form (Mathis et al., 1977; Weingartner, 2001) \[n_{g}(r)=cr^{-\alpha}\] (3) where \(n_{g}(r)dr\) (cm\({}^{-3}\)) is the density of grains with radii in the range \((r,r+dr)\) in the cloud. This distribution is bounded between the upper cutoff \(r_{\rm max}=0.25\mu{\rm m}\) and the lower cutoff \(r_{\rm min}=5{\rm nm}\). The exponent is \(\alpha\simeq 3.5\)(Draine & Lee, 1984). In general, the normalization constant is given by \[c={{3M_{g}(4-\alpha)}\over{4\pi\rho_{g}(r_{\rm max}^{4-\alpha}-r_{\rm min}^{4- \alpha})}},\] (4) where \(M_{g}\) (gram cm\({}^{-3}\)) is the mass density of grain material in the cloud. The total number density, \(n_{\rm grain}\) (cm\({}^{-3}\)), of grains is given by \[n_{\rm grain}=\frac{c(r_{\rm min}^{1-\alpha}-r_{\rm max}^{1-\alpha})}{\alpha-1}.\] (5) Recent experiments have shown that the mobility of H atoms on dust analogues under interstellar conditions is dominated by thermal hopping rather than tunneling (Pirronello et al., 1997a, b, 1999; Katz et al., 1999; Roser et al., 2002). As a result, the production efficiency of H\({}_{2}\) molecules is highly dependent on the grain temperature. The efficiency is very high within a narrow window along the temperature axis, with exponential decay on both sides. Theoretical studies have shown that for sufficiently small grains, the production efficiency is strongly dependent on the grain size, namely it decreases as the grain size is reduced (, 2001; Green et al., 2001). The Hollenbach-Werner-Salpeter formula, in which all the surface processes are captured in the parameter \(\gamma\) cannot account for the temperature and grain-size dependence of the production efficiency. In this paper we present a formula for the production rate of H\({}_{2}\) in interstellar clouds, which takes into account explicitly the dependence of the recombination efficiency on the grain temperature and size, integrating the size dependence over the entire distribution of grain sizes. This formula is in very good agreement with the results obtained from the master equation. It applies for a broad range of steady-state and quasi steady-state conditions and

enables the evaluation of the production rate of H\({}_{2}\) in a closed form without the need for any simulation or numerical integration. The paper is organized as follows. In Sec. 2 we present the different approaches to the calculation of reaction rates on surfaces. The dependence of these rates on the grain size and temperature is considered in Sec. 3. In Sec. 4 we introduce a formula that accounts for the formation rate of molecular hydrogen per unit volume of the clouds, integrated over the entire distribution of grain sizes. The results are discussed in Sec. 5 and summarized in Sec. 6. ## 2 Recombination rates on single grains Calculations of reaction rates of H\({}_{2}\) formation and other chemical reactions on dust grains are typically done using rate equation models (Pickles & Williams, 1977; d'Hendecourt et al., 1985; Brown & Charnley, 1990; Hasegawa et al., 1992; Caselli et al., 1993; Willacy & Williams, 1993). These models consist of coupled ordinary differential equations that provide the time derivatives of the populations of the species involved. The reaction rates are obtained by numerical integration of these equations. The production of molecular hydrogen on a single grain of radius \(r\) is described by \[{dN\over dt}=F-WN-2AN^{2},\] (6) where \(N\) is the number of H atoms on the grain. The first term on the right hand side is the flux \(F\) (sec\({}^{-1}\)) of hydrogen atoms onto the grain surface. The second term describes the thermal desorption of H atoms from the surface where \[W=\nu\exp(-{E_{1}/k_{\rm B}T})\] (7) is the desorption rate, \(\nu\) is the attempt rate (standardly taken as \(10^{12}\,{\rm sec}^{-1}\)), \(E_{1}\) is the activation energy barrier for desorption and \(T\) (K) is the grain temperature. The third term in Eq. (6) accounts for the depletion in the number of adsorbed atoms due to formation of molecules. The parameter \(A=a/S\) is the rate at which H atoms scan the entire surface of the grain, where \[a=\nu\exp(-{E_{0}/k_{\rm B}T})\] (8) is the hopping rate between adjacent adsorption sites on the grain, \(E_{0}\) is the energy barrier for hopping, \(S=4\pi r^{2}s\) is the number of adsorption sites on the grain surface and \(s\) (cm\({}^{-2}\)) is their density. The formation rate, \(R_{\rm grain}\) of H\({}_{2}\) on a single grain is given by \(R_{\rm grain}=AN^{2}\)

The limits of small and large grains Expressing the production rate \(R_{grain}\) of Eq. (15) in terms of the size-independent hopping rate \(a=AS\) (sec\({}^{-1}\)) and the incoming flux \(f=F/S\) (monolayer sec\({}^{-1}\)) we obtain \[R_{grain}={{fS^{2}}\over{\left({W\over f}\right)\left[1+S\left({W\over a}+{2f \over W}\right)\right]}}.\] (16) The ratio \(a/W\) is the number (up to a logarithmic correction) of sites that the atom visits before it desorbs (Montroll & Weiss, 1965). The ratio \(W/f\) is roughly the average number of vacant sites in the vicinity of an H atom. Using these parameters we can identify two regimes of grain sizes. For grains that are sufficiently large such that \(S>\min(a/W,W/f)\), the size dependence of the production rate is given by \(R_{\rm grain}\sim S\sim r^{2}\) and the production efficiency is independent of the grain size. This is the range in which rate equations apply. In the limit of small grains, namely when \(S<\min(a/W,W/f)\), the production efficiency depends linearly on \(S\), and \(R_{\rm grain}\sim S^{2}\sim r^{4}\). This is the regime in which the grain size becomes the smallest relevant length-scale in the system and rate equations fail (Biham & Lipshtat, 2002). To illustrate the implications of these results, consider a given mass \(M\) of dust matter. Dividing the mass \(M\) to spherical grains of radius \(r\), the number of grains is given by \(n_{\rm grain}\sim r^{-3}\). In an interstellar cloud, the \(r\) dependence of the production rate of H\({}_{2}\) due to such ensemble differs in the two limits discussed above. For large grains the total production rate is \(R_{M}=n_{\rm grain}R_{grain}\sim r^{-1}\). Reducing the grain size increases their total surface area, and as a result the production rate goes up. In the limit of small grains the efficiency decreases as the grain size is reduced and thus \(R_{M}\sim r\). This indicates that there is an intermediate grain size for which the production rate is maximal. In Fig. 1 we present the total production rate \(R_{M}\) (sec\({}^{-1}\)) for a total dust mass of \(M=1\) (gram) which is divided into spherical grains of dradius \(r\). Clearly, there is an optimal grain size for which the production rate is maximal. This optimal radius depends on the grain composition and temperature and is given by \[r_{\rm opt}=\sqrt{S_{\rm opt}/4\pi s}\] (17) where \(S_{\rm opt}=({W/a}+2f/W)^{-1}\). For typical interstellar conditions this optimal grain radius is of the order of tens of nm, with several thousand adsorption sites. ## 4

The overall production rate of molecular hydrogen As discussed above, interstellar grains exhibit a broad size distribution of the form \(n_{g}(r)\sim r^{-\alpha}\). For \(\alpha>2\) the surface area is dominated by the small grains, while for \(\alpha>3\) even the grain mass is dominated by the small grains. Therefore, these small grains are expected to contribute significantly to H\({}_{2}\) formation. Taking this size distribution into account we find that the production rate on grains with radii in the range \((r,r+dr)\) is given by \[n_{g}(r)R_{\rm grain}(r)dr=\left\{\begin{array}[]{ll}c_{1}r^{4-\alpha}dr:&\ { \rm small\ grains}\\ c_{2}r^{2-\alpha}dr:&\ {\rm large\ grains}\end{array}\right.\] (18) where \[c_{1}=\frac{(4\pi sf)^{2}c}{W}\] (19) and \[c_{2}=\frac{4\pi saf^{2}c}{W^{2}+2af}\] (20) are obtained directly from Eq. (16) in the limits of \(S\ll S_{\rm opt}\) and \(S\gg S_{\rm opt}\), respectively. Eq. (16) is expected to be highly accurate in the limit of small grains. For large grains its accuracy may be limited because its derivation requires to impose a cutoff on the master equation. For large grains the rate equations apply, and therefore one can use \[c_{2}={4\pi sW^{2}c\over 16a}\left(-1+\sqrt{1+8{af\over W^{2}}}\right)^{2},\] (21) which is obtained directly from the exact solution of the rate equation (6) under steady state conditions [(, 1998)]. To evaluate the total production rate of molecular hydrogen per unit volume in an interstellar cloud, one should take into account the size distribution of dust grains, and the dependence of the production efficiency on the grain size and temperature. The total production rate is given by \[R_{total}=\int_{r_{min}}^{r_{max}}n_{g}(r)R_{grain}(r)dr\] (22) where \(n_{g}(r)dr\) is the density of grains with radii in the range \((r,r+dr)\), and \(R_{grain}(r)\) can be taken either from the exact result of Eq. (13) or from the approximate result of Eq. (16). Assuming a power law distribution of grain sizes, given by Eq. (3), and the result of of Eq. (16) one can divide the range of integration into two parts, namely the domain of small grains, \(r_{\rm min}<r<r_{\rm opt}\), and the domain of large grains, \(r_{\rm opt}<r<r_{\rm max}\). Integrating each one of them separately, for \(\alpha\neq 3\), we obtain

\[R_{\rm total}={c_{1}\over{5-\alpha}}\left(r_{\rm opt}^{5-\alpha}-r_{\rm min}^{ 5-\alpha}\right)+{c_{2}\over{3-\alpha}}\left(r_{\rm max}^{3-\alpha}-r_{\rm opt }^{3-\alpha}\right),\] (23) In the special case of \(\alpha=3\), the total production rate is \[R_{\rm total}={c_{1}\over 2}\left(r_{\rm opt}^{2}-r_{\rm min}^{2}\right)+c_{2} \ln\left({r_{\rm max}/{r_{\rm opt}}}\right).\] (24) In Fig. 2 we present the total production rate obtained from Eq. (23) for flux \(f=6.88\times 10^{-9}\) (ML sec\({}^{-1}\)), which corresponds to gas temperature of 90 K and hydrogen density \(n_{\rm H}=10\) (cm\({}^{-3}\)). The results of this formula are shown for the case in which the parameter \(c_{2}\) is taken from Eq. (20) (\(\circ\)) and for the case in which it is taken from Eq. (21) (\(+\)). Both results are in very good agreement with those obtained from the master equation (solid line). The rate equation results (dashed line) are found to significantly over-estimate the total production for most of the temperature range. The results obtained (using the master equation) under the assumption that the same total grain mass is divided into grains of identical size (0.17 \(\mu m\)) are also shown (dotted line). For the range of grain temperatures in which the H\({}_{2}\) production is efficient, this assumption leads to an under-estimate of the total production rate by about an order of magnitude. This indicates that within this temperature range the broad size distribution of the grains tends to enhance the production rate due to the increase in grain-surface area. ## 5 Discussion The formula introduced in this paper [Eq. (23)] enables us to calculate the formation rate of molecular hydrogen in interstellar clouds for a broad range of conditions without the need to perform computer simulations or numerical integration. It applies both in the case of diffuse clouds in which the H\({}_{2}\) formation takes place on bare silicate and carbon grains and for molecular clouds in which the grains are coated by ice mantles. The formula applies directly for grain size distributions that can be approximated by a power-law of the form of Eq. (3). For other distribution functions for which the integration cannot be done analytically one can solve Eq. (22) by numerical integration. The relaxation time for H\({}_{2}\) formation processes on dust grains can be obtained from Eq. (6). It is given by \(\tau=(W^{2}+8AF)^{-1/2}\). Under typical conditions, this time is extremely short compared to the time scales of interstellar clouds. Therefore, the formula can be used even in the context of evolving clouds. The time dependence can be taken into account by updating the input parameters to the formula as the physical conditions in the cloud vary.

At very low grain temperatures below \(T_{0}\), the mobility of H atoms on the surface is suppressed and the rate of H\({}_{2}\) formation is sharply reduced. In this limit, H atoms keep accumulating on the surface, the relaxation time \(\tau\) increases and the behavior may no longer be well described by steady state calculations. In this limit the coverage is relatively high and thus the rate equations are valid. However, the Langmuir rejection of atoms that hit the grain in the vicinity of already adsorbed atoms should be included. This is done by replacing the flux term \(F\) by \(F(1-N/S)\). The formula introduced in this paper, Eq. (23), is valid only for grain temperatures higher than \(T_{0}\). To extend its validity below \(T_{0}\) one should incorporate the Langmuir rejection term into it, by replacing all the appearances of \(W\) in Eqs. (19) - (21) by \(W+f\). In Eq. (23) it is assumed that all the grains are at the same temperature. This assumption does not apply in photon dominated regions (PDR's), where small grains exhibit large temperature fluctuations. In general, the formation of molecular hydrogen in PDR's is not well understood. The typical grain temperatures in these regions is significantly higher than the temperature range in which the formation of H\({}_{2}\) on olivine, carbon and ice is found to be efficient. Several approaches have been considered in attempt to explain this puzzle. One approach is based on the assumption that chemisorbed H atoms play a role in the formation of H\({}_{2}\)(Cazaux & Tielens, 2002, 2004). Other explanations may ivolve porous grains that capture H atoms more strongly within pores or with the temperature fluctuations of small grains. ## 6 Summary We have presented a formula for the evaluation of the formation rate of molecular hydrogen in interstellar clouds, taking into account the composition and temperature of the grains as well as their size distribution. The formula is found to be in excellent agreement with the results of the master equation. It enables us to obtain reliable results for the production rates without the need to perform computer simulations or numerical integrations. It is found that for an astrophysically relevant range of grain temperatures the broad size distribution of the grains provides an enhancement of the H\({}_{2}\) formation rate compared to previous calculations. ## 7

acknowledgments We thank E. Herbst, H.B. Perets, G. Vidali and V. Pirronello for helpful discussions. This work was supported by the Israel Science Foundation and the Adler Foundation for Space Research.

**On the distribution of the modulation frequencies of RR Lyrae stars** **Johanna Jurcsik\({}^{1}\), Bela Szeidl\({}^{1}\), Andrea Nagy\({}^{1}\), and Adam Sodor\({}^{1}\)** \({}^{1}\) Konkoly Observatory of the Hungarian Academy of Sciences P.O. Box 67, H-1525 Budapest, Hungary jurcsik,szeidl,nagya,sodor@konkoly.hu ###### Abstract For the first time connection between the pulsation and modulation properties of RR Lyrae stars has been detected. Based on the available data it is found that the possible range of the modulation frequencies, i.e, the possible maximum value of the modulation frequency depends on the pulsation frequency. Short period variables (\(P<0.4\) d) can have modulation period as short as some days, while longer period variables (\(P>0.6\) d) always exhibit modulation with \(P_{mod}>20\) d. We interpret this tendency with the equality of the modulation period with the surface rotation period, because similar distribution of the rotational periods is expected if an upper limit of the total angular momentum of stars leaving the RGB exists. The distribution of the projected rotational velocities of red and blue horizontal branch stars at different temperatures shows a similar behaviour as \(v_{rot}\) derived for RR Lyrae stars from their modulation periods. This common behaviour gives reason to identify the modulation period with the rotational period of the modulated RR Lyrae stars. Stars: variables: RR Lyr - Stars: oscillations - Stars: horizontal-branch ## 1 Introduction Different type modulations, which appear as close frequency component(s) in the vicinity of the radial mode frequency in the Fourier spectrum of RR Lyrae stars, seem to be a common property of both fundamental and first overtone variables. The classical Blazhko (BL) phenomenon is just one special case when the spectrum is characterized by equidistant triplets at the frequencies of the radial mode and its harmonics. Modulation manifests in doublet (\(\nu_{1}\)) and non-equidistant triplet (\(\nu_{2}\)) structure of the Fourier spectrum, as well. The transition between the different type modulations seems to be, however, continuous. The strong asymmetry of the amplitudes of the side frequencies of the triplets as seen in many Blazhko stars, indicates that one of the side peaks may even vanish to the noise level. In this case doublet structure of the spectrum is detected. Though, according to our present knowledge, it cannot be excluded for sure that different physics govern the different types of modulation, a natural expectation is trying to find first a common explanation of the phenomenon. Nonradial modes triggered by resonance effects or magnetic field seem to be the most promising solution for the modulation. For a recent detailed summary of the problems of the

theoretical explanations of the Blazhko effect see e.g., the Introduction in Dziembowski & Mizerski (2004). All attempts to find any connection between the pulsation and modulation properties of RR Lyrae stars have been yet failed. To find the correct answer of the modulation such a relation would be of great importance. Its benefit would be also to control the reality of model predictions. In this short note we have made a new attempt to find such a relation. Our recent observations at Konkoly Observatory led to the unexpected discovery of extreme short modulation periods of RR Geminorum and SS Cancri. This fact directed our interest to the distribution of the modulation frequencies. ## 2 The data We have collected all the available data on the observed modulations of RR Lyrae stars. The large surveys (MACHO, OGLE) distinguish between the different types of modulation based on the structure of the Fourier spectrum of the stars. Variables exhibiting doublet structure in their spectra (\(\nu_{1}\) variables) are most probably a special, border-line case of those showing the equidistant triplet characteristics of the classical Blazhko behaviour. The actually observed characteristics of the spectrum may be seriously affected by data length, distribution, S/N etc. For an example, MACHO-9.4632.731 was classified as an RR1 variable in Alcock et. al (2000) from 6.5 years long 'r' data. According to the revision of the Alcock et. al (2000) results utilizing the 8-year 'b' band MACHO data (Nagy & Kovacs, 2005) the spectrum of this star shows in fact asymmetric triplet structure. However, even in the 8 years of 'r' data, because of its worse S/N properties, instead of a triplet seen in the 'b' residual spectrum, only \(\nu_{1}\), doublet structure can be resolved (see Fig. 1). We have also checked the public MACHO database for hidden triplet structure of the residual spectra of some of the fundamental mode \(\nu_{1}\) variables classified in Alcock et. al (2003). Fig. 2 shows two examples that these stars are also intrinsically classical Blazhko variables showing triplets in their spectra. The complete revision of the modulation properties of e.g. the MACHO RR Lyrae stars is, however, far beyond the scope of this note. We would only like to stress that somewhat better S/N statistics, more data, different treatment of filtering, etc., can lead to a different classification of the modulation. Thus it can be supposed, that hidden triplet structure of the \(\nu_{1}\) variables may probably be a common property. In Jurcsik et al. (2005a) we have also shown a similar example. The extended data (N=3000) of RR Gem show symmetric triplets, while analyzing only 1000 datapoints, the residual spectrum becomes strongly asymmetric, indicating that with even a bit worse noise statistics, only one modulation component could have been detected. (For comparison, MACHO data are typically of \(800-1000\) measurements / star.) The modulation of the BL and \(\nu_{1}\) variables can be characterized by a single modulation period. As our interest is focused on the distribution of the modulation periods, we restrict the data involved to these variables. Variables exhibiting modulations with different periodicities (\(\nu_{2}\) variables)

are quite rare, and might represent an indeed different type of modulation behaviour. The list of galactic field Blazhko stars (Smith, 1995, Table 5.2) has been completed with new data given in Table 1. In some globular clusters (M5, M55, M68, NGC 6362, and \(\omega\) Cen) first overtone variables showing frequency doublets or triplets has been identified (Olech et al., 1999a,b; Walker, 1994; Olech et al., 2001; Clement & Rowe, 2000). V12 in M55 shows definite \(\nu_{2}\) characteristics, thus it is not involved in this study. V5 in M68 though clearly shows unstable light curve, its data have not been analyzed by Walker (1994). Using those data we have found that the modulation period of this star is 7.45 d (frequency separation \(\Delta f=0.134\) c/d). Data of variables in the LMC, galactic bulge, and Sagittarius dwarf galaxy and its field were taken from Alcock et al. (2000), Alcock et al. Figure 1: _Amplitude spectra of the prewhitened ’r’ (top), and ’b’ (bottom) data of MACHO-9.4332.731, an RR1 star with \(f1=3.60295\) c/d pulsation frequency. This stars was classified as a non-modulated RR1 variable in Alcock et al. (2000). The residual spectrum of the 8-year ’r’ data shows one modulation peak at the short frequency side of the removed pulsation frequency (i.e, doublet, \(\nu_{1}\) spectrum), while in the ’b’ data modulation components both at the shorter and the longer frequency sides (equdistant triplet, BL spectrum) are evident._

(2003), Moskalik & Poretti (2003), and Cseresnjes (2001), respectively. The modulation frequency has been defined as the frequency separation of the radial mode and the other close frequency appearing in the spectra. The sign of the separation, i.e., that the modulation peak appears at shorter or longer frequency than that of the pulsation, has not been taken into account. Three objects have been eliminated from the sample. WY Dra has been removed from Smith's list of Blazhko stars, as we have found no convincing evidence of its modulation either form the reanalyzis of Chis et al (1975) \(O-C\) and \(M_{max}\) data, or according to the NSVS photometry (Wozniak et. al., 2004). We have found that MACHO 6.6212.1121 is not a modulated fundamental mode variable, but is a superposition of two RRab stars with 0.601390535 d and 0.5602746 d periods, respectively. Its spectrum shows the harmonics of both components up to the 4., 5. order, instead of showing modulation components at the same distance of one of the components and its harmonics. It is a relatively bright RR Lyrae (\(\overline{V}=19.059\) mag, the magnitude range of the bulk Figure 2: _Amplitude spectra of the residuals (after the removal of the fundamental mode pulsation) of two RR0 stars classified as BL1 (\(\nu_{1}\)) variables in Alcock et al. (2003) using MACHO \(V\) data. MACHO-10.3800.1218 (top panel) shows in fact not only an equdistant triplet but also another modulation component with larger frequency separation._

of one of the components and its harmonics. It is a relatively bright RR Lyrae (\(\overline{V}=19.059\) mag, the magnitude range of the bulk of the LMC RRab stars is \(19.0-19.6\) mag) which supports our solution. Another star excluded from the sample is vs4f114, a galactic field star in the area of the Sagittarius dwarf galaxy. The period of this star (0.227 d) is anomalously short for an RRc star. As its distance is not known, we suppose that it is rather a multimode high amplitude \(\delta\) Sct star. The omission of this object has, however, no effect on the results. Alltogether data of 894 RR Lyrae stars which show single periodic modulation are utilized (815 fundamental mode, 79 first overtone variables). The pulsation frequencies of the first overtone variables were fundamentalized in order to obtain a homogeneous sample. ## 3 Distribution of the shortest modulation frequencies Investigating the distribution of the modulation frequencies at different pulsation frequencies we have found that, instead of a uniform distribution, the possible range of the modulation frequencies are wider towards larger pulsation frequencies. The larger the pulsation frequency is, the larger the modulation frequency can be. This tendency does not mean that there would be a correlation between the two frequencies, as the modulation frequencies fill uniformly the \(0-0.04\) c/d range for the large majority of RRab stars with \(1.6-2.2\) c/d pulsation frequency, i.e, the typical modulation period is usually longer than 25 days. The shortest modulation period variables, however, do not follow this uniform distribution, instead, their modulation period is the shorter, the shorter their pulsation period is. This tendency, that the shortest period modulation can be observed among the shortest period variabl \begin{table} \begin{tabular}{l c l l} \hline \hline Star & \(P_{puls.}\) [d] & \(P_{mod.}\) [d] & ref. \\ \hline ASAS 81933-2358.2 & 0.2856 &       8.1 & Antipin \& Jurcsik (2005) \\ SS Cnc & 0.3673 &       5.3 & Jurcsik et al. (2005b) \\ RR Gem & 0.3973 &       7.2 & Jurcsik et al. (2005a) \\ V442 Her & 0.4421 & \(>700\) & Schmidt \& Lee (2000) \\ GSC 6730-0109 & 0.4480 &    26 & Wils \& Greaves (2004) \\ AH Leo & 0.4663 &    29 & Phillips \& Gay (2004) \\ UX Tri & 0.4669 &    43.7 & Achterbert \& Husar (2001) \\ FM Per & 0.4893 & 122 & Lee \& Schmidt (2001a) \\ GV And & 0.5281 &    32 & Lee et al. (2002) \\ NSV 8170 & 0.5510 &    38.4 & Khruslov (2005) \\ DR And & 0.5631 &    57.5 & Lee \& Schmidt (2001b) \\ \hline \end{tabular} \end{table} Table 1: Complementary list of galactic field Blazhko variables with known modulation periods

es is equally evident in the different samples of the data, as shown in Fig. 3, and Fig. 4. We have checked the modulation frequency distributions of RRab and RRc stars separately. Data were divided into a) bins of equal width and b) bins of equal number of stars. The largest modulation frequencies, and the means of the 2, and 3 largest modulation frequencies in each bin are plotted in Fig. 5. Error weighted linear fits to the data are also shown. V104 in M5 has been omitted from the fits, because as discussed in the next paragraph, there may arise some doubt about its classification as a modulated RR Lyrae star. The fitted lines for the shortest modulation period RRab and RRc stars agree within the uncertainty limits in each case, proving that the pulsation frequency dependence of the shortest modulation periods is the same for fundamental and first overtone variables. The united sample of all the 894 RR Lyrae shown in Fig. 6 defines the limiting modulation frequency value as a linear function of the pulsation frequency according to : MAX \((f_{mod})=0.125f_{0}-0.142\). This relation is indicated by a dotted line in Fig. 6. There is only one outlyer with too large modulation frequency, V104 in M5. Th Figure 3: _The modulation frequencies (frequency separation) versus the pulsation frequency (fundamentalized for first overtone variables) of the different samples of modulated RR Lyrae stars. Gray dots are for fundamental mode, while open circles denote first overtone variables. Each plot indicates clearly that short period modulation exists only in case of shorter period variables. The envelope of the data indicates that the shorter the period of the pulsation is the shorter the period of the modulation can be._

is star has been already classified as a possible double mode variable (Reid, 1996), W UMa type (Drissen & Shara, 1998), and as an RRc with two close frequencies (Olech et al., 1999b) allowing some suspect that its frequency solution used is indeed correct. The connection found between the possible range of the modulation frequencies and the pulsation frequency is the first direct link between the pulsation and modulation properties of RR Lyrae stars. As any idea which try to explain the modulation connects it somehow to the rotation of the star, we suspect that the detected relation reflects also the rotational properties of the stars. In order to check this possibility, we compared the data of RR Lyrae stars with projected rotational velocity (\(v\sin i\)) observations of field blue and red horizontal branch stars (BHB, RHB). To do so, we applied a crude transformation on the pulsation and modulation frequency data to get statistically valid temperature and rotational velocity values. The pulsation period was converted to temperature assuming that fundamental mode variables with the shortest periods have \(T_{eff}=7500\) K temperature while the longest period ones are at \(T_{eff}=5500\) K (i.e., \(\log T_{eff}=3.97-0.289P_{0}\)). The rotational velocity was derived from the \(P_{0}\sqrt{\rho}=0.038\) pulsation equation assuming uniform \(M=0.55\) M\({}_{SUN}\) mass of the stars and that the observed modulation frequency (frequency separation) corresponds to the rotational period. It can be easily seen that these approximations lead to a simple form of \(v_{rot}\), namely \(v_{rot}=362f_{mod}\times f_{0}^{-2/3}\). Projected rotational velocities of field BHB and RHB stars are taken Figure 4: _The same as Fig 3, but the 815 fundamental mode and the 79 first overtone RR Lyrae stars are shown in separate plots. Again, both plots show, that the frequency of the pulsation defines the possible range of the modulation frequencies._

from Behr (2003b), Carney et al. (2003) and Kinman et al. (2000). For stars with multiple \(v\sin i\) measurements, the mean of the published values were considered. Rotational properties of globular cluster BHB stars were studied, among others, by Behr (2003a), and Peterson et al. (1995). These are the only studies where both temperature and \(v\sin i\) data are available for BHB stars, therefore globular cluster data are taken from these sources. Fig. 8 in Behr (2003b), and Fig. 5 in Recio-Blanco (2004) indicate already that the maximum possible \(v\sin i\) of both BHB and RHB stars show a temperature dependence, the hotter stars can rotate faster both in the \(3.7<\log T<3.77\) RHB and in the \(3.87<\log T<4.00\) BHB temperature ranges. The similar dependence of the possible largest rotational velocity val Figure 5: _Distribution of the modulation frequencies of the 1, 2, and 3, (from top to bottom) variables with the shortest modulation periods. Filled and open circles correspond to the RRab and the RRc samples shown in Fig. 4, respectively. RRc sample including V104/M5 are shown by gray symbols. In the left panels bins are of equal widths (6 bins for RRab and 4 for RRc stars), while in the right panels of equal number of stars (136 for RRab, 20 for RRc stars). Error bars indicate bin width, as because of the unknown intrinsic distribution of the pulsation and modulation periods and the different biases affecting the samples used, a real estimate of the errors is impossible. Weighted linear fits to data (excluding V104/M5) are shown. In each plot the linear fits to the RRab and RRc data agree within the uncertainty limits, proving that the distribution of the shortest modulation period variables is the same for fundamental and first overtone variables._

ues on the temperature as shown for BHB, RR Lyrae and RHB stars in Fig. 7 gives a convincing proof of our assumption that the modulation periods of RR Lyrae stars equal to their rotational period. Behr (2003b) has already noticed the temperature dependence of the \(v\sin i\) of RHB stars and connected it to a fixed value of the total angular momentum on the horizontal branch. The combined sample of BHB, RR Lyrae and RHB stars points to that, there may be a common upper limit of the total angular momentum of HB stars, most probably due to the mass/angular momentum loss of these stars during the termination of their RGB evolution. ## 4 Concluding remarks In this note we have shown that the possible range of the modulation periods of RR Lyrae stars depends on the pulsation period, i.e., on the physical properties of the stars. The hotter, smaller, short period (\(P<0.45\) d) variables' modulation period can be as short as some days, while for the cooler, larger, long period (\(P>0.6\) d) variables the modulation period cannot be shorter than \(\sim 20\) d. This behaviour can be explained by a unique maximum value and a similar distribution of the angular momentum of the stars at different temperatures on the horizontal branch. The distribution of the projected rotational velocity measurements of RHB and BHB stars is a strong confirmation of the validity of this idea. Though rotation has been connected to the modulation periods of RR Lyrae stars already in many theoretical works, no direct evidence of rotation of RR Lyrae stars has yet been found. Peterson et al. (1996) Figure 6: _The observed frequency separation versus the pulsation frequency for RR Lyrae stars with known modulation frequencies are plotted. Gray dots denote fundamental, open circles first overtone (with fundamentalized period) variables. Except one outlyer (V104/M5), the joint sample traces out a linear envelope for the possible modulation frequency as a function of the pulsation frequency._

gave an upper limit \(v\sin i<10\) km/s for each of the RR Lyrae stars they studied. The shortest known modulation period galactic RRab stars are SS Cnc, RR Gem, AH Cam, and Z CVn. The rotational velocities of AH Cam, and Z CVn are about 21 and 14 km/s assuming 4.5, and 6.5 \(R_{SUN}\) radius, respectively (according to their periods), and applying the simple formula \(v_{rot}{\rm{[km/s]}}=50R{\rm{[R_{SUN}]}}\times f_{rot}{\rm{[1/d]}}\). The rotational velocities of RR Gem and SS Cnc would be \(30-40\) km/s. For all these stars Peterson et al. (1996) found \(v\sin i<10\) km/s. The similar behaviour of the rotational properties of RHB, BHB and RR Lyrae stars as shown in Fig. 7 is a direct evidence that the modulation period reflects, indeed, the rotational period of RR Lyrae stars. We suggest that the contradiction between the predicted and observed values of the rotational velocities arises from projection effect, the modulation period corresponds to the true \(v_{rot}\) of the stars, while \(v\sin i\) is spectroscopically observed. The very small modulation amplitudes of RR Gem and SS Cnc support this explanation. A circumspect spectroscopic analyses of the line broadenings of the modulated RR Lyrae stars would be anyway of great importance in solving the mystery of the Blazhko phenomenon. Figure 7: _The observed rotational properties (\(v\sin i\)) of field blue and red horizontal branch stars (BHB, RHB – open circles) and rotational velocities of RR Lyrae stars (dots), – assuming that the detected modulation frequency corresponds to the surface rotational velocity of the star –, are plotted versus \(\log T_{eff}\). The three samples follow the same trend, the hotter the stars are the higher their rotational velocity can be. There are one RHB star (HD 195636) and one globular cluster RR Lyrae star (V104/M5) with rotational velocity in excess to the global tendency defined by the tree samples. The same trend of the projected rotational velocities of BHB and RHB stars as seen from the modulation periods of RR Lyrae stars is the first direct evidence that the modulation period reflects, indeed, the rotational period of the stars._

**Acknowledgements.** This research has made use of the SIMBAD database, operated at CDS Strasbourg, France. The financial support of OTKA grants T-043504, T-046207 and T-048961 is acknowledged. This paper utilizes public domain data obtained by the MACHO Project, jointly funded by the US Department of Energy through the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48, by the National Science Foundation through the Center for Particle Astrophysics of the University of California under cooperative agreement AST-8809616, and by the Mount Stromlo and Siding Spring Observatory, part of the Australian National University. This publication makes use also of the data from the Northern Sky Variability Survey created jointly by the Los Alamos National Laboratory and University of Michigan. The NSVS was funded by the Department of Energy, the National Aeronautics and Space Administration, and the National Science Foundation. ## REFERENCES * Achterberg, H., & Husar, D. 2001 , _IBVS_, **No. 5210**. * Alcock, C., et al. 2000 , _Astrophys. J._, **542**, 257. * Alcock, C., et al. 2003 , _Astrophys. J._, **598**, 597. * Antipin, S. & Jurcsik, J. 2005 , _IBVS_, **No. 5632**. * Behr, B. B. 2003a , _Astrophys. J. Suppl. Ser._, **149**, 67. * Behr, B. B. 2003b , _Astrophys. J. Suppl. Ser._, **149**, 101. * Carney, B. W., Latham, D. W., Stefanik, R. P., Laird, J. B., & Morse, J. A. 2003 , _Astron. J._, **125**, 293. * Chis, D., Chis, G., & Mihoc, I. 1975 , _IBVS_, **No. 960**. * Clement, C., & Rowe, J. 2000 , _Astron. J._, **120**, 1579. * Cseresnjes, P. 2001 , _Astron. Astrophys._, **375**, 909. * Drissen, L., & Shara, M. M. 1998 , _Astron. J._, **115**, 725. * Dziembowski, W. A. & Mizerski, T. 2004 , _Acta Astron._, **54**, 363. * Jurcsik, J., Sodor, A., Varadi, M., Szeidl, B., et al. 2005a , _Astron. Astrophys._, **430**, 1049. * Jurcsik, J. et al. 2005b , _in preparation_ . * Khruslov, A. V. 2005 , _IBVS_, **No. 5699**. * Kinman, T., Castelli, F., Cacciari, C., Bragaglia, A., Harmer, D., & Waldes, F. 2000 , _Astron. Astrophys._, **364**, 102. * Lee, K. M., & Schmidt, E. G. 2001a , _P.A.S.P._, **113**, 835. * Lee, K. M., & Schmidt, E. G. 2001b , _P.A.S.P._, **113**, 1140. * Lee, K. M., Schmidt, E. G., & Tangan, S. T. 2002 , _P.A.S.P._, **114**, 546. * Moskalik, P., & Poretti, E. 2003 , _Astron. Astrophys._, **398**, 213. * Nagy, A., & Kovacs, G. 2005 , _in preparation_, , . * Olech, A., Kaluzny, J., Thompson, I. B., Pych, W., Krzeminski, W., & Schwarzenberg-Czerny, A. 1999a , _Astron. J._, **118**, 442. * Olech, A., Wozniak, P. R., Alard, C., Kaluzny, J., & Thompson, I. B. 1999b , _MNRAS_, **310**, 759. * Olech, A., Kaluzny, J., Thompson, I. B., Pych, W., Krzeminski, W., & Schwarzenberg-Czerny, A. 2001 , _MNRAS_, **321**, 421. * Peterson, R. C., Rood, T. R., &, Crocker, D. A. 1995 , _Astrophys. J._, **453**, 214. * Peterson, R. C., Carney, B. W., &, Latham, D. W. 1996 , _Astrophys. J._, **465**, L47. * Phillips, J., & Gay, P.L. 2004 , _AAS_, **205**, 5404. * Recio-Blanco, A., Piotto, G., Aparicio, A., & Renzini, A. 2004 , _Astron. Astrophys._, **417**, 597. *

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# Initial Conditions for Massive Star Birth - Infrared Dark Clouds K. M. Menten T. Pillai F. Wyrowski Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D-53121 Bonn, Germany (2005; ?? and in revised form ??) ###### Abstract We summarize the properties of Infrared Dark Clouds, massive, dense, and cool aggregations of interstellar gas and dust that are found througout the Galaxy in projection against the strong mid-infrared background. We describe their distribution and give an overview of their physical properties and chemistry. These objects appear to be the progenitors of high-mass stars and star clusters, but seem to be largely devoid of star formation, which however is taking place in localized spots. keywords: stars: formation, ISM: clouds, ISM: molecules, infrared: general, radio lines: ISM, masers + Footnote †: editors: R. Cesaroni, E. Churchwell, M. Felli, & C.M. Walmsley, eds. + Footnote †: editors: R. Cesaroni, E. Churchwell, M. Felli, & C.M. Walmsley, eds. + Footnote †: editors: R. Cesaroni, E. Churchwell, M. Felli, & C.M. Walmsley, eds. ## 1 Introduction Observations of dust and molecules provide almost all of the accessible information on deeply embedded high-mass (pre-)protostars, whose emission is frequently not detected even at mid-infrared wavelengths. As evidenced by, a.o., many contributions to this symposium, much current effort is expended on extensive surveys of unequivocal signposts of high-mass star formation, such as sources with tell-tale far-infrared spectral energy distributions and hot, dense molecular cores highlighted by maser emission in the methanol and water molecules. All the regions traced by these signposts are containing already formed (proto)stars and only recently have clouds with the potential of forming high-mass stars and/or clusters, but still yet largely devoid of stellar objects, been identified: Infrared Dark Clouds, whose observational status we shall summarize here. ## 2 Infrared Dark Clouds First recognized in mid-infrared images from the Infrared Space Observatory (ISO) and Midcourse Space Experiment (MSX) satellites Infrared Dark Clouds (IRDCs) appear in silhouette against the Galactic mid-infrared (MIR) background, frequently in filamentary shapes. Perault et al. (1996) report that ISOGAL1 images show "unexpectedly, a number of regions which are optically thick at \(15\mu\)m which are likely due to absorption" and "a convincing correlation with a depletion in \(2\mu\)m source counts". They estimate \(A_{V}>25\) and put forward "that these would be good candidates for precursors of star formation sites." Even before IRDCs became generally known as a distinct class of objects, Lis & Menten (1998) found absorption in the 45 \(\mu\)m ISO LWS detector band against the MIR background and emission in the 173 \(\mu\)m band toward M0.25+0.11, the low Galactic longitude end of the Galactic center "dust ridge', a string of submillimeter (submm) condensations found by Lis & Carlstrom (1994) which terminates with the prominent Sgr B2 star-forming region at its high longitude end. M0.25+0.11 was studied, even

earlier, in detail by Lis et al. (1994), who found very little, if any (a weak H\({}_{2}\)O maser) signs of star formation in it. Lis & Menten performed grey body spectral fits to the far-infrared data combined with their previous 350 - 800 \(\mu\)m submillimeter measurements and obtained a low temperature, \(\sim 18\) K, for the bulk of the dust in M0.25+0.11's core. In addition, they found that the grain emissivity is a very steep function of frequency (\(\nu^{2.8}\); see SS4.1). Lis & Menten derived a gigantic mass of \(1\times 10^{6}\)\(M_{\odot}\) for this object, comparable to the core of the "mini starburst region" Sgr B2. Footnote 1: ISOGAL is a 7 and \(15\mu\)m survey with ISOCAM (the ISO 3 – \(20\mu\)m camera) of ∼12∘ in the Galactic Plane interior to |l|=45∘. The first extensive dataset on IRDCs was compiled with the SPIRIT III infrared telescope aboard the Midcourse Space Experiment (MSX; see Price 1995), which surveyed the whole Galactic plane in a b=+-5 wide strip (Price et al. 2001) in four MIR spectral bands between 6 and 25 \(\mu\)m at a spatial resolution of \(\sim 18{\hbox to 0.0pt{.\hss}}\) \({}^{\prime\prime}\) \(\!3\). In an initial census of a ~180 long strip of the Galactic plane (between 269<l<91,b=+-0.5), Egan et al. (1998) find \(\sim 2000\) "compact objects seen in absorption against bright mid-infrared emission from the Galactic plane. Examination of MSX and IRAS images of these objects reveal that they are dark from 7 to 100 \(\mu\)m." The IRDCs are best identified in the \(8\mu\)m MSX "A" band, because, first, the 7.7 and 8.6 \(\mu\)m PAH features associated with star-forming regions contribute to a brighter background emission and, second, the MSX A band is more sensitive than the satellite's other bands. M0.25+0.11 and the other condensations of the Galactic center dust ridge also appear conspicuously in absorption on an \(8\mu\)m MSX image presented by Egan et al. 1998. Hennebelle et al. (2001) in a systematic analysis of the ISOGAL images extracted a total of \(\sim 450\) IRDCs, for which they derive \(15\mu\)m opacities of 1 to 4. The four newly-detected massive and dense cold cores identified by Garay et al. (2004; see also his contribution to these proceedings) also represent an interesting sample of IRDCs. These objects are not mid-IR but mm-contiumm selected: The 1.2 mm dust emission reveals massive (\(M>400M_{\odot}\)) and cold (\(T<16\) K) cores. How do IRDCs compare to the Orion Molecular Cloud I (OMC-1), probably the best-studied high-mass molecular cloud/star-forming region complex? In Fig. 1, we show the 1.2 mm dust continuum emission from OMC-1 mapped with MAMBO2 and the 850\(\mu\)m SCUBA3 dust continuum map of IRDC G11.11-0.12 (Johnstone at al. 2003). At a distance of 3.6 kpc (see SS4.1) G11.11-0.12 has a remarkable resemblance with the integral-shaped Orion filament, both, in structure and in dimensions. The bright MIR emission along the Galactic plane favours the identification of a massive cold cloud as infrared dark, which the OMC-1 region is not due to the absence of a MIR background caused by its location outside of the Galactic plane. One glaring difference though exists between the two maps: the prominent maximum in OMC-1, marking the very active BN/KL high-mass stars-forming region (see SS5). Footnote 2: The **MA**x-Planck **M**illimeter **BO**lometer array is operated at the IRAM 30m telescope on Pico Veleta, Spain. Footnote 3: The **S**ubmillimeter **C**ommon **U**ser **B**olometer **A**rray is operated at the 15 m James-Cleck-Maxwell Telescope on Mauna Kea, Hawaii. ## 3 Galactic distribution and distances Using a standard Galactic rotation curve, Carey et al. (1998) determined kinematic distances for some of the IRDCs in their sample. They obtain distances between 2.2 and 4.8 kpc, proving without a doubt that the clouds are not local. Their distances agree with those of HII regions in their vicinity. Recently, Simon et al. (2004) prepared a catalogue of \(\sim\) 380 IRDCs identified from th

e MSX survey, based on the morphological correlation of MIR extinction and \({}^{13}\)CO emission, as observed in the BU-FCRAO Galactic ring survey (GRS) of the inner Milky Way. They find that the majority of the dark clouds are concentrated in the Galactic ring at a galactocentric radius of 5 kpc. The kinematic distances derived range from 2 - 9 kpc. In Table 1, we list the source parameters of all the IRDCs for which data at wavelengths other than the MIR have been collected. The cloud sizes as reported by Carey et al. (1998) are from 0.4 - 15 pc while Teyssier at al. (2002) report structures of filaments down to sizes \(\leq 1\) pc. ## 4 Physical parameters or IRDCs ### Density, column density and temperature Based on observations of the formaldehyde molecule (H\({}_{2}\)CO), Carey et al. (1998) argue that IRDCs objects are dense (\(n>10^{5}\) cm\({}^{-3}\)), cold (\(T<20\) K) cores, apparently without surrounding envelopes. However, later work by Teyssier at al. on a different IRDC sample report that large field maps obtained with the 4-m Nanten telescope in the \({}^{13}\)CO J\(=1-0\) line, which probes relatively low densities, (Zagury et al., unpublished data) indicate that at least these IRDCs may indeed have lower density envelopes. We have confirmed this for the Carey et al. sample with hitherto unpublished \({}^{13}\)CO \(J=1-0\) maps retrieved from the GRS. Carey et al. (1998) conclude that the IRDCs they have studied have extinctions in excess of 2 mag at 8 \(\mu\)m. Using the infrared (visual through \(30\mu\)m) extinction law Lutz et al. (1996) derived for the Galactic center, this indicates visual extinctions of \(>30\) mag. How representative Lutz et al.'s law is for other lines of sight is unknown. Certainly it does lack the pronounced minimum for standard graphite-silicate mixes in the 4 - 8 \(\mu\)m range predicted by Draine & Lee (1984), which seems well-established by observations toward various lines-of-sight (see references therein). Actually, IRDC opacities at two wavelengths (e.g. 7 and 15 \(\mu\)m) can be used as a check on the extinction curve and its possible variation with different lines of sight; see Teyssier et al. 2002. These authors find a (marginally) lower 7 to 15 \(\mu\)m opacity ratio for clouds located away from the Galactic center compared to clouds that appear in the Galactic center direction. For the latter value they derive \(\sim 1\), which is consistent with Lutz et al.'s law. Using the relation given by Bohlin et al. (1978), assuming that all the hydrogen is in Figure 1: _Left panel:_ 1.2 mm dust continuum map of the Orion Molecular Cloud 1 (courtesy T. Stanke). _Right panel:_\(850~{}\mu\)m map of G11.11-0.12 (Johnstone et al.2003)

molecular form and a "standard" ratio of total to selective extinction of 3.1, hydrogen column densities in excess of \(3\times 10^{22}\) cm\({}^{-3}\) is derived. An independent H\({}_{2}\) column density estimate can be obtained from observations of (sub)millimeter dust emission, which, in addition, also allow determination of the cloud (gas+dust) mass (see, e.g., Mezger et al. 1987, 1990; Lis & Menten 1998). At (sub)millimeter wavelengths the dust emission is generally optically thin over most of the volume of an interstellar cloud. Thus, at wavelength \(\lambda\) the measured flux density, \(S_{\lambda}\), is given by \(\int B_{\lambda}(T_{\rm D})(1-e^{-{\tau}_{\lambda}}){\rm d}\Omega\), where \(T_{\rm D}\) is the temperature of the dust, \({\tau}_{\lambda}\) its optical depth and \(B_{\lambda}\) is the Planck black body brightness. The integration is either over the beam solid angle for a point-like source or over the source's angular extent, if the latter is extended. \({\tau}_{\lambda}\) is proportional to the hydrogen column density, \(N({\rm H}_{2})\), and the dust absorption cross section per hydrogen atom \(\sigma_{\lambda}\), which itself is assumed to be proportional to \(\lambda^{-\beta}\). Using all of the above, one finds that the H\({}_{2}\) column density is related to \(S_{\lambda}\) as \(N({\rm H}_{2})\propto S_{\lambda}\lambda^{3+\beta}(e^{hc/\lambda T_{\rm D}}-1)\). The cloud mass, \(M\), is proportional to \(N({\rm H}_{2})D^{2}\), where \(D\) is the cloud's distance. Carey et al. (2000) imaged a sample of 8 IRDCs in \(450\) and \(850\mu\)m dust emission using \begin{table} \begin{tabular}{l l l c c c c} Name & R.A. & Decl. & \(V_{\rm LSR}\) & d & \(N({\rm H+H_{2}})\) & \(T_{\rm kin}\) \\ \hline & (J2000.0) & (J2000.0) & (km s\({}^{-1}\)) & (kpc) & (\(10^{22}~{}{\rm cm^{-2}}\)) & (K) \\ \hline DF+04.36-0.06 \({}^{t}\) & 17:55:53.07 & \(-\)25:13:18.7 & \(11.4\) & \(3.5\) & \(-\) & \(-\) \\ DF+09.86-0.04 \({}^{t}\) & 18:07:37.22 & \(-\)20:25:54.5 & \(17.7\) & \(2.8\) & \(6.1\) & \(10.0\) \\ DF+15.05+0.09 \({}^{t}\) & 18:17:37.87 & \(-\)15:48:59.9 & \(29.9\) & \(3.1\) & \(12.6\) & \(-\) \\ DF+18.56-0.15 \({}^{t}\) & 18:25:19.52 & \(-\)12:49:57.0 & \(50.5\) & \(4.0\) & \(-\) & \(8.0\) \\ DF+18.79-0.03 \({}^{t}\) & 18:25:19.84 & \(-\)12:34:23.1 & \(-\) & \(3.6\) & \(-\) & \(-\) \\ DF+25.90-0.17 \({}^{t}\) & 18:39:10.13 & \(-\)06:19:58.8 & \(-\) & \(5.5\) & \(-\) & \(-\) \\ DF+30.23-0.20 \({}^{t}\) & 18:47:13.16 & \(-\)02:29:44.7 & \(104.7\) & \(6.7\) & \(11.1\) & \(8.0\) \\ DF+30.31-0.28 \({}^{t}\) & 18:47:39.03 & \(-\)02:27:39.8 & \(-\) & \(6.3\) & \(-\) & \(-\) \\ DF+30.36+0.11 \({}^{t}\) & 18:46:21.16 & \(-\)02:14:19.0 & \(96.1\) & \(5.9\) & \(-\) & \(-\) \\ DF+30.36-0.27 \({}^{t}\) & 18:47:42.37 & \(-\)02:24:43.2 & \(-\) & \(6.9\) & \(-\) & \(-\) \\ DF+31.03+0.27 \({}^{t}\) & 18:47:00.39 & \(-\)01:34:10.0 & \(77.8\) & \(4.9\) & \(11.1\) & \(10.0\) \\ DF+36.95+0.22 \({}^{t}\) & 18:57:59.51 & +03:40:33.3 & \(-\) & \(5.0\) & \(-\) & \(-\) \\ DF+51.47+0.00 \({}^{t}\) & 19:26:12.74 & +16:26:12.6 & \(54.7\) & \(5.3\) & \(7.7\) & \(10.0\) \\ G353.85+0.23 P1 \({}^{c}\) & 17:29:16.5 & \(-\)34:00:06 & \(-\) & \(-\) & \(-\) & \(-\) \\ G353.51-0.33 P1 \({}^{c}\) & 17:30:26.0 & \(-\)34:41:48 & \(-\) & \(-\) & \(-\) & \(-\) \\ G357.51+0.33 P1 \({}^{c}\) & 17:40:49.9 & \(-\)31:14:50 & \(-\) & \(-\) & \(-\) & \(-\) \\ G10.74-0.13 P1 \({}^{c}\) & 18:09:45.9 & \(-\)19:42:04 & \(-\) & \(-\) & \(-\) & \(-\) \\ G11.11-0.12P1\({}^{p}\) & 18:10:29.27 & \(-\)19:22:40.3 & \(29.2\) & \(3.6\) & \(1.7\) & \(13.5\) \\ G19.30+0.07 \({}^{p}\) & 18:25:56.78 & \(-\)12:04:25.0 & \(26.3\) & \(2.2\) & \(-\) & \(18.5\) \\ G24.72-0.75 \({}^{p}\) & 18:36:21.07 & \(-\)07:41:37.7 & \(56.4\) & \(3.6\) & \(-\) & \(20.3\) \\ G24.63+0.15 \({}^{p}\) & 18:35:40.44 & \(-\)07:18:42.3 & \(54.2\) & \(3.6\) & \(-\) & \(14.4\) \\ G28.34+0.06P1\({}^{p}\) & 18:42:50.9 & \(-\)04:03:14 & \(78.4\) & \(4.8\) & \(3.3\) & \(16.6\) \\ G28.34+0.06P2\({}^{p}\) & 18:42:52.4 & \(-\)03:59:54 & \(78.4\) & \(4.8\) & \(9.3\) & \(16.0\) \\ G33.71-0.01\({}^{p}\) & 18:52:53.81 & +00:41:06.4 & \(104.2\) & \(7.2\) & \(-\) & \(17.2\) \\ G79.27+0.38 \({}^{p}\) & 20:31:59.61 & +40:18:26.4 & \(1.2\) & \(1.0\) & \(8.3\) & \(11.7\) \\ G79.34+0.33 \({}^{p}\) & 20:32:26.20 & +40:19:40.9 & \(0.1\) & \(1.0\) & \(8.8\) & \(14.6\) \\ G81.50+0.14 \({}^{p}\) & 20:40:08.29 & +41:56:26.4 & \(8.7\) & \(1.3\) & \(-\) & \(16.6\) \\ \hline \end{tabular} Notes: Columns are name, right ascension, declination, LSR velocity, distance, total column density, and kinetic temperature. In souces with a distance ambiguity, the near distance was chosen. \({}^{t}\) refers to sources from Teyssier et al. 2002, \({}^{c}\) from Carey et al. (2000), ’P1/P2’ refers to the brightest submm peaks of Carey et al. (2000), \({}^{p}\) means that the position of the brightest ammonia peak is given rather than the submm peak position (see Pillai et al. 2005a). \end{table} Table 1: List of all IRDCs with (sub)mm-wavelength data

SCUBA. Since it impossible to determine, both, \(T_{\rm D}\) and \(\beta\) with just two data points, Carey et al. calculated dust color temperatures for three different values of \(\beta\), 1.5, 1.75, and 2 and note that higher \(\beta\)-values (meaning lower temperatures) yield a better fit to the low temperatures Carey et al. (1998) obtained from H\({}_{2}\)CO observations. The (high) column densities implied by choosing \(\beta=2\) are around \(5\times 10^{22}\) cm\({}^{-2}\) for 4 sources of their sample and around \(13\times 10^{22}\) cm\({}^{-2}\) for three. Three of the cores corresponding to the brightest submm peaks have masses around 100 \(M_{\odot}\), two other have 400 and 1200 \(M_{\odot}\), respectively. Two clouds in the Cygnus region have masses around 40 \(M_{\odot}\), but we note that distance estimates for that region are very uncertain and probably a short distance (1 kpc used by Carey et al. 1998) was chosen for the latter calculations. For \(\beta=1.75\), all these values are to be reduced by a factor of 2. As reported above (see SS2), for M0.25 Lis & Menten derive a very high value of \(\beta\) of 2.8. They take that to indicate the presence of dust grains covered with thick ice mantles. The values for the high densities and low temperatures deduced by Egan et al. (1998) are confirmed by Carey et al. (1998), who made, for 10 IRDCs, millimeter-wavelength observations of H\({}_{2}\)CO, which is a well-established density probe (Mangum & Wootten 1993; Mundy et al. 1987). Since they observed several transition, they were able, using a Large Velocity Gradient method, to determine temperatures and abundances. Unfortunately, these authors do not discuss their results source by source, but only give general statements. Leurini in her dissertation (Bonn University; see also Leurini et al. 2004) has shown that methanol (CH\({}_{3}\)OH) is a highly useful interstellar density and temperature probe. Consequently, she conducted observations of IRDCs in a selected series of lines of that molecule, which she showed to be overabundant in these sources (see SS4.3) and, thus, easy to detect. Leurini also corroborates the high densities (\(\sim 10^{5}\) - \(10^{6}\) cm\({}^{-3}\)) indicated by the H\({}_{2}\)CO data. However, she only observed positions of submillimeter emission peaks, some of which (if not all) harbour embedded sources. Her analysis does, thus, not necessarily apply to general, cool IRDC material, but to gas that is influenced by embedded protostars (see SS5). This is reflected most directly in the high-velocity outflows seen in some sources, e.g, G11.11-0.12 and in the high kinetic temperatures of order 40 to 60 K she derives for these. ### Morphology A significant fraction of IRDCs (although no all) are filamentary. Are IRDCs really filaments, i.e. elongated cylinders, or are they sheets seen edge-on? This is actually an important question linked to their evolutionary state. Larson (1985), using theoretical arguments and numerical simulations, argues that fragmentation is unlikely to occur in an initially uniform cloud. Either an initial anisotropy or rotation or a magnetic field will in general cause the cloud to collapse toward a flattened or filamentary structure. Once overall collapse has been halted and approximate equilibrium has been established, gravitational instability can cause the resulting sheet or filament to break into fragments of a characteristic mass that depends on the temperature and the surface density of the cloud. Larson's arguments are supported by the work of Miyama et al. (1987a,b), who investigated the fragmentation instability of an isothermal gas layer, in order to see whether the observed structures of many dense interstellar clouds are the results of fragmentation of sheet like clouds. Linear perturbation theory predicts fragmentation of a parent sheet-like cloud in elongated structures, and using further nonlinear analysis they found that, if fragments are initially elongated, they become elongated more and more as they go on collapsing, ending up as very slender cylinders, which fragment further.

The G11.11-0.12 IRDC has a distinct filamentary appearance (see Figs. 1 and 4). Using a sophisticated computational technique Fiege et al. (2004) compared observations to three different models of self-gravitating, pressure-truncated filaments, namely the non-magnetic Ostriker (1964) model, and two magnetic models from the literature. Analysing the \(850\mu\)m SCUBA observations of G11.11-0.12, Johnstone et al. (2003) concluded that this source has a much steeper r-a,(a>~3) radial density profile than other (lower moss, lower extinction) filaments, where the density varies approximately as \(r^{-2}\), This steep density profile is consistent with the Ostriker model. After a wider search of parameter space, Fiege et al. conclude that the observed radial structure of G11.11-0.12 can be understood in the context of all three models. Discrimination between the different models may be possible with polarization measurements as the magnetic models predict dominant poloidal magnetic fields that are dynamically significant; G11.11-0.12 may be radially supported by a poloidal field. Fiege et al. predict polarization patterns expected for both magnetic models, which produce different polarization patterns. Polarimetry should, thus, be able to distinguish between the two magnetic models or a non-magnetic model. An instrument of choice will be PolKa, the Polarization Kamera designed to be used together with the bolometer arrays developed at the Max-Planck-Institut f r Radioastronomie, for example with the 295 element \(870\mu\)m Large APEX BOlometer CAmera (LABOCA), which is soon to be installed at the 12m Atacama Pathfinder EXperiment telescope (Siringo et al. 2004). To decide the sheet or cylinder question, let us consider G11.11-0.12. That cloud is at a distance of 3.6 kpc (Carey et al. 1998). The elongated submillimeter emission has an extent of 24 pc in the long and an average \(\sim 0.8\) pc in the short axis. The density is uncertain: values between 10\({}^{5}\) and 10\({}^{6}\) cm\({}^{-3}\) have been derived by Carey et al. (1998) from their H\({}_{2}\)CO data, Johnstone et al. (2003) argue for a few times \(10^{4}\) cm\({}^{-3}\). The H\({}_{2}\) column density is between 0.2 and 2\(\times 10^{22}\) cm\({}^{-2}\) (Carey et al. 2000). Using the extremes of these values, we find that the extent along the line of sight must be between a few times \(10^{-3}\) and 0.5 pc, definitely ruling out a sheet seen edge on. ### Chemistry of IRDCs Complex organic (i.e. O- and C-bearing) molecules in the interstellar medium are mostly found in hot, dense cores surrounded by high-mass protostars. They frequently have very high over abundances (factors of 100 - 1000) compared to dark cloud values. These are usually explained by the evaporation of icy dust grain mantles on which these molecules are formed in a cooler phase in the clouds lifetime by hydrogenation of CO to H\({}_{2}\)CO. Further hydrogenation leads to even more complex species. (Relatively) complex molecules are also found in cold dark clouds, with TMC-1 being a prominent nearby example (See, e.g. Kaifu et al. 2004). However, in the latter they all have very small abundances and are observable only because of TMC-1's proximity (yielding a high filling factor) and its moderately high density (\(~{}10^{4}\) cm\({}^{-3}\)) leading to substantial beam-averaged column densities. This makes exotic (but not organic in the strict sense of the work) species detectable, such as the polyyene carbon chains (Kaifu et al. 2004). What is the organic content of normal molecular clouds? This, essentially, is an unanswered question (the one example TMC-1 aside). Its answer has profound impact on astrochemistry (are grain mantles really needed to form these molecules?) and even astrobiology. Their high column densities make IRDCs ideal laboratories to address this question and potentially detect complex molecules. Such species might be present and widespread in many clouds, but would be rendered undetectable because of the modest column densities of ordinary clouds: Lines from almost all molecules significantly rarer

than NH\({}_{3}\) or CH\({}_{3}\)OH will most likely be optically thin, which makes their line intensity directly proportional to the column density. Observations of molecules in IRDCs so far have concentrated on just a few species: CO (several isotopomers), H\({}_{2}\)CO, CH\({}_{3}\)OH, and NH\({}_{3}\). In addition, Teyssier et al. (2002) observed several HC\({}_{3}\)N lines and two \(k\)-series of CH\({}_{3}\)CCH. The latter, a symmetric top, can be used as a temperature probe and its observations yield values for the kinetic temperature, \(T_{\rm kin}\), between 8 and 25 K; the higher values found toward embedded objects. Large Veloity Gradient (LVG) model calculations of HC\({}_{3}\)N, \({}^{13}\)CO, and C\({}^{18}\)O yield densities larger than \(10^{5}\) cm\({}^{-3}\) in the densest parts. Teyssier et al. ascribe the relatively low observed intensities (a factor of a few lower than in TMC-1) to a very low kinetic temperature (difficult to understand, as TMC-1 is cold, too, \(\approx 10\) K), a small filling factor or depletion on grains. In Fig. 2, we show the spectra of different molecules observed towards the brightest submm peak position of G11.11-0.12 (P1). The NH\({}_{3}\) and CH\({}_{3}\)OH observations produced interesting results: CH\({}_{3}\)OH and NH\({}_{3}\) are overabundant by factors of 5 - 10 relative to "normal"(= lower density) and less turbulent dark clouds , such as TMC-1 (Leurini, dissertation and 2005, Pillai et al. 2005a in prep.). In contrast, H\({}_{2}\)CO is _under_abundant by a factor of \(\sim 50\) (Carey et al. 1998). Given this situation it is completely unclear which molecules might be detectable and which ones not. Could it be that species with emission sufficiently strong and widespread to be easily detectable have until now been completely missed? Systematic searches for other molecules will yield a more complete picture of the chemistry of IRDCs, which, while certainly interesting in itself, will also shed light on general formation mechanisms of complex molecules. Moreover, they might help identify new temperature and density tracers and allow studies of (molecule-)selective depletion.

#### 4.3.1 Ammonia To exploit NH\({}_{3}\)'s properties as an excellent molecular cloud thermometer (Danby et al. 1988) 10 IRDCs were studied in the course of T. Pillai's dissertation (see also Pillai et al. 2005): They were mapped in the \((J,K)=\) (1,1) and (2,2) transitions near \(1.3\) cm wavelength (\(\sim 23.7\) GHz) with the MPIfR Effelsberg 100m telescope. The FWHM beam size at the frequencies of the NH\({}_{3}\) lines was \(40^{\prime\prime}\). The NH\({}_{3}\) emission correlates very well with MIR absorption and ammonia peaks (in the following referred to as "cores") distinctly coincide with dust continuum peaks, as shown in Fig. 3. Several compact sources were detected within the clouds with sizes smaller than the \(\approx 40^{\prime\prime}\) FWHM beam size. The total gas masses derived for entire clouds from NH\({}_{3}\) data range from 10\({}^{3}\) - 10\({}^{4}\)\(M_{\odot}\). We can constrain the average gas temperatures to \(10\mathrel{\hbox{\raise 2.15277pt\hbox{$<$}\hbox to 0.0pt{\hss\lower 2.15277pt \hbox{$\sim$}}}}T\mathrel{\hbox{\raise 2.15277pt\hbox{$<$}\hbox to 0.0pt{\hss \lower 2.15277pt\hbox{$\sim$}}}}20\) K. The temperature distribution within clouds has also been analysed and we find significant temperature gradients, with the temperature rising in outward direction, in all of the cases where we have a good signal-to-noise ratio throughout the map. This outward rise in temperature we find in all except one core can be readily interpreted as influence of the strong external UV field warming up the cloud. The only case where we find a positive correlation between the gas temperature and the integrated intensity is also the only case where the turbulence seems to increase towards the core. This one has the most evolved core and is also the most massive in our sample. We observe large line widths (\(1\leq\Delta v\leq 3.5\)) km s\({}^{-1}\), hence turbulence plays an important role in the stability of this IRDC. The column densities translate to extremely high \(A_{V}\) of 55 - \(450\) mag, therefore early star formation, if any, would be deeply embedded. The virial parameter defined as \(\alpha={\frac{{5}{\sigma^{2}}{R}}{GM}}\) is \(1.7\leq\alpha\leq 4\) for most of the clumps. Hence the cores appear to be unstable against gravitational collapse; in fact Figure 3: MSX images of the clouds at 8\({\mu}m\)_(greyscale)_ with NH\({}_{3}\) (1,1) integrated intensity as contours. The contour levels are 2, 4, and 6 times the \(1\sigma\) noise level. Tick marks are coordinate offsets (in arcseconds) relative to the positions given in Table 1 (from Pillai et al. 2005a). The bar marks a distance of 1 pc.

direct evidence for collapse might be revealed from VLA observations we have recently obtained. The fractional abundance of NH\({}_{3}\) (relative to \(\rm H_{2}\)) is \(1-6\times 10^{-8}\). This together with the excellent correlation in morphology of the dust and gas is consistent with the time dependant chemical model for NH\({}_{3}\) of Bergin & Langer (1997) and implies that NH\({}_{3}\) remains undepleted. We can constrain the ages of IRDCs based on this model to \(\geq 10^{7}\) years for \(\rm H_{2}\) densities \(\geq 10^{4}\) cm\({}^{-3}\), assuming that the NH\({}_{3}\) has reached its chemical equilibrium abundance. The time scales we derive for the clouds to disperse due to their own internal motions, of a few Myrs, provide a better upper limit to the life time of these clouds. There are significant velocity gradients observed between the cores but we find that they are not attributable to rotation. The effects of external shock/outflow tracers need to be investigated. Based on the observed line widths, the derived gas temperatures and the NH\({}_{3}\) column densities, we made a comparison of IRDC condensations with objects representing more evolved stages of high-mass star formation like the High-mass Protostellar Objects (HMPOs) studied by Sridharan et al. (2002) and Beuther et al. (2002). There is a clear trend in temperature from the low temperatures of the IRDCs to typical temperatures of 20 - 30 K for the HMPOs without (significant) HII region to the higher temperatures of UCHII/hot core regions. The line widths in the HMPOs are generally higher than those in the IRDCs. ### Magnetic fields Theoretical studies suggest that magnetic fields play a crucial role in the star formation process. But contrary to other parameters like density, temperature, the velocity field, and molecular abundances, it has been notoriously difficult to determine \(B\)-fields in any regime of the interstellar medium (ISM) from diffuse clouds to dense star-forming cores (see, e.g., Crutcher 1991 and these proceedings). Virtually the only method for a direct determination of \(B\) is the Zeeman effect, which causes a frequency shift of the right-circularly polarized (RCP) relative to the left circularly polarized (LCP) component of a spectral line from a molecule with a suitable electronic structure and also from the 21 cm line of the hydrogen atom. One of the few interstellar molecules with detectable Zeeman splitting is hydroxyl (OH), whose ground-state hyperfine structure (hfs) transitions near 18 cm wavelength (at 1665, 1667, 1612, and 1720 MHz) have measurable splittings. OH is found in the general molecular interstellar medium and can be detected in clouds with densities \(\geq\) a few \(10^{3}\) cm\({}^{-3}\). However, it is also found, at elevated abundance, in the dense, expanding envelopes of ultracompact HII regions, which have densities \(\geq 10^{7}\) cm\({}^{-3}\) (Hartquist et al. 1995). \(B\) fields of order a few tens of \(\mu\)G have been found from OH Zeeman measurements of low density dark clouds (see, e.g. Goodman et al. 1989; Crutcher & Troland 2000), while much stronger, few mG, fields are derived for the much denser maser regions (see, e.g., Fish et al. 2003). While it is relatively easy to measure Zeeman-splitting in OH masers, over the years, large amounts of observing time have been dedicated to measuring Zeeman-splitting in lower density clouds with few, but precious results. A picture has emerged in which the \(B\)-field strength increases with density, \(n\), i.e. \(|B|\propto n^{\kappa}\). From theoretical arguments (conservation of magnetic flux and mass) one expects \(\kappa=2/3\) for a collapsing cloud if the \(B\)-field is unimportant throughout the collapse and \(\kappa=1/2\) in the opposite case (Crutcher 1991). Models of ambipolar diffusion-driven cloud contraction deliver \(\kappa\approx 0.47\) (Fiedler & Mouschovias 1993).

See Fig. 1 of from Padoan & Nordlund 1999 for a recent compilation of measured \(B\)-field strengths vs. density. It is apparent from this figure that there is a dearth of \(B\)-field data points for densities between \(10^{5}\) and \(10^{6}\) cm\({}^{-3}\). \(B\)-field measurements of IRDCs will probe just this highly interesting portion of parameter space. A preliminary survey with the Effelsberg 100m telescope showed OH absorption in both the 1665 and the 1667 MHz hyperfine lines with total (Stokes \(I\)) intensities of order \(-1\) K or deeper in several IRDCs. Given the IRDCs' densities cited above we would expect \(B\) of order several hundred mG, similar to the values found in high-mass star-forming regions. A 2 hour integration on one source, G yielded an upper limit of 135 \(\mu\)G at a 99% (3\(\sigma\)) confidence level, consistent with the upper limits derived by Crutcher at al. (1993) for regions of similar density. The \(B\)-field morphology will be determined from submillimeter polarization observations (see 4.2). Feldman et al. (2003) report in an abstract SCUBA polarization observations of MSX IRDCs where they quote very high percentage polarizations (\(\sim 6\)%) and find that inferred magnetic field directions are correlated with the cloud structure. There seems to be trend for \(B\) to align along the direction of a filament. Bright, compact sources in the filaments are much less polarized, and their inferred \(B\)-field directions are perpendicular to the orientation of the filaments. ## 5 Ongoing star formation in IRDCs While large volumes of IRDCs appear to be devoid of signposts of ongoing star formation, such as ultracompact HII regions and/or CH\({}_{3}\)OH, OH or H\({}_{2}\)O masers, isolated centers of high or intermediate star formation are found in many clouds. Teyssier et al. (2002) found that OH and class II CH\({}_{3}\)OH masers et al. (1995) are associated with positions of (not overly pronounced) peak emission from the column density tracer C\({}^{18}\)O in the IRDCs DF+9.86-0.04 and DF+30.23-0.20. These are close to dust emission peaks. Since CH\({}_{3}\)OH masers are unambiguous tracers of high-mass star formation, we have obtained data on the 6.7 GHz CH\({}_{3}\)OH maser transition, towards a sample of \(\sim\) 50 dark clouds with a high (\(>\) 25%) rate of detections. Maybe to date the best-studied example of a star-forming core in an IRDC is the 850 \(\mu\)m emission peak in G11.11-0.12 studied in detail by Pillai et al. (2005a; in press). Coincident with a compact dust continuum source are both, an H\({}_{2}\)O and a CH\({}_{3}\)OH maser as shown in the inset of Fig. 4. Interferometric imaging with the Australia Telescope Compact Array show the CH\({}_{3}\)OH emission, which has a total velocity spread of \(\approx 11\) km s\({}^{-1}\) to have a velocity gradient with emission at different velocities aligned in a line, reminiscent of a disk. Other persuasive arguments for an embedded source are the detection of emission in the high excitation (3,3) line of ammonia with a wider linewidth than the lower excitation (1,1) and (2,2) lines (see Fig. 2). Model fits to all three NH\({}_{3}\) lines indicate a compact source with a size of \(\approx 3^{\prime\prime}\), characterized by a rotation temperature of 60 K, while the more extended emission from the ambient cloud has a rotation temperature of 15 K. The NH\({}_{3}\) column density of the hot, compact component is 9 times higher than that of the cool extended one. Finally, the infrared spectral energy distribution is best modelled by a source with a luminosity of 1200 \(L_{\odot}\), corresponding to a ZAMS star of mass 8 \(M_{\odot}\). \(K_{s}\)-band 2MASS data show what possibly is reflected light emanating from the protostellar source, which is embedded in a compact mm-wavelength dust continuum source imaged with the Berkeley-Illinois-Maryland Array (BIMA)

. ## 6 Conclusions The earliest phases of high-mass star formation are expected to be massive (a few hundred to thousand M\({}_{\odot}\)), cold (10 - 20 K) and quiescent clouds, emitting primarily at (sub)mm wavelenghts and containing no obvious IR sources or star formation tracers. One approach to identify the earliest, cold phases of massive star formation is to search for objects which appear in absorption at MIR wavelengths. Thus IRDCs are the most potential candidates for studying these initial conditions. Centimeter through submm observations reveal that typical IRDCs have gas densities \(>10^{6}~{}{\rm cm}^{-3}\), temperatures \(<20~{}{\rm K}\) and sizes of 1 - 10 pc but studies of their star formation content are still rare. Studies up to now seem to show that they are not all cold and quiescent. IRDCs appear to harbour sources of different evolutionary stages, not all of them necessarily in the high-mass regime. A better classification scheme based on molecular gas content, MIR contrast and extend is needed to compare IRDCs with local molecular cloud complexes (not clouds). Extensive studies of their energetics, kinematics and chemistry are essential to ascertain their role in forming stars, massive or otherwise. These would be the ideal test grounds for testing the present theories of forming massive stars via turbulent cores (McKee & Tan 2003; see also their contributions to these proceedings). We will need large, Galaxy wide surveys to understand the formation of IRDCs and their lifetimes. We would like to thank Malcolm Walmsley for comments on the manuscript. ## References * [Bergin and Langer (1997)] Bergin, E.A. and Langer, W.D.1997, _ApJ_, 486,316 * [Beuther et al.(2002)] Beuther, H., Schilke, P., Menten, K. M., Motte, F., Sridharan, T. K., & Wyrowski, F. 2002, _ApJ_, 566, 945 * [Bohlin et al.(1978)] Bohlin, R. C., Savage, B. D., & Drake, J. F. 1978, _ApJ_ 224, 132 * [Carey et al.(1998)] Figure 4: _Left:_ The \(8~{}\rm\mu m\) image of G11.11-0.12 with the SCUBA \(850~{}\rm\mu m\) map (Carey et al. 2000) overlaid. _Right:_ Southern filament of the SCUBA map in grey scale. The bar marks a distance of 1 pc. The _square_ delineates the position of the active star formation site P1, details of which are shown in the right upper corner inset. Here the _greyscale_ shows a BIMA 3 mm continuum image and a 2MASS \(K_{s}\) band image in shown in dashed contours. The _star_ denotes the H\({}_{2}\)O maser position and the _filled circle_ the CH\({}_{3}\)OH maser position (from Pillai et al. 2005b).

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# * Planar Integrated Optics and astronomical interferometry Optique Integree planaire pour l'interferometrie appliquee a l'astronomie 1 Footnote 1: institutetext: Laboratoire d’Astrophysique de l’Observatoire de Grenoble BP 53, 38041 Grenoble Cedex 9, France 2 Footnote 2: institutetext: Laboratoire d’Electromagnétisme Microondes et Optoélectronique BP 257, 38016 Grenoble Cedex 1, France 3 Footnote 3: institutetext: CSO mesure,70 rue des Martyrs, 38000 Grenoble, France Pierre Kern 11 Jean Philippe Berger 22 Pierre Haguenauer 2233 Fabien Malbet 11 Karine Perraut 11 ###### Abstract Integrated optics (IO) is an optical technology that allows to reproduce optical circuits on a planar substrate. Since 1996, we have investigated the potentiality of IO in the framework of astronomical single mode interferometry. We review in this paper the principles of IO, the requirements for interferometry and the corresponding solutions offered by IO, the results of component characterization and the possible fields of application. **Keywords:** Interferometry, Optical aperture synthesis, Integrated Optics, Planar Optics, Single mode optics. ###### Abstract L'optique integree est une technologie qui permet de reproduire des circuits optiques sur un substrat planaire. Depuis 1996, nous menons des recherches sur les potentialites de l'optique integree dans le contexte de l'interferometrie monomode en astronomie. Dans cet article, nous passons en revue les principes de l'optique integree, les specifications propres a l'interferometrie et les solutions correspondantes offertes par cette technologie, les resultats de caracterisations de composants ainsi que les domaines d'application. **Mots cles :** interferometrie, synthese d'ouverture optique, optique integree, optique planaire, optique monomode. ## 1 Introduction The use of guided optics for stellar interferometry was introduced to reduce constraints while combining coherent beams coming from several telescopes of an interferometer. Claude Froehly proposed in 1981 [1] to use single mode fibers to solve the problems linked to the beam transportation and high number of degrees of freedom of such an instrument. Laboratory developments [2][3] and on the sky experiments [4] have shown the important improvements introduced by guided optics. More than experimental setup simplification, s

ingle mode guided optics introduces modal filtering which allows translation of the phase disturbance for the incoming wavefronts into calibrable intensity fluctuations. The analysis of existing fiber-based experiments led us to propose planar integrated optics (hereafter IO) as a solution for some of the remaining difficulties linked to fiber optics properties or to the general instrument setup [6],[7]. In this paper, we present a review of the work done since 1996 by the team composed of partners from research laboratories (Laboratoire d'Astrophysique de l'Observatoire de Grenoble - LAOG, CEA/LETI and Laboratoire d'Electromagnetisme Microondes et Optoelectronique - LEMO) and from industrial laboratories (GeeO, CSO). Section 2 presents the principle of planar IO and an introduction to the related technology. This section presents also typical available IO functions. Section 3 summarizes the requirements for an interferometric instrument and the solutions offered by IO. Section 4 presents the results obtained during that period and shows how IO can be a convenient solution for the instrumentation for interferometry. The last section gives some perspectives of our developments. ## 2 Integrated Optics technology ### Planar optics principle Optical communications using single mode fiber optics for long distance connection impose periodic signal amplification. Triggered by telecommunications industry requirements, major efforts have been done to manufacture compact single chip repeaters directly connected to fibers avoiding multiple signal conversion [8].This has lead to develop techniques able to integrate complex optical circuits, as for integrated electronics, on small chips. The main technological breakthrough resided in the ability of integrating single-mode waveguides in a given substrate. In a planar waveguide (Fig. 1a) optical guidance is guaranteed by the three step-index infinite planar layers (\(n_{2}>n_{1}\) and \(n_{3}\)) [9]. The core layer thickness of index \(n_{3}\) ranges between \(\lambda/2\) and \(10\lambda\) depending on index difference \(\Delta n\). A large \(\Delta n\) leads to better light confinement. A fu Figure 1: Principle of mode propagation within a waveguide.

ll electromagnetic field description, shows that the modal beam propagation applies in waveguide structure [9]. The main part of the carried energy lies in the waveguide core, but evanescent field propagates in lateral layers and contribute to the mode propagation. A guiding structure with a given thickness and layers refractive index is characterized by a cut-off wavelength \(\lambda_{c}\), separating the single mode propagation (\(\lambda>\lambda_{c}\)) where only the fundamental mode propagates and the multimode propagation condition (\(\lambda\leq\lambda_{c}\), Fig. 1b). Only the single mode regime is considered in our developments. However multimode guided structures have been tested [10] for stellar interferometry. ### Waveguide manufacturing The guided area is obtained by _ion exchange technique [11]_. The Na+ ions of the glass substrate are exchanged by diffusion process with ions K+, Ti+, Ag+ of molten salts and result in an increase of the refractive index, producing the three-layer structure (air / ions / glass) capable to confine vertically the light. The implementation of the optical circuit is obtained by standard photomasking techniques (see Fig. 2 left) to ensure the horizontal confinement of the light. While ion exchange occurs at the surface of the glass, an additional step of the process can embed the guide, either by applying an electric field to force the ions to migrate inside the structure or by depositing a silica layer. The waveguide core is the ion exchange area and the cladding the glass substrate or the glass substrate and air. Depending on the type of ions, \(\Delta n\) can range between 0.009 and 0.1. This technology produced in Grenoble by LEMO and GeeO/Teem Photonics is commonly used for various components used in telecom and metrology applications. The waveguide structure can also be obtained by the _etching_ of silica layers [12] of various refracting indices (phosphorus-doped silica or silicon-nitride). As for other techniques photomasking is required to implement the optical circuit (see Fig. 2 right). The manufacturing process allows to choose either a high \(\Delta n\) (\(\Delta n\geq 0.5\)) to implement the whole circuit on a very small chip with small radii curves, or very low (\(0.003\leq\Delta n\leq 0.015\)) for a high coupling efficiency with optical fibers. This technology is used at CEA / LETI to produce components for various industrial applications (telecommunication, gyroscopes, Fabry-Perot cavities or interferometric displacement sensors). Single mode waveguide structure are also produced by UV light inscription onto _polymers_. The transmission of the obtained components are still too small for our applications. A technology based on \(LiNbO_{3}\) cristal doping by metals allows to produce single-mode waveguides with interesting electro-optical properties but this has not been tested yet for our specific applications.

### Planar optics functions Several functions working at standard telecom wavelengths (\(0.8\mbox{ $\mu$m}\), \(1.3\mbox{ $\mu$m}\) and \(1.5\mbox{ $\mu$m}\)) are available with the different technologies. Figure 3 displays an example of IO chip used in an interferometric displacement sensor [13]. It nicely illustrates IO capability because it contains nearly all basic functions. The reference channel of the interferometer head and the measurement channel are provided by splitting the He-Ne light by a direct Y-junction. The light of the measurement channel, retroreflected is injected again in the waveguide and directed to the interferometer head thanks to a directional coupler. The interferometer head is a large planar guide fed by two tapers. Interference between the two beams produces fringes which are sampled by four straight guides, providing measurements with \(\lambda{\rm/4}\) phase difference at the same time. The most common functions are listed below: * *Direct Y-junctions for achromatic 50/50 power splitting. * *Reverse Y-junctions for elementary beam combination as bulk optics beam splitters with only one output. The flux to the second interferometric state in phase opposition is radiated into the substrate. * *Directional couplers allow the transfer of the propagated modes between neighbour guides. The power ratio division in each output beam is linked Figure 2: Ion exchange (LEMO) and etching (LETI/CEA) techniques

to the guide separation, the interaction length and the wavelength. Symmetrical couplers ensure a chromatic separation of the signal. Achromatic separation requires an asymmetrical design. * *X-crossings with large angles (\(\geq 10^{\circ}\) ) for guide crossing with negligible cross-talk effects. Smaller angles favor power exchange between the guides; * *Straight waveguides. * *Curved waveguides give flexibility to reduce the component size. Possible curvature radii depend on the core and substrate index difference. * *Tapers or adiabatic transitions, thanks to smooth transition of the guide section, adapt propagation from a single mode straight waveguide to a larger waveguide. Consequently light propagates and remain in the fundamental mode of the multimode output waveguide. These components reduce the divergence of the output beam. ## 3 Instrumental requirements in stellar interferometry ### Functional requirements The wavefront distortion, due to atmospheric transmission or to instrumental aberrations, induces fringe visibility losses. The main errors can be corrected by an adaptive optics system or by an appropriate optical design adjusting the entrance pupil diameter to the local value of atmospheric coherence area diameter for the considered wavelength. The remaining phase errors on the incoming wavefront can be removed using a _spatial or modal filtering_[5]. The high spatial frequencies introduced by the wavefront distortion are rejected by a field stop in the Fourier plane. The diffraction limited image of an unresolved object leads to a beam etendue of \(S\Omega=\lambda^{2}\). It corresponds to Figure 3: Planar Optics displacement sensor developed by LEMO [13] and corresponding function list.

single mode propagation with no longer pupil and focal plane position. This fundamental mode is properly directed by a single-mode waveguide (fiber optics or planar waveguide) when it meet the \(\lambda^{2}\) beam etendue condition. If higher modes enter the waveguides they are rejected out of the core according to propagation laws. This modal filtering is wavelength dependent. Current simulations are in progress [21] to determine the appropriate dimensions of the guide to operate an efficient filtering: waveguide diameter, required guide length, operating wavelength range. When a _modal filtering_ is applied, phase distortions are translated into intensity variations in the waveguide. To calibrate the contrast of the fringe pattern, a photometric correction can be applied on the recorded interferometric signal taking into account the flux variations for each incoming beam. The variation of the telescope fluxes are monitored together with the interferometric signal. Associated to the modal filtering, _photometric calibration_ allows significant improvements of the fringe visibility estimation. This principle has been applied successfully with accuracy down to 0.3% with the FLUOR instrument [4]. Observation over _atmospheric spectral bands_ are required in many applications. Wavelength dependent parameters may affect the extraction of the interferometric signal. The bias introduced by differential chromatic dispersion between interferometer arms due to optical components must be compensated or calibrated. Instrumental differential rotations and phase shifts between the polarization directions can affect the fringe visibility. Symmetric optical design allows to reduce polarization effects but high contrasts require the compensation of the _differential effects on polarizations [22]_ by Babinet compensators suggested by Reynaud [23] or Lefevre fiber loops. The _optical path equalization_ is necessary from the interference location to the stellar object with a sub-micrometer accuracy. Delay lines operates this optical function. Fiber optics solution have been proposed and tested in laboratory [24], [25]. Differential fiber dispersion remains the limiting factor of the proposed concept. ESO prototype fringe sensor unit [26] uses a fiber optics delay line. Finally, _very high OPD stability_ is mandatory, especially for phase closure. Variations of the OPD leads to phase relationship loss and reduce the image reconstruction capability. The opto-mechanical _stability_ of the instrument strongly affects the fringe complex visibility. ### System requirements The _beam combiner_ ensures visibility and phase coding of the interference pattern. Telescope combiner for more than 3 telescopes are required to obtain synthesized images. The image reconstruction implies very accurate phase difference control between the interferometer arms. The beam combination

can be done either using single mode or multimode optical field. In each case, the combination is performed using coaxial or multi-axial beams. The _spectral dispersion_ of the fringes is used for either astrophysical parameter extraction, or for fringe detection. Stellar interferometry is generally performed within the standard atmospheric spectral windows of ground-based observation. The spectral analysis is achieved either by using optical path difference modulation (double Fourier Transform mode) [14] in coaxial mode or with dispersive components. In the latter case, the fringe light is focused on the spectrograph slit using a cylindrical optics [15] to concentrate the flux along the slit. A _fringe tracker_ allow longer acquisition times and increase the instrument sensitivity. Time dependent behaviors affect the central white fringe position: sidereal motion, instrument flexures and fine telescope pointing decay on smaller scale. Finally atmospheric turbulence affects ground based observations inducing atmospheric piston at the interferometer baseline scale. The fringe tracker ensures the fringe stability thanks to a suitable delay-line controlled with a proper sampling of the OPD fluctuations at a frequency compatible with the considered time scale. It avoids visibility losses due to fringe blurring. The fringe sensor is part of the fringe tracker, it is aimed to measure the central fringe location of the interference pattern with suitable accuracy. Various principles have been proposed [16], [17], [18]. Multi-axial mode allows a complete sampling in a single acquisition, while coaxial mode requires an OPD active modulation. Astrometrical mode requires milli-arcsecond positioning accuracy on simultaneous observations on two distant stars. Such measurements require an appropriate _metrology control_ of the optical path length for the two stars, from the telescope entrance to the fringe detection device. More recently for search of faint objects around bright stars, instruments using interferometry have been proposed [19]. The on-axis star light is extinguished thanks to a \(\pi\) phase delay on one of the interferometer arms before combination, providing a _nulling interferometer_. Fringe separation is adjusted to place the central fringe of the off-axis searched object interference pattern on the black fringe position. Interferometer pupil arrangement is optimized to obtain enhanced central star light rejection. ### IO: a promising solution Intrinsic properties of planar IO solve a large part of the functional requirements described above of an instrument dedicated to interferometry mostly due to its ability to propagate only the fundamental mode of the electromagnetic field: * *Single mode propagation within a half octave without significant losses [29].

* *Broad band transmission if the used functions are compatible with an achromatic transmission (available for individual J, H and K atmospheric bands) [29], [30]. * *Intrinsic polarization maintaining behavior for most of the cases [31]. * *High optical stability on a single chip [31]. * *Accurate optical path equality (\(leq2\mu{m}\)) if suitable care is applied in the design and in the component manufacturing [32]. * *Reduced differential effects between interferometric paths, since they are all manufactured during the same process on the same substrate [32]. * *Photometric calibration easily implemented using existing basic functions (direct Y junction, directional coupler) * *Measurements performed at LEMO shows that temperature constraints applied on a component only introduces l/90000/ mm/C) phase shift compatible with phase closure requirements [31]. Moreover, existing IO systems are also able to provide part of the required subsystem for interferometry in astronomy: * *Beam combination can be achieved either in coaxial mode by reverse Y-junction, directional couplers, Multi Mode Interferometer [33] (MMI) and/or by tapers in multi-axial mode (see Fig. 4). * *The output of a taper interferometer produces an illumination along a single direction suitable for spectrograph entrance slit. * *Using beam combiner for fringe sensing, many solutions may be applied: * **-**A coaxial combiner with 2 outputs in phase opposition, or 4 outputs with a \(\pi/4\) phase difference provides the proper fringe sampling [40]. More phase samples can be provided by small OPD modulation. * **-**A suitable sampling of the dispersed output of a taper interferometer can also be used on an array detector for a fringe sensing using the Koechlin arrangement [17]. * *Several interferometric displacement sensors have been proposed and even offer for sell using planar optics. The existing concepts are directly applicable to metrology for interferometry [13]. * *Nulling interferometry requires a \(\pi\) phase shift. Interferometer including such functionality has been tested for industrial use with laser. ## 4 Main results A strong collaboration between LAOG and IO specialists (LEMO, LETI, GeeO, Teem Photonics) have given us the oportunity to propose a complete development program. Starting from available off-the-shelves components, we demonstrated the ability of the concept to meet the requirements of interferometry [27], [28]. From the first analysis, we have developed adapted components for astronomy, with suitable designs. Systema

tic tests were performed on first set of components realized with ion exchanged and etching technique [29], [30]. We are starting now developments leading to new functions or new waveguide technology. We will then be able to propose first concepts of fully integrated instrument. Theoretical investigations are also in progress to optimize the combiner parameters [21] and analyze the influence of guided beam on interferometric scientific data. ### Instrumental testbeds Systematic measurements have been performed on our components to check their ability to fulfill interferometry requirements: * *Photometric measurements to characterize all our components transmission over the whole spectral band and the transmission of each function implemented on the corresponding substrate. * *A waveguide mode characterization and cut-off wavelength determination has been performed thanks to an analysis of the intensity spread out in the image of the exiting mode and spectral analysis of the output signal for the whole bandwidth [29]. * *A Mach Zehnder bench is used for interferometric qualification (Fig. 5a). A collimator illuminated by a fiber optics produces a plane wave. It is illuminated either with a He-Ne laser (alignment needs), a laser diode (fringe localization) or a white light source (broad band characterization). The Figure 4: Available beam combiners. For the reverse Y-junction (a) part of the signal, in phase opposition, is radiated inside the substrate. Directional coupler (b) provides two outputs in phase opposition. MMI design (c) corrects this functional loss, providing three outputs. Each external guide collects 1/4 of the interferometric signal and provide modulated light in phase opposition with the central guide (which contains 1/2 of the interferometric signal). The taper interferometer (d) ensures spatial encoding of the fringes whose sampling depend on the two taper characteristics (angles, dimensions).

collimated light is splitted by one or several bulk optics beam splitters. The provided channels are imaged on fiber connected to the inputs of the component. * *A stellar interferometer simulator (Fig. 5b) for phase closure characterization. In this bench the incoming wavefront is sampled by several apertures with baseline / pupil ratio compatible with real stellar interferometer conditions. It provides unresolved images of a complex object for individual aperture, which can be resolved by the simulated baselines. * *In any case the polarization behavior has to be carefully characterized. For all of these test benches, polarizers associated with polarization maintaining fibers ensure the polarization control of the light. ### Results with off-the-shelves components For a first validation step, part of an existing component was used in order to combine two beams in coaxial mode. This component contains 2 direct Y-junctions providing a 50/50 beam splitting for photometric calibration for both inputs and one reverse Y-junction to provide the interferometric combination. This component obtained by ion exchange technique (Ag +) was fully characterized [28], [29] (see Figure 6). For these tests special care were given to the components / fiber optics connection. These components were produced and connected by GeeO. It provides 92% fringe contrast on the whole H atmospheric band. The optimized contrasts was obtained thanks to excellent polarization behavior, with a contrast stability over several hours as low as 2%. The photometric transmission is 43%. The main loss of this component is due to the Y-junction. Using optimized component, this transmission can reach 60% with Y-junction and 80% transmission with an adapted beam combiner [29], [36], [28]. ### Design of specific components Based on those encouraging results we designed specific masks for broad band and low flux level uses. Components for 2, 3 and 4 telescope combination Figure 5: Interferometric characterization benches: a) Mach Zehnder bench (amplitude separation ) for interferometric characterization of the components (right) b) Interferometer simulator (wavefront separation) for image reconstruction (left).

were produced with both silica-on-silicon and ion exchange techniques. The purpose of this work is to provide a realistic comparison of several beam combiners possible designs [32]. It is the first time an experimental program can cover such a wide range of multi-axial and coaxial solutions, pair-wise and all-in-one solutions. The component geometry is chosen to match the fiber and detector dimensions. The LETI components (silica-on-silicon) allowed the characterization of asymmetrical couplers, by a systematic analysis couplers parameters influence. These components provide two interferometric outputs in phase opposition. The obtained design allows quasi-achromatic splitting ratio for the whole H band [30]. Component limitations were identified in terms of transmission and chromaticity and will be taken into account for next realizations [36]. One of the obtained components produce pair-wise combinations of 3 telescopes input beams (see Figure 7). Its excellent performances lead us to propose it as a solution for the IOTA 3-way new beam combiner. The LEMO components allowed an analysis of several beam combinations modes: Y junctions, multi-axial, MMI. 2, 3 and 4 telescopes beam combiners we Figure 6: Coaxial beam combiner (LEMO/GeeO component) and corresponding broad band interferogram before correction with both photometric channels (left) and corrected from photometric fluctuations (right) [28], [29]. Figure 7: 3 telescope beam combiner produced using LETI facilities. Beam combiners are asymmetrical couplers optimized for the whole H band [30]. The obtained interferograms show 90% contrast through the H band, and a throughput higher than 60%

re produced. An example of mask can be seen in figure 8. IO technology allows cut the chip to at different input guide position in order to test all the beam combiners integrated stages. For a first series of experiments all the beam combiners inputs were linked together thanks to suitable Y-junctions [32]. In this case interference signal depends only on internal component behaviors independently of the feeding optics resulting in a characterization of IO specific properties. The obtained results show the low influence to external constraints on the component, and the good symmetry of the optical path within the chip [32]. ### Validation of the concept on the sky Observations using 2 telescope components have been successfully performed using IOTA facilities at Mount Hopkins, Arizona [34]. Further observations using 3-telescope facilities are foreseen in a second step to validate 3-input components operation. Possible installation at Chara is currently under consideration. ## 5 Perspectives The proposed technology [7] shows many advantages for instrumentation design applied to astronomical interferometry. Furthermore it gives a unique solution to the problem beam combination of an array with large number of telescopes. The full instrument concept can be adapted from the planar optics structure and properties. ### Planar optics advantages Planar optics was proposed in the context of single mode interferometry. It offers solutions to outline limitations of the fibers. Fiber optics introduces decisive inputs with a reduction of the number of degrees of freedom of the instrumental arrangement and the modal filtering. Planar optics introduces additional arguments. Its application is limited to the combiner instrument itself and is not suitable for beam transportation and large optical path modulation. We can summarize its main advantages: Figure 8: Mask produced with LEMO facilities containing tests components for telescope beam combination (2, 3 and 4 telescope) either in coaxial and multi-axial mode (left). Half part of the chip (right), contains all the components.

* *Compactness of the whole instrument (typically 40 mm x 5 mm). * *Low sensitivity to external constraints * *Implementation in a cryostat * *Extremely high stability * *No tuning or adjustment requirement but the signal injections in the component, while all the instrument is embedded in a single chip * *Combiner alignment difficulty reported on the component mask design * *Reduced complications while increasing the number of telescopes, all difficulty is reported on the mask design [31] * *Intrinsic polarization capabilities * *The major cost driver is reported on the mask design and optimization phase. Existing component duplication may be realized at low cost. ### Application for aperture synthesis Extrapolation of the tested design to larger number of telescopes is investigated [31]. All elements exist to propose 8-telescope combiner in an optimized design, as an interesting concept for the whole VLTI coherencing mode. It offers a unique imaging capability for large interferometric arrays. This important issue imposes accurate phase stability inside the components who can be provided by IO. ### Fringe sensor For more than 3 telescope operation, mainly for imagery, a fringe tracker is mandatory for each baseline. IO provides a compact solution, for instance with all the component outputs corresponding to the baselines, imaged on the same detector array, in a single cryostat leading to a significant system simplification. ### Fully integrated instrument The achievable compactness opens attractive solutions for fully cooled instrument. In most of the case a chilled detector is required, that needs to be installed inside a cryostat. Low temperature of the environment is required to improve the detector efficiency and to avoid pollution by background emission. An integrated instrument allows to replace the cryostat window with a fiber feed through. The instrument is also confined in a protected volume, and then can be locked in a tuned position. In this case the component outputs are imaged directly on the detector array through relay optics. Even future optimized design may not require any relay optics while gluing an array detector on the substrate end [38] or implementing a STJ device directly on the substrate [35]. We investigate technological points to be solved for the installation of the whole instrument inside the camera cryostat in front of the detector [39]. In our prototype a relay optics is implemented in order to keep flexibility, for engineering tests.

### IO for larger wavelengths Extrapolation of the operating technology to larger wavelengths is an other important issue. The LEMO mask can be used directly to produce all available components for K band operation. Material transmission is compatible with our requirement up to \(2.5\mu{\rm m}\)[37]. The development requires a tuning of the ion exchange parameters. Extrapolation of the operating wavelength to the thermal IR, (\(>2.5\mu{\rm m}\) ) is a more critical issue. A current analysis will identify materials with sufficient transmission. At the present time no single mode fiber optics for \(10\mu{\rm m}\) are available in catalogs, and even laboratory components transmission imposes length shorter than a few millimeters. Investigations are in progress to produce planar guides for the N band (\(10\mu{\rm m}\)) [11]. Thermal IR instrument, as MIDI for the VLTI or Darwin / IRSI (ESA space interferometer), may include planar optics components as modal filters. The instrument thermal constraints can be reduced thanks to an implementation of the component inside a cryostat close to the detection head, and by reducing optical interfaces between subsystem optical components. IO solutions for thermal IR could allow a reduction of the modulation effects due to system operation (background subtraction, OPD modulation). The availability of small range delay lines using planar optics (up to tens of \(\mu{\rm m}\)) for fringe trackers could reduce thermal modulation of the environmental background. Furthermore instrumental thermal emission can be fully controlled by design for the guided part. ### Space based applications IO is a very attractive solution for a space-based technological testbed. The IO techniques allows, accurate, robust and extremely light concept. Such concept is compatible with a prototype dedicated to principle demonstrations for complex mission as Darwin or other foreseen preparation mission. ## 6 Acknowledgments The authors are grateful to Pierre Benech and Isabelle Schanen for their strong collaboration to this work and P. Pouteau, P. Mottier and M. Severi (CEA/LETI - Grenoble) for their contribution in LETI components realization, F. Reynaud for fruitful discussions, and to E. Le Coarer and P. Feautrier for the idea of combining IO and STJ. These works have partially been funded by PNHRA/INSU, CNES, CNRS / Ultimatech and DGA/DRET. ## References * [1] Froehly, C., (1981) In: Ulrich M.H., Kj r K. (eds.) Proc. ESO conf., Science Importance of High Angular Resolution at Infrared and Optical Wavelengths. ESO, Garching, 28

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the Jupiter-forming region (Mumma et al. Mumma (2001)). This would require that CN originates from refractory compounds aggregated in the protosolar cloud. In fact, the discrepancy between the nitrogen isotope ratios derived from millimeter HCN and optical CN and the independence of the \({}^{14}\)N/\({}^{15}\)N ratio on heliocentric distance has led us (Arpigny et al. Arpigny (2003), Manfroid et al. Manfroid (2005)) to suggest that the dominant source of CN -the carrier of \({}^{15}\)N- could be refractory organics. Good candidates are HCN polymers (Rettig et al. Rettig (1992), Kissel et al. Kissel (2004), Fray Fray (2004)), or grains containing organic macromolecules and reminiscent of "cluster" interplanetary dust particles (IDPs) known to have low \({}^{14}\)N/\({}^{15}\)N ratios (Messenger Messenger (2000), Aleon et al. Aleon (2003), Keller et al. Keller (2004)). The hypothesis involving HCN polymers implicitly assumes that their degradation may directly and predominantly produce CN radicals, which is not inconsistent with current experimental limits (Fray Fray (2004), and references therein). Besides, according to Rettig et al. (Rettig (1992)), the physico-chemical properties of HCN polymers indicate that these compounds can likely release CN (and NH\({}_{2}\)) radicals by dissociation. The \({}^{14}\)N/\({}^{15}\)N ratio measured on HCN in comet Hale-Bopp (\(\sim\)330) might be the result of a mixture between unprocessed HCN with protosolar value (\(\sim\)450, in the sense of Owen et al. Owen (2001)) and \({}^{15}\)N-enriched HCN released from HCN polymers (characterized, as the CN we observe, by \({}^{14}\)N/\({}^{15}\)N \(\sim\)145). The difference between the nitrogen isotopic ratios measured for CN and HCN may indicate isotope fractionation in the protosolar cloud. A few mechanisms based on ion-molecule and gas-grain reactions in a cold interstellar medium have been proposed to explain \({}^{15}\)N enhancement with respect to the isotope abundance in N\({}_{2}\) which is usually thought to be the major nebular reservoir of nitrogen (Terzieva & Herbst Terzieva (2000), Rodgers & Charnley Rodgers (2004)). But it is not clear whether such mechanisms can quantitatively reproduce the nitrogen isotopic ratio derived from CN, its uniform distribution throughout the protosolar cloud whatever the fluctuations in temperature and density, and how it can be incorporated into CN-bearing grains. Moreover, the proposed mechanisms seem to be efficient at low temperature (\(\sim\)10 K, Terzieva & Herbst Terzieva (2000), Charnley & Rodgers Charnley (2002)). Kawakita et al. (Kawakita (2005)), by considering the very similar spin temperatures measured for various molecules in comets of both Oort Cloud and Jupiter-family types, have recently proposed that the Solar System was born in a warm dense molecular cloud near 30 K rather than a cold dark cloud at 10 K. A higher protosolar temperature was also suggested by Meier & Owen (Meier (1999)) on the basis of cometary deuterium-to-hydrogen data. More work is therefore needed to assess the reality of fractionation -still very attractive- namely in warmer interstellar clouds. Mass-independent nitrogen fractionation based on selective photo-dissociation may also be worth investigating, as done for example by Yurimoto & Kuramoto (Yurimoto (2004)) to explain oxygen isotopic anomalies. On the other hand, the small \({}^{14}\)N/\({}^{15}\)N ratio we measure in comets could originate from an external source and, for some reason, be preferentially locked in refractory organics. \({}^{15}\)N enhancement may be attributed to a contamination by nucleosynthesis products ejected by nearby massive stars, as observed in the Large Magellanic Cloud and starburst galaxies (Henkel & Mauersberger Henkel (1993), Chin et al. Chin (1999), Wang et al. Wang (2004)). This would be consistent with a \({}^{14}\)N/\({}^{15}\)N ratio smaller than the interstellar medium (ISM) value at the solar circle: \({}^{14}\)N/\({}^{15}\)N \(\simeq\) 450\(\pm\)22 (Wang et al. Wang (2004)). A contamination by massive stars could also slightly increase the \({}^{12}\)C/\({}^{13}\)C ratio with respect to \({}^{12}\)C/\({}^{13}\)C \(\simeq\) 77\(\pm\)7 measured in the local ISM (Henkel & Mauersberger Henkel (1993)), as observed. Isotopic contamination by massive stars is independently suggested by the study of extinct radionuclides in meteorites (e.g. Cameron et al. Cameron (1995)). Interestingly enough, the higher temperature of the protosolar cloud proposed by Kawakita et al. (Kawakita (2005)) would necessitate the vicinity of sites of formation of massive stars. Massive stars also provide large amount of ultraviolet radiation which may initiate HCN polymerization as suggested by Rettig et al. (Rettig (1992)). If this polymerization (or another, unknown, mechanism) locked up the \({}^{15}\)N-enriched nitrogen in a solid phase before it spreads throughout the protosolar cloud, this could ex Figure 1: A section of the spectrum of the CN (0,0) band in comet 88P/Howell. _Thick line:_ Observed spectrum; _thin (red) line:_ synthetic spectrum of \({}^{12}\)C\({}^{14}\)N, \({}^{12}\)C\({}^{15}\)N and \({}^{13}\)C\({}^{14}\)N with the adopted isotopic abundances. The lines of \({}^{12}\)C\({}^{15}\)N are identified by the short ticks and those of \({}^{13}\)C\({}^{14}\)N by the tall ticks. The quantum numbers of the \(R\) lines of \({}^{12}\)C\({}^{14}\)N are also indicated.

plain the nitrogen isotopic differences observed between different molecules in comets and among the various objects and reservoirs in the Solar System (Owen et al. Owen (2001)). A similar effect could be expected for the carbon isotopes although much smaller and within the errors bars. Apart from the need to identify contamination or fractionation processes appropriate to either type of CN progenitors, polymers or organic macromolecules, it will also be very important to measure the \({}^{14}\)N/\({}^{15}\)N ratio in different N-bearing molecules to establish a complete inventory of nitrogen isotopes in comets: HCN (for which a single measurement has been possible so far), NH\({}_{3}\) and/or NH\({}_{2}\) (which is a direct product of ammonia), N\({}_{2}\), C\({}_{2}\)N\({}_{2}\) if present. Some variation may be expected depending on the mechanisms of \({}^{15}\)N enrichment and the sizes of the various nitrogen reservoirs. A comparison with accurate measurements of the solar-wind isotopes from samples collected by the Genesis space mission should help to distinguish between the possible scenarios. ## References * (1) Aleon, J., Robert, F., Chaussidon, M., Marty, B. 2003, Geochim. Cosmochim. Acta., 67, 3773 * (2) Arpigny, C., Jehin, E., Manfroid, J., et al. 2003, Science, 301, 1522 * (3) Biver, N., Bockelee-Morvan, D., Crovisier, J., et al. 2002, Earth Moon and Planets, 90, 323 * (4) Cameron, A.G.W., Hoflich, P., Myers, P.C., Clayton, D.D. 1995, ApJ, 447, L53 * (5) Charnley, S.B., Rodgers, S.D. 2002, ApJ, 569, L133 * (6) Chin, Y., Henkel, C., Langer, N., Mauersberger, R. 1999, ApJ, 512, L143 * (7) Fernandez, J.A., Tancredi, G., Rickman, H., Licandro, J.L. 1999, A&A, 352, 327 * (8) Fouchet, T., Irwin, P.G.J., Parrish, P., et al. 2004, Icarus, 172, 50 * (9) Fray, N. 2004, Ph.D. thesis (available at http://tel.ccsd.cnrs.fr) * (10) Gomes, R. 2003, Nature, 426, 393 * (11) Hashizume, K., Chaussidon, M., Marty, B., Robert, F. 2000, Science, 290, 1142 * (12) Henkel, C., Mauersberger, R. 1993, A&A, 274, 730 * (13) Jehin, E., Manfroid, J., Cochran, A.L., et al. 2004, ApJ, 613, L161 * (14) Jewitt, D.C., Matthews, H.E., Owen, T., & Meier, R. 1997, Science, 278, 90 * (15)Kallenbach, R., Robert, F., Geiss, J., et al. 2003, Space Sci. Rev., 106, 319 * (16) Kawakita, H., Watanabe, J., Furusho, R., Fuse, T., Boice, D.C. 2005, ApJ, 623, L49 * (17) Keller, L.P., Messenger, S., Flynn, G.J., et al. 2004, Geochim. Cosmochim. Acta., 68, 2577 * (18) Kissel, J., Krueger, F.R., Silen, J., Clark, B.C. 2004, Science, 304, 1774 * (19) Levison, H.F., Morbidelli, A. 2003, Nature, 426, 419 * (20) Manfroid, J., Jehin, E., Hutsemekers, D., et al. 2005, A&A, 432, L5 * (21) Meier, R., Owen, T.C. 1999, Space Sci. Rev., 90, 33 * (22) Messenger, S. 2000, Nature, 404, 968 * (23) Mumma, M.J., Dello Russo, N., DiSanti, M.A., et al. 2001, Science, 292, 1334 * (24) Mumma, M.J., DiSanti, M.A., Dello Russo, N., et al. 2003, Adv. Space Res., 31, 2563 * (25) Owen, T., Mahaffy, P.R., Niemann, H.B., Atreya, S., Wong, M. 2001, ApJ, 553, L77 * (26) Rettig, T.W., Tegler, S.C., Pasto, D.J., Mumma, M.J. 1992, ApJ, 398, 293 * (27) Rodgers, S.D., Charnley, S.B. 2004, MNRAS, 352, 600 * (28) Terzieva, R., Herbst, E. 2000, MNRAS, 317, 563 * (29) Wang, M., Henkel, C., Chin, Y., et al. 2004, A&A, 422, 883 * (30) Weissman, P.R. 1999, Space Sci. Rev., 90, 301 * (31) Woodney, L.M., Fernandez, Y.R., Owen, T.C. 2004, BAAS, 36, 1146 * (32) Yurimoto, H., Kuramoto, K. 2004, Science, 305, 1763 * (33) Zinner, E. 1998, Annu. Rev. Earth Planet. Sci., 26, 147 * (34) Ziurys, L.M., Savage, C., Brewster, M.A., et al. 1999, ApJ, 527, L67

# Probing the birth of the first quasars with the future far infrared mission 1 Footnote 1: A survey with five different sky-area/flux limit combinations, designed to provide good sampling of redshift-luminosity space. M. J. Page ###### Abstract It is now widely recognised that massive black holes must have had a fundamental influence on the formation of galaxies and vice versa. With current and imminent missions we aim to unravel much of this relationship for the last 10 Gyr of cosmic history, while the quasar population waned and star formation died down. The picture at earlier times will be more difficult to reconstruct, but will likely be even more exciting: when the first stars shone, the first dust was formed, and quasars were a vigorously rising population. One of the primary goals of XEUS is to allow us to find and study the earliest quasars, however deeply buried in gas and dust they may be. But to understand fully the astrophysical context of these objects, their significance in the grand picture, we must learn how they relate to their environments and their host galaxies. The ESA future Far-InfraRed Mission (FIRM) will provide much of the data we require, revealing the dust heated by star formation in the host galaxy, the relative evolutionary stages of spheroid and black hole, and the total energy budgets posessed by these first quasars. FIRM will reveal star formation in the immediate proto-cluster environment of the quasar and so tell us how the formation of the first galaxies and quasars coupled to the earliest large scale structures. keywords: Stars: formation - Galaxies: formation - Galaxies: evolution - Quasars: general ## 1 Introduction Three hundred and eighty thousand years after the big bang, the first atoms formed, and the primordial background radiation scattered for the last time. As the radiation cooled, the Universe entered a dark age that would last for half a billion years. Eventually, the first stars, or the first quasars re-lit the Universe with optical and ultraviolet radiation. Whether the Universe was illuminated first by stars or by quasars is still unknown. However, what has become clear in the last decade is that these two sources of radiation are intimately linked within the galaxies that host them. Quasars are extremely luminous, compact sources of radiation found at the centres of galaxies. They derive their power from the accretion of surrounding material onto a massive (\(>10^{6}\) M\({}_{\odot}\)) black hole. Stars, on the other hand, are powered by nuclear fusion, e.g. of hydrogen into helium, in their cores. The two processes, accretion and nuclear fusion, have been responsible for almost all of the energy that has been generated and radiated since the first atoms formed. In this paper, I will discuss the value of ESA's future Far InfraRed Mission (FIRM) for understanding the relationship between stars and quasars. I will begin by outlining our basic understanding of the evolution of the stellar and black hole components of galaxies. ## 2 The evolution of black holes and stars There is now overwhelming evidence that the creation and fuelling of quasars is related to galaxy formation. The quasar population has evolved strongly with cosmic epoch, declining dramatically since its heyday at redshift \(\sim 2\) (e.g. Page et al. 1997, Croom et al. 2004). Data from a variety of sources suggest that star formation also peaked at redshift 1-2 (Bunker et al. 2004, Blain et al. 1999 and references therein). These redshifts correspond to the epoch at which galaxies are expected to have assembled according to the hierarchical cold dark matter cosmology (Kauffmann 1996). The discovery of massive dark objects, remnants of once-luminous quasars in the bulges of many nearby galaxies, further demonstrates that the creation and fuelling of quasars is inextricably linked to the formation of galaxies (Magorrian et al. 1998). Present day massive, quiescent black holes are found to have mass roughly proportional to that of the surrounding galaxy spheroid (Merritt & Ferrarese 2001). The simplest scenario one can imagine to produce such coupled stellar and black hole components in present-day galaxies is for the stellar bulge and the massive black hole to grow at the same time, from the same gas. In this scenario we would expect quasars, which are black holes that are growing quickly, to be hosted by stellar bulges that are rapidly growing their stellar mass, and are therefore experiencing episodes of prodigious star formation. However, recent observations show that the relationship between star formation and black hole growth is more complex than this. I will return to this question in Sections 5 and 6. First, I will describe briefly the use of X-ray ob

servations to identify quasars, and the use of far infrared observations to measure star formation. ## 3 Searching for quasars Material accreted by a quasar reaches a large velocity as it falls into the gravitational well of the black hole, and forms a disc where some of the kinetic energy is thermalised and radiated. Much of this energy emerges in the extreme ultraviolet region of the spectrum, but it cannot be observed because of photoelectric absorption by interstellar hydrogen in our Galaxy. Close to the event horizon of the black hole, particles are accelerated to very high temperatures, and inverse-Compton scatter radiation from the disc, forming an X-ray emitting corona. This X-ray emission accounts for \(\sim\)10% of the bolometric output of a typical quasar, a much larger fraction than is emitted in X-rays by normal stars and galaxies. Furthermore, as X-rays are very penetrating, they allow us to find quasars even when they are quite heavily obscured by gas and dust. Surveys of the X-ray sky therefore prove to be an extremely good (probably the best) method of locating and identifying quasars. It turns out that the vast majority of sources that are detected in X-ray surveys are quasars (e.g. Fig. 1). ## 4 Searching for star formation In star forming regions massive, short lived stars usually dominate the overall radiative output. These stars emit most of their power in the rest-frame ultraviolet, and so starburst galaxies are often identifiable by their strong ultraviolet emission. However, the most vigorous starburst galaxies are often so dusty that only a tiny fraction of their ultraviolet radiation manages to escape. The spectral energy distribution of one such galaxy, Arp 220, is shown in Fig. 2. In this case, almost all of the energy emerges in the infrared part of the spectrum, between 20 and 200\(\mu\)m. It would be impossible to determine the energy output of this galaxy without measurements spanning the far infrared part of the spectrum. The spectral energy distribution of Arp 220 is thought to be fairly typical for the most powerful starburst galaxies, and so surveys in the far infrared provide the most reliable means of finding and identifying starburst galaxies. ## 5 Star formation in quasar host galaxies In total we expect the accreting black hole to emit about 1/5 as much energy as the stars forming in the surrounding galaxy spheroid. A far greater mass of gas is converted into stars, but accretion onto a black hole is a much more efficient means of producing radiation than nuclear fusion. Detecting the optical and ultraviolet radiation from the host galaxies of distant quasars is extremely challenging, because the quasar dominates the radiation in these wavebands. However, powerful star forming regions al Figure 1: _XMM-Newton_ image of the 13\({}^{H}\) deep field, a 30 arcminute diameter region of sky which has very little intervening Galactic material. Almost all the X-ray sources in the image are quasars. Figure 2: Spectral energy distribution of the luminous starburst galaxy Arp 220. The spectrum is plotted as the product of wavelength (\(\lambda\)) and the flux per unit wavelength (\(F_{\lambda}\)) so that constant energy per decade in wavelength would be a horizontal line. The energy output is completely dominated by the thermal dust emission between 20 and 200\(\mu\)m (shaded).

most always contain large quantities of dust, which absorb much of the starlight. Most of the energy is re-emitted as thermal radiation in the far-infrared. Observations at long wavelengths can therefore reveal major bursts of star formation from their strong dust emission. In recent years some such observations have become feasible from the ground, exploiting the atmospheric transmission windows between 350\(\mu\)m and 1.1mm. Pioneering millimetre and submillimetre observations of the most powerful quasars, at very high redshift (\(z>3\)), suggested that high star formation rates may be an ubiquitous characteristic of quasar host galaxies (McMahon et al. 1994, Omont et al. 1996, Isaak et al. 2003). However, if we look at the distribution of quasar luminosities (their 'luminosity function') over a range of cosmic time, it is straightforward to determine the luminosity range, and the period of cosmic history, that contributed the most to present day black hole mass. The luminosity function has a distinctive knee or break in its shape at a luminosity which changes with cosmic time (Page et al. 1997, Croom et al. 2004). At luminosites higher than this knee, quasars drop rapidly in numbers, so that the most powerful objects are exceedingly rare compared to their lower luminosity cousins. At luminosities lower than the knee, quasars are more numerous, but not by a large amount. The contribution of any part of the luminosity function to the growth of black hole mass is proportional to product of the numbers and luminosities of the objects. This product is a maximum at the knee of the luminosity function, and \(\sim 70\%\) of the instantaneous black hole mass growth rate comes from \(\pm 0.7\) dex of the break. The quasar population has changed dramatically with cosmic time, peaking in the \(1<z<3\) epoch, when the typical luminosity of a quasar was \(\sim\)20 times larger than it is in the present day Universe. Therefore in terms of contribution to the present day mass density of black holes, the most important quasars by far are those in the redshift interval \(1<z<3\), with luminosities around the break in the luminosity function. Submillimetre observations of quasars in this luminosity and redshift range rule out the simple co-evolution models because the quasars that are responsible for most of the black hole growth are undetectable in the submillimetre. This means that they cannot be undergoing star formation episodes of sufficient magnitude for the spheroid to build up most of its mass in the same timespan as the black hole (Page et al. 2004). However, quasars at similar redshifts and luminosities, with normal quasar spectra in the optical and UV, but with significant absorption in their X-ray spectra, are found to be luminous submillimetre sources, undergoing major bursts of star formation (Page et al. 2001). This suggests an evolutionary sequence in which X-ray absorbed quasars are at an earlier stage in their evolution than the unabsorbed quasars, in line with a number of theoretical models (Fabian 1999, Hopkins et al. 2005). The luminosities of the X-ray absorbed quasars imply that they have already built up a significant fraction of their ultimate black hole mass - both the X-ray absorbed and unabsorbed quasar phases are relatively late in the active quasars lifetime. The relative numbers of X-ray absorbed and X-ray unabsorbed quasars suggest that the X-ray absorbed phase is short, marking the transition from an earlier heavily obscured phase to the emergence of a luminous, naked quasar. When the quasar runs out of fuel, it ceases to shine, leaving an elliptical galaxy with a quiescent massive black hole in the centre. ## 6 Black hole growth in starburst galaxies In the last 10 years, ground based surveys at submillimetre wavelengths have revealed a remarkable population of ultraluminous starburst galaxies, found at high redshift (Smail, Ivison & Blain 1997, Hughes et al., 1998, Barger et al. 1998). These objects are thought to be massive galaxies undergoing their major episodes of star forma

tion (Smail et al. 2002). Recently, using the deepest X-ray observations ever taken, it has been possible to show that the majority of these objects contain active accreting black holes at their centres, often obscured behind large column densities (\(>10^{23}\) cm\({}^{-2}\)) of gas and dust (Alexander et al. 2005). The black holes in these objects appear to be a factor of a few less massive and less luminous than the quasars around the break in the luminosity function, placing them earlier in the quasar evolutionary sequence. Nevertheless, with black holes of \(10^{7}\) M\({}_{\sun}\) and larger, these objects are already most of the way through their major black hole growth phases. If we put together the observations of star formation in quasars, and of black hole accretion in powerful starburst galaxies, we come to the following picture: * *Submillimetre galaxies, X-ray absorbed quasars, X-ray unabsorbed quasars and elliptical galaxies appear to form an evolutionary sequence. * *So far, we have only observed (or at least recognised) the last \(\sim 30\%\) of the quasar lifespan. * *Absorption increases as we look further back in the sequence; the black hole is likely to be very heavily obscured for the majority of its main growth phase. This picture has several implications for our way forward. As we look earlier in the history of a galaxy, the black hole gets more heavily buried in gas and dust, so we need a more powerful X-ray telescope to be able to see through the murk to the earlier stages of black hole growth. Most of the accretion power will be absorbed by the surrounding gas and dust, and will be reradiated in the infrared, but the galaxy will already be a bright source of infrared emission because of the intense dust-enshrouded star-formation that will be taking place. We can only disentangle the infrared quasar emission from the infrared starburst emission using spatial resolution or detailed spectroscopy. Therefore we will need a far-infrared observatory with very fine spatial resolution, excellent spectroscopic sensitivity, or both. The Far InfraRed Mission (FIRM) identified in ESA's Cosmic Visions programme, fits the bill exactly. ## 7 Quasars and the growth of structure In the currently favoured hierarchical cosmology, galaxy formation is a consequence of the gravitational collapse of positive fluctuations in the large scale density field. Small, galaxy-sized structures form first. Larger scale overdensities grow with time, drawing in matter from their surroundings, ultimately producing the filamentary "soap bubble" distribution seen in present day galaxies (Peacock et al. 2001). As the large scale structure develops, small galaxies merge to form larger galaxies, experiencing substantial bouts of star formation in the process; further mergers produce successively larger galaxies. The most massive galaxies end up in the most overdense regions: those which are destined to become clusters of galaxies by the present day. The black holes that once shone as powerful quasars now lie in the hearts of massive elliptical galaxies, which in turn lie in clusters. By searching for merger-induced starbursts within the environments of redshift \(\sim 2\) quasars, we can examine how the growth and evolution of massive black holes relate to the build up of large scale structure. At present, with ground based observations, we can probe only the most luminous starbursts in the most massive galaxies. A 450\(\mu\)m image of the environment of the X-ray absorbed quasar RXJ094144 (Stevens et al. 2004) is shown in Fig. 4. The image reveals a chain of ultraluminous infrared galaxies around the quasar, with enough star formation taking place for each starburst to evolve into a massive elliptical galaxy within 1 Gyr. In this case, the X-ray absorbed phase of the quasar coincides with the formation of the massive cluster galaxies. However, to measure the dust emission and star formation rates of the many smaller galaxies that will ultimately lie within the cluster will require much more sensitive observations, at much higher spatial resolution. Indeed most black holes lie in lower mass galaxies, and these within groups rather than clusters of galaxies (our own Milky Way for example, lies within a group of galaxies). With FIRM, we will be able to probe energy production and star formation in these numerous galaxies, and determine how the growth of black holes relates to the build up of structure in these smaller, more typical environments. Figure 4: 450\(\mu\)m image of a 2.5 arcminute region around the X-ray absorbed quasar RXJ094144 (Stevens et al. 2004), revealing a chain of ultraluminous starburst galaxies. The X-ray position of the quasar is marked by the cross in the centre of the image.

## 8 A step into the far-IR with Herschel The Herschel Space Observatory (Pilbratt 2003) will probe the Universe in the 60-600 \(\mu\)m region. Due for launch in late 2007, with both spectroscopic and imaging instruments, it will represent a huge advance in this part of the spectrum. With its deep extragalactic surveys, it is set to measure the star formation for a large portion of cosmic history, and resolve a significant fraction of the far infrared background into discrete sources. Figure 5 shows the anticipated coverage of a 5-tier "wedding cake" survey1 at 250\(\mu\)m. Herschel should perform extremely well in detecting luminous infrared galaxies in the wavelength ranges where the bulk of their bolometric power is emitted, out to redshifts of 2-3. This corresponds to a large period of cosmic history (\(>10\) Gyr), but for the majority of this period star formation has been declining. Similarly, accretion onto massive black holes has been waning continuously since redshift 2; the powerful quasars are past their prime, and each successive generation is less luminous than the last. Footnote 1: A survey with five different sky-area/flux limit combinations, designed to provide good sampling of redshift-luminosity space. An earlier epoch, between 1 and 3 Gyrs after the big bang, is a much more exciting period in the story of black hole growth. Star formation was becoming more vigorous with time, and the massive black holes of the most powerful quasars were growing exponentially, limited only by the radiation pressure from their own central engines. From this period of black-hole gluttony emerged the massive compact objects that today lurk at the centres of the greatest elliptical galaxies. Unfortunately, it can be seen in Fig. 5 that Herschel will only detect a small number of objects at the tail-end of this epoch. Principally, Herschel is limited by the angular resolution that is achievable with its 3.5m primary mirror: source confusion will make it impossible to detect the weaker, high redshift objects against the large sky density of brighter, foreground sources. If we are to study the epoch of black hole growth, we will require a more sensitive far-infrared observatory, with much better angular resolution: FIRM. ## 9 Chicken or egg at redshift 20? Which came first, stars or black holes? How did the first black holes come about? Did the first stars become the first black holes, seeds around which whole galaxies of stars would ultimately form? These are arguably the most fundamental of questions about massive black holes, and to answer them we will have to make observations stretching right back into the dark ages of the Universe, before reionisation. The initial results from the WMAP satellite suggest that reionisation occurred at redshift \(z=17\pm 5\) (Bennett et al. 2003), so the first stars and/or black holes must have formed at \(z\sim 20\). Not yet polluted by metals synthesised in stars, the primordial gas would have consisted almost entirely of hydrogen and helium. The first collapsing gas clouds must therefore have cooled primarily through molecular hydrogen (H\({}_{2}\)) line emission. These emission lines are the key to identifying the first epoch of star formation. The strongest lines predicted have rest frame wavelengths of 2-3 and 8-10\(\mu\)m (Mizusawa, Nishi & Omukai 2004, Ripamonti et al. 2002, Kamaya & Silk 2002). Although the highest instantaneous luminosities are reached in the 2-3\(\mu\)m lines during the main accretion phases of individual protostars, the 8-10\(\mu\)m lines are longer lived, and therefore more likely to be detected from an assembly of star forming clouds. At redshifts of 15-20, the strongest lines will be observed at 130-200\(\mu\)m: only with a facility such as FIRM can we hope to detect these lines and determine the time when the first stars formed. There are a whole variety of possibilities for the formation of the first black holes. They could result from supernova explosions of the first generation of stars, or they

could form directly within primordial gas clouds. The latter possibility requires the suppression of H\({}_{2}\) within the cloud, perhaps due to UV radiation from the first stars (Bromm & Loeb 2003). Such clouds could be identified by the amount of atomic H I cooling relative to H\({}_{2}\) emission. FIRM observations will thus be key to timing and identifying the formation of the first black holes relative to the formation of the first stars. ## 10 What do we need FIRM to be? If we are to use FIRM to explore the origin, birth and growth of massive black holes, we can identify the most basic requirements as follows: It must provide sensitive spectroscopy in the far infrared (25-300\(\mu\)m) wavelength range. * *It must be in space. * *It must have a cold aperture. It must have high enough spatial resolution that it is not confusion limited. * *It could be a large (\(>10\)m) single dish. * *It could be a multi-element interferometer. The most important decision to be taken, for the shape and capabilities of FIRM, is whether to fly a single dish, or a multi-spacecraft interferometer. At present both options are being considered. A single dish would have superior surface brightness sensitivity, but the interferometer wins out in spatial resolution. The two configurations present different technical challenges, and these will have to be taken into account along with the scientific trade-offs when the decision is made. ## 11 XEUS and FIRM as partners Quasars are multiwavelength phenomena, emitting throughout the electromagnetic spectrum, and our current understanding of them is the result of observations in every waveband. In the 2015-2025 timeframe, FIRM will be operating alongside a number of exceptionally capable ground-based facilities covering a wide range of wavelengths, including the Atacama Large Millimetre Array (ALMA), the Square Kilometre Array (SKA) and extremely large (100m) optical/near-IR telescopes such as the European Southern Observatory's OWL telescope. In addition, the gravitational wave observatory LISA may be making a significant contribution to our understanding of black hole growth via an entirely different form of radiation. However, for the study of the birth and growth of massive black holes, it is in conjunction with ESA's next generation X-ray observatory XEUS that FIRM has the greatest potential. The very large throughput of XEUS will enable it to detect small, young quasars even when they are embedded in very dense cocoons of gas and dust. Most of their radiation will be absorbed and re-emitted by the surrounding material, and it is FIRM that will detect this radiation, so telling us the total energy budgets of these quasars. FIRM will measure the bolometric output from star formation in their host galaxies, telling us the relative evolution of the black hole and the stellar components. The cryogenic spectrometers on XEUS will identify outflows and winds from young quasars, that may terminate the star formation by sweeping the cool gas from the host galaxy. FIRM spectroscopy will provide the other half of the picture, by revealing the mass, temperature, ionization state and dynamics of this cool gas. As large scale structures developed, hot gas filled the potential wells of clusters and groups that hosted powerful quasars. XEUS will detect this intracluster medium, and will allow us to measure the conditions and elemental abundances as the gas built up. With FIRM we will learn when, and how this relates to the star formation in the galaxies of the cluster. FIRM will tell us the abundances and physical conditions of cool gas within the galaxies so that we can follow the enrichment history of the intracluster gas. The combination of XEUS and FIRM will allow us to determine the role of feedback from both quasars and starbursts in galaxy formation, and in the heating of the intergalactic medium. ## 12 Conclusions In all directions X-ray telescopes reveal massive black holes at great distances, in an earlier epoch, when they accreted material and shone as quasars. In the present day Universe, these black holes lie silent in the centres of galaxies, with mass proportional to that of their surrounding stellar spheroids. This is most easily explained if the formation of the two components was coeval, i.e. if the black hole was built up by accretion of the same gas that rapidly formed the stars of the spheroid. However, the picture is more complex observationally: quasars which had redshifts and luminosities in the interval responsible for most of today's black hole mass lived, for the most part, in quiescent, finished host galaxies. The formation of the spheroid appeared to overlap the growth of the black hole only in quasars which were hidden within cocoons of gas and dust, with absorption increasing as we look to earlier times in the growth of the black hole. Most of the black hole growth phase was probably heavily obscured, suggesting that we have so far observed and recognised only the final 30% of the evolutionary sequence of a typical quasar. To detect quasars in the earlier stages of their lives, we need a more powerful X-ray telescope, XEUS, which can penetrate the dense gas and dust in which they are buried. However to get the complete picture, we will also require the Far InfraRed mission (FIRM). FIRM will have a combination of sensitivity and spatial resolution that will allow it to survey the Universe when the first galaxies were taking shape, when quasars were still a vigorously rising

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###### Abstract A bar rotating in a pressure-supported halo generally loses angular momentum and slows down due to dynamical friction. Valenzuela & Klypin report a counter-example of a bar that rotates in a dense halo with little friction for several Gyr, and argue that their result invalidates the claim by Debattista & Sellwood that fast bars in real galaxies require a low halo density. We show that it is possible for friction to cease for a while should the pattern speed of the bar fluctuate upward. The reduced friction is due to an anomalous gradient in the phase-space density of particles at the principal resonance created by the earlier evolution. The result obtained by Valenzuela & Klypin is probably an artifact of their adaptive mesh refinement method, but anyway could not persist in a real galaxy. The conclusion by Debattista & Sellwood still stands. keywords: Galaxies: kinematics and dynamics -- galaxies: halos -- dark matter Anomalously Weak Dynamical Friction in Halos ## 1 Introduction It is now well established that a bar rotating in a halo loses angular momentum through dynamical friction. This topic has received a lot of attention recently for two important reasons: (1) it offers a constraint on the density of the DM halo (Debattista & Sellwood 1998, 2000), and (2) it may flatten the density cusp (Weinberg & Katz 2002). Both these claims have been challenged. Realistic bars in cuspy halos produce a mild density decrease at most (Holley-Bockelmann _et al._ 2003) or even a slight increase (Sellwood 2003), but we leave this issue

aside here and concentrate instead on the density constraint. Holley-Bockelmann & Weinberg (2005) announce a preliminary report of simulations with weak friction in halos having uniform density cores, but we focus here on the older counter-example claimed by Valenzuela & Klypin (2003; hereafter VK03) of a bar that experiences little friction in a cusped dense halo. VK03 kindly made available the initial positions and velocities of all the particles of their model A\({}_{1}\), in which the bar did not slow for 2-3 Gyrs after it had formed and settled. We have used our code (Sellwood 2003) to rerun this simulation many times, and the pattern speed evolution in many of these runs is shown in Figure 1. It is striking that in most cases, the bar slowed earlier than VK03 found, but in one anomalous case, the bar stayed fast for about 10 Gyr! The anomalous result is not a consequence of some inadequate numerical parameter, since many of the other cases are from models with parameters that bracket those of the anomalous case - _i.e._ longer and shorter time steps, coarser and finer grids, _etc._ Note that apart from the crucial delay in the onset of friction in the case by VK03 and the one anomalous case we find, the evolution is generally very similar. In particular, whenever the bar slows, it slows Figure 1: The time evolution of the bar pattern speed in a number of resimulations of model A\({}_{1}\) of VK03. The evolution reported by VK03 is reproduced as the dot-dashed line; all other lines are from simulations from the same initial particle load, but run with our code using many different sets of numerical parameters.

at a similar rate. The following sections account for the discrepancies between the results shown in Fig. 1. ## 2 Frictional Torque In a classic paper, Tremaine & Weinberg (1984) laid out the mathematical apparatus for friction in a spherical system. Following the precepts of Lynden-Bell & Kalnajs (1972), they derived a formula for the torque experienced by a rotating perturbation potential, \(\Phi_{p}\). They work in action-angle variables (see Binney & Tremaine 1987, SS3.5). In a spherical potential, there are two non-zero actions: the total angular momentum per unit mass \(L\equiv J_{\phi}\) and the radial action \(J_{r}\), each associated with two separate frequencies, \(\Omega\) and \(\kappa\), which are generalizations to orbits of arbitrary eccentricity of the usual frequencies of Lindblad epicycles familiar from disk dynamics. In the limit that a constant amplitude perturbation rotates steadily at \(\Omega_{p}\), they showed that the net LBK torque is \[\tau_{\rm LBK}\propto\sum_{m,k,n}\left(m{\partial f\over\partial L}+k{\partial f \over\partial J_{r}}\right)|\Phi_{mnk}|^{2}\delta(n\Omega+k\kappa-m\Omega_{p}),\] (1) where \(f\) is the usual distribution function and \(\Phi_{mnk}\) is a Fourier coefficient of the perturbing potential. The Dirac delta function implies that the net torque is the sum of the separate contributions from resonances, where \(n\Omega+k\kappa=m\Omega_{p}\). Because the bar pattern speed decreases, as a result of the frictional torque, this expression needs to be generalized to a time-dependent forcing (see Weinberg 2004), but the revised expression for the torque still contains the same derivatives of the distribution function. Lynden-Bell (1979) offered a clear insight into how an orbit is affected when close to a resonance. The unperturbed orbit, which is a rosette in an inertial reference frame, closes in any frame that rotates at the rate \[\Omega^{\prime}=\Omega+k\kappa/m,\] (2) for any pair \(k,\,m\). [See _e.g._ Kalnajs (1977) for illustrations of several of the most important shapes.] When the pattern speed of the bar is close to \(\Omega^{\prime}\) for some pair \(k,\,m\), the orbit can be regarded as a closed figure that precesses at the slow rate \[\Omega_{s}\equiv(\Omega^{\prime}-\Omega_{p})\ll\Omega_{p}.\] (3) Under these circumstances, the "fast action" is adiabatically invariant, while the "slow action" can suffer a large change. Things are particularly

ers and losers is soon established, and the bar can rotate in a dense halo with little friction, which we describe as a "metastable state". In fact, \(\Omega_{p}\) declines slowly because of weak friction at other resonances, and normal friction resumes when the slope of \(F\) at the main resonance changes, as shown in the last frame of Fig. 4. ## 5 Self-consistent Simulations If we now re-examine Fig. 1, we see that the period of weak friction is preceded by a small rise in the bar pattern speed in both the simulation of VK03 (dot-dashed line) and in the anomalous case we found. It is likely therefore that friction stopped for a while in both cases because the local density gradient across the principal resonance became flat, as just described. Analysis of our simulation that displayed this behavior suggests that \(\Omega_{p}\) rose because of an interaction between the bar and a spiral in the disk, which caused the bar to gain angular momentum. Such an event is rare; spirals generally remove angular momentum from the bar at most relative phases. It is possible that VK03 were unlucky to have such an event in their case, but they report similar behavior in their model B making a chance event unlikely. Figure 4: The mean density of particles as a function of \(L_{\rm res}\) at several different times in the simulation shown in Fig. 3.

One significant difference between our code and that used by VK03 (Kravtsov, Klypin & Khokhlov 1997) is that their resolution is adaptive, which causes gravity to strengthen at short range when the grid is refined. The increase in the local density as the bar amplitude rises causes the code to refine the grid, strengthening gravity and thereby causing the bar to contract slightly and to spin-up. We have found that a reduction of softening length in our code at this epoch also leads to a metastable state. It is likely, therefore, that their anomalous result is an artifact of their adaptive code. ## 6 The Metastable State is Fragile Whatever the origin of the bar speed-up in simulations, it remains possible that the metastable state could occur in real galaxies. If friction in a dense halo can be avoided for this reason, then the observed pattern speeds will provide no constraint on the halo density. However, further experiments in which we perturbed our model in the metastable state very slightly, revealed that the state is highly fragile. For example, a satellite of merely 1% of the galaxy mass flying by at 30kpc is sufficient to jolt the system out of the metastable state. We therefore conclude that anomalously weak friction is unlikely to persist for long in nature. ## 7 Conclusions Tremaine & Weinberg (1984) showed that angular momentum is transferred from a rotating bar to the halo through resonant interactions. We find that friction is dominated by a single resonance at most times, and that corotation is most important for a bar with realistic pattern speed - _i.e._ when the bar extends almost to corotation. Friction arises because the phase space density is a decreasing function of angular momentum in normal circumstances, causing an excess of particles that gain angular momentum over those that lose. While this process would tend to flatten the density gradient if the pattern speed remained steady, the decreasing angular speed of the bar prevents this steady state from being reached. Instead we find that the density of particles in phase space develops a shoulder, with the resonance holding station on the high-angular momentum side of the shoulder as the feature moves to larger \(L_{\rm res}\). However, if the bar is spun up slightly for some reason after a period of normal friction, the rise in the pattern speed may move the resonance to the other side of the pre-constructed shoulder. The change in the local gradient of particle density at the dominant resonance causes

friction to become very weak for a while, allowing the bar to rotate almost steadily. Mild friction persists because of contributions from other, sub-dominant resonances, and normal friction resumes once the pattern speed has declined sufficiently for the gradient at the main resonance to become favorable for friction once more. A state in which strong friction is suspended for this reason is "metastable", both because it relies on a local minimum in the phase space density, and because the state is fragile. A very mild jolt to the system is sufficient to cause normal friction to resume. The absence of friction in the simulation A\({}_{1}\) reported by Valenzuela & Klypin (2003) is probably an artifact of their code. Their adaptive grid causes gravity to strengthen as the bar density builds up, making the pattern speed of the bar rise for a purely numerical reason. Thus their claimed counter-example to the argument of Debattista & Sellwood (1998, 2000) is a numerical artifact of their method. _Pace_ Holley-Bockelmann & Weinberg (2005), our constraint on halo density still stands: A _strong_ bar in a _dense_ halo will quickly become unacceptably slow through dynamical friction. ###### Acknowledgements. We thank Anatoly Klypin for providing the initial positions and velocities of the particles in his model, and for many discussions. This work was supported by NASA (NAG 5-10110) and the NSF (AST-0098282). 1 ## References * [1] Binney, J. & Tremaine, S. 1987, _Galactic Dynamics_ (Princeton: Princeton University Press) * [2] Debattista, V. P. & Sellwood, J. A. 1998, _Ap. J. Lett._, **493**, L5 * [3] Debattista, V. P. & Sellwood, J. A. 2000, _Ap. J._, **543**, 704 * [4] Hernquist, L. 1990, _Ap. J._, **356**, 359 * [5] Holley-Bockelmann, K., Weinberg, M. D. & Katz, N. 2003, astro-ph/0306374 * [6] Holley-Bockelmann, K. & Weinberg, M. D. 2005, DDA abstract 36.0512 * [7] Kalnajs, A. J. 1977, _Ap. J._, **212**, 637 * [8] Kravtsov, A. V., Klypin, A. & Khokhlov, A. M. 1997, _Ap. J. Suppl._, **111**, 73 * [9] Lin, D. N. C. & Tremaine, S. 1983, _Ap. J._, **264**, 364 * [10] Lynden-Bell, D. 1979, _MNRAS_, **187**, 101 * [11] Lynden-Bell, D. & Kalnajs, A. J. 1972, _MNRAS_, **157**, 1 * [12] Sellwood, J. A. 2003, _Ap. J._, **587**, 638 * [13] Sellwood, J. A. 2004, astro-ph/0407533 * [14] Tremaine, S. & Weinberg, M. D. 1984, _MNRAS_, **209**, 729 * [15] Valenzuela, O. & Klypin, A. 2003, _MNRAS_, **345**, 406 * [16] Weinberg, M. D. 2004, astro-ph/0404169 * [17] Weinberg, M. D. & Katz, N. 2002, _Ap. J._, **580**, 627

# Multiple CO lines in SMM J16359+6612 - Further evidence for a merger 1 Footnote 1: institutetext: IRAM, Avenida Divina Pastora 7, 18012 Granada, Spain 2 Footnote 2: institutetext: IRAM, 300 rue de la Piscine, 38406 St-Martin-d’Héres, France 3 Footnote 3: institutetext: MPIA, Königstuhl 17, 69117 Heidelberg, Germany 4 Footnote 4: institutetext: MPIfR, Auf dem Hügel 69, 53121 Bonn, Germany A. Weiss 1144 D. Downes 22 F. Walter 33 C. Henkel 44 Using the IRAM 30 m telescope, we report the detection of the CO(3-2), CO(4-3), CO(5-4) and CO(6-5) lines in the gravitational lensed submm galaxy SMM J16359+6612 at \(z=2.5\). The CO lines have a double peak profile in all transitions. From a Gaussian decomposition of the spectra we show that the CO line ratios, and therefore the underlying physical conditions of the gas, are similar for the blue and the redshifted component. The CO line Spectral Energy Distribution (SED; i.e. flux density vs. rotational quantum number) turns over already at the CO 5-4 transition which shows that the molecular gas is less excited than in nearby starburst galaxies and high-z QSOs. This difference mainly arises from a lower average H\({}_{2}\) density, which indicates that the gas is less centrally concentrated than in nuclear starburst regions in local galaxies. We suggest that the bulk of the molecular gas in SMM J16359+6612 may arise from an overlap region of two merging galaxies. The low gas density and clear velocity separation may reflect an evolutionary stage of the merger event that is in between those seen in the Antennae and in the more evolved ultraluminous infrared galaxies (ULIRGs) like e.g. Mrk 231. Key Words.: **galaxies: formation - galaxies: high-redshift - galaxies: ISM - galaxies: individual (SMM J16359+6612) - cosmology: observations** ## 1 Introduction The intensity of the far-infrared (FIR) background indicates that emission from warm dust contributes significantly to galaxies' overall energy output over the Hubble time (Puget et al. puget96 (1996), Fixsen et al. fixsen98 (1998)). Recent surveys at submm and mm wavelengths with SCUBA at the JCMT and MAMBO at the IRAM 30 m telescope have identified part of the underlying galaxy population responsible for the strong FIR emission. Up to now several hundred submm/mm galaxies (SMGs) have been identified (e.g. Smail et al. smail97 (1997), Bertoldi et al. bertoldi00 (2000), Ivison et al. ivison02 (2002), Webb et al. webb03 (2003), Greve et al. greve04 (2004)). These surveys, however, are limited by confusion and therefore only trace the bright part of the SMG luminosity function (Blain et al. blain02 (2002)). Observations of CO, providing valuable information on the dynamics, size and mass of the molecular reservoirs in these objects, have only been reported for 12 SMGs so far (e.g. Frayer et al. frayer98 (1998), Ivison et al. ivison01 (2001), Downes & Solomon downes03 (2003), Genzel et al. genzel03 (2003), Neri et al. neri03 (2003), Greve et al. greve05 (2005)). Due to their selection based on the mm/submm continuum, all these sources, however, are intrinsically luminous, and not representative of the faint end of the SMG luminosity function that dominates the FIR background. Recently Kneib et al. (kneib04 (2004)) discovered the strongly lensed submillimeter galaxy SMM J16359+6612 towards the galaxy cluster A 2218. This source is lensed by the cluster into 3 discrete images and the large magnification (14, 22 & 9 for images A, B & C respectively) implies that its intrinsic submm flux density (\(S_{850{\mu{\rm m}}}=0.8\) mJy, corresponding to \(L_{\rm FIR}\approx 10^{12}\,{L_{\odot}}\) (Kneib et al. kneib04 (2004))) is below the confusion limit of existing 850 \(\mu\)m surveys (\(\approx 2\) mJy, Blain et al. blain02 (2002)). It therefore provides a unique opportunity to investigate a source which is presumably more representative for the submm population. Detections of CO towards SMM J16359+6612 have been reported by Sheth et al. (sheth04 (2004), CO 3-2) and Kneib et al. (kneib05 (2005), CO 3-2 & 7-6). In this letter we report on the detection of the CO 3-2, 4-3, 5-4 & 6-5 lines towards the strongest lensed component B. For the derived quantities in this paper, we use a \(\Lambda\) cosmology with \(H_{\rm 0}=71\) km s\({}^{-1}\) Mpc\({}^{-1}\), \(\Omega_{\Lambda}=0.73\) and \(\Omega_{m}=0.27\) (Spergel et al. spergel03 (2003)). ## 2 Observations Observations towards SMM J16359+6612 B were made with the IRAM 30 m telescope during nine runs between

Jan. and March 2005 in mostly excellent weather conditions. We used the AB and CD receiver configuration with the A/B receivers tuned to the CO(3-2) (\(98.310\) GHz, 3 mm band) and CO(6-5) (\(196.586\) GHz 1 mm band) and C/D to CO(4-3) or CO(5-4) (\(131.074,161.637\) GHz, 2 mm band). The beam sizes/antenna gains for increasing observing frequencies are 25\({}^{\prime\prime}\)/6.1 Jy K\({}^{-1}\), 19\({}^{\prime\prime}\)/6.5 Jy K\({}^{-1}\), 15\({}^{\prime\prime}\)/6.9 Jy K\({}^{-1}\) and 12.5\({}^{\prime\prime}\)/7.7 Jy K\({}^{-1}\). Typical system temperatures were \(\approx\) 120 K, 220 K, and 270 K (\(T_{\rm A}^{*}\)) for the 3, 2, and 1 mm observations. The observations were done in wobbler switching mode, with switching frequencies of 0.5 Hz and a wobbler throw of \(50^{\prime\prime}\) in azimuth. Pointing was checked frequently and was found to be stable to within \(3^{\prime\prime}\). Calibration was done every 12 min using the standard hot/cold-load absorber measurements. The planets Uranus and Neptune were used for absolute flux calibration. We estimate the flux density scale to be accurate to about \(\pm\)10-15%. Data were taken with the 1 MHz filter banks on the A/B 3mm receivers (512 channels, 512 MHz bandwidth, 1 MHz channel spacing) and the 4 MHz filter banks for the 2 and 1.3 mm observations (256 channels, 1 GHz bandwidth, 4 MHz channel spacing). The data were processed with the CLASS software. We omitted scans with distorted baselines, and only subtracted linear baselines from individual spectra. Their average was then regridded to a velocity resolution of 50 km s\({}^{-1}\) (CO 3-2, 4-3, 5-4 ) and 55 km s\({}^{-1}\)(6-5) leading to rms noise values (\(T_{\rm A}^{*}\)) of 0.26 mK (1.6 mJy), 0.47 mK (3.0 mJy), 0.6 mK (4.1 mJy) and 0.38 mK (2.9 mJy) respectively. The total observing time in the final spectra is 8.7h, 6.8h, 4.7h and 8.2h for the 3-2 to 6-5 lines, respectively. The final spectra are presented in Fig. 1. We also generated an averaged CO spectrum by averaging all individual CO transitions, with equal weight. This spectrum is shown at a velocity resolution of 15 km s\({}^{-1}\) in Fig. 2. ## 3 Results We detected all observed CO transitions from SMM J16359+6612 B. The line profiles for all four lines are similar, and show the characteristic double peak (see Fig. 1) already recognized in previous interferometric studies (Sheth et al. sheth04 (2004), Kneib et al. kneib05 (2005)). The small separation between the lensed images A and B of \(15.0^{\prime\prime}\) (Kneib et al. kneib04 (2004)) implies that our spectra also have a contribution from component A. Taking the relative integrated flux densities between component A/B and the beam size of the 30 m telescope at the four observing frequencies into account, we estimate the contribution from component A to the integrated line intensities of our spectra to be 24%, 12%, 4% and 2% for the 3-2 to 6-5 transitions respectively. These corrections have been applied to the following quantitative analysis. Due to the larger distance to component C and its lower magnification, the contribution from this component is negligible. Figure 1: Spectra of the CO(3–2), CO(4–3), CO(5–4) and CO(6–5) lines towards SMM J16359+6612 B, with Gaussian fit profiles superposed. The velocity scale is relative to a CO redshift of \(z=2.5174\). The velocity resolution is 50  km s\({}^{-1}\) (3–2, 4–3, 5–4) and 55  km s\({}^{-1}\)(6–5). All spectra are shown with the same flux scale. Figure 2: Averaged spectrum of all four CO lines at a velocity resolution of 15  km s\({}^{-1}\) with Gaussian fit profile superposed. All CO lines have equal weight. The velocity scale is relative to \(z=2.5174\). The total integration time for the spectrum is 28.4 hours (on + off)

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# The aperture for UHE tau neutrinos of the Auger fluorescence detector using a Digital Elevation Map Gennaro Miele Sergio Pastor Ofelia Pisanti Dipartimento di Scienze Fisiche, Universita di Napoli "Federico II" and INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cinthia, I-80126 Napoli, Italy Instituto de Fisica Corpuscular (CSIC-Universitat de Valencia), Ed. Institutos de Investigacion, Apdo. 22085, E-46071 Valencia, Spain ###### Abstract We perform a new study of the chances of the fluorescence detector (FD) at the Pierre Auger Observatory to detect the tau leptons produced by Earth-skimming ultra high energy \(\nu_{\tau}\)'s. We present a new and more detailed evaluation of the effective aperture of the FD that considers a reliable fiducial volume for the experimental set up. In addition, we take into account the real elevation profile of the area near Auger. We find a significant increase in the number of expected events with respect to the predictions of a previous semi-analytical determination, and our results show the enhancement effect for neutrino detection from the presence of the near mountains. keywords: PACS: 95.85.Ry, 13.15.+g, 96.40.Tv, 95.55.Vj, 13.35.Dx DSF-17/2005, IFIC/05-36 , , Neutrinos constitute one of the components of the cosmic radiation in the ultra high energy (UHE) regime. Since we have detected ultra high energy cosmic rays (UHECR), the presence of a secondary UHE neutrino flux is guaranteed as a result of the \(\pi\)-photoproduction, due to the interaction of hadronic UHECR with the cosmic microwave background. The detection of these _cosmogenic neutrinos_[1, 2], in addition to a possible primary neutrino flux, would provide precious information on the physics and position of their powerful astrophysical sources. On the other hand, copious neutrino fluxes are also predicted in more exotic _top-down_ scenarios where relic massive particles, produced at the first moments of the Universe, decay into UHE lighter particles, among which neutrinos and photons are expected. In any case, the detection of UHE

neutrinos would significantly contribute to unveiling the still unknown origin of UHECR. Due to the very low expected fluxes and the small neutrino-nucleon cross section, neutrinos with energies of the order of \(10^{18}\) eV and larger are hardly detectable even in the new generation of giant array detectors for cosmic radiation, like the Pierre Auger Observatory (Auger, in short) [3, 4]. The detection of UHE neutrinos inducing inclined air showers was recently reviewed in [5]. In particular, a promising strategy concerning the detection of the tau leptons produced by Earth-skimming UHE \(\nu_{\tau}\)'s has been analyzed in a series of papers [6]-[19]. UHE \(\tau\)'s, with energies in the range \(10^{18-21}\) eV, have a decay length not much larger than the corresponding interaction range. Thus, if a UHE \(\nu_{\tau}\) crosses the Earth almost horizontally (Earth-skimming) and interacts in the rock, the produced \(\tau\) has a chance to emerge from the surface and decay in the atmosphere, producing a shower that in principle can be detected as an up-going or almost horizontal event. The aim of this letter is to perform a new, more refined, estimate of the effective aperture of the fluorescence detector (FD) at Auger to Earth-skimming UHE \(\nu_{\tau}\)'s. A calculation of the number of possible up-going \(\tau\) showers detectable with the FD has already been performed in ref. [15] by using a semi-analytical computation. Our analysis represents a considerable improvement with respect to the estimate of this last work, since it uses a different method for calculating the number of \(\nu_{\tau}\)/\(\tau\) events, which now includes a class of tracks neglected in the previous calculation. An additional improvement in our analysis comes from considering the effects of the topology around the Auger observatory site, by using a Digital Elevation Map (DEM) of the area around the experiment. A detailed DEM of the Earth surface is provided by ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer) [20] which is an imaging instrument that is flying on Terra, a satellite launched in December 1999 as part of NASA's Earth Observing System. The available elevation map, GTOPO30, is a global digital model where the elevations are regularly spaced at 30-arc seconds. We show in Fig. 1 a 3D map of the relevant region around Auger. We will use this DEM to produce a realistic and statistically significant sample of possible \(\nu_{\tau}\)/\(\tau\) tracks crossing the fiducial volume of Auger, that will be used later to evaluate the real aperture of FD at Auger. We will define the Auger _fiducial_ volume as that limited by the the six lateral surfaces \(\Sigma_{a}\) (the subindex \(a=W\), \(E\), \(N\), \(S\), \(U\) and \(D\) labels each surface through its orientation: West, East, North, South, Up, and Down), and with \(\Omega_{a}\equiv(\theta_{a},\phi_{a})\) a generic direction of a track entering \(\Sigma_{a}\), as shown in Fig. 2. We have considered a simplified Auger area, given by a \(50\times 60\) km rectangle (an approximation to the real one, see ref. [4]), while th

e height of the fiducial volume was fixed to 10 km in order to be within the range of detection of the FD eyes. This is a conservative estimate, since we expect that the effective fiducial volume for the detection at the FD will be larger. Let \(\Phi_{\nu}\) be an isotropic flux of \(\nu_{\tau}+\overline{\nu}_{\tau}\). By generalizing the formalism developed in ref. [13], the number of \(\tau\) leptons emerging from the Earth surface with energy \(E_{\tau}\), going through \(\Sigma_{a}\) and showering in the fiducial volume per unit of time (thus potentially detectable by the FD), is given by Figure 1: A 3D map in longitude and latitude of the area around Auger with the elevation (not to scale) expressed in meters. The Auger position and surface, approximated to a rectangle, is indicated in red. Figure 2: A simplified scheme of the Auger fiducial volume is represented (height not to scale). The lateral surfaces are labelled by their orientation. Two examples of entering tracks are also shown.

the formalism developed in ref. [13], the number of \(\tau\) leptons emerging from the Earth surface with energy \(E_{\tau}\), going through \(\Sigma_{a}\) and showering in the fiducial volume per unit of time (thus potentially detectable by the FD), is given by \[\left(\frac{dN_{\tau}}{dt}\right)_{a} = D\,\int d\Omega_{a}\int dS_{a}\,\int dE_{\nu}\,\,\frac{d\Phi_{ \nu}(E_{\nu})}{dE_{\nu}\,d\Omega_{a}}\,\] (1) xdEt(Et)cos(tha)ka(En,Et;r-a,Oa), where \(D\) is the duty cycle and \(\epsilon(E_{\tau})\) is the detection efficiency of the FD, respectively [3]. The minimum energy for the \(\tau\) leptons, \(10^{18}\) eV, is chosen taking into account the energy threshold for the flourescence process [15]. The kernel \(k_{a}(E_{\nu}\,,E_{\tau}\,;\vec{r}_{a}\,,\Omega_{a})\) is the probability that an incoming neutrino crossing the Earth with energy \(E_{\nu}\) and direction \(\Omega_{a}\), produces a lepton emerging with energy \(E_{\tau}\), which enters the fiducial volume through the lateral surface \(dS_{a}\) at the position \(\vec{r}_{a}\) and decays inside this volume (see Fig. 2 for the angle definition). In Eq. (1), due to the very high energy of \(\nu_{\tau}\), we can assume that in the process \(\nu_{\tau}\,+\,N\rightarrow\tau\,+\,X\) the charged lepton is produced along the neutrino direction. As already shown in details in ref. [15], this process can occur if the following conditions are fulfilled, * 1)the \(\nu_{\tau}\) with energy \(E_{\nu}\) has to survive along a distance \(z\) through the Earth; * 2)the neutrino converts into a \(\tau\) in the interval \(z,z+dz\); * 3)the created \(\tau\) emerges from the Earth before decaying with energy \(E_{\tau}\); * 4)the \(\tau\) lepton enters the fiducial volume through the lateral surface \(\Sigma_{a}\) at the point \(\vec{r}_{a}\) and decays inside this volume. 1) The probability \(P_{1}\) that a neutrino with energy \(E_{\nu}\) crossing the Earth survives up to a certain distance \(z\) inside the rock is \[P_{1}=\exp\left\{-\frac{z}{\lambda_{CC}^{\nu}(E_{\nu})}\right\}\,\,\,,\] (2) where \[\lambda_{CC}^{\nu}(E_{\nu})=\frac{1}{\sigma_{CC}^{\nu N}(E_{\nu})\,\varrho_{s} \,N_{A}}\] (3) is the charged current (CC) interaction length in rock (\(\varrho_{s}\simeq 2.65\) g/cm\({}^{3}\)). A detailed discussion of an updated evaluation of the neutrino-nucleon cross section, \(\sigma_{CC}^{\nu N}(E_{\nu})\), can be found in ref. [15]. The dependence of \(\lambda_{CC}^{\nu}\) on the particular track direction can be safely neglected, since it is well known that

m before entering in the fiducial volume, and then decays inside it), preferred by the lateral surfaces due to the \(\cos\left(\theta_{i_{a}}\right)\) term in Eq. (17), were not included in the calculation of ref. [15], while they are present in this analysis. In Fig. 4 the different contributions from each surface are plotted together with the results of ref. [15] (thin solid line). As one can notice, the contribution coming from the tracks going through the Down surface (thick solid line) is in nice agreement with our previous calculation. Moreover, it is possible to distinguish a North-South effect and, more consistent, a West-East effect. It is worth observing the different high energy behavior of the aperture corresponding to the D surface, \(A_{D}\), with respect to the others. The increase of the neutrino energy would select the almost horizontal tracks, which however are depressed, for the D-surface only with respect to the lateral ones, by the factor \(\cos\left(\theta_{i_{D}}\right)\). We can use the expression in Eq. (14) to obtain the yearly number of \(\tau\) showering events at the FD of Auger (assuming a duty cycle \(D=10\%\)). In Table 1 these rates are reported for the same UHE neutrino fluxes considered in section 2 of ref. [15] (see in particular figs. 1 and 2), and described in a series of papers [22, 23, 24, 25, 26, 27, 28]. The three GZK fluxes refer to three possible scenarios for cosmogenic neutrinos, which are those produced from an initial flux of UHE protons. Instead the NH (New Hadrons) and TD (Topological Defects) cases are two examples of exotic models capable of generating the UHECR above \(10^{10}\) eV, with large associated neutrino fluxes. For each neutrino flux (fixed column), we list the total number of ye Figure 4: The effective apertures \(A_{a}(E_{\nu})\) defined in Eq. (15) are plotted versus the neutrino energy. The thin solid line corresponds to the same quantity as obtained in ref. [15] for \(H=30\) km.

arly events as well as the contributions from each lateral surface. Some comments are in turn. The number of events crossing the bottom surface is in fair agreement with the previous analytical result of ref. [15]. However, the total number of events is a factor 4-6 larger (depending on the model considered), showing that the main contribution to the number of events is coming from almost horizontal showers, where the \(\tau\) emerges from Earth surface far away from the Auger fiducial volume and decays inside it. The enhancement factor depends on the different features of the fluxes used in the analysis. For example, for the three GZK models in Table 1, this factor ranges from 3.7 to 6.2, corresponding to a hardening of the differential fluxes in energy (see Figs. 1 and 2 of ref. [15]). Instead, the enhancement is roughly the same for the last two models in Table 1 despite the fact that they have a different spectrum in the high energy range, due to the suppression of the very high energy neutrino events which escape without showering. As one can see from Table 1, a significant difference in the number of events exists between the Surfaces W (facing the Andes) and E, which shows a _mountain_ effect. This enhancement is mainly due to the largest amount of rock encountered by horizontal tracks coming from the west side. If we define, as a measure of the effect of mountains, the difference of the number of expected events entering the volume from W-surface and E-surface, divided by their average, the effect can be quite remarkable (even order 30%). This effect would also be larger by comparing the exclusive apertures, but in this case the difference in the apertures, which is larger for larger neutrino energy, should compel the fast decreasing with energy of neutrino fluxes. Of course, on the total number of events this 30% effect is diluted because it concerns only one surface among four lateral ones. Moreover, a similar but smaller effect (of order \(\sim\) 20-25%) is \begin{table} \begin{tabular}{|c|c|c|c|c|c|} \hline & GZK-WB & GZK-L & GZK-H & NH & TD \\ \hline Surface D & 0.016 & 0.040 & 0.095 & 0.246 & 0.100 \\ Surface S & 0.012 & 0.037 & 0.098 & 0.214 & 0.094 \\ Surface N & 0.015 & 0.046 & 0.125 & 0.267 & 0.120 \\ Surface W & 0.022 & 0.066 & 0.181 & 0.380 & 0.174 \\ Surface E & 0.008 & 0.024 & 0.061 & 0.139 & 0.060 \\ \hline Total & 0.074 & 0.213 & 0.560 & 1.245 & 0.548 \\ \hline \hline Ref. [15] & 0.02 & 0.04 & 0.09 & 0.25 & 0.11 \\ \hline \end{tabular} \end{table} Table 1: Yearly rate of Earth-skimming events at the FD for the different neutrino fluxes considered in ref. [15]. The number of \(\tau\)’s showering into the fiducial volume that enter through each lateral surface are reported, as well as the total number of events for each flux. For comparison, we include the corresponding results from ref. [15].

## Acknowledgments We thank M. Ambrosio, F. Guarino, L. Perrone and R. Vazquez for useful discussions. This work was supported by a Spanish-Italian AI, the Spanish grants BFM2002-00345 and GV/05/017 of Generalitat Valenciana, as well as a MEC-INFN agreement. SP was supported by a Ramon y Cajal contract of MEC. ## References * [1] V.S. Berezinsky and G.T. Zatsepin, Phys. Lett. B **28** (1969) 423. * [2] V.S. Berezinsky and G.T. Zatsepin, Sov. J. Nucl. Phys. **11** (1970) 111 [Yad. Fiz. **11** (1970) 200]. * [3] Pierre Auger Coll., _The Pierre Auger Project Design Report_, FERMILAB-PUB-96-024. * [4] J. Abraham et al. [Pierre Auger Coll.], Nucl. Instrum. Meth. A **523** (2004) 50. * [5] E. Zas, New J. Phys. **7** (2005) 130. * [6] K.S. Capelle, J.W. Cronin, G. Parente and E. Zas, Astropart. Phys. **8** (1998) 321. * [7] F. Halzen and D. Saltzberg, Phys. Rev. Lett. **81** (1998) 4305. * [8] D. Fargion, A. Aiello and R. Conversano, contribution to ICRC 1999, Salt Lake City (August 1999) [astro-ph/9906450]. * [9] F. Becattini and S. Bottai, Astropart. Phys. **15** (2001) 323. * [10] D. Fargion, Astrophys. J. **570** (2002) 909. * [11] A. Letessier-Selvon, AIP Conf. Proc. **566** (2000) 157. * [12] X. Bertou et al., Astropart. Phys. **17** (2002) 183. * [13] J.L. Feng, P. Fisher, F. Wilczek and T.M. Yu, Phys. Rev. Lett. **88** (2002) 161102. * [14] D. Fargion, P.G. De Sanctis Lucentini and M. De Santis, Astrophys. J. **613** (2004) 1285. * [15] C. Aramo et al., Astropart. Phys. **23** (2005) 65. * [16] Z. Cao, M.A. Huang, P. Sokolsky and Y. Hu, J. Phys. G **31** (2005) 571. * [17] G. Miele, L. Perrone and O. Pisanti, Nucl. Phys. Proc. Suppl. **145** (2005) 347. * [18] M.M. Guzzo and C.A. Moura, hep-ph/0504270.

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# High-speed, multi-colour optical photometry of the anomalous X-ray pulsar 4U 0142+61 with ULTRACAM V. S. Dhillon,\({}^{1}\) T. R. Marsh,\({}^{2}\) F. Hulleman,\({}^{3}\) M. H. van Kerkwijk,\({}^{3,4}\) A. Shearer,\({}^{5}\) S. P. Littlefair,\({}^{1}\) F. P. Gavriil,\({}^{6}\) V. M. Kaspi \({}^{6}\) \({}^{1}\)Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK \({}^{2}\)Department of Physics, University of Warwick, Coventry CV4 7AL, UK \({}^{3}\)Astronomical Institute, Utrecht University, PO Box 80000, 3508 TA Utrecht, The Netherlands \({}^{4}\)Department of Astronomy and Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada \({}^{5}\)Computational Astrophysics Group, Department of Information Technology, National University of Ireland, Galway, Ireland \({}^{6}\)Department of Physics, Rutherford Physics Building, McGill University, 3600 University Street, Montreal, Quebec H3A 2T8, Canada E-mail: vik.dhillon@shef.ac.uk (Submitted on 2005 May 26.) ###### Abstract We present high-speed, multi-colour optical photometry of the anomalous X-ray pulsar 4U 0142+61, obtained with ULTRACAM on the 4.2-m William Herschel Telescope. We detect 4U 0142+61 at magnitudes of \(i^{\prime}=23.7\pm 0.1\), \(g^{\prime}=27.2\pm 0.2\) and \(u^{\prime}>25.8\), consistent with the magnitudes found by Hulleman et al. (2004) and hence confirming their discovery of both a spectral break in the optical and a lack of long-term optical variability. We also confirm the discovery of Kern & Martin (2002) that 4U 0142+61 shows optical pulsations with an identical period (\(\sim 8.7\) s) to the X-ray pulsations. The rms pulsed fraction in our data is \(29\pm 8\)%, 5-7 times greater than the 0.2-8 keV X-ray rms pulsed fraction. The optical and X-ray pulse profiles show similar morphologies and appear to be approximately in phase with each other, the former lagging the latter by only \(0.04\pm 0.02\) cycles. In conjunction with the constraints imposed by X-ray observations, the results presented here favour a magnetar interpretation for the anomalous X-ray pulsars. keywords: pulsars: individual: 4U 0142+61 - stars: neutron ## 1 Introduction More than 100 X-ray pulsars are currently known. The vast majority of these are found in low-mass and high-mass X-ray binaries (LMXBs and HMXBs), and are hence powered by accretion onto a rotating, magnetised neutron star. There exists a small group of 8 X-ray pulsars, however, that exhibit properties very much at variance with those of the accreting pulsars in X-ray binaries. These so-called Anomalous X-ray Pulsars (AXPs) all have \(\sim 5-12\) s spin periods which decrease steadily with time, soft (and relatively low-luminosity) X-ray spectra, no radio emission, and tend to be associated with supernova remnants in the galactic plane. Most importantly, the AXPs show no evidence of a binary companion. For a recent review of AXPs, see Woods & Thompson (2004). This latter fact prompted a variety of models based on isolated neutron stars and white dwarfs (see the review by Israel et al. 2002), but these run into difficulty on energetic grounds: the loss of rotational energy, which powers radio pulsars like the Crab, is orders of magnitude too small to power the observed X-ray luminosity of the AXPs. An additional energy source is therefore required, for which two competing models seem to have emerged: accretion from a fossil disc or ultra-strong magnetic fields. In the former scenario, an isolated neutron star accretes from a fossil disc, such as might be produced through fall-back of material after a supernova explosion or left over from a common-envelope phase which destroyed the companion star. In the latter scenario, AXPs are "magnetars", isolated neutron stars with enormous (\(B\sim 10^{14}-10^{15}\) G) magnetic fields. It is the decay of the magnetic field which heats the neutron star surface, causing it to emit thermal radiation in the X-rays. Non-thermal emission is then produced by particles accelerated in the magnetosphere by the Alfven waves from small-scale fractures on the neutron star surface (Thompson & Duncan, 1996) or Comptonization of thermal photons by magnetospheric currents (Thompson et al., 2002).

The magnetar model has begun to dominate the literature in recent years. There are sound theoretical reasons for why this is so, as the magnetar model now appears to be able to explain the observational properties of several categories of supposedly young neutron stars that are not powered by rotation, including the AXPs and the Soft Gamma Repeaters (SGRs). Such unification is supported by the recent discovery of SGR-like bursts in AXPs (Gavriil et al. 2002; Kaspi et al. 2003), which suggests there might be an evolutionary link between AXPs and SGRs (see Mereghetti et al. 2002 and references therein). But what other observational evidence is there to support the magnetar model of AXPs? Belief in the magnetar model rests partly on the failure of the accretion model to explain the faintness of the optical/infrared counterparts, which sets strong limits on the size of an accretion disc (e.g. Hulleman et al. 2000), and the fact that the pulsed fraction of optical light is significantly greater than it is in X-rays, ruling out reprocessing of X-rays in a disc as its origin (Kern & Martin 2002; but see Ertan & Cheng 2004). Both of these optical constraints have been obtained via observations of the brightest known AXP, 4U 0142+61. In this paper we report on new high-speed, multi-colour optical observations of this object, obtained with the aim of confirming the high optical pulsed fraction observed by Kern & Martin (2002). ## 2 Observations and data reduction The observations of 4U 0142+61 presented in this paper were obtained with ULTRACAM (Dhillon & Marsh 2001, Beard et al. 2002) at the Cassegrain focus of the 4.2-m William Herschel Telescope (WHT) on La Palma. ULTRACAM is a CCD camera designed to provide imaging photometry at high temporal resolution in three different colours simultaneously. The instrument provides a 5 arcminute field on its three \(1024\times 1024\) E2V 47-20 CCDs (i.e. 0.3 arcseconds/pixel). Incident light is first collimated and then split into three different beams using a pair of dichroic beamsplitters. For the observations presented here, one beam was dedicated to the SDSS \(u^{\prime}\) (3543A) filter, another to the SDSS \(g^{\prime}\) (4770A) filter and the third to the SDSS (7625A) \(i^{\prime}\) filter. Because ULTRACAM employs frame-transfer chips, the dead-time between exposures is negligible: we used ULTRACAM in its two-windowed mode, each of \(100\times 200\) pixels, resulting in an exposure time of 0.48 s and a dead-time of 0.025 s. A total of 30 618 and 31 304 frames of 4U 0142+61 were obtained on the nights of 2002 September 10 and 12, respectively, with each frame time-stamped to a relative accuracy of better than 50 \(\mu\)s using a dedicated GPS system.1 Both sets of data were obtained in photometric conditions, with no moon and \(i^{\prime}\)-band seeing of 0.75 and 0.65 arcseconds on 10/09/02 and 12/09/02, respectively. Footnote 1: The absolute timing accuracy of ULTRACAM was verified with contemporaneous observations of the Crab pulsar. Our observed time of optical pulse maximum was found to agree with the ephemeris of Lyne et al. (2005) to better than 1 millisecond (the quoted error in the Crab pulsar ephemeris during September 2002). A portion of the summed \(i^{\prime}\) image from the night of 12/09/02 is shown in figure 1. The vertical streaks are due to light from bright stars falling on the active area of the chip above the CCD windows. The data we obtained on 10/09/02 (not shown in figure 1) suffer from streaks passing through the position of 4U 0142+61, increasing the background noise level significantly. As a result, we rotated the Cassegrain rotator in advance of our observations on 12/09/02 so that no streaks passed through 4U 0142+61. For this reason, the data obtained on 12/09/02 are of a much higher quality than the data obtained on 10/09/02. Note that the vertical streaking problem has since been rectified in ULTRACAM by provision of an adjustable focal-plane mask which blocks the light from bright stars (and the sky) above the CCD windows (Stevenson, 2004). The data were reduced using the ULTRACAM pipeline software. All frames were first debiased and then flat-fielded, the latter using the median of twilight sky frames taken with the telescope spiralling. We then extracted light curves of 4U 0142+61 using two different techniques: ### Technique (i) Kern & Martin (2002) obtained their light curve of 4U 0142+61 by synchronising the CCD clocks in their camera to the X-ray spin period of 4U 0142+61, resulting in the accumulation of 10 on-chip phase bins. This has the advantage of reducing detector noise, but the potential disadvantage that a period must be assumed before the data have been taken and, if the period is wrong, the true pulse profile is unrecoverable. To mimic the Kern & Martin (2002) technique, we assumed a spin period for 4U 0142+61 on 12/09/02 of 8.688473130 s, which was calculated from the updated X-ray ephemeris given in table 1. Note that this ephemeris spans our WHT observations and is hence more reliable for our purposes than using the ephemeris of Gavriil & Kaspi (2002) adopted by Kern & Martin (2002). Each ULTRACAM data frame was then added to one of 10 evenly-spaced phase bins covering the spin cycle of 4U 0142+61, resulting in 10 high signal-to-noise data frames. An optimal photometry algorithm (Naylor, 1998) was then used to extract the counts from 4U 0142+61 and a bright comparison star 24 arcseconds to the east of the AXP (see \begin{table} \begin{tabular}{l r} \hline BMJD range & \(51\,610.636-53\,401.184\) \\ TOA arrival points & 79 \\ \(\nu\) (Hz) & 0.11509507445(18) \\ \(\dot{\nu}\) (\(10^{-14}\) Hz s\({}^{-1}\)) & –2.66478(36) \\ \(\ddot{\nu}\) (\(10^{-24}\) Hz s\({}^{-2}\)) & 5.08(23) \\ Epoch (BMJD) & 52 506.9748874274228 \\ rms residual (cycles) & 0.031 \\ \hline \end{tabular} \end{table} Table 1: Updated ephemeris for 4U 0142+61 spanning the optical observations described in section 2, based on the monitoring campaign described in Gavriil & Kaspi (2002). BMJD refers to the Barycentric-corrected Modified Julian Date on the Barycentric Dynamical Timescale (TDB). TOA refers to the pulse time of arrival (see Gavriil & Kaspi (2002) for details). The errors on the last two digits of each parameter are given in parentheses.

figure 1), the latter acting as the reference for the profile fits and transparency-variation correction. The position of 4U 0142+61 relative to the comparison star was determined from a sum of all the images, and this offset was then held fixed during the reduction so as to avoid aperture centroiding problems. The sky level was determined from a clipped mean of the counts in an annulus surrounding the target stars, and subtracted from the object counts. ### Technique (ii) The second approach we took to light curve extraction was identical to that described above, except that we omitted the phase-binning step and simply performed optimal photometry on the 61922 individual ULTRACAM data frames. In other words, we made no assumption about the spin period of 4U 0142+61. ## 3 Results ### Magnitudes We were unable to detect 4U 0142+61 in \(u^{\prime}\), at a detection limit of \(u^{\prime}>25.8\). We did, however, clearly detect it in \(g^{\prime}\) and \(i^{\prime}\) on both nights at magnitudes of \(g^{\prime}=27.2\pm 0.2\) and \(i^{\prime}=23.7\pm 0.1\), as shown in figure 1. Hulleman et al. (2004) measured \(g^{\prime}\sim 26.9\) and \(i^{\prime}\sim 23.7\) (where we have converted their \(BVRI\) Johnson-Morgan-Cousins magnitudes to SDSS magnitudes using the transformation equations of Smith et al. 2002), indicating that 4U 0142+61 was approximately the same magnitude during our observations. ### Pulse profiles The two data reduction techniques described in section 2 result in two different pulse profiles for 4U 0142+61. #### 3.2.1 Technique (i) The first technique produced the pulse profiles shown in the top panel of figure 2. As expected, the light curve of 12/09/02 is of a significantly higher quality than that of 10/09/02, but both show approximately the same morphology as the optical pulse profile presented by Kern & Martin (2002), exhibiting a broad (arguably double-humped) structure with peaks around phases 0.65 and 1.15 and a minimum around phase 0.35. These phases are different to the corresponding phases in the pulse profile of Kern & Martin (2002), but this is to be expected given that, as discussed by Kern & Martin (2002), their optical observations were obtained outside the span of the ephemeris they used and the source does exhibit some timing noise (Gavriil & Kaspi, 2002). Our timing solution, on the Figure 1: Left: Summed \(i^{\prime}\) image from the night of 12/09/02, with a total exposure time of 15046 s (\(\sim 4\) h). Star A is 4U 0142+61 and star B is the comparison/reference star (see Hulleman et al. (2004) for coordinates and magnitudes). The orientation arrows represent 10 arcseconds on the sky. For clarity, only a portion of the two ULTRACAM windows is shown. Note that there is no gap between the windows, but a faint discontinuity between them can be seen running down the centre of the image, due to the fact that each window is read out via a separate channel. Right: Higher contrast plots of the field around 4U 0142+61 (star A), showing the summed \(i^{\prime}\) (top) and \(g^{\prime}\) images (bottom) from the night of 12/09/02. The box in the left-hand image shows the portion of the field shown (at the same scale) in the right-hand images.

other hand, is based on the updated ephemeris for 4U 0142+61 presented in table 1, which spans our WHT observations and is hence reliable. There is some similarity in the morphologies of the optical pulse profile shown in the top panel of figure 2 and the 2-10 keV X-ray pulse profile shown below it, where the latter is an updated version of the data presented by Gavriil & Kaspi (2002). Both profiles share a similar broad/double-humped morphology. Moreover, since the X-ray light curve shown in figure 2 has also been phased using the ephemeris given in table 1, it can be seen that the optical and X-ray pulse profiles are approximately in phase with each other. To quantify this, the optical pulse profile was cross-correlated with the X-ray pulse profile. The resulting peak in the cross-correlation function was fitted with a parabola to derive a shift of \(0.04\pm 0.02\) cycles (i.e. \(0.35\pm 0.17\) s), where a positive phase shift implies that the optical pulse profile lags the X-ray pulse profile. This result is only marginally significant (at the 2\(\sigma\) level), due to the low signal-to-noise and time resolution of the optical data, and additional data will be required in order to confirm that the phase shift is significantly different from zero (discounting the unlikely situation in which the time delay is approximately equal to some multiple of the spin period). The modulation amplitude of the pulses presented in figure 2 can be measured using a peak-to-trough pulsed fraction, \(h_{pt}\), defined as follows: \[h_{pt}=\frac{F_{max}-F_{min}}{F_{max}+F_{min}},\] (1) where \(F_{max}\) and \(F_{min}\) are the maximum and minimum flux in the pulse profile, respectively. We find a value of \(h_{pt}=58\pm 16\)% on 12/09/02, higher than the pulsed fraction of \(h_{pt}=27\pm 8\%\) derived by Kern & Martin (2002), although the difference between the two values is only marginally significant (\(31\pm 18\%\), i.e. \(<2\sigma\)). There are a number of factors which might contribute to a higher optical pulsed fraction in our data: * *The pulsed fraction measured from our data refers to the \(i^{\prime}\) band, whereas that of Kern & Martin (2002) is for white light (4000-10000A). If the optical pulsed fraction varies with wavelength, this could be the source of the discrepancy. Note that our \(g^{\prime}\) data were too faint to extract a pulse profile from, unfortunately, so we are not in a position to test this explanation. * *Even a small error in the assumed period on which the data is phase-binned can result in a smearing of the pulse profile and hence a reduction in the measured pulsed fraction. We have simulated this effect and find that to reduce our pulsed fraction to the level observed by Kern & Martin (2002), the period must be in error by greater than \(\sim 0.003\) s. This is three orders of magnitude greater than the timing accuracy achieved by the instrumentation used by Kern & Martin (2002) and hence an error in the period used to phase bin the data is an unlikely source of the discrepant pulsed fractions. * *The higher pulsed fraction in our data might be due either to a decrease in the unpulsed optical component or an increase in the pulsed optical component. Hulleman et al. (2004) found no evidence for long-term \(R\)-band variability in 4U 0142+61, down to a 2-\(\sigma\) limit of 0.09 magnitudes, and our magnitude estimates (section 3.1) appear to support this conclusion. Note, however, that Hulleman et al. (2004) did find long-term variability of \(\sim 0.5\) magnitude in their \(K\)-band observations of 4U 0142+61, which they tentatively attributed to the occurence of SGR-like bursts in 4U 0142+61. X-ray observations of this source have not shown such bursts, but this might be due to their (expected) low amplitude and the efficiency of the X-ray monitoring. * *The peak-to-trough pulsed fraction defined in equation 1 effectively adds any noise present in the light curve to the true pulsed fraction, thereby tending to increase the resulting measurement. A more robust estimate is given by the root-mean-square (rms) pulsed fraction, \(h_{rms}\), defined as follows: \[h_{rms}=\frac{1}{\bar{y}}\left[\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\bar{y})^{2}- \sigma_{i}^{2}\right]^{\!\frac{1}{2}},\] (2) where \(n\) is the number of phase bins per cycle, \(y_{i}\) is the number of counts in the \(i^{\rm th}\) phase bin, \(\sigma_{i}\) is the error on \(y_{i}\) and \(\bar{y}\) is the mean number of counts in the cycle. As expected, measuring the optical pulsed fraction in this way gives a lower value of \(h_{rms}=29\pm 8\)%. This is much closer to the value derived by Kern & Martin (2002), but it should be stressed that these authors measured the peak-to-trough Figure 2: Top: Pulse profiles of 4U 0142+61 in the \(i^{\prime}\)-band on 12/09/02 (solid line), obtained using technique (i) (section 2.1). The dotted line shows the poorer quality light curve we obtained on the night of 10/09/02, demonstrating the repeatability of the pulse profile. Each pulse profile was first corrected for transparency variations using the comparison star (star B in figure 1), although the correction made only a negligible difference to the light curves. The pulse profiles were then normalised by dividing by the mean number of counts. Note that the formal error bars on these pulse profiles were unreliable (most probably due to the vertical streaks shown in figure 1), and hence the error bars shown have been calculated from the scatter in the light curve extracted using technique (ii) (section 2.2). Bottom: Averaged X-ray pulse profile of 4U 0142+61 in the 2–10 keV energy band, which is an updated version of the profile presented in Gavriil & Kaspi (2002). Note that it is not possible to estimate the X-ray pulsed fraction from this profile as the background level (i.e. the minimum flux) in the X-ray pulse profile is unrelated to the pulsar – see section 4 for details). For this reason, no scale is given on the ordinate.

pulsed fraction (equation 1), not the rms pulsed fraction (equation 2). * *The higher pulsed fraction in our data could be due to some systematic problem with the sky subtraction. We consider this to be unlikely, however, as one would not then expect our magnitude estimates to agree with those of Hulleman et al. (2004). #### 3.2.2 Technique (ii) The second data reduction technique (section 2.2) can be used to provide a check on the reliability of the optical pulse profile shown in figure 2. To do this, it is first necessary to fold the extracted light curve on the pulse period. Rather than do this by adopting the X-ray ephemeris given in table 1, as we did in figure 2, we can instead determine the pulse period directly from our optical data using a periodogram and then fold the data on this period. Figure 3 shows the Lomb-Scargle periodograms (Press & Rybicki, 1989) for the 30 618 and 31 304 points in the \(i^{\prime}\) light curves obtained on 10/09/02 and 12/09/02, respectively. The \(g^{\prime}\) light curves were unfortunately too noisy to perform such an analysis. The light curves were first corrected for transparency variations and then detrended by subtracting their mean level. The highest peak in the resulting periodogram of 12/09/02 occurs at a period of \(8.687\pm 0.002\) s, where the error is given by the width (\(\sigma\)) of a Gaussian fit to the peak in the periodogram. This period is consistent with the X-ray pulse period given in table 1. Although noisier, an equivalent peak is also present in the periodogram of 10/09/02, with a period of \(8.688\pm 0.002\) s, thereby confirming that we have indeed detected the X-ray pulsation of 4U 0142+61 in the optical. We further tested the robustness of our period detection by constructing 10000 randomised light curves from the original light curves by randomly re-ordering the \(y\)-axis points. Only 0.12% of the resulting 10000 periodograms for the 12/09/02 dataset showed a higher peak at 8.687 s, and only 0.38% showed a higher peak at 8.688 s in the 10/09/02 dataset. Folding the \(i^{\prime}\) light curve of 12/09/02 on the derived optical pulse period of 8.687 s gives the pulse profile shown in figure 4. The same data folded on the X-ray pulse period of 8.688473130 s is shown for comparison. Note that the phasing of both profiles can be directly compared to that in figure 4, as all of the data were folded using the zero point given in table 1. As one would expect, the \(i^{\prime}\)-data folded on the X-ray pulse period (dotted line in figure 4) is in excellent agreement with that presented in figure 2, in terms of morphology, phasing and pulsed fraction (\(h_{pt}=50\pm 20\)%). The \(i^{\prime}\)-data folded on the optically-determined pulse period (solid line in figure 4) shares approximately the same phase of pulse maximum and pulsed fraction (\(h_{pt}=56\pm 16\)%), but the morphology is slightly different. In particular, the shape and phase of pulse minimum is very different, This is to be expected, however, given that the data have been folded on the optically-derived period of 8.687 s, which is much less accurate than the X-ray period due to the lower quality of the optical data. ## 4 Discussion and conclusions Using two different data reduction techniques we have shown that the optical light from 4U 0142+61 pulsates on the X-ray period, thereby confirming the discovery of Kern & Martin (2002). The morphologies of the 2-10 keV and \(i^{\prime}\) pulse profiles are quite similar, both exhibiting a broad/double-humped structure. The optical lags the X-rays by only \(0.04\pm 0.02\) cycles (\(0.35\pm 0.17\) s), i.e. there is no strong evidence for a phase shift between the two pulse profiles. The most reliable value we have derived for the optical pulsed Figure 4: Pulse profiles of 4U 0142+61 in the \(i^{\prime}\)-band on 12/09/02, obtained using technique (ii) (section 2.2) and folding the resulting data on the optically-determined period of \(8.687\) s (solid line) and on the X-ray period of 8.688473130 s (dotted line). The data were first corrected for transparency variations using the comparison star (star B in figure 1). The pulse profiles were then normalised by dividing by the mean number of counts. Note that the formal error bars on these pulse profiles were unreliable (most probably due to the vertical streaks shown in figure 1), and hence the error bars shown have been calculated from the scatter in the unfolded light curve. Figure 3: Lomb-Scargle periodograms of 4U 0142+61 in the \(i^{\prime}\)-band on 10/09/02 (top panel) and 12/09/02 (bottom panel), obtained using the light curves from technique (ii) (section 2.2). The dotted line shows the predicted X-ray pulse frequency of 0.11509502130 Hz on 12/09/02, calculated from the ephemeris given in table 1.

fraction is \(h_{rms}=29\pm 8\)%, as this is the more robust rms figure (as opposed to the peak-to-trough value) and has been obtained by folding the best dataset, that of 12/09/02, on the accurately known X-ray period (see figure 1). The X-ray pulsed fraction of 4U 0142+61 cannot be measured from the X-ray pulse profile shown in figure 2, unfortunately, as the background level (i.e. the minimum flux) in these data is unrelated to the pulsar. This is because the X-ray data were obtained with the Proportional Counter Array (PCA) on the Rossi X-ray Timing Explorer (RXTE), which has approximately a 1\({}^{\circ}\) field of view and no imaging capability. Instead, we turn to the work of Patel et al. (2003), who reported X-ray pulsed fractions for 4U 0142+61 of \(h_{rms}=4.6\pm 0.5\)% between 0.2-1.3 keV, \(h_{rms}=4.1\pm 0.4\)% between 1.3-3.0 keV and \(h_{rms}=5.6\pm 1.0\)% between 3.0-8.0 keV; Patel et al. (2003) also quote corresponding peak-to-trough pulsed fractions of \(h_{pt}=8.4\pm 1.6\)%, \(h_{pt}=7.4\pm 1.2\)% and \(h_{pt}=11.7\pm 3.2\)%. These values demonstrate that the optical rms pulsed fraction we have measured is 5-7 times greater than the X-ray rms pulsed fractions, consistent with the factor of 5-10 times derived by Kern & Martin (2002) from their peak-to-trough pulsed fraction measurements. We have measured \(g^{\prime}\) and \(i^{\prime}\) magnitudes consistent with the \(BVRI\) magnitudes found by Hulleman et al. (2004), supporting their finding that, although variable in the infrared and X-rays, 4U 0142+61 does not appear to show long-term variability in the optical part of the spectrum. Moreover, the fact that we have used the \(B\) and \(V\) magnitudes of Hulleman et al. (2004) to derive a \(g^{\prime}\) magnitude consistent with our own confirms that the spectral break between \(B\) and \(V\) found by Hulleman et al. (2004) is real. The optical observations presented in this paper therefore lend additional weight to the arguments given by Hulleman et al. (2000), Kern & Martin (2002) and Hulleman et al. (2004) that the AXP's are best explained by the magnetar model, mainly thanks to the failure of most alternative models to explain the observations (a notable exception is the disc-star dynamo gap model of Ertan & Cheng 2004). In particular, fall-back accretion disc models (e.g. Perna et al. 2000) fail because the optical flux is assumed to be due to reprocessing of the X-ray flux in the disc and therefore would not be expected to show either an optical pulsed fraction significantly in excess of the X-ray pulsed fraction (see Kern & Martin 2002) or a non-thermal spectral energy distribution in the optical. 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# A COMPLETE Look at The Use of IRAS Emission Maps to Estimate Extinction and Dust Temperature Scott L. Schnee, Naomi A. Ridge, Alyssa A. Goodman Jason G. Li Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA, 02138, USA ###### Abstract We have created new dust temperature and column density maps of Perseus, Ophiuchus and Serpens using 60 and 100 \(\mu\)m data from the IRIS recalibration of IRAS data. We describe an optimized method for finding the dust temperature, emissivity spectral index, and optical depth using optical and NIR extinction maps. The creation of these temperature and extinction maps (covering tens of square degrees of molecular clouds) is one of the first results from the ongoing COordinated Molecular Probe Line Extinction Thermal Emission (COMPLETE) Survey of Star Forming regions. However, while the extinctions derived from the IRIS emission maps are globally accurate, we warn that FIR emission is not a good proxy for extinction on the scale of one pixel (\(\sim\)5'). In addition to describing the global dust properties of these clouds, we have found two particularly interesting features in the column density and temperature maps. In the Ophiuchus dark cloud complex, the new dust temperature map shows a little known warm (25 K) dust ring with 2 pc diameter. This shell is approximately centered on the B star \(\rho\)-Ophiuchus, 1\({}^{\circ}\) north of the well-studied \(\rho\)-Oph star-forming cluster. In Perseus, the column density map shows a 10 pc diameter ring, a feature not apparent in the filamentary chain of clouds seen in molecular gas. These rings are further discussed in detail in companion papers to this one. ISM: clouds -- dust, extinction -- surveys + [FOOTNO

TE:+][ENDFOOTNOTE] ## 1 Introduction The goal of the COMPLETE Survey is to use a carefully chosen set of observing techniques to fully sample the density, temperature and velocity structure of three of the five large star-forming complexes observed in the NASA-sponsored Spitzer Legacy Survey "From Molecular Cores to Planet-forming Disks" (c2d) described in Evans et al. (2003). The c2d Survey, started in late 2003, is producing high-resolution infrared spectroscopy, and near- through far-infrared images of each of its 5 pc scale target complexes. COMPLETE is providing fully-sampled milimeter spectral-line, extinction, and thermal emission maps for the same regions, at arcminute resolution or better (Goodman, 2004). Phase II of COMPLETE, begun recently, provides higher-resolution observations using the same suite of techniques for a large subset of the high-density cores evident at lower resolution. In this paper we present new temperature and extinction maps of the Perseus, Serpens and Ophiuchus star-forming regions, produced from 60 and 100 \(\mu\)m flux-density maps obtained from IRIS (Improved Reprocessing of the _IRAS_ Survey), and normalized using optical/NIR extinction maps generated by Alves, Lombardi & Foster (2005) and Cambresy (1999). Previous all-sky thermal dust emission maps by Schlegel, Finkbeiner & Davis (1998) [SFD] include these regions. However, the SFD maps were based on low-resolution temperature data and optimized for low extinction regions. It has been established that the SFD maps lose accuracy at \(A_{V}>0.5\) mag (Arce & Goodman, 1999; Cambresy et al., 2005), so they are not adequate for mapping column density in the high-extinction areas targeted in the COMPLETE survey. We show here that reanalysis of the IRAS data can yield column density and color temperature maps that are more accurate at high and low levels of extinction on the large scale, though their use on the scale of the data (\(\sim\) 5') is more limited. In Section 2 we describe the IRIS flux measurements and NIR/optical-based extinction maps. In Sections 3 and 4 we present and explain the equations used to determine the the dust optical depth and conversion to visual extinction, and the parameters needed in those equations. In Section 5 we compare the results of our analysis technique to those from other extinction tracers. The results are summarized in Section 6

. ## 2 Data ### IRAS/IRIS IRIS1 images of flux-density at 60 and 100 \(\mu\)m were obtained for each of our three target regions from the IRIS website (Miville-Deschenes & Lagache, 2005). Image details are given in Table 1. The maps have units of MJy sr\({}^{-1}\), are made with gnomic projection and have spatial resolution smoothed to 4.3' at 100 \(\mu\)m. Footnote 1: IRIS comprises a machine-readable atlas of the sky in the four IRAS bands at 12, 25, 60, and 100 \(\mu\)m IRIS data offer excellent correction for the effects of zodiacal dust and striping in the images and also provide improved gain and offset calibration. Earlier releases of the IRAS data did not have the appropriate zero point calibration, which can have serious consequences on the derived dust temperature and column density (Arce & Goodman, 1999). To test the zero point calibration of the IRIS data, we allowed two free parameters in the fit (one each for the 60 and 100 micron zero points) to convert IRIS fluxes to visual extinction (see Section 4). We find that values of the free parameters are consistent with zero, and thus provide independent evidence that the zero point calibrations of the IRIS data at 60 and 100 um are correct. ### Optical and NIR Extinction Maps Here we describe the NIR and optical extinction maps used to recalibrate the IRIS maps presented in this paper. We have obtained extinction maps of Serpens and Ophiuchus from Cambresy (1999), which are based on an optical star counting method with variable resolution (but we regrid these maps to the constant resolution of the IRIS images). The optical photometry data used by Cambresy come from the USNO-PMM catalogue (Monet, 1996). Extinction maps of Perseus and Ophiuchus have been constructed from the 2MASS point source catalog as part of COMPLETE by Alves, Lombardi & Foster (2005) using the "NICER" algorithm, which is a revised version of the NICE method described in Lada et al. (1994) and Lombardi & Alves (2001). NICE and NICER combine direct measurements of near-infrared color excess and certain techniques of star counting to derive mean extinctions and map the dust column density distribution through a cloud (Lombardi & Alves, 2001). The 2MASS survey provides the NIR \(J,H\) and \(K_{s}\) colors of background stars that have been reddened by the molecular cloud. With these measured colors, and knowledge of the intrinsic colors of these stars (measured in a nearby, non-reddened contol field), the amount

of obscuring material along the line of sight to each star can be determined. In NICER, the extinction values are calculated for a fixed resolution, which means uncertainties vary from pixel to pixel. Maps of uncertainty for the regions considered are shown in Alves, Lombardi & Foster (2005). In the Ophiuchus molecular cloud, we have both 2MASS/NICER and optical star counting based extinction maps. It is important to note that the two methods _do not_ give equivalent extinctions. A plot of the optical vs NIR extinctions is shown in Figure 1. A linear fit to the data shows that the slope of the line relating the two quantities is very close to unity (as expected), _but_ there is an offset of roughly 0.71 magnitudes of visual extinction, with the 2MASS derived data points being systematically higher than the optically derived extinctions. The 1\(\sigma\) scatter on the least squares fit between the two methods is 0.7 magnitudes in \(A_{V}\). Because these methods produce such different results, care must be taken when using any one extinction map as a model to determine dust properties as described in Section 3. In Ophiuchus, where we have both optical and NIR extinction maps, we run the global fitting algorithm for each data set separately, and report both sets of results in Table 2. In Perseus we only have a NIR based extinction map, and in Serpens we only have an optically derived extinction map, so no intercomparison of the calibration methods is possible for these clouds. We expect that the 2MASS derived extinctions are more accurate than the star counting method of Cambresy, although in both cases the zero point calibration can be difficult to assess. The optical star counting method chooses the average minimum value in the map as the "zero level" of extinction (Cambresy, 1999), and the NICER method uses the average minimum H-K color to determine the minimum extinction in the map. Both methods rely on the minimum in their map actually corresponding to zero extinction, which if untrue, will cause both methods to underestimate the true extinction. In Ophiuchus, because the NICER algorithm gives higher extinctions, it is likely that the optical star counting algorithm has underestimated the true extinction by approximately 0.71 magnitudes. Our decision to trust the NIR based extinctions over the star counting extinctions is supported by discussion with Drs. Cambresy and Alves (private communication). To account for the 0.71 mag offset, we have added 0.71 magnitudes to the extinction values derived by Cambresy (1999) in our optically calibrated calculations for Ophiuchus in Sections 3 and 4. We expect the Serpens extinction map to suffer from the same "zero level" problem as the Ophiuchus optical extinction map, and therefore include a free parameter in the fit between the optical extinction map and the IRIS emission maps to account for this possibility. We find the best fit occurs between the emission based extinction map and the optical star count based extinction map when the latter map has a constant value of 2.4 magnitudes of

visual extinction added to each pixel. ## 3 Basic Formulae The basic method that we use to calculate the dust color temperature and column density from the IRAS 60 and 100 \(\mu\)m flux densities is similar to Wood, Myers & Daugherty (1994) and Arce & Goodman (1999). The temperature is determined by the ratio of the 60 and 100 \(\mu\)m flux densities. The column density of dust can be derived from either measured flux and the derived color temperature of the dust. The calculation of temperature and column density depend on the values of three parameters: two constants that determine the emissivity spectral index, and the conversion from 100 \(\mu\)m optical depth to visual extinction. We are able to solve for these parameters explicitly because we have an independent estimate of visual extinction, as will be explained in Section 4. The dust temperature \(T_{d}\) in each pixel of a FIR image can be obtained by assuming that the dust in a single beam is isothermal and that the observed ratio of 60 to 100 \(\mu\)m emission is due to blackbody radiation from dust grains at \(T_{d}\), modified by a power-law emissivity spectral index. The flux density of emission at a wavelength \(\lambda_{i}\), is given by \[F_{i}=[\frac{2hc}{\lambda_{i}^{3}(e^{hc/(\lambda_{i}kT_{d})}-1)}]N_{d}\alpha \lambda_{i}^{-\beta}\Omega_{i},\] (1) where \(N_{d}\) represents column density of dust grains, \(\alpha\) is a constant that relates the flux to the optical depth of the dust, \(\beta\) is the emissivity spectral index, and \(\Omega_{i}\) is the solid angle subtended at \(\lambda_{i}\) by the detector. Following Dupac et al. (2003), we use the equation, \[\beta=\frac{1}{\delta+\omega T_{d}}\] (2) to describe the observed inverse relationship between temperature and the emissivity spectral index. The parameters (\(\delta\) and \(\omega\)) are derived separately for each cloud and subregion considered in this paper. With the assumptions that the dust emission is optically thin at 60 and 100 \(\mu\)m and that \(\Omega_{60}\simeq\Omega_{100}\) (true for IRIS images), we can write the ratio, \(R\), of the flux densities at 60 and 100 \(\mu\)m as \[R=0.6^{-(3+\beta)}\frac{e^{144/T_{d}}-1}{e^{240/T_{d}}-1}.\] (3) Once the appropriate value of \(\beta\) is known, one can use Equation 3 to derive \(T_{d}\). The value of \(\beta\) depends on such dust grain properties as composition, size, and compactness. For

reference, a pure blackbody would have \(\beta=0\), amorphous layerlattice matter has \(\beta\sim 1\), and metals and crystalline dielectrics have \(\beta\sim 2\). Once the dust temperature has been determined, the 100 \(\mu\)m dust optical depth can be calculated as follows: \[\tau_{100}=\frac{F_{\lambda}(100\mu m)}{B_{\lambda}(100\mu m,T_{d})},\] (4) where \(B_{\lambda}\) is the Planck function and \(F_{\lambda}(100\mu m)\) is the 100 \(\mu\)m flux. The 100 \(\mu\)m optical depth can then be converted to V-band extinction using: \[A_{V}=X\tau_{100}\] (5) where \(X\) is a parameter relating the thermal emission properties of dust to its optical absorption qualities. ## 4 Derivation Of Constants We can derive the values of the three parameters (\(\delta\), \(\omega\) and \(X\)) from the IRIS emission maps and extinction maps from Cambresy (1999) and Alves, Lombardi & Foster (2005). Each optical and NIR extinction map described in Section 2.2 is used as a "model" extinction map to fit the IRIS-implied column density map using the three adjustable parameters which are explained in Section 3. The IDL task AMOEBA was used to simulateously fit all three parameters with the downhill simplex method of Nelder & Meade (1965). Each combination of these three parameters is used to determine the dust temperature and column density at each point in the map (using the formulae in Section 3). The parameter values determined by this method are those that create a FIR-based extinction map that best matches the NIR color excess or optical star count derived extinction map. This is a statistical point-by-point match, not a spatial match to features in the NIR/optical extinction map. As explained in Section 2.2, we solve for a fourth parameter in Serpens, which is the zero level of the optical extinction map. Each cloud is considered separately, so the values of \(\delta\), \(\omega\) and \(X\) are different for each cloud. Because Ophiuchus has two independent extinction maps, one from optical star counting (adjusted by the 0.71 mag offset) and one from the NIR color excess method, it has two sets of constants derived for it. In this paper we assume that the values of the three parameters are constant within each image, though of course this does not have to be the case. For instance, it may be the case that areas of especially high or low column density do not share the same visual extinction conversion factor, \(X\). Our values for the three parameters for each region fit (four in Serpens) are presented in Table 2. ## 5

Results and Discussion ### Assumption of Thermal Equilibrium The derivations of dust temperature and column density from IRIS data rely on the assumption that the dust along each line of sight is in thermal equilibrium. However, the dust models of Desert et al. (1990) show that the emission at 60 and 100 um have contributions by big dust grains (BGs) and very small dust grains (VSGs). The VSGs are not in thermal equilibrium, and emit mostly in the 60 micron band, while the BGs are the primary contributors at 100 microns and longer. Because of the emission from the VSGs, determining the temperature of the dust from the ratio of 60 and 100 um fluxes can yield temperatures that are systematically high. An empirical method for determining the color temperature and optical depth of dust using the 60 and 100 micron bands from IRAS is presented in Nagata et al. (2002), but as this method has been calibrated for galaxies and not molecular clouds, we do not employ their method. In order to remove the contribution of VSGs to the 60 um flux, we calibrate our temperature maps to those derived by Schlegel, Finkbeiner & Davis (1998) [SFD], which are not currupted by VSG emission because they used maps at 100 um and longer to derive their temperatures. We smooth the IRIS images to the resolution of the SFD temperature maps, and calculate the temperature based on 100% of the 100 um flux and a lesser percentage of the 60 um flux, assuming that \(\beta=2\) (as assumed by SFD). The fraction of the 60 um flux was chosen so as to best match our derived temperatures with the SFD temperatures. The remaining 60 um flux comes from the VSGs. Note that the temperatures we use in our calculations of column density do not assume that \(\beta=2\); we use the temperature dependent form of \(\beta\) described in Section 3. However, the 60 um flux used in Section 3 is adjusted by this determination. By comparison to the SFD temperature maps, we find that the average VSG contribution to the 60 um flux is 74%, 72% and 85% in Perseus, Ophiuchus and Serpens, respectively. ### Assumption of Uniform Dust Properties The equations in this paper rely on the assumption that the dust along each line of sight is characterized by a single temperature, emissivity spectral index and emissivity. This is a simplification that our method requires, though we recognize that real molecular clouds are much more complicated. In their FIR study of interstellar cold dust in the galaxy, Lagache et al. (1998) have found

that there are at least two temperature components to the dust population. They find that the warmer component, associated with diffuse dust, has a temperature around 17.5 K, while the colder component, associated with dense regions in the ISM, has a temperature around 15 K. The molecular clouds we study here are expected to have a range of temperatures along some lines of sight that is even wider than seen in Lagache et al. (1998) because the FIRAS data used in this study has a beam size of 7\({}^{\circ}\), which is larger than the size of the maps for each cloud studied in this paper. The color temperature that we derive from our isothermal assumption is therefore biased, as is the optical depth. This problem is especially relevant in Serpens, which is only a few degrees above the galactic center, so there are certainly multiple environments integrated into each IRAS beam. A method for determining the amount of 100 um flux associated with the cold component of the BGs in a molecular cloud is explained in Abergel et al. (1994), Boulanger et al. (1998) and Laureijs et al. (1991). Nevertheless, Jarrett, Dickman & Herbst (1989) find in Ophiuchus that there is a very tight linear correlation between FIR optical depth (determined in much the same way as presented here) and visual extinction for \(A_{V}\leq 5\), so we trust that the errors introduced by our method are not prohibitively large. ### Temperature and Column Density Maps The dust color temperature and column density maps derived from our parameter fits and IRIS data are among the first publicly available data products distributed by the COMPLETE team. Temperature and extinction maps of Perseus, Ophiuchus and Serpens derived from the IRIS data are shown in Figures 2, 3 and 4. FITS files of these maps can be downloaded from the COMPLETE web page2. Footnote 2: http://cfa-www.harvard.edu/COMPLETE In Perseus, there is a striking ring of emission that is centered on a region of warm material. This ring has been discussed by Andersson et al. (2000), Pauls & Schwartz (1989) and Fiedler et al. (1994) and is discussed in more detail in a companion paper to this one (Ridge et al., 2005). The Perseus ring does not stand out in the NICER extinction map as visibly as in the IRIS column density map because it is not a true column density feature. It is difficult to determine from emission maps alone if individual features are the result of changing dust properties or column density enhancements. A warm dust ring is evident in Ophiuchus in the temperature map, centered at the position 16:25:35, -23:26:50 (J2000). This ring was reported by Bernard, Boulanger & Puget (1993) in a discussion of the far-infrared emission from Ophiuchus and Chameleon, but they

did not investigate its nature or possible progenitor. The B star \(\rho\)-Ophiuchus and a number of X-ray sources are projected to lie within this shell of heated gas. The Ophiuchus ring will be further discussed in a future paper (Li et al., 2005). ### Temperature and Extinction Distributions In Figure 5 we show histograms of the dust temperature in Perseus, Serpens, and Ophiuchus. Each distribution peaks near 17 K, and all except Serpens have a spread of several degrees. The dust temperatures that we derive are, to an extent, calibrated with those derived by Schlegel, Finkbeiner & Davis (1998) (see Section 5.1). It has been shown for Taurus by Arce & Goodman (1999) that using IRAS 60 and 100 \(\mu\)m flux densities to determine dust column density gives results consistent with other methods, such as the color excess method (e.g. NICE/NICER), star counts (e.g. Cambresy (1999)), and using an optical (V and R) version of the average color excess method used by Lada et al. (1994). Here we compare the IRIS derived extinction maps of Perseus, Serpens, and Ophiuchus with maps created by some of these other methods. Our method requires the FIR-derived extinction to best match the NIR or optical-derived extinction, and the global agreement can be seen in Figure 6. However, the point-to-point extinction values can be significantly different between the two methods, as shown in Figure 7. The large scatter in these extinction plots (\(1\sigma\simeq 1\) mag \(A_{V}\)) is likely the result of the various assumptions used in our calculations. For instance, it is unlikely to be the case that all of the dust along a given line of sight can be well characterized by a single temperature or emissivity spectral index, especially along lines of sight through the denser regions of the molecular clouds. It is also likely that the dust optical depth to visual extinction conversion factor (\(X\)) is not constant throughout a cloud volume. The flux detected by IRAS comes preferentially from warmer dust, while the extinction maps made from NIR and optical data have no temperature bias, so it is also possible (and in many regions likely) that the dust doing most of the FIR emitting is not the same dust responsible for most of the extinguishing at shorter wavelengths. The scatter for each cloud is shown in Table 3. As a test to see if the parameters determined for one cloud can be successfully used to describe another, we used the Perseus fits for \(\delta\), \(\omega\) and \(X\) for the Ophiuchus 60 and 100 \(\mu\)m IRIS maps and compared the derived extinction to the 2MASS extinction map of Ophiuchus. The median point-to-point difference was 0.8 magnitudes of visual extinction, with a standard deviation of 1.9 magnitudes. When the optimized parameters for Ophiuchus are used, the median point-to-point difference is only 0.2 mag, with a scatter of 1.2 mag.

We conclude that _the fits for one cloud are unlikely to be appropriate for other clouds_, and therefore caution should be used in attempts to estimate extinction within molecular clouds from IRAS emission maps alone. We have derived separate values for \(\delta\), \(\omega\) and \(X\) for various regions within Perseus to see if the dust properties are significantly different there than in the cloud as a whole. The regions considered were B5, IC348, NGC1333, the emission ring, and the area surveyed by the c2d Spitzer Legacy project. The locations and sizes of the Perseus sub-regions are shown in Table 1. The values of \(\delta\), \(\omega\) and \(X\) for these sub-regions are shown in Table 2 and displayed in Figure 2. The value of \(\delta\) varies by about 10 percent, \(\omega\) varies by about 20 percent and \(X\) varies by 20 percent in these sub-regions of Perseus. NGC1333 varies much more significantly from the other sub-regions of Perseus. We conclude that the method described here for converting dust emission to visual extinction can be used with confidence to find regions with high or low extinction and to determine the average extinction in large areas (\(\sim\)0.25 square degrees). However, the extinction determined in any individual 5' pixel _should not be trusted_ to represent the true absolute extinction to better than \(\sim\) 2.5 magnitudes (2\(\sigma\)) of visual extinction. This is made clear by the significant variability in the emissivity spectral index of dust and the conversion from dust optical depth to visual extinction between clouds and within clouds, as shown in Tables 2 and 3. ### Emissivity Spectral Index The emissivity spectral index that we use in this paper varies with temperature as shown in Equation 2. The values that we find for the parameters \(\delta\) and \(\omega\) are shown in Table 2. Their values as determined by Dupac et al. (2003) are 0.4 and 0.008 respectively, which comes from a much broader range of environments and many more measurements of the FIR/sub-mm flux. Figure 8 shows the emissivity spectral index that we find for each cloud plotted along with the curve from Dupac et al. (2003). The emissivity spectral index is considerably larger in Ophiuchus than in Serpens, which is somewhat higher than \(\beta\) in Perseus. The best-fit curve to the wider range of environments in Dupac et al. (2003) falls between our Serpens and Ophiuchus curves. ## 6

Summary We have described a new method that uses NIR color excesses or optical star counts to constrain the conversion of IRIS 60 and 100 \(\mu\)m data into color temperature and column density maps. Our method also derives the dust emissivity spectral index and the conversion from dust 100 um optical depth to visual extinction. We test the IRIS 60 and 100 um zero points and confirm that, unlike earlier releases of IRAS data, the IRIS recalibration is properly zero point corrected. We find the the very small grain contribution to the 60 um flux is significant. The dust temperature maps of Perseus, Serpens and Ophiuchus available through the COMPLETE website should be the best dust temperature maps of large star forming regions at 5' resolution created to date. The dust temperatures derived here are dependent on the emissivity spectral index of the dust, which is solved globally for each molecular cloud, and recorded in Table 2. Our work here indicates that one can not confidently convert dust 100 um optical depth to visual extinction without the benefit of having an extinction map made in an alternative manner to use as a model because the conversion constant \(X\) varies significantly from cloud to cloud, and even within a cloud (see Table 2). Using the values for the dust emissivity spectral index and visual extinction conversion derived for one cloud results in a significant miscalculation of the extinction in other clouds. Even with the NICER and optical star counting extinction maps used here to calibrate the IRAS data, there is significant point-to-point variation between the two estimates (see Figure 1). In fact, we have shown that in Ophiuchus the optical star count method employed by Cambresy (1999) has an offset from the NICER method applied to the 2MASS data set of \(\sim\) 0.71 magnitudes in A\({}_{V}\), with a scatter of 0.7 magnitudes, so the issue is not simply one of dealing with the FIR dust properties in molecular clouds. In addition, we have identified two ring structures, one in Perseus and one in Ophiuchus, which are discussed in upcoming papers (Ridge et al., 2005) and (Li et al., 2005) respectively. We would like to thank the referee Laurent Cambresy for many useful comments. This research has made use of the NASA/ IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National

# Discovery of a Magnetic White Dwarf/Probable Brown Dwarf Short-Period Binary1 Footnote 1: It is strictly a “pre”-Polar. Gary D. Schmidt2 , Paula Szkody3 , Nicole M. Silvestri3 , Michael C. Cushing2 4 , James Liebert2 , and Paul S. Smith2 Footnote 2: And possibly at Na I D \(\lambda\)5893, but it is clear from the near-IR portion of this spectrum that sky-subtraction is not excellent. Footnote 3: affiliation: Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195-1580. Footnote 3: affiliation: Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195-1580. Footnote 2: And possibly at Na I D \(\lambda\)5893, but it is clear from the near-IR portion of this spectrum that sky-subtraction is not excellent. Footnote 4: affiliation: Spitzer Fellow Footnote 2: And possibly at Na I D \(\lambda\)5893, but it is clear from the near-IR portion of this spectrum that sky-subtraction is not excellent. Footnote 2: And possibly at Na I D \(\lambda\)5893, but it is clear from the near-IR portion of this spectrum that sky-subtraction is not excellent. gschmidt@as.arizona.edu, mcushing@as.arizona.edu, jliebert@as.arizona.edu, psmith@as.arizona.edu szkody@astro.washington.edu, nms@astro.washington.edu ###### Abstract The magnetic white dwarf SDSS J121209.31+013627.7 exhibits a weak, narrow H\(\alpha\) emission line whose radial velocity and strength are modulated on a period of \(\sim\)90 minutes. Though indicative of irradiation on a nearby companion, no cool continuum component is evident in the optical spectrum, and IR photometry limits the absolute magnitude of the companion to \(M_{J}>13.37\). This is equivalent to an isolated L5 dwarf, with \(T_{\rm eff}<1700\) K. Consideration of possible evolutionary histories suggests that, until \(\sim\)0.6 Gyr ago, the brown dwarf orbited a \(\sim\)1.5 \(M_{\sun}\) main seqeunce star with \(P\sim 1\) yr, \(a\sim 1\) AU, thus resembling many of the gaseous superplanets being found in extrasolar planet searches. Common envelope evolution when the massive star left the main sequence reduced the period to only a few hours, and ensuing angular momentum loss has further degraded the orbit. The binary is ripe for additional observations aimed at better studying brown dwarfs and the effects of irradiation on their structure. stars: low mass, brown dwarfs -- stars: individual (SDSS J121209.31+013627.7) -- binaries: close -- magnetic fields + Footnote †: slugcomment: To appear in ApJ (Letters) ## 1 Introduction Detached binary systems consisting of a white dwarf plus a nearby low-mass, unevolved companion are of importance because they represent the immediate precursors to cataclysmic variables (CVs) and because their properties allow inferences into the mechanisms and dependencies of common-envelope (CE) evolution. For example, it has been suggested that the lack of magnetic white dwarf + nonmagnetic main-sequence pairs in current catalogs of detached binaries could be due, in part, to the role that a magnetic field on the compact core might play in facilitating the removal of angular momentum (Lemagie et al. 2004; Liebert et al. 2005). The classification process itself is plagued by selection effects, including the larger mean mass (smaller radius) of magnetic _vs._ nonmagnetic white dwarfs (e.g., Liebert et al. 2003), which reduces their detectability against the light of a companion. A strong magnetic field (\(B\gtrsim 50\) MG) on a white dwarf also enables the efficient capture of the wind from a low-mass companion, and the resulting weak accretion (\(\dot{M}\sim 10^{-13}\)\(M_{\sun}\) yr\({}^{-1}\)) is detectable as optical/IR cyclotron emission long before the donor's Roche lobe contacts the stellar surface (Schmidt et al. 2005). The binary therefore may escape classification as a detached system, and be included in the Polar class of magnetic CVs1. To date, 6 such binaries have been cataloged from spectroscopic searches like the Sloan Digital Sky Survey (SDSS). Footnote 1: It is strictly a “pre”-Polar. In this paper we report the discovery and followup observations of a detached binary with an orbital period of \(\sim\)90 minutes that contains a magnetic white dwarf and what appears to be a brown dwarf secondary. The lack of ongoing accretion and the relative youth of the white dwarf suggest that the components may have emerged from the CE with an orbital period of only a few hours. The system thus represents an interesting new wrinkle in the tapestry of binary star evolution. ## 2 Observational Data The star SDSS J121209.31+013627.7 (hereafter SDSS 1212) was reported as a magnetic white dwarf with an equivalent dipolar magnetic field of \(B_{d}=13\) MG by Schmidt et al. (2003). In the 1 hr SDSS spectrum, obtained on 2002 Jan. 8 and reproduced here as Figure 1, very weak emission appears to be present at H\(\alpha\)2. This indicates the presence of a nearby companion that is not apparent as a cool continuum component in the optical spectrum. The emission line was confirmed through spectroscopy at the APO 3.5 m telescope using the DIS spectrograph on 2004 Mar. 28 and 2005 May 14, where the regions \(\lambda\lambda 4000-5200\) and \(\lambda\lambda 5950-7600\) were observed in the two spectrograph channels with a resolution of 2A. Spectropolarimetry was added on 2005 Apr. 14 and 2005 May 16 with the instrument SPOL (Schmidt et al. 1992) at the Bok 2.3 m telescope, covering the region \(4200-8400\) A at a resolution of 16A. Though one of the above runs extends as long as 2.2 hr, no existing data set is ideal for characterizing the behavior of the line emission

due to low time resolution, clouds, or strong moonlight. Footnote 2: And possibly at Na I D \(\lambda\)5893, but it is clear from the near-IR portion of this spectrum that sky-subtraction is not excellent. The H\(\alpha\) emission and Zeeman-split absorption lines are best displayed in the APO results from 2005 May 14 shown in Figure 2. The combined effects of periodic variations in strength and radial velocity that are apparent in the right panel cause the emission line to appear doubled when spectra are coadded over the hour-long sequence. Separations of the principal triplet components of H\(\alpha\) and H\(\beta\) indicate a mean surface field of \(B_{s}=7\) MG. A hint of variation in the shapes of the Zeeman profiles through the series is confirmed by other data sets, and results in smearing across the higher Balmer lines in long exposures. In an effort to detect the companion star in the infrared, imaging was conducted on 2005 May 20 UT with SpeX, the facility near-IR medium-resolution spectrograph (Rayner et al. 2003) at the 3.0 m NASA Infrared Telescope Facility on Mauna Kea. The spectrograph was configured to an imaging mode using the guiding camera as the detector, which is equipped with a 512\(\times\)512 InSb array, to image SDSS 1212 in the Mauna Kea Observatories Near-Infrared \(J\) and \(K\) bands (Tokunaga et al. 2002). The observations consisted of sequences of dithered 240 s and 120 s exposures for \(J\) and \(K\), respectively, using the UKIRT faint standard FS 132 (Hawarden et al. 2001) for photometric calibration. The \(J\)-band measurements were obtained in clear conditions and yielded \(J=17.91\pm 0.05\) for 10 integrations. The \(K\)-band results exhibit the systematic effects of rapidly rising humidity that eventually terminated the observations in fog, and will not be reported here. ## 3 Orbital Period In all data sets of sufficient length, modulations in the equivalent width (EW) and radial velocity of the narrow H\(\alpha\) emission line are apparent. Least-squares sinusoidal fits to the velocities individually yield periods of \(\sim\)0.065 d (\(\sim\)90 minutes), with uncertainties of \(\sim\)0.01 d. Unfortunately, at this precision the gaps between observing runs cannot be bridged without cycle-count ambiguities, so the period cannot be refined at this time. However, as a consistency check, all data sets were phased onto a period of 0.065 d and individual phase offsets were applied to register each set to a common curve. The results are plotted in the bottom panel of Figure 3 together with a sinusoid of semiamplitude \(K_{2}=320~{}(\pm 20)\) km s\({}^{-1}\). The velocity offset shown, \(\gamma=+40\) km s\({}^{-1}\), is probably not significant. The shape and amplitude of the variation are reproducible and consistent with the radial velocity curve of a low-mass companion orbiting a white dwarf at a rather high inclination. Indeed, because positive zero-crossing corresponds to inferior conjunction, disappearance of the emission around this phase (see also Fig. 2) supports a high inclination and implies that the line emission is confined to the inner, radiatively-heated hemisphere of the companion. It might be expected that the line strength would then peak near superior conjunction (\(\varphi=0.5\)), but the EW values in the top panel are inconclusive on this point. The variation in Zeeman structure on a similar timescale as the emission-line variation that was noted in SS2 suggests that the white dwarf spin may be synchronized to the orbital period, as in the Polars. Best estimates for the pertinent parameters of SDSS 1212 are collected together with "psf" magnitudes from the SDSS and our \(J\)-band photometry in Table 1. ## 4 The Stellar Components By comparing the survey photometry with colors of nonmagnetic DA spectral models (Bergeron et al. 1995) computed in SDSS filter bands, Schmidt et al. (2003) estimated a temperature of \(T_{\rm eff}=10,000\) K for the white dwarf in SDSS 1212. The Zeeman effect tends to increase the EW of (particularly) H\(\alpha\) and H\(\beta\), thereby depressing \(g\) and to a lesser extent \(r\). However, the magnetic field is also known to alter the continuum opacities, at least for fields \(B\gtrsim 100\) MG (Merani et al. 1995). Lacking an adequate solution for the entire problem for a magnetic white dwarf photosphere, we adopt the temperature indicated by the nonmagnetic models and quote a liberal uncertainty of \(\pm 1,000\) K. The predicted absolute magnitude in SDSS \(r\) of \(12.27\pm 0.31\) (\(\log g=8\), as indicated by the colors) then implies a distance modulus \(m-M=+5.80\pm 0.31\), or \(d=145\pm 20\) pc, with the error bar dominated by the uncertainty in temperature. Absolute \(J\)-band magnitudes for the same DA white dwarf models range between \(12.29-11.95\) for \(T_{\rm eff}=9,000-11,000\) K, respectively. Therefore, with a predicted \(J_{\rm wd}=17.90\pm 0.14\), the white dwarf alone can account for the total light of the binary (\(J=17.91\pm 0.05\)) at the coolest end of our allowed range. We can set an upper limit for the brightness of the companion by choosing the hottest permissible white dwarf (largest distance modulus; \(T_{\rm eff}=11,000\) K) and allowing 3\(\sigma\) uncertainties on the photometry, i.e. \(J_{\rm min}=17.76\). With these assumptions, we find that the companion can contribute at most 21% of the light at 1.25\(\mu\)m, or \(J_{2}>19.44\). The implied absolute magnitude is \(M_{J,2}>13.37\). By comparison with the mean characteristics of field L and T dwarfs (Vrba et al. 2004) this corresponds to a spectral type no earlier than L5, \(T_{\rm eff}<1700\)K, and \(\log L/L_{\sun}\leq-4.22\). Of course, the presence of modulated H\(\alpha\) emission signifies the importance of irradiation by the white dwarf. We cannot directly utilize the line flux to estimate a radiating area, but we point out that the blackbody temperature for reprocessing on the surface of a companion at the implied separation of 0.6 \(R_{\sun}\) is only 1400 K, even assuming an 11,000 K white dwarf, synchronous rotation, and zero albedo. Thus, the consideration of radiative heating cannot yet be used to further constrain the nature of the companion. The very low inferred luminosity for the companion in SDSS 1212, its large radial velocity amplitude, the presence of hydrogen at its surface, and the length of its orbital period argue that the star is a low-mass object near the cool end of the main sequence, as opposed to, e.g., the eroded core of a double-degenerate (white dwarf + white dwarf) binary. The stellar properties derived from the \(J\)-band flux are actually near the terminus of hydrogen-burning stars (\(M_{2}=0.07-0.09~{}M_{\sun}\); e.g., Chabrier & Baraffe 2000), but the fact that the \(J\)-band luminosity is an upper limit coupled with the high degree of irradiation prompt us to refer to the companion star as a brown dwarf. ## 5 Nature of the Binary We can imagine two possible evolutionary histories for the SDSS 1212 system. The first takes the binary to be an

# Measurement of Noisy Absorption Lines using the Apparent Optical Depth Technique Andrew J. Fox, Blair D. Savage, & Bart P. Wakker Department of Astronomy, University of Wisconsin - Madison, 475 North Charter St., Madison, WI 53706 fox@astro.wisc.edu ###### Abstract To measure the column densities of interstellar and intergalactic gas clouds using absorption line spectroscopy, the apparent optical depth technique (AOD) of Savage & Sembach (1991) can be used instead of a curve-of-growth analysis or profile fit. We show that the AOD technique, whilst an excellent tool when applied to data with good S/N, will likely overestimate the true column densities when applied to data with low S/N. This overestimation results from the non-linear relationship between the flux falling on a given detector pixel and the apparent optical depth in that pixel. We use Monte Carlo techniques to investigate the amplitude of this overestimation when working with data from the _Far Ultraviolet Spectroscopic Explorer_ (_FUSE_) and the Space Telescope Imaging Spectrograph (STIS), for a range of values of S/N, line depth, line width, and rebinning. AOD measurements of optimally sampled, resolved lines are accurate to within 10% for _FUSE_/LiF and STIS/E140M data with S/N\(\gtrsim\)7 per resolution element. Subject headings: techniques: spectroscopic ## 1. Introduction The apparent optical depth (AOD) method (Savage & Sembach, 1991; Sembach & Savage, 1992) has gained substantial popularity as a means of converting velocity-resolved flux profiles into column density measurements for interstellar and intergalactic absorption lines. The method offers a quick and convenient way of determining reliable interstellar column densities from unsaturated lines without having to follow a full curve-of-growth analysis or detailed component fit, and without demanding prior knowledge of the component structure. Accurate column densities are important for studies of elemental abundances and physical conditions in diffuse gas in space. In the AOD method, a velocity-resolved flux profile \(F(v)\) is converted to an apparent optical depth profile \(\tau_{a}(v)\) using the relation: \[\tau_{a}(v)={\mathrm{l}n}[F_{c}(v)/F(v)],\] (1) where and \(F(v)\) and \(F_{c}(v)\) are the observed line and continuum fluxes at velocity \(v\), respectively. This apparent optical depth profile can then be converted to an apparent column density profile according to \[N_{a}(v)=3.768\times 10^{14}(f\lambda)^{-1}\tau_{a}(v)\,\mathrm{cm^{-2}\,(km\, s^{-1})^{-1}},\] (2) where \(f\) is the oscillator strength of the transition and \(\lambda\) is the transition wavelength in Angstroms (Savage & Sembach, 1991). The total apparent column density between two velocity limits \(v-\) and \(v+\) is then simply \(N_{a}=\int_{v-}^{v+}N_{a}(v)\mathrm{d}v\). When two lines of different strength of the same ionic species are available, the AOD method can also be used to assess and correct for the level of saturation in the data, by comparing the apparent column density derived from the stronger line with that derived from the weaker line (Savage & Sembach, 1991; Jenkins, 1996). The AOD method was originally developed for application to measurements of reasonably high signal-to-noise spectra (S/N\(\gtrsim\)20 per resolution element). The technique offers excellent results in these cases. However, spectroscopists are now using the method even when analyzing relatively low S/N data (e.g. Wakker et al., 2003). This paper deals with accounting for a systematic error that is introduced when applying the AOD method to noisy data, which can lead to an overestimation of the true column density of the absorbing species. The error arises because the logarithmic relationship between \(\tau_{a}(v)\) and \(F(v)\) (Eq. 1) will distort a Poisson noise component in the flux when converting into column density space, giving undue weight to the pixels where the noise has resulted in high optical depths; this effect tends to exaggerate the estimate of \(N_{a}\). We present simulations investigating the accuracy of \(N_{a}\) determinations as a function of line depth and S/N, together with the separate effects of line width and rebinning. ## 2. Simulations We ran Monte Carlo simulations of the measurement of noisy absorption lines to investigate the amount by which noise in the data leads to overestimation of \(N_{a}\). Our models were run with two simulated experimental setups, representing the _Far Ultraviolet Spectroscopic Explorer_ (_FUSE_) LiF (Sahnow et al., 2000) and Space Telescope Imaging Spectrograph (STIS) E140M (Woodgate et al., 1998) configurations. The _FUSE_/LiF setup is parameterized by a Gaussian instrumental line spread function with FWHM=20 km s\({}^{-1}\) (\(\sigma_{ins}=8.5\) km s\({}^{-1}\)) and velocity pixels 2.0 km s\({}^{-1}\) wide. The STIS/E140M configuration has FWHM=6.8 km s\({}^{-1}\) (\(\sigma_{ins}=2.9\) km s\({}^{-1}\)) and 3.2 km s\({}^{-1}\) pixels. Our models simulate the measurement of an absorption line whose intrinsic optical depth profile is a single-component Gaussian, centered for convenience at 0 km s\({}^{-1}\), and normalized to a peak optical depth of \(\tau_{0}\), i.e. \(\tau(v)=\tau_{0}e^{-v^{2}/2\sigma_{line}^{2}}\). We run models for two line width cases: resolved (\(\sigma_{line}=2\sigma_{ins}\)) and marginally resolved (\(\sigma_{line}=\sigma_{ins}\)) The AOD method is known to underestimate the column density for unresolved lines, when no allowance is made for the effects of unresolved