From the result of the χ2 minimization, we found that the minimized χ2 values agree with the expected values, i.e. the computed χ2 are typically in the range of ($\mathrm{d.o.f.}-\sqrt{2 \mathrm{d.o.f.}}$, $\mathrm{d.o.f.}+\sqrt{2 \mathrm{d.o.f.}}$), where d.o.f. is the number of degrees of freedom. This means that the fits describe the observed data rather well. The only exception is with χ2 ≈ 20, which occurs for nearby AGN, z  0.2, and for the highest energy band, E > 10 GeV. Note that there is a strong contribution of the source, Mrk 421, in the first redshift interval at high energies, E > 10 GeV for quiescent states. Mrk 421 is a very hard spectrum γ-ray source with a photon index of ≈1.77 and its semiminor and semimajor axes at 68 per cent confidence are of 0$_{.}^{\circ}$0067 as derived in Nolan et al. (2012). Semiminor and semimajor axes of many 2FGL sources are derived with one order of magnitude higher uncertainties than those for Mrk 421 in the 2FGL catalogue (Nolan et al. 2012). We noted that the discrepancy between the observation and model is particularly strong in the annular bin, r  0$_{.}^{\circ}$05, for the redshift interval z  0.2 and for the highest energy band, E > 10 GeV. If we exclude photons from Mrk 421, then the minimized χ2 value is 7.5 and is consistent with the expected one. In the limit of a large number of counts in each bin, the likelihood is given by $\mathcal {L}=\text{exp}(-\chi ^{2}/2)$, so that minimizing χ2 is equivalent to maximizing the likelihood, $\mathcal {L}$. We found that the inclusion of a pair halo component in the model does not improve the likelihood value sufficiently to establish the presence of this pair halo component in the data. Therefore, we derived the one-sided 95 per cent upper limit on the fraction of photons attributable to a pair halo component by fitting the normalization of this component, for which we increase its normalization until the maximum likelihood decreases by 2.71/2 in logarithm. The computed upper limits are between 2 and 6 per cent depending on energy band and redshift interval. These upper limits are stronger than those obtained before. Note that the model for a point-like source used in the likelihood analysis is considered to be precisely established, however, the number of photons recorded during flaring states is close to those numbers of photons recorded during quiescent states for each of these redshift intervals. The expression, such as equation (1), leads to more conservative upper limits on the fraction of photons attributable to a pair halo component, since it takes the error bars assigned to the model into account. If the point-like source model is considered well established, then the error bars shown in Table 3 would decrease by a factor of ≈1.5.


Returning to the case of HL Tau, where the possible contribution of an infalling envelope is not an issue, how can one reconcile the strong indication of a dominant radial field component in the polarization map with the expectation that the bulk of the mm-wavelength emission originates near the disc mid-plane, where the azimuthal field component dominates? One possibility is that the non-negligible optical depth inferred in the bright emission rings of HL Tau at mm-wavelengths (Jin et al. 2016; Pinte et al. 2016) shifts the emission centroid to finite disc elevations where the magnetic field already has a measurable radial component. However, in view of the very small scale height inferred for the mm-emitting dust in this source, this is unlikely to be the main explanation. Perhaps a more likely possibility is that, even in this comparatively young source, the grains near the mid-plane, which dominate the total intensity, have already grown to sizes that exceed the maximum size $a_\mathrm{max} = \lambda /2\pi$ for producing polarized emission at wavelength λ (e.g. Cho & Lazarian 2007; for λ = 1.25 mm, amax = 0.2 mm), while the smaller grains (with sizes a amax), which contribute efficiently to the polarized flux, remain suspended at high elevations (where the field is predominantly radial). Another effect that could lower the polarized emission from grains that have settled to the mid-pane is the likelihood that grains become less elongated as they grow (e.g. Hughes et al. 2009), which would tend to reduce the value of the coefficient C in equation (2) (C → 0 as the grain axis ratio → 1).7 This interpretation is supported by the finding in the high-resolution observations of IRAS 4A (Cox et al. 2015) of an average polarization of 15 per cent at 8 mm and 10 per cent at 10 mm, with a peak fractional polarization of ∼20 per cent. If the intrinsic degree of mm-wavelength polarization in HL Tau is also of the order of 20 per cent, then it may be possible to explain the factor of ∼10 lower value of P measured in this source at 1.25 mm8 in terms of a dilution of the polarized emission from a ≲ 0.1 mm grains at high disc elevations by weakly polarized emission of larger grains residing near the mid-plane. In this scenario, most of the grains that are responsible for the mm-wavelength flux have settled to the mid-plane and grown to sizes a ≳ 1 mm.9 Although a fraction of these grains may have sizes in excess of 1 mm and would therefore emit less efficiently at that wavelength than a ≲ 1 mm grains (e.g. Miyake & Nakagawa 1993), the mid-plane region should still dominate the total mm-wavelength flux if most of the a ≳ 1 mm grains are concentrated there. Grains of size a ≲ 0.1 mm may be kept at high elevations by turbulent motions that can persist below the wind-driving surface layers (e.g. Simon et al. 2013, 2015; Bai 2015) as well as by the emerging outflows within these layers (see Safier 1993), with porosity effects (e.g. Ormel, Spaans & Tielens 2007) possibly also helping to mitigate gravity's pull towards the mid-plane. This scenario of course needs to be backed by detailed calculations and observational tests. One such test would be to obtain a polarization map of HL Tau at longer ( ≳ 1 cm) wavelengths: if the above picture is correct and the grains in the mid-plane region are aligned, such a map could reveal a stronger (or even dominant) contribution from the azimuthal and (especially if Λ0 ≪ 1) vertical field components.10 It is, however, conceivable that the large grains in this source are not well aligned because the radiative torque mechanism does not operate efficiently on them: this could happen if the characteristic wavelength of the anisotropic component of the local radiation field were much smaller than the mid-plane grain sizes (e.g. Cho & Lazarian 2007) or if the anisotropic radiation component inside the dust disc were weak due to finite optical depth effects. Note that the possibility of the mid-plane grains not being well aligned provides another reason for why the polarized mm-wavelength emission from this region could be weak.


In both of these approaches, disc–planet interactions causing planet migration are modelled using analytical formulae for the disc torque experienced by the planet. This gravitational torque consists of two components. The differential Lindblad torque results from the angular momentum exchange between the planet and the spiral density waves it generates inside the disc. For sufficiently low-mass planets, it scales linearly with disc mass and planet mass and as the inverse square of the disc aspect ratio (Tanaka, Takeuchi & Ward 2002). Although its sign depends on the density and temperature gradients inside the disc, the differential Lindblad torque is generally negative for typical disc models and is therefore responsible for inward migration. The corotation torque is due to the torque exerted by the material located in the coorbital region of the planet. It is composed of a barotropic part which scales with the vortensity (i.e. the ratio between the vertical component of the vorticity and the disc surface density) gradient (Goldreich & Tremaine 1979) plus an entropy-related part which scales with the entropy gradient (Baruteau & Masset 2008; Paardekooper & Papaloizou 2008). A negative vortensity (resp. entropy) gradient gives rise to a positive vortensity (resp. entropy) related corotation torque. It has been shown that for mildly positive surface density gradients or negative entropy gradients, a positive corotation torque can eventually counteract the effect of a negative differential Lindblad torque, which may stall or even reverse migration (Masset, D'Angelo & Kley 2006; Paardekooper & Papaloizou 2009). In isothermal discs, the corotation torque is a non-linear process generally referred as the horseshoe drag and whose amplitude is controlled by advection and diffusion of vortensity inside the horseshoe region. In non-isothermal discs, the corotation torque is also powered by singular production of vortensity due to an entropy discontinuity on downstream separatrices (Masset & Casoli 2009; Paardekooper et al. 2010). In the absence of any diffusion processes inside the disc, vortensity and entropy gradients across the horseshoe region tend to flatten through phase mixing, which causes the two components of the horseshoe drag to saturate. Consequently, desaturating the horseshoe drag requires that some amount of viscous and thermal diffusions are operating inside the horseshoe region. In that case, the amplitude of the horseshoe drag depends on the ratio between the diffusion time-scales and the horseshoe libration time-scale and its optimal value, also referred as the fully unsaturated horseshoe drag, is obtained when the diffusion time-scales are approximately equal to half the horseshoe libration time (e.g. Baruteau & Masset 2013). In the limit where the diffusion time-scales become shorter than the U-turn time-scale, the corotation torque decreases and approaches the value predicted by linear theory. Therefore, the corotation torque can be considered as a linear combination of the fully unsaturated horseshoe drag and the linear corotation torque with coefficients depending on the ratio between the diffusion time-scales and the horseshoe libration time-scale. Corotation torque formulae as a function of viscosity and thermal diffusivity were recently proposed by Paardekooper, Baruteau & Kley (2011) and Masset & Casoli (2010).


To complement our study, we also analyzed GLOSTAR continuum images toward sites with maser emission. A full description of the GLOSTAR continuum data calibration and imaging is given in Brunthaler et al. (2021), while the full analysis of continuum images of Cygnus X will be presented in a forthcoming paper. Here, we briefly discuss the imaging strategy. The calibration and imaging of the continuum data was performed with the Obit package (Cotton 2008). The 2 GHz bandwidth was first rearranged into nine frequency subbands, which were used to image each pointing individually. Then, for each frequency subband the pointings were combined into large individual mosaics to cover the entire observed area. Finally, we combined the different frequencies to obtain the image at the reference frequency, which has circular beams of 19″ and 1.5″ in the D and Bconfiguration, respectively. Continuum and methanol line maps from Effelsberg observations have also been obtained as part of the GLOSTAR survey (Brunthaler et al. 2021, Rugel et al., in prep.) We note that continuum images were constructed for Effelsberg data, the VLA D configuration, the VLA B configuration, a combination of the VLA D and B (D+B) configurations, and a combination of the VLA D configuration and Effelsberg observations. The central frequency of these images is 5.8 GHz. Here, we only use B-configuration continuum maps to study the region of the investigated methanol maser positions and D+B maps of the region around DR21 (see Sect. 4.5). Methanol line data from Effelsberg were also inspected to look for flux variations in the VLA-detected masers (Sect. 4.4). The noise in the continuum images is not uniform, but rather varies across the mapped region, and can be high around strong sources with complex or extended emission. We locally measured the noise in regions close to the maser locations, resulting in 1σ values in the range from 0.056 to 0.43 mJy beam−1 for B-configuration images. For the D configuration, the 1σ rms noise ranges from 0.10 to 2.6 mJy beam−1. The higher values measured in D-configuration data are due to bright extended emission, which is present across the Cygnus X region, and are resolved out by the array in the B configuration. The highest local rms noise occurs around the strong radio source, DR21, a compact HII region.


On the CND scales displayed in Fig. 12, the CO(3–2) emission in this highly inclined (i = 59°; Appendix D) barred Seyfert 2 galaxy is detected at every single position inside r  200 pc. However, a sizeable fraction of the molecular gas appears concentrated in a nuclear ring of ∼200 pc (deprojected) radius. Molecular gas in this nuclear ring is feeding an active star formation episode detected at optical as well as near and mid IR wavelengths. The molecular gas ring is the likely signature of the gas response to the ∼140″ (16 kpc) long stellar bar at its ILR region. The bar, detected in the NIR by Quillen et al. (1997) and Buta et al. (2009), shows a prominent boxy-shape morphology. At the larger radii imaged inside the ALMA FOV (Fig. 10), molecular gas shows a two-arm spiral structure that is connected to the nuclear ring. Closer to the Seyfert 2 nucleus (r  50 pc), molecular gas probed by CO is concentrated in an asymmetric ringed disk of ∼30 − 40 pc radius located around the AGN and oriented along ∼160°. The molecular disk shows a similar orientation to the extended component of the 351 GHz continuum emission detected by ALMA (PAGauss ∼ 160° −162°; Table 4). The CO disk appears to be partly incomplete: its southwest hemisphere is on average a factor of 3 weaker than its northeast counterpart. The V − H map shows a dusty ring feature in excellent correspondence with the morphology of the CO ringed disk. There is nevertheless significant molecular gas inside the ring: CO emission is detected toward the position of the AGN defined by the position of the ALMA 351 GHz continuum point source. This implies values for the molecular gas mass and H2 column densities of Mgas[r ≤ 7 − 9 pc]  ∼ (1.5 − 2.9)×105 M⊙ and N(H2)∼(3.5 − 3.6)×1022 cm−2, respectively. The galaxy shows a bright ionization cone southwest of the nucleus oriented along PAout ∼ 235° −245° and characterized by blueshifted velocities, which betray an outflow (Morris et al. 1985; Storchi-Bergmann & Bonatto 1991; Davies et al. 2016; Ricci et al. 2018a). The northeast ionization cone appears to be obscured by the host galaxy. The orientation of the 70 − 90 pc-size disk detected by ALMA in continuum and CO is therefore equatorial (torus-like).


The marginalized probability for Mgal and Mhalo is shown in Fig. 6. The contours correspond to the 68% and 95% intervals and the black dot marks the position of the best model. We note that the best model is outside the 68% region of the marginalized probability. The N-dimensional likelihood near the best model forms a shallow valley that extends toward the 68% confidence region. The best models clearly prefer a relatively narrow region in the Mgal − MDM space. An interesting result from this figure, is that a baryon-only model (i.e., MDM = 0) does not perform much worse than a model with a DM halo, although the data prefers a model with a DM halo. The relatively weaker dependence with the DM component may be a consequence of the small size of the Einstein ring, since at this radius the baryon component dominates the projected mass (see Table 1 below). The inferred mass of the galaxy (baryons) in the best model (5.4 × 1010 M⊙) is marginally consistent with the estimated stellar mass derived from the velocity dispersion – stellar mass correlation (Hyde & Bernardi 2009; Zahid et al. 2016; Cannarozzo et al. 2020). Assuming the velocity dispersion in Mörtsell et al. (2020), and the models in Zahid et al. (2016), Cannarozzo et al. (2020), the predicted stellar mass is ≈2.5 × 1010 M⊙. This is about a factor two less than the stellar mass inferred from the lens model. However, a factor two uncertainty is typical in mass estimations from the velocity dispersion (see the references above). Since the galaxy and halo masses are partially degenerate (see Fig. 6), it is possible that the galaxy mass is lower than the one at the maximum of the likelihood. Another possibility is that the gas mass is similar to that of the stars, increasing the baryonic mass by a factor two compared with the stellar mass. This is in principle feasible based on the gas to stellar mass ratios, which is close to 1 for early type galaxies (similar to the lens considered in this work) and stellar masses ∼1010 M⊙ (Calette et al. 2018). However, in the central part of the galaxy the stellar component is still expected to dominate, especially if a bulge is present, as suggested by the data. An alternative way of estimating the contribution from the gas is by comparing with galaxies of similar morphological type. According to Casasola et al. (2020), and considering a morphological type for the lens galaxy between Sa and Sb, the gas fraction for this type of galaxy is ≈20%. In Schruba et al. (2011), gas and molecular surface densities as high as O(100) M⊙ pc−2 can be found in areas with large star formation rates. In the most extreme cases of star formation rates, gas surface densities of ≈1000 M⊙ pc−2 can be found. However, even at these extreme star formation rates, the contribution from the gas to the baryonic mass is still subdominant with respect to the stellar contribution from our fiducial model.


These new limits, in conjunction with the inconsistency of isotropic flux interpretations, leave no room for an astrophysical interpretation of AAEs in the context of the standard model for time windows as short as 103 s. However, it has been shown that these events can be explained using physics beyond the standard model, as many models suggest that AAEs lend support for axionic dark matter, sterile neutrinos, supersymmetry, or heavy dark matter (Anchordoqui et al. 2018; Connolly et al. 2018; Dudas et al. 2018; Fox et al. 2018; Huang 2018; Abdullah et al. 2019; Anchordoqui & Antoniadis 2019; Borah et al. 2019; Chauhan & Mohanty 2019; Cherry & Shoemaker 2019; Chipman et al. 2019; Cline et al. 2019; Collins et al. 2019; Esmaili & Farzan 2019; Esteban et al. 2019; Heurtier et al. 2019a, 2019b; Hooper et al. 2019). Many of these models, excluding the axionic dark matter explanation (Esteban et al. 2019) or those heavy dark matter scenarios that are tuned to prevent signatures in IceCube (Hooper et al. 2019), can be constrained by this nonobservation at IceCube. Dedicated tests to quantify these constraints are beyond the scope of this work and may be the focus of a future study. In addition to explanations that incite new physics, it has recently been suggested that AAEs could be explained by downward-going CR-induced EASs that reflected off of subsurface features in the Antarctic ice (Shoemaker et al. 2019). Another possible explanation could be coherent transition radiation from the geomagnetically induced air shower current, which could mimic an upgoing air shower (Motloch et al. 2017; de Vries & Prohira 2019). Explaining these anomalous events with systematic effects or confirming the need for new physics requires a deeper understanding of ANITA’s detection volume. Efforts such as the HiCal radio frequency pulser, which has flown alongside ANITA on the last two flights (Prohira et al. 2018), are already underway to try to characterize the various properties of the Antarctic ice surface.


The existence of winds is shown by blueshifted absorption lines from highly ionized ions. These are only seen in soft state but not in hard state (Ponti et al. 2012), anticorrelated with the radio jet which is seen in the hard state but not in the soft. This was thought to be evidence that the wind was magnetically driven by the same field as was responsible for the jet, but in a different geometric configuration (Miller et al. 2012). However, in Tomaru et al. (2019, hereafter Paper I) we show instead that thermally driven winds can explain this switch (see also Done, Tomaru & Takahashi 2018; Shidatsu & Done 2019). Thermal driving produces a wind by irradiation from the central source heating the surface of accretion disc up to the Compton temperature ($T_\text{IC} \sim 10^7 \!-\!10^8\, \text{K}$), which is hot enough for its thermal energy to overcome the gravity at large radii. The characteristic radius at which the wind can be launched is called the Compton radius, defined by RIC = μmpGM/kTIC ∼ 105 − 106Rg (Begelman, McKee & Shields 1983). Paper I show the first modern radiation hydrodynamic simulations of thermal (and thermal-radiative) winds designed to investigate the switch in wind properties between the hard and soft states changing illumination spectra. These simulations were tailored to the BHB system H1743−332, where there is Chandra high-resolution data in both states giving detailed spectral information on the wind or its absence (Miller et al. 2012; Shidatsu & Done 2019). They incorporate radiation force on the electrons, both bound and free, as they show that this is important factor driving the escape of the thermal wind in the fairly high Eddington fraction (L/LEdd ∼ 0.2–0.3), fairly low Compton temperature (TIC ∼ 0.1 × 108 K) characteristics of the soft state. The only other modern hydrodynamic simulation of thermal winds (e.g. Luketic et al. 2010; Higginbottom & Proga 2015; Higginbot et al. 2016) has not included radiation pressure, which is important in setting the velocity structure for L ≥ 0.3LEdd as required here (Paper I).


Combining different samples from various instruments at different redshifts therefore inevitably introduces ENLR size–luminosity relations with different slopes α depending on the details of target selection and analysis approaches. Slopes ranging from α = 0.22 ± 0.04 (Greene et al. 2012), α = 0.25 ± 0.02 (Liu et al. 2013b), α ∼ 0.3–0.4 (Hainline et al. 2013; Chen et al. 2019a), to α ∼ 0.5 (Bennert et al. 2002; Husemann et al. 2014) are reported in the literature. The slopes solely inferred from the CARS data are consistent with those reported by Greene et al. (2012) and Liu et al. (2013b) and are therefore on the shallower side of previous estimates. Nevertheless, the scatter in the observed relation is significant and measured slope variations might be entirely attributed to the observationally induced biases as discussed above. A slope of α = 0.5 is reminiscent of the BLR size-luminosity relation, but would require a constant ionization parameter U that demands a constant density with radius. This is not observed for the ENLR on kiloparsec scales (e.g., Bennert et al. 2006; Kakkad et al. 2018) and more detailed photoionization calculations are required to predict the shallower slopes inferred for most studies (Dempsey & Zakamska 2018). We cannot study the radial variations of U as our snapshot MUSE observations are not deep enough to map the electron density given the too low S/N of the [S II] doublet on kpc scales. However, the photoionization calculations do not take into account variable ionizing flux from AGN on 105 yr time scales (Schawinski et al. 2015) and the various geometrical intersections of the ionizing radiation field with the gas distribution of the galaxies. The CARS survey is least biased with regard to RENLR given the narrow redshift range and large dynamic range offered by MUSE (see Fig. 13). Therefore, the CARS survey is one of the best data set to explore the origin of the significant scatter in ENLR size–luminosity relation and search for additional factors or more fundamental parameters controlling the ENLR size.


Capturing the full information content of the cosmic large-scale structure requires a field-based approach to infer the entire three-dimensional cosmic large-scale structure from observations. This poses a particular challenge for the analyses of Ly-α forest observations, which provide sparse inherently one-dimensional information along the lines of sight. Various approaches to perform three-dimensional density reconstructions from one-dimensional Ly-α forests have been proposed in the literature (e.g. Kitaura et al. 2012; Cisewski et al. 2014; Stark et al. 2015a; Ozbek et al. 2016; Horowitz et al. 2019). Gallerani et al. (2011) and Kitaura et al. (2012) proposed a Gibbs sampling scheme to jointly infer density and velocity fields and corresponding power-spectra. However, these approaches assume matter density amplitudes to be log-normally distributed. The log-normal distribution reproduces one- and two-point statistics but fails to reproduce higher-order statistics associated with the filamentary dark matter distribution. In an attempt to extrapolate information from one-dimensional quasar spectra into the three-dimensional volume, Cisewski et al. (2014) applied a local polynomial smoothing method. Ozbek et al. (2016) and Stark et al. (2015a) employed a Wiener filtering approach to reconstruct the three-dimensional density field between lines of sight of Ly-α forest data. In order to reproduce higher-order statistics, Horowitz et al. (2019) recently used a large-scale optimization approach to fit a gravitational structure growth model to Ly-α data, showing that this approach allows recovering the more filamentary structure of the cosmic web. Although the approach improves over linear and isotropic Wiener filtering approaches, it shows systematic deviations of reconstructed matter power-spectra and underestimates density amplitudes at scales corresponding to the mean separation between lines of sight (Horowitz et al. 2019).


The problem we are facing consists in the reconstruction of two maps of a given region of an astrophysical object: the former consists in point sources, such as stars, of very high intensity, the latter of smooth structures surrounding these sources. The standard approach, i.e. simply solving Eq. (2), fails since the presence of the point sources destroys all the information about the smooth structures. Hence, the main idea is to consider the object x as the sum of two components, namely x = xP + xE, where xP represents the point sources and xE the extended source. This approach was proposed for the first time in De Mol & Defrise (2004), assuming that the positions of the point sources are known. Denoting by pj the position of the jth source, we can write (4)\begin{equation} \label{2:point} x_{\rm P}=\sum_{j=1}^qc_j\delta(p_j) , \end{equation}xP=∑j=1qcjδ(pj),where q is the total number of sources, cj is the jth unknown intensity, and δ(pj) is the delta function centred in pj. Thus, xP is a vector with zero entries except in the q positions corresponding to the known locations of the sources. Then, instead of computing f1 on the whole object x in Eq. (2), we only regularize the extended source, since the structure induced on xP already works as a regularization. This requires a slightly modification in the computation of f0. We introduce the vector c = (c1,c2,...,cq)t containing the intensities of the sources, and we define \hbox{$\overline{x} = (c^t,x_{\rm E}^t )^t$}x=(ct,xEt)t and the matrix \hbox{$\mathcal{H}=[\overline{H}, H]$}ℋ=[H,H], where \hbox{$\overline{H}=[h_{p_1},h_{p_2},\dots,h_{p_q}]$}H=[hp1,hp2,...,hpq], with hj denoting the jth column of H. We are hence led to solve(5)\begin{equation} \label{2:solve} \tilde{x} =\arg\min_{x\in\mathcal{C}} KL(\mathcal{H} \overline x+b;g)+\beta f_1\left(x_{\rm E}\right) . \end{equation}˜x=argminx∈𝒞KL(ℋx+b;g)+βf1(xE).It may happen that \hbox{$\tilde x$}˜x has a loss in contrast, even using the optimal value for β. To overcome this difficulty, we then propose the use of the inexact Bregman procedure, which permits the use of an overestimation of the regularization parameter, and at the same time allows us to obtain a contrast enhancement.


However, the sensitivity limits of most current submillimeter surveys only allow for the study of the most extremely star-bursting systems (e.g., Asboth et al. 2016; Geach et al. 2017; Simpson et al. 2019), which may represent merely a tip of an iceberg of dust-obscured star formation in the early Universe. A potential population of more typical dusty star-forming galaxies at high-z is still to be found (Wang et al. 2017). The Atacama Large Millimetre/submillimetre Array (ALMA) has now opened a new avenue to refine our understanding of dusty galaxies at high redshifts, enabling to uncover faint SMGs down to a flux level of 0.1–1 mJy. Several ALMA blind surveys have been performed and allowed to detect and characterize the faint SMGs across cosmic times (e.g., Aravena et al. 2016; Wang et al. 2016b; Dunlop et al. 2017; Umehata et al. 2017; Franco et al. 2018; Williams et al. 2019; Yamaguchi et al. 2019; González-López et al. 2020). Based on the ALMA survey of GOODS-South field over an area of 69 arcmin2, Franco et al. (2018) found that 20% of the 1.1 mm sources are not detected with HST down to a depth of H ∼ 28 mag, and suggested that they are massive main-sequence star-forming galaxies at z > 4 (see also, Yamaguchi et al. 2019; Umehata et al. 2020). A similar fraction of HST-dark galaxies has also been found in the ALMA [C ii] survey of main-sequence galaxies at 4.4  z  5.9 (∼14%, Gruppioni et al. 2020). Conversely, the existence of such HST-dark galaxies can also be uncovered by focusing the reddest galaxies in the IRAC and H bands (H-[4.5 μm] > 4.0), namely H-dropouts (Huang et al. 2011; Caputi et al. 2012; Wang et al. 2016a). Follow-up continuum observations with ALMA of a sample of 63 H-dropouts have yielded detections of 39 sources down to an 870 μm flux density of 0.6 mJy (Wang et al. 2019). They further suggested that the ALMA-detected H-dropouts are the bulk populations of massive (M
⋆ ≳ 1010.3
M
⊙) star-forming galaxies at z > 3 with the contribution to star formation rate density an order of magnitude higher than that of equivalently massive LBGs. To uncover the nature of H-dropouts and the critical role they play in the cosmic evolution of massive star-forming galaxies, we need to explore the fainter population that might have even fainter (sub)millimeter fluxes.


Figure 13 shows the temporal evolution of the density, ρ, plasma flow velocity, vx, position of the wave crest, PosA, phase speed, vw, and magnetic field component in the z-direction, Bz, for the primary waves in every different case of initial amplitude, ρIA. In Figure 13(a), we observe that the amplitude of the density remains approximately constant at their initial values until the time when the shock is formed and the density amplitude of the primary wave starts decreasing (see Vršnak & Lulić 2000), i.e., at t ≈ 0.03 (blue), t ≈ 0.04 (red), and t ≈ 0.055 (green). For the case of ρIA = 1.3 (magenta), a decrease of the amplitude of the primary can hardly be observed, as expected for low-amplitude wave (Warmuth 2015). One can see that the larger the initial amplitude, ρIA, the stronger the decrease of the primary wave’s amplitude, which is consistent with observations (Warmuth & Mann 2011; Muhr et al. 2014; Warmuth 2015). The amplitudes decrease to values of ρ ≈ 1.6 (blue), ρ ≈ 1.5 (red), and ρ ≈ 1.4 (green) until the primary wave starts entering the CH. Due to the fact that the waves with larger initial amplitude enter the CH earlier than those with small initial amplitude, we can see in Figure 13(a) that the tracking of the parameters of the faster waves stops at an earlier time than the one for the slower waves. A similar behavior to the one of the density, ρ, can be observed for the plasma flow velocity, vx, in Figure 13(b) and the magnetic field component, Bz, in Figure 13(e). Here, the amplitudes decrease from vx = 0.75, Bz = 1.9 (for ρIA = 1.9, blue), vx = 0.6, Bz = 1.7 (for ρIA = 1.7, red), vx = 0.45, Bz = 1.5 (for ρIA = 1.5, green), and vx = 0.27, Bz = 1.3 (for ρIA = 1.3, magenta) to vx = 0.55, Bz = 1.6 (for ρIA = 1.9, blue), vx = 0.46, Bz = 1.5 (for ρIA = 1.7, red), vx = 0.36, Bz = 1.4 (for ρIA = 1.5, green), and vx = 0.25, Bz = 1.25 (for ρIA = 1.3, magenta). Figure 13(c) shows how the primary waves propagate in the positive x-direction. In all four cases of different initial amplitude, ρIA, the phase speed decreases slighty (consistent with observations; see Warmuth et al. 2004 and Warmuth 2015) until the waves enter the CH at different times, i.e., the values for the phase speed start at vw ≈ 2.2 (for ρIA = 1.9, blue), vw ≈ 1.9 (for ρIA = 1.7, red), vw ≈ 1.7 (for ρIA = 1.5, green), and vw ≈ 1.4 (for ρIA = 1.3, magenta) and decrease to vw ≈ 1.5 (for ρIA = 1.9, blue), vw ≈ 1.39 (for ρIA = 1.7, red), vw ≈ 1.2 (for ρIA = 1.5, green), and vw ≈ 1.13 (for ρIA = 1.3, magenta).


Interestingly, from ∼11:33:40 UT, the PAD of the suprathermal electrons changes to cigar type, in association with a dramatic drop of electron flux (Figure 2(a)). This change of electron PAD and flux is related to a magnetic dip structure that is manifested by a conspicuous decrease of the magnetic field strength (Figure 2(b)). In contrast to the magnetic field enhancement observed at ∼11:33:08 UT, the magnetic dip structure should arise from the local expansion of flux tubes, which are driven by the two opposite flows (see the shaded region in Figure 2(c)). The observed electron cigar distribution and the associated magnetic dip are a strong indication of the betatron cooling effect. This betatron-mediated cigar distribution has been suggested in previous studies (Fu et al. 2011b, 2012c, 2013b; Liu et al. 2017c) but never clearly observed. These observations, for the first time, show a direct link between the cigar distribution and betatron cooling. Note that in the trailing edge of the magnetic dip region, a magnetic hump structure, indicated by the sharp enhancement of magnetic field, is observed at ∼11:33:55 UT (Figure 2(b)). This magnetic hump, reminiscent of the Earthward-propagating dipolarization-front structure typically generated by magnetic reconnection in the midtail (Fu et al. 2012d, 2012e, 2013a, 2015, 2016, 2017; Liu et al. 2013, 2018a, 2018b, 2018c; Cao et al. 2017; Peng et al. 2017; Yao et al. 2017; Chen et al. 2018), was possibly formed due to the local contraction of flux tubes driven by the ion flow with an increasing velocity in the Earthward direction (Figure 2(c)). Associated with this magnetic hump, a very weak pancake distribution of suprathermal electrons is observed (Figure 2(a)), and strong waves near the electron gyrofrequency are also observed (Figures 2(e) and (f)). These waves are whistler-mode; they indicate that the betatron acceleration inside the magnetic hump was accompanied by non-adiabatic effects (Fu et al. 2009, 2010a, 2010b, 2012a, 2012b) and is still ongoing (Fu et al. 2011a; Khotyaintsev et al. 2011; Wang et al. 2017; Yang et al. 2017).


The distances to planetary nebulae (PNe) have always faced the difficulty that nearby targets were lacking that could be reached well by direct methods. Trigonometric parallaxes have been obtained in a homogeneous long time-line campaign by the US Naval Observatory (USNO; Harris et al. 2007) and from the Hubble Space Telescope (HST; Benedict et al. 2009). Other studies (Acker et al. 1998; Smith 2015) showed that Hipparcos spacecraft parallaxes do not seem to be reliable. It was assumed that contamination by the emission of the surrounding nebulae caused these problems. Another model-independent method for distances to PNe are a cluster membership, as studied extensively by Majaess et al. (2007, 2014), and as discussed in Frew et al. (2016). In addition to these model-independent methods, a wide variety of statistical, model-dependent individual distance scales have been derived. The most frequently used of these are certainly those that are based on surface brightness versus angular sizes. They sometimes include optical depth corrections. All these methods have to be calibrated against a data set of nebulae with known distances. The older, widely used method is based on the 6 cm radio continuum flux, either using the ionized mass concept of Daub (1982) in the calibrations of Cahn et al. (1992) and Stanghellini et al. (2008), or by means of the radio continuum brightness temperature as used by van de Steene & Zijlstra (1994) and calibrated with a Galactic bulge sample. The newest model developed by Frew et al. (2016) is based on similar ideas, but makes use of the optical Hα surface brightness and a wide set of various calibrators. Moreover, they use a completely homogeneous data set for the brightness data derived earlier by themselves (Frew et al. 2013). Smith (2015) and Frew et al. (2016) described the underlying physics and assumptions for all these methods in detail. With the upcoming Gaia project (Gaia Collaboration 2016), a new era was expected to start for many classes of objects. The first step into this was described by Stanghellini et al. (2017) based on the combined Tycho + Gaia DR1 solution called TGAS (Michalik et al. 2015). With the second Data Release of Gaia (hereafter GDR2; Gaia Collaboration 2018), a complete homogeneous data set based only on Gaia measurements is available now for the first time. We present here the comparison of this new data set with common previous calibrations of PNe distances. Moreover, we compare it to the preliminary TGAS results in Stanghellini et al. (2017). Finally, we discuss possible caveats using the current GDR2.


In Fig. 7 we compare UGC 1378’s SFR density versus gas surface density (the Schmidt–Kennicutt relation) to data in the literature. The gas surface density corresponds to H i calculated from the 0th moment map from Mishra et al. (2017) in the same areas as SFR density. Points for the HSB and LSB discs are plotted as black and grey circles, respectively. We plot the mean SFR and H i surface density for the entire galaxy with a large open circle. The black line corresponds to the relation with an exponent of 1.4 found by Kennicutt (1998). Triangles give results for LSB galaxies published by Wyder et al. (2009), and bright and faint crosses show normal spiral galaxies from Kennicutt (1998) – total and H isurface densities. A blue line shows the best-fitting relation for the H isurface density of Bluedisk galaxies from Roychowdhury et al. (2015). We also plot the SFR in the outer regions of spiral galaxies (Bigiel et al. 2010, square symbols). In Fig. 7 the UGC 1378 measurements lie between normal spirals and LSB galaxies. The HSB disc data lie above the relation plotted for normal spirals, possibly indicating that the SFR is boosted by the bar driving gas to the star-forming rings. We cannot account for molecular gas since there are no available measurements for UGC 1378. The contribution of molecular gas would likely move the HSB disc of UGC 1378 towards the locus of normal galaxies. Because the HSB SFR of UGC 1378 is close to the predicted SFR from the Kennicutt (1998) relation obtained from H i densities (faint crosses in Fig. 7). The LSB disc of UGC 1378 lies below the correlation and accounting for molecular gas would only increase the deviation from the normal Schmidt–Kennicutt relation. Similar deviations are observed in ‘classical’ LSB galaxies, Bluedisk galaxies (Roychowdhury et al. 2015), outer parts of HSB spiral galaxies (Bigiel et al. 2010), and H idiscs in early-type galaxies (Yıldız et al. 2017). These deviations for LSB galaxies are at least partially explained by their lower gas densities leading to lower SFRs (Abramova & Zasov 2011). A recent episode of gas accretion on to the disc of UGC 1378 may also contribute to a lower SFR if the gas is not yet fully participating in the star formation. Lutz et al. (2017) studied a sample of very H i rich galaxies and proposed that very high specific angular momentum in H irich galaxies prevents the accreted gas from being transported to the mid-plane of the disc and being converted into stars. This mechanism may act to preserve giant gaseous discs.

Similar deviations are observed in
outer parts of HSB spiral galaxies


Relatively few such global convective dynamo studies have been conducted in the domain of M-dwarf stars. Early work by Browning (2008) considering lower mass FC M dwarfs found that the deep CZ could support very strong nonaxisymmetric fields, which strongly quenched the star’s differential rotation. Later, more turbulent simulations of FC M-dwarf stars led to a number of interesting results. Yadav et al. (2015a) found strong, axisymmetric fields which were statistically steady in time and recovered many of the observed characteristics of M-dwarf surface fields. A somewhat slower rotating model (Yadav et al. 2015b) revealed that flux concentration by merging downflow lanes could lead to the formation of large, persistent high-latitude starspots in these stars. A still slower rotating model (Yadav et al. 2016) built large-scale, axisymmetric, cycling magnetic fields of somewhat lower amplitude which did not eliminate the star’s differential rotation, reminiscent of the distributed αΩ-type dynamos prevalent in solar-like contexts. Brown et al. (2020) presented the first simulation of a stratified, rotating FC star whose computational domain extended to r = 0, finding a preference for hemispheric dynamo states. Similar models were recently explored by Käpylä (2021) for a broad range of rotation rates, which yielded a variety of results. At slow rotation, differential rotation was antisolar, and dynamo action dipole dominant. Moderate rotation rates yielded solar-like profiles, which were then magnetically quenched in the fastest rotators, yielding nonaxisymmetric dynamos. In Bice & Toomre (2020; hereafter BT20), we presented an exploration of the influence exerted by a tachocline in more massive, shell-convecting M-dwarf stars as a contributing factor to the break in observed magnetic activity across the tachocline divide. Our models produced a wide variety of field configurations, nearly all of which led to quenching of the differential rotation to a significant degree. We found that including a tachocline in models of early M-dwarf stars led to their surface fields being more favorable for rapid stellar spin-down, which may contribute to the formation of the tachocline divide.


At quasi-perpendicular shocks, the average shock structure is dominated by a foot of reflected ions, which is upstream of the shock ramp where the major thermalization and deceleration occurs. Non-stationarity in the form of rippling of the surface or steepened whistler waves (Moullard et al. 2006; Lobzin et al. 2007) is an intrinsic feature of the shock, but this is generally manifest as minor perturbations on top of an otherwise stationary shock ramp. Simulations have predicted that if the fraction of ions reflected by the shock front becomes sufficiently high, the quasi-perpendicular shock can become periodically reforming on timescales of the ion gyroperiod. Various theories have been suggested for such non-stationarity, including self-reformation where a new shock ramp grows at the edge of the foot (Biskamp & Welter 1972a; Lembège & Dawson 1987), whistler-induced reformation (Biskamp & Welter 1972b; Scholer & Burgess 2007), kinetic instabilities such as the Buneman and modified two-stream instability (e.g., Cargill & Papadopoulos 1988; Matsukiyo & Scholer 2003, 2006b; Scholer et al. 2003; Scholer & Burgess 2007; Matsumoto et al. 2013), and gradient catastrophe of nonlinear whistler waves due to steepening (Krasnoselskikh et al. 2002). However, it has not been until recently that such non-stationarity has been confirmed with in situ spacecraft observations. In a survey of Cassini shock crossings at Saturn, Sulaiman et al. (2015) found evidence of a periodically reforming shock, pulsating at a period near 0.3 of the ion gyroperiod in the unperturbed upstream medium. This period agrees with the time taken for a specularly reflected proton to gyrate across the foot and return to the main shock ramp. Sulaiman et al. (2015) also report that these periodic non-stationary shocks are primarily found in the very high Mach number regime, which gives evidence for a relation between Mach number and reformation. The main processes behind the non-stationary behavior of these very high Mach number shocks, such as the details of the ion- and electron-scale processes acting within the shock transition, remain elusive.


There are some indications that available models of the post-AGB and CSPN phases are not accurate enough. First, the two available grids of post-AGB models (Vassiliadis & Wood 1994; Blöcker 1995a) do not agree with each other on the predicted timescales (Zijlstra et al. 2008). Second, consistency between the masses of white dwarfs and those of CSPNe seems to require faster evolutionary speeds than predicted by both sets of models (Gesicki et al. 2014). Third, present models of the CSPNe phase are unable to explain why the cut-off of the PNe luminosity function is constant in most galaxies (Marigo et al. 2001, 2004). Lastly, post-AGB stellar evolution models, computed with updated physics in a reduced mass range (Kitsikis 2008; Weiss & Ferguson 2009), show a strong disagreement with the previous grids. This is not a surprise since many improvements have been carried out in the field of stellar physics in recent decades. Most importantly, available grids have been computed with opacities, which are now 45 years old (Cox & Stewart 1970b,a) before the big changes introduced by the OPAL (Iglesias & Rogers 1996), and Opacity Project (Seaton 2007) redeterminations. Similarly, nuclear reaction rates, equation of states, conductive opacities, and neutrino emission rates adopted in the models date from the early eighties and even earlier. In addition, Herwig et al. (1997) showed that the existence of carbon stars at low luminosities can be explained by the addition of mixing beyond the formal convective boundaries during the thermal pulses (TP) on the AGB. Finally, Marigo (2002) showed that C-rich molecular opacities are essential to predict the correct effective temperatures once the AGB models become carbon rich (NC/NO> 1, by number fractions). This is particularly important because of the impact of effective temperatures on the mass loss rates. While all these improvements in stellar modeling have been implemented in AGB stellar models, and very detailed and exhaustive grids and models are available (Weiss & Ferguson 2009; Cristallo et al. 2009, 2011; Ventura & Marigo 2010; Karakas 2010; Lugaro et al. 2012; Constantino et al. 2014; Doherty et al. 2015), the inclusion of these improvements in post-AGB stellar models is still missing. It is time for a recomputation of the post-AGB models in the light of all these advances.


Deriving the completeness limits of the WISE photometry is mandatory to assess the reliability of our catalogue of starless cores. We examined the histograms of the number of mid-infrared (MIR) sources versus magnitude; taking into account the effects of the cuts required to fulfil the criteria of Koenig et al. (2012), rough completeness limits are [3.6] ~ 14, [4.6] ~ 12, [12] ~ 9 and [22] ~ 7. These values are 1–3 mag brighter than the sensitivity limits quoted in the WISE Explanatory Supplement3 for the relevant sky region. Once converted into flux units and, for example, compared with the models of Class I and Class 0 sources of 0.5 M⊙ by Whitney et al. (2004), it can be seen that the completeness limits at 3.6 and 4.6μm are faint enough to detect such objects taking into account a distance of 700 pc and a further foreground reddening up to AV = 20. Even in the worst case of edge-on discs, these objects would be detectable at 3.6 and 22μm. Furthermore, the completeness limit at 22 μm is faint enough to allow detection of Class I and Class 0 sources of even-lower-mass central objects. Alternatively, one can compute the bolometric luminosity following Kryukova et al. (2012). Starting from our completeness limit at 22 μm, after conservatively dereddening it by AV = 20, we assumed a spectral index γ = −2 (see Table 3 for definition) to compute the MIR luminosity from Eq. (6) of Kryukova et al. (2012). Equation (7) of Kryukova et al. (2012) then yields Lbol ~ 1.7–2.8 L⊙, depending on whether the NIR flux is neglected (which may be the case) or extrapolated from γ = −2. A comparison with the birthline of Palla & Stahler (1993) indicates a mass of ~ 0.4–0.5 M⊙ for the central protostar. For the sake of comparison, we can roughly estimate the completeness limit in central masses of the Herschel protostellar cores in Giannini et al. (2012) using their quoted completeness limit at 70 μm of 0.21 Jy and following Dunham et al. (2008). By using Eq. (2) of Dunham et al. (2008), scaled to a distance of 700 pc, we found that the flux density at 70 μm translates into a bolometric luminosity of the central (proto)star Lbol ~ 0.28 L⊙ (we note that Dunham et al. 2008 indicate this luminosity as Lint). We highlight the fact that the 70 μm emission is in principle a more sensitive protostellar tracer than WISE. However, this contrasts with the much lower number of protostellar cores found by Giannini et al. (2012), which may be due to a poorer effective sensitivity because of their selection criteria.


In this paper, we consider resonance scattering on a two-level atom with an infinitely sharp and unpolarized lower level. As for the frequency redistribution, we consider both CRD and angle-averaged PRD. In an unmagnetized one-dimensional spherically symmetric atmosphere, the polarized radiation field is axially symmetric and is described by

. We also take into account the effects of radial velocity fields. We solve the concerned transfer equation in the CMF and in the nonrelativistic regime of velocity fields. To efficiently handle the sphericity effects, we solve the spherical transfer equation in the (p, z) coordinate system (Hummer & Rybicki 1971), which is also called the tangent-ray method. Here z is the distance along the tangent rays and p is impact parameter (see Figure 1 in Megha et al. 2019). Following Frisch (2007), we express the Stokes vector components in terms of their irreducible components. From here on we present all the basic equations in the irreducible basis (see Sampoorna & Trujillo Bueno 2010 for details). The CMF polarized PRD transfer equation for a spherically symmetric medium in (p, z) representation under the nonrelativistic limit is given by (see also Equation (17) of Megha et al. 2019)
1

where x denotes the nondimensional frequency and

 denotes the irreducible Stokes vector with “+” and “−” referring to the outgoing and incoming rays, respectively. The radial optical depth is defined as dτr = −χl(r)dr, where r is the radial distance and χl(r) is the line averaged absorption coefficient. In the CMF the monochromatic optical depth along the tangent ray is given by dτ = [φ(x) + βc]dτr/μ, where φ(x) is the line absorption profile function and βc = χc(r)/χl(r) with χc(r) denoting the continuum absorption coefficient. The direction cosine of the tangent ray about the radius vector of the intercepting radial shell is given by

. In Equation (1),

 denotes the CMF term, which has the form
2

where χ(r, x) = χl(r)φ(x) + χc(r), and
3

The symbol V denotes the ratio of radial (vr) to the thermal (

) velocities. In Equation (1),

 represents the irreducible CMF total source vector and is given by
4

where the line source vector is of the form
5

Here ϵ gives the probability of destruction of photons by inelastic collisions, Bν0 is the Planck function at the line center frequency ν0, and

. The continuum is assumed to be unpolarized. Therefore, the continuum source vector is given by

. The frequency-averaged PRD mean intensity vector is given by
6

where

 is the 2 × 2 nonmagnetic angle-averaged PRD matrix (Domke & Hubeny 1988; Bommier 1997), and
7

The Rayleigh phase matrix

 in the irreducible basis is given in Appendix A of Frisch (2007). It is useful to rewrite Equation (7) as
8

where
9


In this work, we focus on the 56 most massive (M* ≥ 1011 M⊙) galaxies at 1.4 ≤ z ≤ 2, 31 of which have spectroscopic redshifts. Two more objects entered the original sample, but they have been excluded from this study, because their WFC3/HST images are not available, or too noisy to perform SB fitting, due to the proximity of saturated stars. The sample was culled from the K-selected (K(Vega)  22) multiband catalogue of Daddi et al. (2007a, hereafter D07), including data from all the available filters in GOODS-S, i.e. HST/ACS optical, F435W (B), F606W (V), F775W (I), and F850LP(z), VLT/ISAAC near-IR, J, H, K, and Spitzer/Infrared Array Camera (IRAC), 3.6, 4.5, 5.8, and 8.0 μm (for more details on the data sets see Giavalisco et al. 2004). The optical/near-IR photometry was then complemented with the 24 μm catalog (Daddi et al., in preparation), built as summarized in Section 2.1 from the Multi-Band Imaging Photometer for Spitzer (MIPS) images (Rieke et al. 2004). Far-IR fluxes were extracted (Daddi et al., in preparation) from the publicly released PACS 70–160 μm data from Herschel GOODS (Elbaz et al. 2011), and SPIRE 250 μm data from Herschel Multi-tiered Extragalactic Survey (HerMES; Oliver et al. 2010). For objects without spectroscopic information, we used photometric redshifts from the public GOODS-MUSIC catalogue, which agree well with the spectroscopic ones (Δz/(1 + z) ≃ 0.03) for galaxies at z  2 (cf. Grazian et al. 2006, 2007). Although the uncertainties on photometric redshifts could result in the inclusion in the sample of a few lower redshift contaminants, we avoided applying colour criteria to pre-select high-z objects, in favour of completeness. The HST/WFC3/F160W H-band image mosaic (>5σ point source sensitivity for H160  27.7, AB system) drizzled to a pixel scale of 0.06 arcsec, was exploited to study galaxy morphology in the optical rest frame with a very high resolution (FWHM ∼ 0.18 arcsec ≃ 1.5 kpc). For more details on the observations and data reduction see Grogin et al. (2011) and Koekemoer et al. (2011).


The launch of the Fermi Gamma-ray Space Telescope has spurred on the search for pulsars in γ-rays (Grenier & Harding 2015), yielding over 2001 detections and triggering multiwavelength observations. While pulsars are common targets in the X-rays, they are very challenging targets in the optical and very few of them have been identified (see Mignani et al. 2016, and references therein). Here, we report on Large Binocular Telescope (LBT) observations of an isolated pulsar, PSR J2043+2740 (Taylor, Manchester & Lyne 1993), detected by both AGILE (Pellizzoni et al. 2009) and Fermi (Abdo et al. 2010; Noutsios et al. 2011). It was discovered as a radio pulsar (Ray et al. 1996) and later on as an X-ray source by XMM–Newton (Becker et al. 2004), although X-ray pulsations have not yet been found. PSR J2043+2740 is one of the very few non-recycled pulsars older than 1 Myr detected in γ-rays, with a characteristic age τc = 1.2 Myr, inferred from the values of its spin period Ps = 0.096 s and its derivative $\dot{P}_{\rm s} = 1.27 \times 10^{-15}$ s s−1 (Ray et al. 1996). This also yields a rotational energy loss rate $\dot{E}_{\rm rot} = 5.6 \times 10^{34}$ erg s−1 and a surface dipolar magnetic field Bs = 3.54 × 1011 G.2 Although PSR J2043+2740 does not have a very large spin-down power compared to young (∼1–10 kyr) pulsars (∼1036–1038 erg s−1), it is still a factor of 2 larger than that of middle aged γ-ray pulsars (∼0.1–0.5 Myr), such as Geminga, PSR B0656+14 and PSR B1055−52, all detected in the optical, thanks to their distances ≲ 500 pc (Abdo et al. 2013). The distance to PSR J2043+2740 is uncertain owing to the lack of a radio parallax measurement. The radio dispersion measure (DM = 21.0 ± 0.1 pc cm−3; Ray et al. 1996) gives a distance of 1.8 ± 0.3 kpc from the NE2001 model of the Galactic-free electron density (Cordes & Lazio 2002). A slightly smaller distance (1.48 kpc) is inferred from the model of Yao, Manchester & Wang (2017). The hydrogen column density towards the pulsar obtained from the X-ray spectral fits (NH ≲ 3.6 × 1020 cm−2; Abdo et al. 2013) suggests a distance of a few hundred pc (He, Ng & Kaspi 2013), although these estimates depend on the model X-ray spectrum. Such a distance would make PSR J2043+2740 a viable target for deep optical observations, never carried out until now, and might be compatible with the debated association (Noutsios et al. 2011) with the Cygnus Loop supernova remnant (SNR) at $540^{+100}_{-80}$ pc (Blair, Sankrit & Raymond 2005).


Having a line list that is as complete as possible is crucial for doing proper radiative transfer computations in high temperature atmospheric environments. However, computing the line opacities for a large number of lines can be computationally challenging. For example, the ExoMol line list of CH4 contains on the order of 1010 lines (Yurchenko & Tennyson 2014). Computing the exact pressure and temperature broadened Voigt profile for each of these lines is computationally extremely demanding. There are several approximate methods for computing Voigt profiles available in the literature (e.g. Humlícek 1982; Weideman 1994; Zaghloul & Ali 2012). Also, much effort is spend succesfully on making these approximate methods faster and more accurate (see e.g. Poppe & Wijers 1990; Letchworth & Benner 2007). These methods all focus on obtaining a given accuracy of the exact shape of the Voigt profile by applying mathematical approximations to decrease the computation time. While these methods still require significant computation time, they are now routinely applied to compute Voigt profiles in many applications. The fastest code able to compute Voigt profiles of large numbers of lines at this moment is the HELIOS-k code (Grimm & Heng 2015). This code is able to compute ~ 105 lines per second on a dedicated NVIDIA K20 GPU based machine. This implies that the computation of 1010 lines still requires on the order of one day for a single point in pressure temperature space. Usually a grid of pressure and temperature points is required. Thus, there is the need for an even faster method. In addition, we have to make sure that there are no systematic errors in the computations because a small systematic error in a single line can become large when computed for 1010 lines. Thus, we seek a method that is statistically exact, preserves the integrated opacities and the average shape of the lines, and computes the line profile accurately for the stronger lines.


Modern optical imaging surveys measure the positions and ellipticities of millions of galaxies; from them, the galaxy overdensity field as well as the gravitational lensing shear field can be derived. The two-point auto and cross-correlations of these two fields are the two-point correlation functions of cosmic shear, galaxy–galaxy lensing and galaxy clustering. A joint analysis of these correlation functions can break degeneracies between cosmological and nuisance parameters, leading to tighter cosmological constraints (Joachimi & Bridle 2010). Several earlier studies have indeed considered such joint analyses (Cacciato et al. 2013; Mandelbaum et al. 2013; More et al. 2015; Kwan et al. 2017; Nicola, Refregier & Amara 2017), albeit very few in a modified gravity context. Among the latter, Joudaki et al. (2018) recently performed a combined analysis of cosmic shear tomography, galaxy–galaxy lensing tomography, and redshift space multipole power spectra using data from KiDS-450 (∼450 deg2 of cosmic shear data from the KiDS survey) and two overlapping spectroscopic surveys, the 2-degree Field Lensing Survey4 (2dFLenS; Blake et al. 2016) and the Baryon Oscillation Spectroscopic Survey5 (BOSS; Dawson et al. 2013). They found that none of the extended cosmologies considered were simultaneously favoured in a model selection sense and able to resolve the discordance with Planck, except for an evolving dark energy component with a time-dependent w0 − wa equation of state. Amon et al. (2018) presented a measurement of EG, a statistic combining measurements of weak gravitational lensing, galaxy clustering, and redshift space distortions, proposed as a consistency test of General Relativity (Zhang et al. 2007). They determined the value of EG using data from the KiDS, 2dFLenS, BOSS, and Galaxy And Mass Assembly6 (GAMA; Driver et al. 2009, 2011; Liske et al. 2015) surveys; their results show that measurements of the EG statistic cannot be conducted as consistency checks of General Relativity until the aforementioned tension in cosmological parameters is resolved, and their EG measurements favour a lower matter density cosmology than the CMB. Recently, DES Collaboration (2019) presented a combined analysis of galaxy clustering and weak gravitational lensing from the first-year data of the Dark Energy Survey, targeting modifications of the metric potentials that would be a signal of modified gravity. They found that their constraints are compatible with a cosmological constant scenario.


Sunspot light bridges can be formed by the fragmentation of the umbra in the decay phase or during the merging of different magnetized areas during the formation of the sunspot in complex active regions (Bray & Loughhead 1964; Garcia de La Rosa 1987). At the last stages of a sunspot, the photospheric-like conditions are recovered as a consequence of the splitting of the umbra, and a granulation pattern similar to that of the quiet Sun is found in light bridges (Vazquez 1973), although the light-bridge convection cells differ significantly from normal granules (Lagg et al. 2014). Understanding the decay of sunspots requires the study of the magnetic and dynamical structure of light bridges. Previous studies have classified light bridges based on their morphological properties. Light bridges separating two umbral regions are called strong light bridges (e.g., Sobotka et al. 1993, 1994; Jurčák et al. 2006; Rimmele 2008). Their brightness is similar to that of the penumbra, and they typically appear between two regions with the same polarity. Faint light bridges (e.g., Lites et al. 1991; Sobotka et al. 1993) are elongated bright structures that penetrate the umbra. They are composed of rows of bright grains with sizes comparable to umbral dots. Light bridges can exhibit different internal structures. Most of them show several segments along their length that resemble granules (Berger & Berdyugina 2003), while some light bridges are similar to the bright filaments seen in the penumbra (Lites et al. 2004). All types show a weakened magnetic field strength relative to the surrounding umbra and more strongly inclined field lines (e.g. Beckers & Schröter 1969; Lites et al. 1991; Leka 1997), which in some case even exhibit a polarity reversal (Lagg et al. 2014). Observations are consistent with a reduced field strength in the photosphere, with a magnetic canopy extending from either side of the light bridge and merging at the top (Jurčák et al. 2006; Lagg et al. 2014). The velocity field measured in light bridges shows evidence of their convective origin (Rimmele 1997; Hirzberger et al. 2002; Lagg et al. 2014). Recently, Schlichenmaier et al. (2016) have also found evidence that the umbral magnetic field is wrapped around light bridges. The authors defined a new type, the plateau light bridge, with Y-shaped dark canals that resemble penumbral grains and suggest the presence of inclined magnetic fields. Several dynamic phenomena have been detected at the chromosphere above light bridges, including recurrent plasma ejections visible in Hα (Roy 1973; Asai et al. 2001), Ca ii  H (Shimizu et al. 2009), and other bands (AIA 1600 and 1700 Å, IRIS 1330 and 1400 Å, Toriumi et al. 2015), brightness enhancements in the TRACE 1600 Å band (Berger & Berdyugina 2003), or fan-shaped jets observed in Hα (Robustini et al. 2016). All these processes are considered to be caused by the interaction of the light bridge magnetic field with the surrounding atmosphere through magnetic reconnection events.


Using the RADEX3 non local thermodynamic equilibrium (LTE) modeling program (van der Tak et al. 2007) with collisional rate coefficients from Wiesenfeld & Faure (2013), we modeled the relation between the gas kinetic temperature and the measured average of para-H2CO 0.5 × [(322–221 + 321–220)/303–202] ratios, adopting a 2.73 K background temperature, an average observational linewidth of 4.0 km s−1, and column densities N(para-H2CO) = 2.7 × 1012 and 3.7 × 1012 cm−2 for N113 and N159W, respectively. The results are shown in Fig. 5. The values of the para-H2CO column density were obtained with APEX data (beam size ~30″; Tang et al. 2017b), which cover similar regions. Different column densities of para-H2CO only weakly affect derived kinetic temperatures (see Fig. 3 in Tang et al. 2017b or Fig. 4 in Tang et al. 2018a; this was also shown in Fig. 13 and discussed in Sect. 4.3.1 of Mangum & Wootten 1993) as long as all lines are optically thin. Considering that the relation between the gas temperature and the para-H2CO line ratio may vary at different spatial densities (see Fig. 2 in Tang et al. 2017b), we modeled it at spatial densities 104, 105, and 106 cm−3 in Fig. 5. It appears that Tkin at n(H2) = 105 cm−3 is consistently lower than values at 104 and 106 cm−3 by ≲23% and ≲34%, respectively, for Tkin ≲ 100 K. Local thermodynamic equilibrium (LTE) is a good approximation for the H2CO level populations under optically thin and high-density conditions (Mangum & Wootten 1993; Tang et al. 2017a,b, 2018b). Following the method applied by Tang et al. (2017b) in their Eq. (2), we plot the relation between the LTE kinetic temperature, TLTE, and the para-H2CO (3–2) line ratio in Fig. 5. Apparently, TLTE agrees well with Tnon-LTE at volume densities n(H2) ~ 105 cm−3 as long as Tkin ≲ 100 K. Previous observations show that para-H2CO (3–2) is sensitive to gas temperature at density 105 cm−3 (Ginsburg et al. 2016; Immer et al. 2016; Tang et al. 2017b). The spatial density measured with para-H2CO (303–202) and C18O (2–1) in N113 and N159W is n(H2) ~ 105 cm−3 on a size of ~30″ (Tang et al. 2017b). Therefore, here we adopt 105 cm−3 as an averaged spatial gas density in the N113 and N159W regions.


Figure 2 shows the ratios of the relative fluences (element/Mg) measured in Genesis bulk SW (Figure 2(a)) and regime targets (Figure 2(b)) after normalization to the respective solar abundance ratios (Table 7 in Appendix A.5). The bulk SW data for K and Fe in silicon (marked by asterisks in Figure 2(a)) are the preliminary fluences from Rieck (2015), Rieck et al. (2016), and Burnett et al. (2017). If SW had the composition of the solar photosphere, the ordinate value in Figure 2 would be 1 for all elements. The bulk SW shows a fractionation of elemental abundances correlating with FIP, as previously observed by spacecraft (e.g., Geiss 1982; Bochsler 2009). However, the better accuracy and element coverage of Genesis data compared to in situ measurements allows further insights into this FIP-related fractionation. The low-FIP elements (Figure 2(a)) are consistent with a flat pattern, at least below 7 eV, as many pre-Genesis studies suggested. This consistency would make these SW data easier to apply to cosmochemistry, as they would suggest that low-FIP elements are unfractionated relative to each other and hence their SW abundance ratios equal photospheric ratios. However, Figure 2(a) is also consistent with a monotonic increase of the low-FIP elements with decreasing FIP, which could be viewed as a trend continuing that of the high-FIP elements between Ar and C discussed below. The Na abundance given here is about 20% higher than that of Burnett et al. (2017). Na fluences derived from backside depth profiling of diamond-like-C collectors are roughly a factor of 2 lower than ours, which are based on Si collectors (Rieck 2015; Rieck et al. 2016). Jurewicz et al. (2019) propose that diffusion of surface contamination Na might have enhanced fluences from Si collectors. Because the amounts of surface contamination is highly variable, the Na fluences from Si should show significant scatter; however, replicate analyses of bulk and regime samples agree to within 2%–11% (Table 4, Appendix A.1). More analyses are required to resolve this important discrepancy. A ∼20% lower fractionation of K compared to that of Na, if real, would be surprising although within 2σ, both values still overlap.


Wang et al. (2017), motivated by the fact that previous studies on high-eccentricity migration focused only on the total efficiency of HJs formed, analyzed the efficiency of each high-eccentricity mechanism, trying to understand which mechanism is the dominant one in HJ formation. They considered multiplanetary systems containing from two to five planets with equal masses (1MJ), initially in circular and near-coplanar orbits with a host star of $1\, {\rm M}_\odot$ and $1\, {\rm R}_\odot$. Moreover, various initial semimajor axis conditions were considered, depending on the initial mutual separation between the planets. Their numerical simulations were performed using the classical version of the Mercury code (Chambers 1999), which does not include general relativity (GR) effects and tidal interaction with the central star. They studied how the initial number of planets, the spatial separation between them, and the location of the inner planet influence the efficiencies of high-eccentricity mechanisms. As a result, they found that the Kozai–Lidov mechanism plays the most important role in HJ production. The restriction made in the previous study, regarding not including the contribution of GR and realistic initial mass configurations (unequal masses), makes us wonder about the implications of these contributions on the efficiency of each high-eccentricity mechanism in the activation of the HJ production process. The main effect of GR is to cause the apsidal precession of planetary orbit, where the rate of precession is faster for planets close to the star and with eccentric orbits due to the term a5/2(1 − e2) in the denominator, being a and e the planet’s semimajor axis and eccentricity, respectively (Einstein 1916; Misner, Thorne & Wheeler 1973). Studies related to the influence of GR on the dynamic evolution of systems with more than one massive planet have been carried out, but only considering some particular systems (e.g. Adams & Laughlin 2006; Migaszewski & Goździewski 2009; Veras & Ford 2010; Zhang, Hamilton & Matsumura 2013; Marzari & Nagasawa 2019, 2020). Therefore, the aim of our study is to obtain a broader and more detailed description of the efficiency of each high-eccentricity mechanism in the activation of the HJ production process, including the contribution of GR and different initial planetary mass configurations. The analysis is made by solving the numerical simulation of the exact equations of motion, in the context of general N-body problem. Several initial conditions are considered, changing the initial mass and number of planets, the semimajor axis of the inner planet and the location of the other planets in the system.


Astrochemical models have always dedicated special attention to molecular oxygen. With a cosmic abundance twice that of C, atomic O is the third most abundant element in space. In dense clouds, standard gas phase chemical models therefore suggest a comparable ratio of CO and O2 after times ≥ 3 × 105 yr (e.g. Woodall et al. 2007), where O2 is supposed to be formed especially via OH + O → O2 + H. The OH here can be formed by the dissociative recombination of H3O+, H3O+ +e− → OH + 2H. However, observations with the Submillimeter Wave Astronomy Satellite (SWAS) by Goldsmith et al. (2000) towards Orion and with Odin by Larsson et al. (2007) towards ρ Oph A showed a significant difference between model predictions and measurements. The O2 abundances found were more than 100 times smaller than those predicted by models (Goldsmith et al. 2000). Better agreement with observations can be obtained if freeze-out of O atoms onto dust grains is taken into account in gas-grain chemical models (Bergin et al. 2000; Viti et al. 2001), with consequence surface production of H2O and O2, which may trap a significant fraction of oxygen, leaving only some atomic O and CO in the gas phase. Observations conducted by Liseau et al. (2012) led to a O2 column density of N(O2) = 5.5 × 1015 cm−2 with an upper limit of abundance of N(O2)/N(H2) ∼ 5 × 10−8 in warm gas (T > 50 K) and to N(O2) = 6 × 1015 cm−2 with a little higher abundance in cold gas (T  30 K). Liseau et al. (2012) stated that detecting gas phase O2 might be so difficult because the O2 abundance is transient in ρ Oph A and O2 is no longer detectable after ∼2 × 105 yr. A relatively large amount of O2 has only been found with Herschel in Orion as reported by Goldsmith et al. (2011). This source is quite warm (≥180 K), leading to a grain temperature of ≥100 K. At this temperature the grains are warm enough to desorb H2O ice and keep a large amount of oxygen with a big fraction in the form of O2 in the gas phase. Another explanation for the high O2 abundance found by Goldsmith et al. (2000) is that low-velocity C-shocks might be responsible for the increase of molecular oxygen in the gas phase.


We estimate the DPL parameters in equation (9) via Monte Carlo simulations. We compare the real structure function of an AGN to simulations computed from mock light curves generated using the DPL model of equation (9). We generate ‘mock’ light curves using the Timmer & König (1995) method. To create a single mock light curve, pseudo-random numbers are generated using the Fast Mersenne Twister SFMT19937 generator seeded with hardware-generated random numbers (generated using Intel RDRAND instruction) to ensure that the random number sequences are free of artificial correlations (Coddington 1994) induced by poor random seed choices. At this intermediate stage, the mock light curve is oversampled by a factor of 10 i.e. we generate points at 10 × the required cadence in order to avoid sampling issues. To include low-frequency modes that are not adequately characterized by the length of the observed light curve, the intermediate mock light curve is much longer than is ultimately required to make the final mock; mock light curves generated in this manner are capable of exhibiting low-frequency modes longer than the length of the observed data. Fast Fourier Transforms (FFTs) are most efficient for data sequences that are a power of 2; for this reason, we pick the intermediate (including the oversampling) to be of length 223. This results in the intermediate mock light curve being between 15 × to 45 × the length required for the final mock light curve depending on the actual length of the observed light curve. We pick a uniformly distributed random segment of the intermediate overly long light curve that has the same length as the observed light curve and generate another stream of uncorrelated Gaussian random deviates to simulate the white-noise properties of Kepler instrumentation noise. After adding this ‘measurement noise’, we set data points corresponding to the unobserved cadences in the real light curve to 0. This procedure creates a final mock light curve with identical sampling and noise properties to the real light curve. Fig. 8 shows the true light curve (orange) along with an example mock light curve (light green) for the Sy 1 AGN kplr006932990 illustrating what the mock light curves look like for the best-fitting DPL parameters for this object.


HATLAS12-00 had already been identified as a candidate gravitationally lensed galaxy as a result of its high submm flux (i.e. F500 > 100 mJy), red Herschel colours and the lack of a bright optical or radio counterpart (see e.g. Negrello et al. 2010 for a discussion of the selection of lens candidates in H-ATLAS and other Herschel surveys). This source was therefore observed spectroscopically in the submm. A CO spectroscopic redshift of 3.26 was first suggested by Z-spec (Bradford et al. 2004) observations, then subsequently confirmed by observations by the CARMA interferometer (Leeuw et al., in preparation) and the Zpectrometer instrument (Harris et al. 2007) on the Greenbank Telescope (Harris et al. 2012; see also Fu et al. 2012). Additional followup observations in the optical, near-IR, submm and other wavelengths were targeted at the lensed z = 3.26 source and the foreground objects responsible for the lensing, resulting in detailed analyses of this lensing system by Fu et al. (2012) and Bussmann et al. (2013). Their conclusions are that the z = 3.26 source HATLAS12-00 is subject to gravitational lensing, with a magnification of 9.6 ± 0.5 in both the submm continuum and CO, and 16.7 ± 0.8 in the K′ band, by two foreground galaxies, one at a spectroscopically determined redshift of 1.22, and another with photometry suggesting that it lies at a similar redshift. The submm photometry of HATLAS12-00 at 890 μm acquired with the Submillimeter Array (SMA) as part of this programme (Fu et al. 2012; Bussmann et al. 2013) is fully consistent with the 870 μm and 850 μm fluxes derived for this source from the LABOCA and SCUBA2 data to be presented here. The spectral energy distribution (SED) of the lensed source, after correcting for the lensing amplification, is well matched by the optically thick SED model for Arp220 from Rangwala et al. (2011), with a lensing-corrected far-IR luminosity of 1.2 ± 0.2 × 1013 L⊙, and an implied star formation rate of 1400 ± 300  M⊙ yr−1. In many ways the unlensed properties of this object match those of the broader population of bright submm selected galaxies first discovered by the SCUBA submm imager (see e.g. Chapman et al. 2005; Clements et al. 2008; Michałowski, Hjorth & Watson 2010). The unlensed 870 μm flux of this object would be ∼7.7 mJy.


Finally, the multiphase nature of galactic outflows implies that measurements of the outflow properties based on a single gas phase can lead to misleading conclusions (for a discussion, see e.g., Cicone et al. 2018b). Historically, systematic studies of galactic outflows in nearby and high-z galaxies have focused on the ionized gas – for example, as observed as broad wing emission in the spectra of the Hα, [O III] or Paα lines – (e.g., Heckman et al. 1990; Rupke & Veilleux 2013a; Woo et al. 2016; Harrison et al. 2016; Förster Schreiber et al. 2019; Ramos Almeida et al. 2019) and the atomic phase – based on the Na D or Mg II lines in absorption (e.g., Heckman et al. 2000; Rupke et al. 2002, 2005; Weiner et al. 2009; Roberts-Borsani & Saintonge 2019). The molecular component of outflows, on the other hand, has been much more difficult to study. Great progress was made with the Herschel Space Observatory using the OH 119 μm line in absorption to study molecular outflows in Seyfert and luminous infrared galaxies (Fischer et al. 2010; Sturm et al. 2011; Veilleux et al. 2013; Bolatto et al. 2013; Spoon et al. 2013; George et al. 2014; Stone et al. 2016; González-Alfonso et al. 2017; Zhang et al. 2018). More recently, the advent of powerful millimeter-wave interferometers such as the Atacama Large Millimeter/submillimeter Array (ALMA) and the NOrthern Extended Millimeter Array (NOEMA) are rapidly increasing the number of molecular outflows detected based on observations of the CO line (e.g., Combes et al. 2013; Sakamoto et al. 2014; García-Burillo et al. 2014; Leroy et al. 2015; Feruglio et al. 2015; Morganti et al. 2015; Dasyra et al. 2016; Pereira-Santaella et al. 2016, 2018; Veilleux et al. 2017; Fluetsch et al. 2019; Lutz et al. 2020). At high-z, so far only a handful of large-scale, molecular outflows have been studied in QSOs (e.g., Cicone et al. 2015; Vayner et al. 2017; Feruglio et al. 2017; Carniani et al. 2017; Fan et al. 2018; Brusa et al. 2018), sub-millimeter galaxies (e.g., Spilker et al. 2018), and main-sequence, star-forming galaxies (e.g., Herrera-Camus et al. 2019).


Cluster radio relics are usually found in the outskirts of merging galaxy clusters. They exhibit elongated morphologies and high degrees of polarisation above 1 GHz (up to 70%, Ensslin et al. 1998; Bonafede et al. 2014; Loi et al. 2019; de Gasperin et al. 2022). The resolved spectral index in radio relics shows a gradient: it steepens towards the cluster centre and flattens towards the outskirts. Their size can reach up to ∼2 Mpc, and high-resolution observations have revealed filamentary structures within relics themselves (Di Gennaro et al. 2018; Rajpurohit et al. 2020, 2022a,b; de Gasperin et al. 2022). The Largest Linear Sizes (LLS) and radio powers of relics are correlated, as well as the integrated spectral index and the radio power (van Weeren et al. 2009b; Bonafede et al. 2012; de Gasperin et al. 2014). Relics trace ICM shock waves with relatively low (M   3) Mach numbers (Finoguenov et al. 2010; Akamatsu et al. 2013; Shimwell et al. 2015; Botteon et al. 2016). The acceleration of electrons is believed to proceed via diffusive shock acceleration (DSA) in the ICM (Ensslin et al. 1998; Roettiger et al. 1999), in which particles scatter back and forth across the shock front gaining energy at every crossing. Nevertheless, this mechanism has been shown to be rather inefficient in accelerating electrons from the thermal pool (Vazza & Brüggen 2014; Vazza et al. 2016; Botteon et al. 2020a; Brüggen & Vazza 2020; see Brunetti & Jones 2014 for a review). Recently, it has been suggested that seed electrons could originate from the tails and lobes (driven by AGN outflows) of cluster radio galaxies (Bonafede et al. 2014; van Weeren et al. 2017; Stuardi et al. 2019), which alleviates the requirements of high acceleration efficiencies at cluster shocks (e.g., Markevitch et al. 2005; Kang et al. 2012, 2017; Botteon et al. 2016; Eckert et al. 2016). In some cases, double relics have been detected on opposite sides of the cluster centre (e.g., Rottgering et al. 1997; van Weeren et al. 2010, 2012b; Bonafede et al. 2012; de Gasperin et al. 2015a). In these clusters it is possible to constrain the merger history, providing important information about the formation processes of relics.


On the other hand, the line-shift-absence conundrum of ZP74 is easily explained through geometrical considerations. Essentially, the arguments leading to this conundrum assume that the collapse is roughly spherically symmetric and monolithic, so that the infall motions are coherent, and directed towards a single collapse centre, at the geometrical centre of the cloud. This assumption is inconsistent with our current understanding of the structure of MCs, which are known to be far from spherically symmetric, and instead consist of an intricate and inhomogeneous network of filaments and clumps within them (e.g. Bally et al. 1987; Feitzinger et al. 1987; Gutermuth et al. 2008; Juvela, Pelkonen & Porceddu 2009; Myers 2009; André et al. 2010; Henning et al. 2010; Men’shchikov et al. 2010; Molinari et al. 2010; Arzoumanian et al. 2011; Busquet et al. 2013). The central clumps (‘hubs’) appear to accrete from the filaments, while in turn the filaments seem to accrete radially from their surroundings (Schneider et al. 2010; Kirk et al. 2013; Peretto et al. 2014; Gong et al. 2018; Lu et al. 2018; Williams et al. 2018; Shimajiri et al. 2019). Thus, the geometry is far from being spherically symmetric, and therefore the accreting gas is not isotropically distributed around the collapse centres (the hubs). In addition, the velocity field is highly complex and chaotic (e.g. Gómez & Vázquez-Semadeni 2014; Zamora-Avilés, Ballesteros-Paredes & Hartmann 2017; Gómez, Vázquez-Semadeni & Zamora-Avilés 2018), so there is no reason to expect a systematic redshift of the absorption lines produced in the gas surrounding the hubs. Instead, the accretion flow is most directly observed as velocity-centroid gradients along the filaments, directed towards the hubs. Indeed, synthetic CO observations of simulations of the regime often show only marginal or no evidence for infall profiles, due to the chaotic motions and perhaps velocity crowding effects, although the line profiles do look similar to observed ones (e.g. Heitsch et al. 2009; Heiner, Vázquez-Semadeni & Ballesteros-Paredes 2015; Clarke et al. 2018). Nevertheless, recent dedicated searches for evidence of infall signatures in CO lines from GMCs have met with success. For example, Schneider et al. (2015) have found the classical combination of self-absorbed and blue-skewed optically thick lines (12CO (3–2)) together with centrally peaked optically thin (13CO (1–0)) lines, indicating collapse in the molecular gas surrounding IRDC G28.37+0.07, while Barnes et al. (2018) have measured shifts between the lines of 12CO (tracing gas in the outer parts of the cloud) and 13CO (tracing gas deeper into the cloud) in the pc-scale, massive clumps of the CHaMP survey, finding systematic velocity differentials between the two lines that imply an average mass accretion time-scale of ∼16 Myr, consistent with the time-scales we discuss in this paper (cf. Section 7.1 and Fig. 13).


The close approach of a star to a supermassive black hole (SMBH) can lead to the destruction of the stellar body in a process known as a tidal disruption event (TDE; Hills 1975). Gravitationally bound material returns to the black hole and is accreted, giving rise to a flare whose electromagnetic signature peaks in the extreme ultraviolet (EUV) band (Rees 1988; Ulmer 1999). These flares were first detected in the soft X-ray band by ROSAT (Komossa et al. 2004; Bade et al. 1996; Komossa & Greiner 1999; Komossa & Bade 1999), later by XMM-Newton and Chandra (Esquej et al. 2007; Saxton et al. 2012a, 2017; Maksym et al. 2010; Lin et al. 2015) (see review by Komossa 2017), and also in the UV band by GALEX (Gezari et al. 2006, 2008, 2009). In recent years, large-area optical surveys have detected candidate TDEs emitting at temperatures of a few ×104 K (van Velzen et al. 2011; Cenko et al. 2012a; Gezari et al. 2012; Arcavi et al. 2014; Holoien et al. 2016), ostensibly too cool to be coming from an accretion disc (e.g. Bonning et al. 2007). This optical radiation has been interpreted as being due to reprocessing of the accretion radiation by an optically thick screen (Metzger & Stone 2016; Roth & Kasen 2018; Dai et al. 2018) or to emission from shocks (Piran et al. 2015). Super-Eddington accretion in the initial phase of the disruption causes a large-scale, radiation-driven outflow of material from the central engine (Strubbe & Quataert 2009), which Metzger & Stone (2016) showed would initially completely absorb the radiation from the central engine and convert it into optical/UV photons with an effective temperature similar to that observed. In this model, the screen density is expected to drop after a few months to the point where the inner thermal radiation would become visible, with the delay time and ratio of X-ray to optical/UV flux depending on the line of sight (Metzger & Stone 2016; Dai et al. 2018). Observationally, the evidence for differences in the X-ray and UV/optical timescales is mixed. The X-rays may have lagged the UV by ∼32 days in ASASSN-14li (Pasham et al. 2017), but broadly fell on the same timescale (Brown et al. 2017), as they did in 2MASX 0740-85 (Saxton et al. 2017). In SDSS J1201+30 the UV flux did not change, while the X-rays dropped by a factor of 100 (Saxton et al. 2012a), whereas in ASASSN-15oi the X-ray luminosity was quite low (LX ∼ 1041 ergs s−1) at the peak of the optical flare, but 200–300 days later had increased to LX ∼ 1042ergs s−1 (Holoien et al. 2018; Gezari et al. 2017).


The simplest explanation for these metal abundances, i.e., that they reflect the yields of normal core-collapse SNe (averaged over the stellar initial mass function (IMF)), fails to predict anything like the observed stellar abundances of the extremely metal-poor stars ([Fe/H]  −3). Of course, at these low metallicities, the number of progenitor SNe enriching the ISM may be small, so models typically allow for metal-poor or metal-free progenitor stars, and an arbitrary mix of progenitor stellar masses (i.e., assuming the abundances might come from just one or at most a few SNe with individual explosion and progenitor parameters fitted to the observations). However, even with these degrees of freedom, the models still often fail to explain the abundances of certain individual species at the order-of-magnitude level (see, e.g., Nomoto et al. 2006; Heger & Woosley 2010; Lee et al. 2014; Placco et al. 2015), although they undoubtedly explain many of the observed abundance ratios. For the lowest metallicity stars observed ([Fe/H]  −4), and in particular for the CEMP stars, these remaining discrepancies have led to more “exotic” models with a number of free parameters, invoking a mix of normal/faint SNe and hypernovae (with variable explosion energies of ∼1051–1054 erg); jets, prior “failed explosions,” and fallback episodes; rotation and adjustable mixing layers allowing for a tunable stellar abundance profile in the progenitor stars; and pollution of the stars via companions (e.g., Tominaga et al. 2007; Ishigaki et al. 2014; Takahashi et al. 2014; Abate et al. 2015). These additions can improve the agreement with observations; however, there is still no consistent theoretical scenario that simultaneously explains most of the observed stars, and even the best-fit models for many individual stars can still have order-of-magnitude discrepancies with certain outlier elements (see Tominaga et al. 2014; Frebel et al. 2015; Placco et al. 2015, and references therein).


Recently, forms of feedback that are fundamentally different from SNe have been shown to be essential to galaxy formation. Murray, Quataert & Thompson (2010) analysed the dynamical effects of several forms of stellar feedback on parent molecular clouds. In their models they include momentum input from ionized gas in H ii regions, shocked stellar winds, hot gas pressure, protostellar jets and cosmic rays. Murray et al. (2010) conclude that radiation pressure (RP) on dust grains is likely to be the dominant form of feedback in star-forming galaxies. A variety of other studies have reached the same conclusions, placing the combination of RP and photoionization of gas by massive stars as the dominant mechanism for disruption of molecular clouds and internal regulation of the SF process (Indebetouw et al. 2009; Krumholz & Matzner 2009; Murray et al. 2010; Andrews & Thompson 2011; Hopkins, Quataert & Murray 2011; Lopez et al. 2011; Pellegrini, Baldwin & Ferland 2011). RP alone might also be the only mechanism that explains galactic fountains and the warm gas outflows observed in absorption in high-redshift galaxies (Murray, Ménard & Thompson 2011). In addition, recent numerical work by Krumholz & Thompson (2012) shows that radiation feedback fully accounts for the large gas velocity dispersions measured in young star clusters in the MW. There are at least three reasons why radiative feedback is an essential ingredient of the galaxy formation process. First, observations show that molecular clouds begin to disperse shortly after the O stars form and before the first SNe explode and deposit their energy into the gas (Kawamura et al. 2009). Secondly, the total energy output of a stellar cluster is dominated by radiation. The rate of radiative energy output by O and B stars is ∼200 times larger than the average power injected by SNe and stellar winds during the lifetime of the most massive stars. Thirdly, it is difficult to explain the large gas turbulence values observed in star-forming regions without including the momentum input by radiation (Murray et al. 2010).


With our joint analysis of stellar mass fraction and source size, we find a larger stellar mass fraction than earlier statistical studies. In FigureÂ 2, we compare our determination of the stellar surface density fraction to a simple theoretical model and to the best fit of a sample of lens galaxies by Oguri etÂ al. (2014). The simple theoretical model is the early-type galaxy equivalent of a maximal disk model for spirals. We follow the rotation curve of a de Vaucouleurs component for the stars outward in radius until it reaches its maximum and then simply extend it as a flat rotation curve to become a singular isothermal sphere (SIS) at large radius (see details in the Appendix). The ratio of the surface mass density of the de Vaucouleurs component to the total surface mass density is shown as a dashed curve in FigureÂ 2. We also show as a gray band the best fit for the stellar fraction in the form of stars determined by Oguri et al (2014) in a study of a large sample of lens galaxies using strong lensing and photometry, as well as the best model using a Hernquist component for the stars and an NFW halo for the dark matter with and without adiabatic contraction, also from Oguri etÂ al. (2014). We have used the average and dispersion estimates for the Einstein and effective radii available for 13 of the objects in our sample from Oguri etÂ al. (2014), Sluse etÂ al. (2012), Fadely etÂ al. (2010), and LehÃ¡r etÂ al. (2000; see TableÂ 1) as an estimate of RE/Reff in FigureÂ 2. The average value and dispersion of the sample is RE/Reff = 1.8 Â± 0.8. This also averages over the different radii of the lensed images. The agreement of our estimates with the expectations of the simple theoretical model and with estimates from other studies (Oguri etÂ al. 2014) is quite good. For comparison, the estimate of Pooley etÂ al. (2012; using the Einstein and effective radii estimates for 10 out of 14 of their objects from Schechter etÂ al. 2014) seems somewhat lower than expected at those radii. The range of stellar mass fractions from MED09 for source sizes in the range 0.3â15.6 light days is also shown in FigureÂ 2. In this case, the discrepancy between our estimate and their reported value of Î± = 0.05 is completely due to the effect of the source size. Although accretion disk sizes are known to be smaller in X-rays, recent estimates are in the range of 0.1â1 light-days, depending on the mass of the black hole (see Mosquera etÂ al. 2013), and these finite sizes will increase the stellar surface densities implied by the X-ray data. Another possible origin for this discrepancy is that Pooley etÂ al. (2012) use the macro model as an unmicrolensed baseline for their analysis. It is well known that simple macro models are good at reproducing the positions of images, but have difficulty reproducing the flux ratios of images due to a range of effects beyond microlensing. Recently, Schechter etÂ al. (2014) found that the fundamental plane stellar mass densities have to be scaled up by a factor 1.23 in order to be compatible with microlensing in X-rays in a sample of lenses with a large overlap with that analyzed by Pooley etÂ al. (2012). It is unclear how this need for more mass in stars at the position of the images found by Schechter etÂ al. (2014) can be reconciled with the apparently low estimate of mass in stars at those radii by Pooley etÂ al. (2012). Our estimate of the stellar mass fraction agrees better with the results of microlensing studies of individual lenses (Keeton etÂ al. 2006; Kochanek etÂ al. 2006; Morgan etÂ al. 2008, 2012; Chartas etÂ al. 2009; Pooley etÂ al. 2009; Dai etÂ al. 2010) that reported values in the range 8%â25%, and with the estimates from strong lensing studies (see for example Jiang & Kochanek 2007; Gavazzi etÂ al. 2007; Treu 2010; Auger etÂ al. 2010; Treu etÂ al. 2010; Leier etÂ al. 2011; Oguri etÂ al. 2014) which produced stellar mass fractions in the range 30%â70% integrated inside the Einstein radius of the lenses.


The dynamical importance of CRs is even more uncertain. This is in part because most early work on this question focused only on galactic conditions similar to those found locally (Jokipii 1976; Badhwar & Stephens 1977; Ghosh & Ptuskin 1983; Chevalier & Fransson 1984; Boulares & Cox 1990; Ko, Dougherty & McKenzie 1991; Ptuskin 2001), and/or focused largely on the question of how and whether CRs can drive galactic winds originating in the ionized, low-density medium found several scale heights above galactic planes (Ipavich 1975; Breitschwerdt, McKenzie & Voelk 1991; Zirakashvili et al. 1996; Ptuskin et al. 1997; Zirakashvili & Völk 2006; however, for an exception see Breitschwerdt, McKenzie & Voelk 1993). More recent numerical and analytic models have continued in this vein (e.g. Everett et al. 2008; Jubelgas et al. 2008; Samui, Subramanian & Srianand 2010; Wadepuhl & Springel 2011; Uhlig et al. 2012; Booth et al. 2013; Pakmor et al. 2016; Simpson et al. 2016; Recchia, Blasi & Morlino 2016, 2017; Ruszkowski, Yang & Zweibel 2017; Pfrommer et al. 2017; Buck et al. 2019), rather than address the question of whether CRs represent a significant contribution to the support of the neutral material that dominates the total mass budget and occupies at least $\sim 50{{\ \rm per\ cent}}$ of the volume (e.g. Dekel et al. 2019) near the mid-plane. Indeed, the vast majority of published simulations that include CR transport do not resolve the neutral phase or galactic scale heights (∼100 pc), and those that do (e.g. Hanasz et al. 2013; Salem & Bryan 2014; Salem, Bryan & Corlies 2016; Chan et al. 2019) generally assume that CR transport in the neutral ISM is identical to that in the ionized ISM (though see Farber et al. 2018), an assumption that is almost certainly incorrect (e.g. Zweibel 2017; Xu & Lazarian 2017; Krumholz et al. 2020). Only a few published models attempt to address the question of CR pressure support in the neutral ISM for non-Solar neighbourhood (mostly starburst or Galactic Centre) conditions (e.g. Thompson et al. 2006; Socrates, Davis & Ramirez-Ruiz 2008; Lacki, Thompson & Quataert 2010; Lacki et al. 2011; Crocker et al. 2011; Crocker 2012; Lacki 2013; Yoast-Hull, Gallagher & Zweibel 2016; Yoast-Hull & Murray 2019; Krumholz et al. 2020).