Keeping in mind the caveats discussed in Sect. 4.2, a relation between the properties of the jet collimation region and the properties of the accretion disk is suggested by Figs. 5 and 6. According to theoretical models and simulations, both thin disks (e.g., Blandford & Payne 1982; Fendt 2006; Liska et al. 2019) and geometrically-thick hot disks (e.g., Blandford & Begelman 1999; McKinney 2006; Begelman 2012; Mościbrodzka & Falcke 2013; Mościbrodzka et al. 2016) can launch collimated outflows. Due to the higher mass loading and lower speed, the disk-driven jet is expected to dominate the emission in radio galaxies with respect to the de-boosted black hole-launched jet. This is confirmed in observations by the direct imaging of limb-brightened jet structures (e.g., Boccardi et al. 2016a; Mertens et al. 2016; Giovannini et al. 2018) as well as by kinematic studies of radio galaxies, which generally show much lower intrinsic speeds than measured in blazars (Lister et al. 2019). As these properties are observed in high-luminosity and low-luminosity radio galaxies alike, a jet sheath must be produced from disks spanning different accretion regimes. Our results, however, indicate that the disk-driven jet in LERG originates at small disk radii (few RS, as measured in M 87), and indeed the expansion profiles of most of the LERG are well aligned with those of BL Lacs, which are expected to be dominated by the black hole-launched spine (see e.g., Ghisellini et al. 2014). This result is in broad agreement with models of jet launching from ADAFs (e.g., Cao 2011; Yuan & Narayan 2014, and references therein), which predict the formation of a thin and mildly-relativistic outer layer. ADAF models also predict the launch of a nonrelativistic disk-wind component carrying the bulk of the disk mass outflow and spanning a large solid angle. There is no evidence for such a component based on the analyzed VLBI images, at least in the considered frequency regime. The jet profiles in HEG, on the other hand, are all shifted upward, and a back-extrapolation down to the jet base suggests that the jet sheath is launched at larger disk radii. Taking as a reference Cygnus A, which shows the thinnest jet among HEG and for which an initial jet width of ∼200 RS was measured based on GMVA observations (Boccardi et al. 2016b), the present data suggest that thin disks could launch collimated winds with an initial outer radius ≳100 RS. This possible difference in the outer radius of the jet sheath is accompanied by a different extent of the collimation region in HEG and LEG (Fig. 6). Modeling of jet collimation by disk winds, presented by Globus & Levinson (2016), revealed a direct link between the wind outer radius and the collimation radius: for a given wind power, larger wind radii correspond to more extended collimation zones. A sufficiently high ratio (> 0.1) of wind power to jet power is required for this process to be efficient. When this condition is verified in reality, is a matter of debate. In recent simulations presented by Hervet et al. (2017), the diverse kinematic behavior of VLBI knots in blazars of different powers could be well explained by varying this ratio. Except for the least powerful class among BL Lacs (that of the High-frequency peaked BL Lacs, HBLs), whose properties could be reproduced by assuming an absent or very weak wind, ratios larger than 0.3 were suggested for blazars. A question remains concerning the portion of these winds which is actually detected in VLBI observations. When attempting to model the M 87 jet collimation profile, Globus & Levinson (2016) have suggested that the radio emission is produced in the shocked interface between the relativistic jet and the outer wind, which is undetected. Observational constraints on extended disk winds may be provided through other methods. For instance, we note that for all the HERG in our sample (except PKS 1514+00) the detection of ultra-fast outflows was reported based on X-ray observations (Tombesi et al. 2010, 2014; Reynolds et al. 2015). These outflows, whose launching mechanism is unclear, are suggested to be characterized by mildly relativistic speeds, to originate at disk radii of 102 − 104RS (in agreement with our findings), and to carry a significant fraction of the jet kinetic power. Thus collimation via the action of disk winds, where by disk winds we mean a mildly relativistic jet sheath plus possible broader outflows, appears to be a viable mechanism, especially for high-luminosity sources.


We apply our analysis to five open clusters of ages between ∼10 and 100 Myr that were observed within GES (25 Ori, Gamma Vel, NGC 2547, NGC 2451 B, and NGC 2516). These clusters were selected because they cover the age interval in which the effect of radius inflation could be significant, allowing us to investigate how it evolves with age. The 25 Ori cluster is a group of PMS stars that was discovered by Briceño et al. (2005) in the Orion OB1a association, with an estimated age of 6−13 Myr (Downes et al. 2014; Briceño et al. 2019; Kos et al. 2019; Zari et al. 2019); a dispersed, kinematically distinct population was also found in the region using data from the Gaia Second Data Release (DR2; e.g. Zari et al. 2019). Because only a few stars of the secondary population were observed by GES, only the main cluster is considered here. Gamma Vel (age ∼10−20 Myr, Jeffries et al. 2014, 2017) and NGC 2547 (35 ± 3 Myr, Jeffries & Oliveira 2005) are both located in the Vela OB2 association at a relative separation of ∼2°. Both clusters host two kinematically distinct populations (Jeffries et al. 2014; Sacco et al. 2015); the two Gamma Vel populations (Gamma Vel A and B) are also separated by ∼38 pc along the line of sight (Franciosini et al. 2018). NGC 2451 is a double cluster composed of two open clusters of similar age (30−40 Myr, Randich et al. 2018) located at different distances along the same line of sight (Röser & Bastian 1994; Platais et al. 1996). The GES observations cover the background cluster NGC 2451 B and only a few selected regions of the closer and more dispersed NGC 2451 A. For this reason, we considered only NGC 2451 B here. Finally, NGC 2516 is the oldest cluster in our sample, with an age of ∼100 − 140 Myr (e.g. Lyra et al. 2006; Randich et al. 2018), so that most of its members are already close to or at their main-sequence position. All clusters have solar or slightly subsolar metallicities (Biazzo et al. 2011; Jacobson et al. 2016; Spina et al. 2017).


The hot emission line of Fe xxi 1354.09 Å and the cool emission line of Si iv 1402.77 Å have been used in many spectroscopic studies to investigate chromospheric evaporation (e.g., Tian et al. 2014, 2015; Li et al. 2015b, 2017a, 2017b; Brosius et al. 2016; Zhang et al. 2016a, 2016b). It is widely accepted that the forbidden line of Fe xxi 1354.09 Å is a hot (log T ∼ 7.05) and broad emission line during solar flares (Doschek et al. 1975; Cheng et al. 1979; Mason et al. 1986; Innes et al. 2003a, 2003b). Meanwhile, IRIS spectroscopic observations show that Fe xxi 1354.09 Å is always blended with a number of cool and narrow emission lines, which are from neutral or singly ionized species. Those blended emission lines can be easily detected at the position of the flare ribbon, including known and unknown emission lines, such as the C i line at 1354.29 Å, the Fe ii lines at 1353.02 Å, 1354.01 Å, and 1354.75 Å, the Si ii lines at 1352.64 Å and 1353.72 Å, and the unidentified lines at 1353.32 Å and 1353.39 Å (e.g., Li et al. 2015a, 2016a; Polito et al. 2015, 2016; Tian et al. 2015, 2016; Young et al. 2015; Tian 2017). In order to extract the hot line of Fe xxi 1354.09 Å and the cool line of C i 1354.29 Å (log T ∼ 4.0; Huang et al. 2014), we apply a multi-Gaussian function superimposed on a linear background to fit the IRIS spectrum at the “O i” window (e.g., Li et al. 2015a, 2016a), which has been pre-processed (i.e., IRIS spectral image deformation, bad pixel despiking and wavelength calibration) with the standard routines in Solar Soft Ware (SSW; Freeland et al. 2000). In short, the line positions and widths of these blended emission lines are fixed or constrained, and their peak intensities are tied to isolated emission lines from similar species. More details can be found in our previous papers (Li et al. 2015a, 2016a). On the other hand, the cool line of Si iv 1402.77 Å (log T ∼ 4.8) at the “Si iv” window is relatively isolated, and it can be well fitted with a single-Gaussian function superimposed on a linear background (Li et al. 2014, 2017a). Using the relatively strong neutral lines (i.e., “O i” 1355.60 Å and “S i” 1401.51 Å), we also perform an absolute wavelength calibration for the spectra at the “O i” and “Si iv” windows, respectively (Tian et al. 2015; Tian 2017). Finally, the Doppler velocities of Fe xxi 1354.09 Å, C i 1354.29 Å, and Si iv 1402.77 Å are determined by fitting line centers removed from their rest wavelengths (Cheng & Ding 2016b; Guo et al. 2017; Li et al. 2017a). As the hot Fe xxi line is absent in the non-flaring spectrum, the rest wavelength for the Fe xxi line (i.e., 1354.09 Å) is determined by averaging the line centers of the Fe XXI profiles which were used in the previous IRIS observations (Brosius & Daw 2015; Polito et al. 2015, 2016; Sadykov et al. 2015; Tian et al. 2015; Young et al. 2015; Brosius et al. 2016; Lee et al. 2017), while the rest wavelengths for the C i and Si iv lines, i.e., 1354.29 Å and 1402.77 Å, respectively, are determined from their quiet-Sun spectra (Li et al. 2014, 2015a).


Selected as part of ESA’s Cosmic Vision programme, Athena will study the evolution of large scale structure through the detection of WHIM filaments to trace the missing baryons in the local universe. Athena aims to measure the local cosmological baryon density in the WHIM to better than 10% and to constrain structure formation models in the low-density regime by measuring the redshift distribution and the physical parameters of 200 filaments against bright background sources. To achieve this, Athena will detect 200 filaments in the WHIM through absorption, 100 towards active galactic nuclei (AGN), and 100 towards bright gamma-ray burst (GRB) afterglows, up to redshifts of z = 1 (Kaastra et al. 2013). The WHIM can be detected by observing the absorption of highly ionised elements such as C, N, O, Ne, and possibly Fe (e.g. O VII, O VIII, Ne IX, Fe XVII). The strongest lines expected correspond to the H-like and He-like oxygen ions of the O VII 1s−2p X-ray resonance line (574 eV) and the unresolved O VIII 1s−2p X-ray doublet (653.5 eV, 653.7 eV). A bright X-ray background source such as an AGN (e.g. Padovani et al. 2017) or a GRB (e.g. Willingale & Mészáros 2017) can be used to detect the WHIM by producing absorption features in its energy spectra (Perna & Loeb 1998; Hellsten et al. 1998; Fiore et al. 2000). These sources provide a high probability of detection for the WHIM because they are sufficiently bright and distant to obtain a large statistical sample of lines. Bright AGN are common but are typically nearby, having an average redshift of z ≈ 0.8 for flat-spectrum radio quasars (FRSQ) and z ≈ 0.3 for BL-Lacs (Ackermann et al. 2011) and so, they probe relatively short lines of sight. Gamma-ray bursts occur at an average redshift of z ≈ 2 (Evans et al. 2009) and have been detected out to redshifts of 9.4 (Cucchiara et al. 2011). This allows for the probing of long lines of sight and can potentially provide multi-filament detections in a single observation. In addition, GRBs occur at an approximate rate of 1 GRB per day, with Fermi-GBM detecting ≈250 per year with a ≈70% sky coverage (Bhat et al. 2016). Both sources provide similar fluences in the 0.3−10 keV energy range, but GRBs can provide this fluence in much shorter integration times. The challenge associated with the use of GRBs as background sources is their transient nature, emitting a considerable percentage of the soft X-ray photons within the first hour of their afterglow phase. Therefore, an instrument capable of having a high efficiency to react on target of opportunity (ToO) events is required to probe the WHIM with GRBs. In spite of this, GRBs should allow Athena to perform its science mission of tracing the missing baryons in GRB afterglow spectra throughout its four-year mission lifetime.


The multiwavelength spectral data of 13 SNRs with hard γ-ray spectra. The γ-ray spectra are fitted with a hadronic model with the normalization of the individual spectrum as free parameters. The model assumes that protons have a single power-law energy distribution with an exponential high-energy cutoff. Note that the TeV spectra of G78.2+2.1 (HAWC) and N132D (HESS) cut off at relatively lower energies, and the soft spectral component of GeV of HESS 1912+101 may be from other contributors and are not considered in SED fitting. The best-fit model parameters are indicated in the figure. References for the observational data are as follows: RX J0852.0−4622: radio (Duncan & Green 2000), GeV (Tanaka et al. 2011), X-ray (Aharonian et al. 2007), TeV (H.E.S.S. Collaboration et al. 2018c); RX J1713.7−3946: radio (Lazendic et al. 2004), X-ray (Tanaka et al. 2008), GeV and TeV (H.E.S.S. Collaboration et al. 2018a); HESS J1731−347: radio (Tian et al. 2008), GeV (Condon et al. 2017; Guo et al. 2018), X-ray (Doroshenko et al. 2017), TeV (H.E.S.S. Collaboration et al. 2011); RCW 86: radio (Clark et al. 1975; Lemoine-Goumard et al. 2012), X-ray (Lemoine-Goumard et al. 2012), GeV (Ajello et al. 2016), TeV (H.E.S.S. Collaboration et al. 2018d); SN 1006: radio Dyer et al. 2009, X-ray (Bamba et al. 2008), GeV (Condon et al. 2017), TeV (Acero et al. 2010); G150.3+4.5: radio (Gerbrandt et al. 2014), X-ray and GeV (Devin et al. 2020); G296.5 + 10.0: radio (Milne & Haynes 1994), GeV (this work), HESS J1534−571: radio (Maxted et al. 2018), GeV (Araya 2017), X-ray and TeV (H.E.S.S. Collaboration et al. 2018b); RCW 103: radio (Dickel et al. 1996), GeV (Xing et al. 2014); G78.2+2.1: radio (Wendker et al. 1991; Zhang et al. 1997; Kothes et al. 2006; Gao et al. 2011), X-ray (Leahy et al. 2013), GeV (Abeysekara et al. 2018) and TeV (Fleischhack 2019); G279.0+1.1: radio (Woermann & Jonas 1988; Duncan et al. 1995), GeV Araya (2020); N132D: radio (Dickel & Milne 1995), X-ray (Hughes et al. 1998; Bamba et al. 2018), GeV (Y. L. Xin et al. 2020, in preparation), and TeV (H.E.S.S. Collaboration et al. 2015).


The metallicity calculated for HD 212869 is higher than that estimated prior to using high-resolution spectra. The iron abundance is found to be [Fe/H] =

 0.2 dex on the basis of ionized lines that are almost free from NLTE effects. The carbon abundance was found to be high in the atmosphere of HD 112869,

 = 8.3 ±  0.1 dex. The nitrogen abundance is

 = 6.55 ± 0.2 dex. With the obtained abundances [C/Fe] = +2.2 dex and [C/N] = +1.15, HD 112869 occupies the region of CEMP-s stars on the plots [C/Fe] versus [Fe/H] and [C/N] versus [Fe/H] (see Figures 5 and 6 in Campbell & Lattanzio 2008). However, the s-process elements Sr, Y, and Ba are not enhanced significantly, thus confirming by definition (Beers & Christlieb 2005) the CEMP-no status of HD 112869. However, the Nd abundance seems to be enhanced relative to iron, and a similar overabundance was recognized for lanthanum and samarium. From inspection of the Eu ii line at 6645.127 Å, the upper limit was set for the r-process element europium, [Eu/Fe] ≲ +0.8 dex. According to calculations carried out by Bisterzo et al. (2011), the abundances of three s-peaks are strongly dependent on the choice of the

-pocket, as well as on the initial mass and the metallicity. [ls/Fe], [hs/Fe] and [Pb/Fe] do not follow a linear behavior with decreasing metallicity and can cover a large range of values. For the low-mass models the enhancement of the first s-process peak is low or absent. A spectrum of very high resolution is needed to estimate the abundances for a large number of the second s-process peaks and to recognize an overabundance of the third s-process peak. With the adopted oxgen abundance, [O/Fe] = +0.8 dex, the carbon-to-oxygen ratio was found to be very high for HD 112869, C/O

 12.6. The isotopic lines of C2 and CN are too week to be detected in the crowded spectrum, and the lower limit of isotopic ratio was found to be extremely high,

 1500. A large isotopic ratio is not typical of CEMP stars. However, for low-mass AGB stars the CN processing is not expected after the second dredge-up and a total amount of

 dredged-up during the AGB phase leads to a high [C/N] ratio and a high

 ratio observed for HD 112869. On the contrary, intermediate-mass AGB stars with a hot bottom burning should have low both [C/N] and

 ratios.


AGN-driven outflows. Another possible effect of the AGN activity on the molecular gas is through outflows. This possibility is supported by observations of individual objects: For example, Carniani et al. (2017), Brusa et al. (2018) and Loiacono et al. (2019) find low gas fractions in powerful AGN at cosmic noon hosting high-velocity molecular and ionized outflows (but see also Herrera-Camus et al. 2019). AGN feedback in action in these targets could be depleting the molecular gas reservoir (Brusa et al. 2015). Förster Schreiber et al. (2019), studying outflows in a large sample of 0.6  z  2.7 galaxies through integral field spectroscopy of the Hα emission line, find that incidence, strength, and velocity of AGN-driven winds are strongly correlated with the stellar mass. In particular, they find that high-velocity (∼1000–2000 km s−1) AGN-driven outflows are commonly detected at masses above log(M*/M⊙) = 10.7, and present in up to 75% of the population for log(M*/M⊙) > 11.2. Interestingly, above this stellar-mass threshold we find a significant CO luminosity deficit in our AGN sample with respect to inactive galaxies (Fig. 3, bottom). Moreover, our AGN show on average gas fractions 0.57 dex (by using uniform assumptions, Sect. 4) lower than inactive galaxies at the 2.2σ level. Quantitatively, this translates into Mgas, mol/M* ≈ 0.3 for AGN (0.16 if we use r31 = 0.92; Kirkpatrick et al. 2019) and ≈1 in inactive galaxies. This representative value for our AGN is in line but not as low as previous work targeting extremely powerful sources (e.g., Mgas, mol/M*  0.05 in Brusa et al. 2018). Our team is performing a systematic investigation of ionized gas outflows with SINFONI as part of the SUPER survey, and 11 targets of our ALMA sample have complementary good quality SINFONI data (Kakkad et al. 2020; Perna et al., in prep.). For some of them we measured [O III] line widths larger than 600 km s−1, interpreted as a clear signature of the presence of an AGN-driven outflow in these objects (Kakkad et al. 2020). A detailed comparison between outflow and CO properties for these targets will be presented in a future work. Distinguishing among the scenarios described above is challenging with the current dataset. AGN feedback could proceed in different ways and different mechanisms likely overlap in shaping the properties of the molecular gas reservoir. For example, AGN radiation could both heat and/or dissociate CO molecules. In this case, AGN would produce a feedback mechanism that does not require outflows but would potentially work toward inhibiting further star formation. As for AGN-driven outflows, they could impact the gas content by ejecting material out of the galaxy (e.g., Travascio et al. 2020), or they could produce CO heating or dissociation due to shocks. Additionally, numerical simulations predict that AGN-driven outflows may heat via shocks a significant quantity of the gas in the ISM, reaching the high temperatures required for the excitation of high-J CO transitions (Costa et al. 2018). To reach a deeper understanding of the impact of AGN on the molecular gas reservoir, also on longer timescales, predictions from simulations providing the spatial scales and effects of AGN activity on CO properties as a function of cosmic time are needed.


Critical luminosity (Lcrit) is the luminosity above which a state transition from subcritical to supercritical takes place. The subcritical state (LX Lcrit) is known to be the low luminosity state whereas the supercritical state is high luminosity state (LX > Lcrit) (Becker et al. 2012). The critical luminosity is crucial to determine whether the radiation pressure of the emitting plasma is capable of decelerating the accretion flow (Basko & Sunyaev 1976; Becker et al. 2012). The luminosity during the 2020 giant outburst reached a record high, which was significantly higher than the critical luminosity (Reig & Nespoli 2013). The source entered a supercritical regime from a subcritical regime during the outburst. In the supercritical regime, radiation pressure is high enough to stop the accreting matter at a distance above the neutron star, forming a radiation-dominated shock (Basko & Sunyaev 1976; Becker et al. 2012). For the subcritical regime, accreted material reaches the neutron star surface through nuclear collisions with atmospheric protons or through Coulomb collision with thermal electrons (Harding 1994). These accretion regimes can also be probed by noting changes in the cyclotron line energies, pulse profiles, and changes in the spectral shape (Parmar, White, & Stella 1989; Reig & Nespoli 2013). During the transition from the subcritical to the supercritical regime, sources show two different branches in their hardness–intensity diagram (HID) which are known as horizontal branch (HB) and diagonal branch (DB) (Reig & Nespoli 2013). The HB implies the low-luminosity state of the source, which is represented by spectral changes and high X-ray variability. The DB corresponds to the high-luminosity state that appears when the X-ray luminosity is above the critical limit. The classification HB and DB depends on HID patterns that the source follows. The HB pattern is generally observed in the subcritical regime and the DB pattern is observed in the supercritical regime (Reig & Nespoli 2013).


The physical conditions within giant molecular clouds (GMCs) establish the initial conditions for star formation, thus understanding the factors that determine molecular cloud properties is of major interest. A correlation between the size and line width, of the form σv ∝ Rα with α ≈ 0.5, has long been noted in samples of nearby molecular clouds (Larson 1981; Solomon et al. 1987, hereafter S87). This correlation, hereafter referred to as the R–σv relation, is usually interpreted as the result of turbulent motions in the interstellar medium on all scales (Mac Low & Klessen 2004; Falgarone et al. 2009). It closely resembles the turbulent cascade with a power-law slope falling between the Kolmogorov (1941) and Burgers (1939) values for incompressible and highly supersonic turbulence, respectively (see also Falgarone et al. 1994; Brunt & Heyer 2002; Federrath 2013; Kritsuk et al. 2013). At the same time, a study of 13CO emission in the Boston University–FCRAO Galactic Ring Survey (GRS) by Heyer et al. (2009) showed that the normalization of the relation,

, exhibits a linear correlation with the mass surface density, Σ = M/πR2, across more than an order of magnitude in Σ. The data are consistent with a state of virial balance between gravity and turbulent motions, except that the observed normalization, v0, is about a factor of 2 too large. Subsequent work by Field et al. (2011) has suggested that the larger than expected v0 may result from external pressure confinement, although to a lesser extent than has been inferred for clouds in the outer Galaxy (Heyer et al. 2001) or near the Galactic Center (Oka et al. 2001; Shetty et al. 2012). On the other hand, Ballesteros-Paredes et al. (2011) have interpreted the Heyer et al. (2009) result in terms of gravitational collapse near freefall, which differs from the virial equilibrium prediction by a factor of

 in v0 and is thus roughly consistent with the GRS data. A third possibility is that errors in the measured or inferred cloud properties create the appearance of excess kinetic energy when in fact clouds are close to being virialized.


Figures 8 and 9 show the effects of solar activity on the CR parallel λ∥ (blue line), perpendicular λ⊥ (red line), and radial mean free path λrr (gray line) for a proton with rigidity 445 MV (corresponding to a 100 MeV proton) for the inwardly and outwardly directed IMF, respectively. As described in Zank et al. (1998), the parallel mean free path (mfp) based on standard QLT and assuming magnetostatic turbulence is approximated by
13

where

,

, and

. RL is the particle Larmor radius, P is the particle rigidity, and B0 is the mean magnetic field strength. The analytic form of the perpendicular mfp based on NLGC theory is given by (Zank et al. 2004; Shalchi et al. 2010)
14

where a2 = 1/3 is a factor related to the gyrocenter velocity.

 is a constant such that ν = 5/6 yields a Kolmogorov (1941) spectrum. Note that Equation (14) was derived under the assumption of a specific form of 2D wave spectrum, which is a constant at large turbulence scales. It means that the 2D turbulence spectrum is independent of wavenumber in the energy range in Equation (14). Observation of magnetic fluctuations in the SW indicates that omnidirectional power spectra approach a k−1 wavenumber dependence and that low-frequency turbulence exhibits some sunspot cycle variability (Bieber et al. 1991). Based on this, Engelbrecht & Burger (2015) derived the perpendicular mfp by specifying the energy range spectral index of 2D turbulence power spectra as −1. A more general form of the 2D power spectrum with an energy range spectral index q was proposed by Shalchi et al. (2010). They show that the spectral index has a strong influence on the perpendicular diffusion coefficient. In their model, negative values of q correspond to a decreasing spectrum in the energy range, q = 0 corresponds to the constant spectrum we use here, and positive values of q correspond to an increasing spectrum. Matthaeus et al. (2007) presented a similar spectrum in different regimes: energy range, inertial range, and intermediate regime where the spectrum is proportional to k−1 to coincide with observations (Bieber et al. 1991; Goldstein & Roberts 1999). However, Shalchi (2013) argues that a spectrum that behaves like k−1 does not provide a different perpendicular diffusion coefficient (see also Shalchi et al. 2010), since the field lines for such length scales behave superdiffusively as in the inertial range (Shalchi & Kourakis 2007). In view of this uncertainty, we do not take into account a more elaborate spectrum in the present paper. The behavior of the 2D wave spectrum in the energy range, which may also be correlated with the sunspot cycle, is an important factor in deriving the CR perpendicular mfp. A general form (e.g., Shalchi et al. 2010; Shalchi 2013) should be employed in future studies of CR diffusion.


In this section, we consider the plasma properties under the propagation of strong waves. In strong waves, the motion of electrons in the plasma becomes relativistic. However, different from free electrons that have a relativistic drift velocity in the direction of the incident electromagnetic wave (see Section 3.1), in plasma the space-charge potential is important in preventing the drift of electrons (Waltz & Manley 1978). For nonrelativistic electrons in plasma, if the wave duration τ is much larger than c/ωp, where

 is the plasma frequency, the drift velocity would be close to zero (Waltz & Manley 1978; Sprangle et al. 1990b). In this case, electrons in plasma under a strong wave would have a typical Lorentz factor (

) similar to that (γ) in the laboratory frame, so that

 is satisfied. Due to the relativistic and magnetic force effects, the propagation and dispersion properties of an electromagnetic wave depend on its amplitude. For a circular polarized wave, the dispersion relation in the laboratory frame is given by (e.g., Gibbon 2005; Macchi 2013; Macchi et al. 2013; see the Appendix)
11

The dispersion relation of strong electromagnetic waves is altered due to the effective electron mass increased by the relativistic effect (e.g., Sarachik & Schappert 1970; Gibbon 2005; Macchi 2013). One can define the effective plasma frequency as
12

so that the wave can propagate in the region where

. With respect to the nonrelativistic linear case, this is known as relativistically self-induced transparency. We note that since the dispersion depends on the electromagnetic field amplitude in the nonlinear case, the dispersion relation must be taken with care. The propagation of a pulse will be affected by the complicated effects of nonlinear propagation and dispersion, and finally the spatial and temporal shape of the pulse itself would also be modified. In particular, for linear polarization, the relativistic factor γ is not a constant (see Section 3.1). The propagation of the linearly polarized wave with a relativistic amplitude would lead to generation of the higher-order harmonics. Sprangle et al. (1990b) proved that the propagation of the first harmonic component, i.e., of the “main” wave, is still reasonably described by Equation (11) with

. Thus, we will directly adopt Equation (11) in the following discussion.


Each pulsar system in this analysis was observed with XMM-Newton (Jansen et al. 2001), using the European Photon Imaging Camera (EPIC) with the pn detector in full frame mode with thin filters (the data from the MOS and RGS detectors had insufficient counts for analysis). PSR J0337 was observed on 2013 August 1 (observation number 0722920101) for 16.2 ks. An X-ray source was detected 16 away from the radio position of Ransom et al. (2014), consistent with the 2″ astrometric precision of XMM;12

12
See xmm.vilspa.esa.es/docs/documents/CAL-TN-0018.pdf.
 we show an image of the detection in Figure 1. We measured 164 ± 13 background-subtracted counts between 0.2 and 2.0 keV, as determined using calc_data_sum in Sherpa (Freeman et al. 2001; Doe et al. 2007) and uncertainty given by a Poisson distribution.13

13
Note that our count-rate for PSR J0337 is below the 2σ upper limit from Prinz & Becker (2015), who analyzed the same data set. Nonetheless, we are confident in our detection (Figure 1) and do not know the reason for the discrepancy.
 The chance coincidence probability, given the number of sources in the field with similar or higher count rates, is approximately 8 × 10−5. PSR J0636 was observed on 2013 October 13 (observation number 0722920201) for 15.0 ks, and we found an X-ray source within 03 of the radio position of Stovall et al. (2014); see Figure 1. The chance coincidence probability for PSR J0636 is also approximately 8 × 10−5. We measured 170 ± 13 counts between 0.2 and 2.0 keV. Finally, PSR J0645 was observed on 2014 March 29 (observation number 0722920301) for 34.9 ks, but removing a flare from the data reduced the effective observation length to 23 ks. No source was found by the XMM pipeline near the radio position of Stovall et al. (2014, see Figure 1), and we measured only 18 ± 9 source counts between 0.2 and 2.0 keV. The time resolution of 73.4 ms was too coarse to detect pulsations at the rotational periods of the pulsars (2.73, 2.87, and 8.85 ms; Ransom et al. 2014; Stovall et al. 2014), but the observed flux can guide future searches for pulsed X-rays. We reprocessed the data using SAS v13.0.1, specifically epchain. Using HEAsoft v6.14 and CIAO v4.6, and some custom scripts, we extracted the source counts from within a radius of 25″, and background counts from an annular region with radii of 50″ and 125″, restricted to the same CCD chip with other sources removed. We limited the data to events with PATTERN ≤ 4 (singles and doubles), but also experimented with using PATTERN ≤ 12 (singles, doubles, and triples). We found that the change in the results when including triple events was negligible. Because of the high background rate at low energies and the expected softness of the source spectra, we limited our analysis to energies between 0.2 and 2.0 keV. We grouped the counts such that each energy bin had at least 15 events in it and subtracted the background from the source.


Finally, it is worth noting that two-body relaxation and tidal interactions affect the IMF in different ways. The former causes mass segregation with higher-mass stars moving inward and lower-mass stars outward, which enables the lower-mass stars to evaporate from the cluster (see also, e.g., Chandrasekhar 1942; Spitzer 1969; Binney & Tremaine 2008). The cluster then forms a dense core of high-mass stars and once it starts to collapse, binaries form in the centre. These perturb their neighbours, and we begin to observe massive stars escaping from the mass segregated core (see also Hills 1975; Hut 1985). On the other hand, if the relaxation timescales are long, the cluster does not segregate as quickly and the tidal harassment is the dominant reason for mass-loss. Stars are peeled-off from the outer regions independent of their masses. Consequently, the relative contributions of these two processes determine the mass distribution of the escapers. This is shown in Fig. 5, where the mass distribution of escaping stars divided by the original IMF in models R07_Sal13 and R07_Sal13_Nb. When the environment is present, the tidal shocks enhance fraction of escaping stars at intermediate masses. Instead, the loss of massive stars, similar in the two models, can be linked to the relaxation process ongoing in the core that is composed almost exclusively of massive stars and binaries at later times. In our model, the percentage of mass loss is small so this does not significantly affect the mass function of the remaining members. However, the same process happens in protoclusters still embedded in the parent cloud. Their gas density is orders of magnitude higher than our n = 10 cm−3, and structures are closer to the cluster (Kruijssen et al. 2012; Kruijssen 2012). At the same time, the IMF of massive protoclusters is much wider, since massive stars are still on the main sequence, so that the evolutionary timescale is also reduced (Allison et al. 2009; Yu et al. 2011). In the end, the effects we described could indeed play a crucial role when inferring the IMF of young clusters.


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.


3D General Circulation Models (GCMs) with simplified thermal forcing are one possible intermediate step between 3D GCMs with full coupling between radiation and dynamics like those used by Showman et al. (2009) and Amundsen et al. (2016), and shallow water models, i.e. atmosphere models with one atmosphere layer comprising vertically averaged flow (Showman, Cho & Menou 2010). Fully coupled GCMs have the highest accuracy in stellar radiation and flow coupling and thus the highest predictive power. They are, however, computationally much more expensive and their complexity makes it more difficult to test underlying modelling assumptions compared to GCMs with simplified thermal forcing. The latter are thus better suited to run simulations for various scenarios, to understand large-scale flow and circulation properties in 3D climate models under different conditions (Liu & Showman 2013; Mayne et al. 2014; Tsai et al. 2014; Carone et al. 2015, 2016; Komacek & Showman 2016; Hammond & Pierrehumbert 2017; Mayne et al. 2017). Such models have been proven to be very useful: superrotation in hot Jupiters was first inferred by Showman & Guillot (2002) in a 3D GCM with Newtonian cooling. Recently, Showman, Tan & Zhang (2019) used Newtonian cooling to establish a clean, simple environment to diagnose flow dynamics in brown dwarfs, Jupiter, and Saturn-like planets. Shallow water models present an even simpler model framework and represent 3D flow patterns in an atmosphere depth-dependent (2D) formalism (Showman & Polvani 2010, 2011; Penn & Vallis 2017). There are other useful radiative forcing parametrizations such as those using the dual-band radiative scheme, which can also explore a large parameter space and basic assumptions (see e.g. the model used by Komacek et al. 2017). Generally, a hierarchy of models with various levels of complexity has proven to be extremely beneficial to understand complex flow patterns in full 3D climate simulations. Here, we establish a clean, simple environment to understand possible dynamical feedback between the lower boundary and observational flow via Newtonian cooling.


The short-plateau SNe 2006Y, 2006ai, and 2016egz most likely come from partially stripped massive progenitors,36

36
The lack of nebular spectra for SNe 2006Y and 2006ai remains a caveat.
 but a remaining question is their exact formation channel. If it is single-star evolution as assumed in this work, the main theoretical uncertainties are RSG wind mass-loss rates and stellar rotation (e.g., Hirschi et al. 2004; Georgy 2012; Chieffi & Limongi 2013; Meynet et al. 2015; Renzo et al. 2017). We assume no rotation and tweak the wind efficiency by hand, but it is debatable whether such high mass-loss rates are physically plausible. Observationally, there is indeed a wide range of measured RSG wind mass-loss rates (e.g., de Jager et al. 1988; van Loon et al. 2005; Mauron & Josselin 2011; Goldman et al. 2017; Beasor et al. 2020). In addition, recent observational and theoretical studies on RSGs and SNe II indicate that RSG wind mass-loss rates may be independent from metallicity (Goldman et al. 2017; Chun et al. 2018; Gutiérrez et al. 2018). Thus, it could be possible that the short-plateau SNe 2006Y, 2006ai, and 2016egz originate from single-star evolution. However, it is unlikely the case if RSG mass-loss rates are metallicity dependent (as in the main-sequence O/B stars; e.g., Vink et al. 2000, 2001; Mokiem et al. 2007), given the estimated subsolar host metallicities (Table 2). In such a case, interacting binary evolution is more plausible, as Eldridge et al. (2017, 2018) indeed show some interacting binary products also result in short-plateau SNe. It is also important to note that any mass-loss models need to reproduce the observed populations of not only SNe II but also RSGs. For example, Neugent et al. (2020) recently show that the luminosity function of RSGs can be used to constrain their mass-loss rates. Future statistical studies with both RSG and SN II populations at various metallicities are required to distinguish the formation channels of short-plateau SNe.


We have developed the simplest spherical void lens model based on the recently developed embedded lens theory. We have assumed a uniform mass profile for the void, compensated by a thin bounding shell. The infinitesimally thin bounding shell was chosen for convenience (Maeda & Sato 1983a, 1983b). To investigate other void profiles such as a non-uniform void interior or a finite-thin bounding ridge (Colberg et al. 2005; Lavaux & Wandelt 2012; Pan et al. 2012; Sutter et al. 2012; Hamaus et al. 2014; Kantowski et al. 2015) is straightforward; one has only to evaluate the Fermat potential of Equation (1) or equivalently the potential part of the time delay of Equation (4). It is also possible to build embedded void lens models with non-spherically symmetric density profiles given that the lowest-order embedded lens theory is applicable to any distributed lens (Kantowski et al. 2013). It is well accepted by the lensing community that small overdensities attract light, whereas small underdensities repel light. This fact can be rigorously proved using general relativistic perturbation theory (Sachs & Wolfe 1967) assuming

. However, the repulsive nature of lensing by a large and deep underdense region (i.e., cosmic voids) as described by the rigorously derived but simply implemented embedded lens formalism did not appear until Kantowski et al. (2013). In the case of large density contrasts, i.e.,

 approaching its lower bound −1 for cosmic voids, the repulsive lens equation follows naturally from the embedded lensing theory. This theory is based on Swiss cheese models (Einstein & Straus 1945), which are exact solutions of Einstein’s field equations containing inhomogeneities with large density contrasts (Chen et al. 2010, 2011, 2015; Kantowski et al. 2010, 2012, 2013). The void-lensing community takes void repulsive lensing as granted (e.g., Amendola et al. 1999; Das & Spergel 2009), whereas the galaxy/cluster strong-lensing community has ignored embedding effects, i.e., the repulsive lensing caused by the large underdense regions surrounding the central overdense lens. Besides correctly predicting repulsive lensing by cosmic voids, our Fermat potential formulation can be used to compute the void-lensing time delay effects, including the ISW effect caused by voids; see Equation (5).


As mentioned above, the magnetic reconnection is introduced as breaking and reconfiguration of the oppositely directed magnetic field lines in highly conducting plasma. The magnetic field lines collapse near the X-point and form an extended magnetic singularities known as a current sheet. There are two mechanism of the current-sheet formation. The first kind of current-sheet formation is associated with the MHD instabilities (e.g., resistive tearing mode and ideal kink mode) known as spontaneous magnetic reconnection (e.g., White 1984; Baty 2000; Vekstein 2017). The second kind of current sheet can be formed in the MHD stable configuration, where some external perturbations trigger the forced magnetic reconnection (Hahm & Kulsrud 1985). The forced magnetic reconnection may be activated by nonlinear MHD waves, which may be caused by explosive solar activities (e.g., Sakai et al. 1984; Dewar et al. 2013; Beidler et al. 2017). The forced magnetic reconnection may be developed due to boundary perturbations, which induce a surface current in such a way that it opposes the progress of the reconnection (Ishizawa & Tokuda 2000, 2001; Fitzpatrick 2003). The multimode simulation approach has been adopted to investigate the thinning of the current sheet induced by forced magnetic reconnection (Birn et al. 2005). The motion of the photospheric footpoints of the coronal magnetic field may also trigger the forced magnetic reconnection, which may be caused by the explosive solar coronal events (e.g., Vekstein & Jain 1998; Jain et al. 2005; Vekstein 2017). Although there is a remarkable development in the theory of the forced magnetic reconnection, Jess et al. (2010) have suggested that there is no observational evidence of explosive flare or coronal activities triggered by forced magnetic reconnection. They have observed a microflare activity driven by forced magnetic reconnection. The lower solar atmosphere (photosphere & chromosphere) is dominated by cool, partially ionized and collision dominated plasma. Most of the energy releases during the forced magnetic reconnection may be consumed by such plasma systems (e.g., Litvinenko 1999; Chen et al. 2001; Chen & Ding 2006; Litvinenko et al. 2007).


The SFR reported in Table C.1 refers to a stellar mass range from Mlow = 0.1M⊙ to Mup = 100M⊙, is averaged over the past Δt = 100 Myr, and was calculated using the standard SFR(LIR) relationship from Kennicutt (1998; here scaled to a Chabrier 2003, IMF) (1)\begin{equation} \label{eq:sfr} \textit{SFR}=10^{-10}\times L_{\rm IR}[{L}_{\sun}]\, {M}_{\sun}~{\rm yr}^{-1}. \end{equation}SFR=10-10×LIR[L⊙] M⊙yr-1.This calibration relies on the starburst synthesis models of Leitherer & Heckman (1995), and it is based on the assumption of solar metallicity, and an optically thick (τdust ≫ 1) starburst region, in which case LIR is a good proxy of the system’s bolometric luminosity (LIR ≃ Lbol), and hence a sound, calorimetric probe of the obscured, current stellar birth rate. A possible caveat is that the contribution to the dust heating by more evolved stellar populations (the cirrus component; e.g. Helou 1986; Lonsdale Persson & Helou 1987; Walterbos & Greenawalt 1996) is not taken into account. If the cirrus ISM component heated by the more general galactic UV radiation field contributes to LIR, then the Kennicutt (1998) relationship overestimates the SFR. Another issue is the fact that some percentage of the UV photons can escape the starburst region without being absorbed, and hence are not reprocessed into IR photons (indeed, some of our SMGs are visible in the rest-frame UV images; Miettinen et al. 2017b). The MAGPHYS code also gives the SFR as an output, and contrary to the aforementioned LIR diagnostic, the model permits for the heating of the dust by older and longer-lasting stellar populations. We found that the SFR(LIR) is somewhat higher on average than SFRMAGPHYS: the SFR(LIR) /SFRMAGPHYS ratio was found to range from 0.47 to 6.92 with a median of \hbox{$1.31^{+0.83}_{-0.17}$}1.31-0.17+0.83, where the ± errors represent the 16th–84th percentile range (see the corresponding panel in Fig. 2). If, instead of Δt = 100 Myr, the aforementioned comparison is done by using the SFRMAGPHYS values averaged over the past Δt = 10 Myr, the median SFR(LIR) /SFRMAGPHYS ratio is found to be \hbox{$1.15^{+0.38}_{-0.27}$}1.15-0.27+0.38, which is consistent with the results obtained by da Cunha et al. (2015). Unless otherwise stated, in our subsequent analysis we use the SFR averaged over the past 100 Myr as calculated using Eq. (1).


On the other hand, a clear physical interpretation of the observed pulse broadening phenomenon requires a good understanding of the interstellar electron density structure. A power-law model of electron density fluctuations is commonly adopted in theoretical constructions on radio wave propagation (Lee & Jokipii 1976; Rickett 1977, 1990) and is compatible with observational indications (e.g., Armstrong et al. 1995). Recent advances in understanding the properties of magnetohydrodynamic (MHD) turbulence (Goldreich & Sridhar 1995; Lithwick & Goldreich 2001; Cho & Lazarian 2002, 2003) stimulate a renewed investigation on density statistics (Beresnyak et al. 2005; Kowal et al. 2007; Lazarian et al. 2008; Burkhart et al. 2009, 2010, 2015; Collins et al. 2012; Federrath & Klessen 2012), which provide important insight into key physical processes such as star formation in the turbulent and magnetized ISM (see reviews by, e.g., McKee & Ostriker 2007; Lazarian et al. 2015). The density spectrum in compressible astrophysical fluids was systematically studied in Kowal et al. (2007) by carrying out an extensive set of MHD numerical simulations with varying compressibility and magnetization. Instead of a single Kolmogorov slope with a power-law index of

, significant variations in the spectral slope of density fluctuations are present. For supersonic turbulence, their results are consistent with earlier findings in both magnetized (Beresnyak et al. 2005) and nonmagnetized (Kim & Ryu 2005) fluids. It shows that the density power spectrum becomes shallower as the sonic Mach number (

) increases, where VL is the turbulent velocity at the outer scale of turbulence and cs is the sound speed in the medium, and there is a significant excess of density structures at small scales in highly supersonic turbulence. This behavior is naturally expected as the gas is compressed in shocks by supersonic flows and the interacting shocks produce local density enhancements (Mac Low & Klessen 2004; Padoan et al. 2004b).


In the supersonic part of WR outflows, the presence of instabilities and inhomogeneities should be taken into account. Invoking density inhomogeneities, or “clumping”, in stellar models has an influence on the mean opacity, due to the enhanced density in clumps (Moffat et al. 1988; Hamann & Koesterke 1998). However, a porous structure could also imply lowered mean opacity, counteracting the effect of small-scale clumping (Shaviv 1998; Oskinova et al. 2007). Assuming that the material near the Fe-opacity peak is clumped, Gräfener et al. (2012) were able to extend the surface radii of their hydrostatic helium star models, in practical terms, by significantly enhancing the iron bump opacity (see also Appendix A). The surface temperatures of such hydrostatic, strongly inflated models computed with plane parallel grey atmospheres are then compared with the fictitious effective temperatures at τ = 20 of the atmosphere calculations performed by Hamann et al. (2006). This effective temperature at τ = 20 should not be confused with the actual blanketed temperature at the base of WNE wind models, which is about a factor of 2 larger (see e.g. Appendix D). As we show in Sect. 4, strongly inflated hydrodynamic solutions imply supersonic flows already at the base of the inflated envelopes for the typical mass-loss rates of WNE stars (cf. the plane parallel atmosphere model in Fig. 4). Moreover, it would be inconsistent to think that the iron opacity bump is simultaneously responsible for both the inflation of the envelope and the acceleration of the flow. While the detailed effects of clumping and porosity remain a subject for future research, we concentrated in this work on the homogeneous case as those instabilities are expected to initiate above the sonic point (Sundqvist et al. 2013; Owocki 2015). If this is not the case and clumping is already present at the relatively high densities and optical depth of the sonic point of massive helium star models, it might affect to some extent the local opacity.


As a first step, we need to specify the photoelectron sheath features. In this course, we first evaluate the steady state potential over the lunar surface (equation 4), and then after, we use this as a boundary condition to solve the Poisson equation (equation 2) and estimate the photoelectron sheath profile. In calculations, Lyman α (λ ∼ 121.57 nm, 10.29 eV, Λ ∼ 3 × 1011 cm–2 s–1) spike of solar photon radiation (Bauer 1973) is considered as the dominant source for the generation of photoelectrons from the lunar surface. The work function of the regolith material is taken from Grobman & Blank (1969), where it is suggested to vary in the range ϕr ∼ (4–6) V for the region across the subsolar point and limb. Moreover, Draine’s formulation is accounted to determine the lunar surface’s photoelectric efficiency (Draine 1978; Draine & Salpeter 1979) – its spectral dependence can be represented as ${\chi _{\nu r}} = {\chi _o}[1 - ({\phi _r}/{E_\nu })]$. For instance, for the Lyman α radiation χνr = 0.042 for optimum efficiency χo = 0.1 (Sickafoose et al. 2001) and ϕr = 6 V (Grobman & Blank 1969). Another significant parameter is the surface temperature which describes the electron population within the lattice available for the photoemission. Lunar Reconnaissance Orbiter based measurements (Williams et al. 2017) suggest that the surface temperature may vary from the equator (∼400 K) to the terminator (poles, ∼150 K). In order to take this account, we use the latitude (θ) dependent empirical relation ${T_\theta } = {T_0}[1 - (5/4\pi )\theta ]$; for instance, at θ = 70°, and To ≈ 205 K. These three parameters, viz., ϕr, To, χν, and Λ drive the photoemission current from the lunar regolith. The nominal solar wind plasma parameters are considered for calculating collection current over lunar regolith; the constituents are considered as40-41nes ≈ nis = 8.7 cm–3 and Tes ≈ Tis = 1.4 × 105 K (Mann et al. 2011; Kureshi et al. 2020). These solar radiation and wind plasma parameters might vary widely during active solar events and alter surface charging and sheath features. Popel et al. (2018) suggest the dust number density may also vary in a wide range depending on lunar altitude and particle size; for instance, nd ∼ 800 cm–3 for the particles of size 100 nm ≤ ao ≤ 200 nm and θ = 77°. Note that the secondary electron emission (Seitz 1940; Misra, Mishra & Sodha 2013) from the lunar regolith (and floating dust) is ignored, as it minimally contributes to the charging of sunlit surfaces (Mishra & Bhardwaj 2020). These parameters, along with equation (4), yield steady state potential over the sunlit locations. This estimate of the surface potential is used as a boundary condition (i.e. at l = 0, υ = υo) alongwith υ’ = υ = 0 as $l \to \infty $ to solve the Poisson equation (equation 2) numerically – using this framework, the sheath structure is derived in terms of electric potential (υ), electric field (Es), and photoelectron population density (npe).


1E 1841–045, located at the center of supernova remnant (SNR) Kes 73 (Vasisht & Gotthelf 1997), is another steady X-ray emitter. The source was monitored with NuSTAR between 2013 September 5 and 21, during which time six bursts were detected (An et al. 2015). In order to eliminate the contamination from the SNR, an annulus region with inner and outer radii of 60″ and 100″ around the source position was selected for background spectral extraction, as was also done in An et al. (2013). We searched for soft X-ray data from 2013 August 1 to October 30, and identified 11 Swift XRT observations, 10 executed in WT mode and 1 short observation in Photon Counting (PC) mode. Note that in WT mode, 10 rows are compressed into a single row, only the central 200 columns are read, and only 1D imaging is preserved. Consequently, it is impossible to resolve the SNR contribution and three SNR related emission lines (Mg, Si, and S) clearly appear in the stacked spectrum of 10 WT data. Since the source emission has been stable for more than 15 years (Dib & Kaspi 2014), we performed the joint fit with the longest, burst-free NuSTAR observations (ObsID = 30001025012) and XMM-Newton observations that were performed ∼11 years earlier. For the XMM-Newton observation, since the MOS1/MOS2 data were performed in the full frame mode and were seriously affected by pile up, we only use the pn data in the following spectral fitting. The joint spectra are fit by our model (STEMS3D+PL) and a 2% systematic error is added to the XMM-Newton data to account for calibration uncertainties. The fit results yielded that 1E 1841–045 has the lowest twist angle (Δϕ ∼ 0.83) and the highest electron velocities in the magnetosphere (β ∼ 0.28) among the four sources studied here. The resulting photon index of the PL component (Γ ∼ 1.23) is consistent with the value reported based on INTEGRAL data (Kuiper et al. 2006). However, due to the short exposure of the XMM-Newton data, in addition to the high interstellar absorption, the parameter values have large uncertainties (see Table 2 and Figure 2). Note that 1E 1841–045 is the only source whose non-thermal component (FP ∼ 5.1 × 10−11 erg s−1 cm−2) dominates the STEMS3D component (FS ∼ 3.6 × 10−11 erg s−1 cm−2) in the range of 1–79 keV.


For the first time, we detected [C ii] 158-μm emission from a GRB host galaxy at z > 2. This is the second detection of [C ii] 158-μm emission among known GRB host galaxies, following GRB 980425 (Michałowski et al. 2016). The [C ii] 158-μm fine structure line is the dominant cooling line of the cool interstellar medium, arising from photodissociation regions (PDR) on molecular cloud surfaces. It is one of the brightest emission lines from star-forming galaxies from FIR to metre wavelengths, almost unaffected by dust extinction. [C ii] 158-μm luminosity, L[C II], has been discussed as an indicator of SFR (e.g. Stacey et al. 2010). If L[C II] scales linearly with SFR, the ratio to FIR luminosity, L[C II]/LFIR, is expected to be constant, since LFIR is a linear function of SFR (e.g. Kennicutt 1998a). However, LC II/LFIR is not constant, but declines with increasing LFIR, known as the ‘[C ii] deficit’ (e.g. Luhman et al. 1998, 2003; Malhotra et al. 2001; Sargsyan et al. 2012; Díaz-Santos et al. 2013, 2017; Spilker et al. 2016). The [C ii] deficit persists when including high-z galaxies (e.g. Stacey et al. 2010; Wang et al. 2013; Rawle et al. 2014). In Fig. 5, we compare the [C ii] deficit in the GRB 080207 host and other star-forming galaxies. Two GRB hosts are shown by stars: GRB 080207 (orange star) and 980425 (blue star). The comparison sample is compiled from the literature up to z ∼ 3 (Malhotra et al. 2001; Cormier et al. 2010, 2014; Ivison et al. 2010; Stacey et al. 2010; Sargsyan et al. 2012; Farrah et al. 2013; Magdis et al. 2014; Brisbin et al. 2015; Gullberg et al. 2015; Schaerer et al. 2015). Active galactic nuclei are separated from star-forming galaxies based on either (i) the explicit description in the literature or (ii) EWPAH 6.2μm  0.1 (Sargsyan et al. 2012). As reported by previous studies (e.g. Maiolino et al. 2009; Stacey et al. 2010), high-z galaxies are located at a different place from local galaxies in the L[C II]/LFIR–LFIR plane.


Despite the considerable scatter in both colors and color gradients (Peletier & Balcells 1996; Taylor et al. 2005; Roediger et al. 2011a), the tight correlation between color and stellar mass of the host galaxies holds true in both the region identified as intermediate and outer in Sect. 7. ETGs form a tight red sequence (see Fig. 10) for both regions and show an average inside-out gradient of ~0.1 mag (Fig. 12, bottom). LTGs form instead two different distributions: the blue cloud of the intermediate (or bulge/bar) region becomes red (i.e., it reaches the red sequences) above 1010 M⊙ while the outer, disk-dominated region never overlaps completely the red sequence. Still, more massive disks are redder than their lower mass counterparts but the difference between the colors of the outer and the intermediate region increases with respect to the total stellar mass. This can be possibly induced by the growth of a red and dead structure in the center of massive disks, i.e. that the central part of galaxies underwent a star formation quenching process that turned them red. Our results on the average properties of color profiles broadly agree with literature data. For example MacArthur et al. (2004) have shown that the radial profile of the average ages of the stellar populations decreases from inside out and that the steepness of the decrease is a function of morphological type. Color templates shown in Fig. 9 exhibit a radial behavior fully consistent with the average age profiles shown by MacArthur et al. (2004). We find there is also a good agreement with the (g−H) color profiles published in Roediger et al. (2011a) for almost all the morphological types, although in their median profiles of early disks they find positive color gradients (and consistently positive age population gradients in their stellar population analysis, Roediger et al. 2011b) that we do not see. Roediger et al. (2011b) do not find any direct link between galaxy morphologies and the observed stellar population gradients. On the contrary, studies such as Cheung et al. (2013) and Gavazzi et al. (2015) have shown that the bar occupation fraction rises steeply above 109.5 M⊙ (as also confirmed by the works done by  Skibba et al. 2012; Masters et al. 2012) and that, above this mass,galaxies are progressively more quenched (red) in their centers, while their disks still sustain SF and hence are blue. These studies therefore highlight that the presence of structures such as bars can indeed produce the color gradients that we observe and likely also the stellar population gradients. These authors thus conclude that a secular bar drives the quenching of the star formation in the central kiloparsecs of galaxies. Moreover massive galaxies undergo bar instability earlier than their lower mass counterparts and thus have more time to grow redder than low mass systems. Moreover, Méndez-Abreu et al. (2012) on a study of the Virgo bar fraction have shown that this rises up to more than 50% above 1010 M⊙, adding a further link between color/stellar populations radial gradients that we observe and structures such as bars (Laurikainen et al. 2010). We stress, however, that disk instabilities can also rejuvinate the central stellar population by, e.g., triggering central star formation in correspondence of the ILRs of spirals or bars (an example could be the one of VCC 508 in Fig. 3a).


Although the origin and evolution of linear-scale clustering is well described by the concordance model (Spergel et al. 2007), gravitational clustering of matter on smaller scales (galaxy clusters and groups) belongs to a non-linear regime of structure formation. This regime is more difficult to understand and to simulate because its evolution must include the role of baryons, which are driven by complex physics. Clusters of galaxies that are the most massive gravitationally bounded structures have been widely used over the past years to probe the cosmic evolution of the large-scale structures in the Universe (Voit 2005; Allen et al. 2011). In the standard model of structure formation driven by gravitation alone, clusters form a self-similar population that is only characterized by their mass and redshift. Including baryon physics introduces some distortions in the scaling relations between the mass and other physical quantities such as temperature, X-ray, or optical luminosity (Kaiser 1986; Giodini et al. 2013). Most recent research works have focused on the relationship between the dominant dark matter and the baryonic matter that forms gas and stars (Lin et al. 2003; Giodini et al. 2009). Both the mass-to-light (M/L) ratio of structures and the halo occupation number (HON, or the number of satellite galaxies per halo) correspond to observables that are easy to compare to predictions from numerical simulations (Cooray & Sheth 2002; Tinker et al. 2005). They are both representative of the way stellar formation occurred in the early stages of halo formation (Marinoni & Hudson 2002; Borgani & Kravtsov 2011). Recent progress on numerical simulations (Murante et al. 2007; Conroy et al. 2007; Aghanim et al. 2009) has also stressed the role of hierarchical building of structures in enriching the intra-cluster medium (ICM) with stars in a consistent way with the observed amount of ICM globular clusters and ICM light. This ICM light, although hardly detectable, can be considered as the extension of the diffuse envelope often seen in the central galaxy in rich clusters of galaxies. It is an important component, although not the only one, that explains the formation of the brightest cluster galaxies (BCG) in the centre of clusters of galaxies (Dubinski 1998; Presotto et al. 2014).


Regardless of their exact composition, particles suspended in these exoplanet environments likely undergo repeated particle–particle collisions in response to atmospheric circulation. Such dynamics have been inferred to drive efficient triboelectrification (e.g., Helling et al. 2013), resulting in electrified cloudy or hazy environments at elevation. As happens within Earth’s clouds, exoplanet clouds are likely gravitationally stratified, meaning that smaller, lighter grains become concentrated at the top of the clouds, while larger, heavier grains remain at lower elevation (see Figures 2 and 8 in Helling et al. 2008; also Helling & Fomins 2013; Helling et al. 2016). Because, as discussed above, the polarity of charge collected by particles from triboelectric processes depends on grain size, this stratification (smaller particles at elevation; larger particles on the bottom) has the ability to set up coherent electric fields. Such charge separation occurs in both thunderstorms and volcanic plumes and ultimately drives spark discharges–lightning–either through conventional breakdown of the gas or via runaway electron avalanche (Kikuchi & Endoh 1982; Gurevich et al. 1992; James et al. 1998; Dwyer 2005; Cimarelli et al. 2014; Dwyer & Uman 2014; Aizawa et al. 2016). On Earth, these discharges support a global electric circuit and have the ability to modulate chemical and physical reactions in the atmosphere (Price 1993; Rakov & Uman 2007; Siingh et al. 2007; Genareau et al. 2015; Wadsworth et al. 2017; Mueller et al. 2018). Indeed, lightning may have been involved in the production of prebiotic molecules in an early-Earth environment (Miller & Urey 1959; Navarro-González et al. 1998) and such lightning has been hypothesized to have been associated within dusty flows (namely, volcanic plumes) rather than hydrometeor clouds (Navarro-González et al. 1998; Segura & Navarro-González 2005; Johnson et al. 2008). If the mineral clouds inferred to exist on extrasolar worlds can be considered analogs to the dusty environments in our own solar systems, charging within these systems may also stimulate a wide array of electrostatic phenomena and help catalyze prebiotic chemistry (Hodosán et al. 2016).


With the real-time pipeline, we also frequently detect eclipsing binaries, due to their significant changes in brightness. Often, when we trigger these sources, PV light curves reveal potentially eclipsing behaviour. In these cases, we can attempt to verify the nature of the variable source by creating Lomb-Scargle periodograms for the light curves38 and inspecting, by eye, the folded light curves that we create using the best periods found. We note that this is done independently of the rest of pipeline; it is not part of the automatic software. An example of an eclipsing binary we found using TUVOpipe is shown in Fig. 32. The strong variability (by over 1 optical magnitude) led us to create a long-term light curve; the PV light curves of all the used UVOT filters are shown in Fig. 33. The source is a known source that appears in many sky survey catalogues, including Gaia, where its G-band magnitude is listed as 14.1 and its inferred temperature is ~5000 K (see Andrae et al. 2018 for how the listed temperature we extract from the Gaia catalogue is inferred from the Gaia data). This G-band magnitude is brighter than the U-UV bands seen in the UVOT light curve, indicating (along with the temperature) that it is a relatively red source. The source is also present in the ATLAS catalogue of variable stars Heinze et al. (2018), where it is denoted as AT J098.1962+05.6837. The ATLAS catalogue gives a period of 1.985 days. However, no classification of the source was so far known, so the cause of the found periodicity is not clear. Our method gave a best period of 1.9899 days, so we used this period to fold the UVOT U-band light curve, which is shown in Fig. 34. The light curve clearly reveals an eclipse in which the source becomes dimmer by around 1.5 magnitudes, and the shape of the light curve confirms it as an eclipsing binary. There may also be additional very weak minima seen halfway between the deep eclipses (see around phase −0.5 and 0.5 in the plot shown). The fact that any potential secondary minima are very weak may suggest that this is an Algol-type system (these are known as EA binaries; see Carmo et al. 2020 for a review of these systems and example light curves; the inferred Gaia temperature is also consistent with this being an EA system).


With improved resolution, in this work we have resolved corrugated swept-up shells as well as small blobs of mixed material in the wind region that were not seen in Paper I. The swept-up shells are much smoother in the simulations including poloidal field, which is related to the stabilization of shear instability by the magnetic field. To check how an even higher resolution can affect the results, we have run simulations for case b2 at a resolution of 3200 × 990. In the upper panel of Figure 9 we present the density map at t = 1000 year for the run without ambient poloidal field. A close comparison to its ordinary resolution counterpart (see the upper left panel of Figure 5) shows that the details of the mixing structures are quite different in the two runs. More complex and fragmented mixing structures are generated in the higher resolution simulation, which indicates that the process producing these structures is not completely resolved at the current resolution (see, e.g., Frank et al. 1996). Despite the different fine structures, the overall outflow shape and the jet structure in the two simulations are in good agreement. In the lower panel of Figure 9 we present the same maps for the run with ambient poloidal field. The smoother and thicker shell seen here is almost identical to its ordinary resolution counterpart (see the lower left panel of Figure 5), and similar feather-like structures are also present near the wind boundary. There is also no sign of intense stochastic behavior like that seen in the upper panel of Figure 9. This suggests that the stabilization of the wind-ambient interface by the poloidal field is quite robust, and this conclusion holds well at least for the resolution we have used. Finally, it should be noted that the wind in the current simulations fans out in all radial directions even at the equator where an accreting inner envelope or disk is instead expected. Whether this setup could have anything to do with the growth of stochastic mixing structures near the inner toroid will need to be resolved in future simulations with more realistic setup of boundary conditions.


Star-forming galaxies at redshifts z ∼ 1–3 probe the cosmic epoch when most of the stellar mass assembly in the universe took place (Madau & Dickinson 2014, and references therein). A better understanding of star formation (SF) during this epoch is therefore imperative to understand SF across cosmic time. Locally, less than 5% of the galaxy population has a star formation rate (SFR) that is significantly higher than the empirical main sequence for star-forming galaxies, i.e., the tight correlation (∼0.3 dex) between the SFR and stellar mass, M⋆ (Brinchmann et al. 2004; Elbaz et al. 2007, 2011; Noeske et al. 2007; Goto et al. 2011; Rodighiero et al. 2011; Sargent et al. 2012; Whitaker et al. 2012, 2014; Salmon et al. 2015). These often-called starburst galaxies, with an IR luminosity LIR ∼ (0.1–5) × 1012 L⊙ (e.g., Sanders & Mirabel 1996; Downes & Solomon 1998), become increasingly more common at high z. In fact, (sub)millimeter number counts reveal that galaxies with LIR > 1012–13 L⊙, at z > 0.5, are many hundreds of times more likely to exist than in the local universe (Blain et al. 2002; Chapman et al. 2005; Berta et al. 2011; Magnelli et al. 2011; Béthermin et al. 2012; Magnelli et al. 2013; Casey et al. 2013, 2014; Geach et al. 2013; Simpson et al. 2014; Strandet et al. 2016; Brisbin et al. 2017). Meanwhile, the cosmic molecular gas density also peaks at z ∼ 1–3 (Decarli et al. 2014, 2016a, 2016b, 2019; Walter et al. 2014; Lentati et al. 2015; Pavesi et al. 2018; Liu et al. 2019; Riechers et al. 2019). This suggests a strong link between molecular gas and SF. Rest-frame far-IR (FIR) measurements of spectral lines and thermal dust continuum emission have been used to investigate the cooling and heating processes of the interstellar medium (ISM) in star-forming galaxies; however, the physical conditions at high z are still, in general, poorly investigated (Popesso et al. 2012; Bothwell et al. 2013; Carilli & Walter 2013; Genzel et al. 2013; Yang et al. 2017; Tacconi et al. 2018, 2020; Aravena et al. 2020; Birkin et al. 2020; Boogaard et al. 2020; Lenkić et al. 2020).


We analyze the 10 BBH mergers reported by LIGO and Virgo in their O1 and O2 observing runs (Abbott et al. 2019a; LIGO Scientific Collaboration & Virgo Collaboration 2019). Before discussing results, it is useful to review expectations from the literature for the spin distributions resulting from different formation scenarios. Isolated binary evolution is predicted to yield black holes with spins preferentially aligned with their orbit. Although spin misalignments may be introduced by natal supernova kicks, episodes of mass transfer and tidal torques serve to realign component spins before the formation of the final black hole binary (Rodriguez et al. 2016; Zevin et al. 2017; Gerosa et al. 2018; Qin et al. 2018; Zaldarriaga et al. 2018; Bavera et al. 2020). The black holes’ spin magnitudes in this scenario are much more uncertain. Recent work indicates that angular momentum is efficiently transported away from stellar cores, leaving black holes with natal spins as low as a ∼ 10−2 (Qin et al. 2018; Fuller & Ma 2019). While tides on the progenitor of the second-born black hole can spin up the progenitor star (Zaldarriaga et al. 2018), this effect can be counteracted by mass loss in stellar winds, and more detailed simulations find only low or moderate spin increases due to tides (Qin et al. 2018; Bavera et al. 2020). Meanwhile, dynamically formed systems in dense stellar clusters have no a priori preferred axis, and so are likely to have random spin configurations (Rodriguez et al. 2016, 2018, 2019; Doctor et al. 2020). Once again, however, the expected spin magnitudes are largely unknown, subject to the same uncertainties mentioned above regarding natal black hole spins. One firm prediction of the dynamical scenario concerns the spins of second-generation binaries, whose components were themselves formed from previous mergers. Regardless of their component spins, black hole mergers generally yield remnants with a ∼ 0.7; thus the effective spin of two such second-generation binaries may be large (Fishbach et al. 2017; Gerosa & Berti 2017; Rodriguez et al. 2018, 2019; Doctor et al. 2020).


Various types of AGNs are known and one among them are the narrow-line Seyfert 1 (NLSy1) galaxies, which are classified based on the presence of narrow Hβ emission line with full width at half-maximum (FWHM) 2000 km s−1 and weak [O iii] emission line, with F([O iii])/F(Hβ) 3 (Osterbrock & Pogge 1985; Goodrich 1989). They are believed to be powered by low-mass black holes (${\sim } 10^7 \, \mathrm{M}_{\odot }$) having higher accretion rate and generally showing strong Fe ii emission compared to their broad line counterparts namely the broad-line Seyfert 1 (BLSy1) galaxies (Xu et al. 2012; Rakshit et al. 2017a). However, from spectro-polarimetric observations of a γ-ray emitting NLSy1 galaxy, PKS 2004 − 447 (Baldi et al. 2016) and accretion disc modelling of a sample of 23 radio-detected NLSy1 galaxies (Calderone et al. 2013) indicate that they have masses similar to the blazar class of AGNs. Other characteristics that make NLSy1 galaxies different from the BLSy1 galaxies are their rapid soft X-ray variability (Pounds, Done & Osborne 1995; Leighly 1999a), steep soft X-ray spectra (Boller, Brandt & Fink 1996; Wang, Brinkmann & Bergeron 1996; Leighly 1999b) and low amplitude optical variability (Grupe 2004; Rakshit & Stalin 2017). Also, the fraction of NLSy1 galaxies detected in radio is much lower (${\sim } 7{{\ \rm per\ cent}}$) compared to the fraction of radio detected BLSy1 galaxies (Komossa et al. 2006; Rakshit et al. 2017a). Among radio-loud NLSy1 galaxies, about a dozen (∼2 per cent) have been detected in γ-ray by the Fermi-Large Area Telescope (e.g. Abdo et al. 2009; D’Ammando et al. 2015; Paliya et al. 2018) suggesting the unambiguous presence of relativistic jets in them. Multiband broad-band SED modelling of these γ-ray detected NLSy1 galaxies indicate that these sources have many properties similar to the blazar class of AGNs (Paliya et al. 2013b) and specifically resembling the flat spectrum radio quasar (FSRQ) category (Paliya et al. 2018). In the radio, these γ-ray emitting NLSy1 galaxies have a compact core jet morphology, high brightness temperature, show superluminal motion and significant radio variability (Doi et al. 2006; Komossa et al. 2006). Detailed investigations of the population of NLSy1 galaxies need to be undertaken to understand more about their peculiar characteristics.


Being a benchmark system H + H2, H + HD, and their isotopic counterparts have received much attention over the last several decades (Marinero et al. 1984; Zhang & Miller 1989; D’Mello et al. 1991; Harich et al. 2002; Gao et al. 2015; Yuan et al. 2018a, b, 2020). Most early experimental and theoretical investigations were centered around benchmarking theory against experiments and providing improved descriptions of the H3 potential energy surfaces (PES; Boothroyd et al. 1996; Mielke, Garrett & Peterson 2002; Yuan et al. 2018a, b). Among the available PESs for the H3 system, the one by Boothroyd et al. (1996) referred to as the BKMP2 PES and by Mielke et al. (2002) referred to as the CCI PES, nearly equally well account for most experimental data for H + H2, H + HD, and D + HD collisions. These PESs have also been able to account for even subtle effects such as the GP (Kendrick et al. 2015; Hazra et al. 2016; Croft et al. 2017; Kendrick 2018, 2019). The GP effect, while not significant at temperatures relevant to astrophysics, is important below 1 K as illustrated in a series of calculations on H + HD (v, j) collisions for vibrational levels v = 4 − 9 (Kendrick et al. 2015; Hazra et al. 2016; Croft et al. 2017; Kendrick 2018, 2019). Though several prior studies of Flower and co-workers  (Flower 1999, 2000; Flower & Roueff 1999; Wrathmall et al. 2007) have reported rate coefficients for H + HD collisions, due to the approximations involved in the scattering calculations (e.g. neglect of hydrogen atom-exchange), the reliability of the available rate coefficients has been a source of debate (Desrousseaux et al. 2018). Recently, Desrousseaux et al. (2018) reported rate coefficients for pure rotational transitions for j ≤ 10 within the v = 0 vibrational level using accurate quantum calculations that include the exchange channel. In this paper, we report rate coefficients for state-to-state rovibrational transitions in HD induced by H atoms between and within the v = 0 and 1 vibrational levels and for temperatures ranging from T = 1–1000 K.


ΓCR can be expressed as the product of three factors – the total cosmic ray ionization rate per H nucleus ζH (including both primary and secondary ionizations), the average energy deposited into the medium per ionization ΔQ, and nH. Both ζH and ΔQ are rather uncertain and can vary considerably over different Galactic environments. Typical values of ζH in dense gas are ∼1–5 × 10−17 s−1 (Dalgarno 2006), but there is evidence from H3+ observations that ζH is considerably higher in the diffuse gas under consideration here (Dalgarno 2006; Indriolo & McCall 2012). Indriolo & McCall (2012) find a mean ζH of 1.8 × 10−16 s−1 in their sample of diffuse molecular sight lines, and values as large as ∼1 × 10−15 s−1 have been reported in the literature (Snow & McCall 2006; Shaw et al. 2008). In this paper, we adopt the value 1.8 × 10−16 s−1. For ΔQ, we use 10 eV, as estimated for diffuse molecular gas from table 6 of Glassgold, Galli & Padovani (2012), although it is important to note that this value can vary by several eV depending on the precise physical and chemical conditions in the cloud. Combining these factors, the cosmic ray heating rate is

(11)

\begin{eqnarray}
\Gamma _{\rm {CR}} &=& \zeta \Delta Q n_{\rm {H}} \nonumber \\
&\approx& 1.9 \times 10^{-25} \left( \frac{n_{\rm {H}}}{30 \hspace{3.0pt} \rm {cm}^{-3}} \right) \hspace{3.0pt} \rm {ergs} \hspace{3.0pt} \rm {cm}^{-3} \hspace{3.0pt} \rm {s}^{-1}.
\end{eqnarray}

For ΓPE, we adopt the expression:

(12)

\begin{equation}
\Gamma _{\rm {PE}} = 1.3 \times 10^{-24} \hspace{3.0pt} n_{\rm {H}} \epsilon G_0 \hspace{3.0pt} \rm {ergs} \hspace{3.0pt} \rm {cm}^{-3} \hspace{3.0pt} \rm {s}^{-1}
\end{equation}

from Wolfire et al. (2003), where G0 is the intensity of FUV light in units of the Habing (1968) field and ϵ is the heating efficiency factor given by equation 20 of Wolfire et al. (2003). For nH = 30 cm−3, T = 100 K, an electron fraction of 1.6 × 10−4, and a FUV field of G0 = 1.1 (Mathis, Mezger & Panagia 1983), ϵ evaluates to 1.8 × 10−2, yielding

(13)

\begin{equation}
\Gamma _{\rm {PE}} = 7.6 \times 10^{-25} \left( \frac{n_{\rm {H}}}{30 \hspace{3.0pt} \rm {cm}^{-3}} \right) \hspace{3.0pt} \rm {ergs} \hspace{3.0pt} \rm {cm}^{-3} \hspace{3.0pt} \rm {s}^{-1}.
\end{equation}


The trends between the LF slope α and the aforementioned parameters, with the addition of the morphological T type, are shown in Fig. 4 together with their Spearman correlation coefficient (ρ) and their p value, indicating the probability that the two sets of data are uncorrelated. We summarize the properties for which we look for a correlation in Table 4. We define a correlation to be negligible when |ρ|=[0 − 0.2], weak when |ρ|=[0.2 − 0.4], moderate when |ρ|=[0.4 − 0.6], strong when |ρ|=[0.6 − 0.8], and very strong when |ρ|=[0.8 − 1]; using the p value to evaluate the probability that, despite showing a correlation, two variables may be uncorrelated. It should be noted that only a handful of studies so far have looked at the correlation between α and global galaxy properties: Kennicutt et al. (1989), Elmegreen & Salzer (1999), Youngblood & Hunter (1999), van Zee (2000), and Thilker et al. (2002) investigated nebular LFs as in this paper, while Liu et al. (2013) identified H II regions via Paα, and Cook et al. (2016) studied the GALEX far-ultraviolet (FUV) LFs of H II regions. While the sample of Cook et al. (2016) includes a few hundred galaxies, the other studies are based on samples ranging from 10 to 35 galaxies, similar to our study. In this section and in Sect. 6.1, we compare our results to those studies that, as in our case, applied a uniform analysis methodology on galaxy samples. It should be noted that using different tracers means probing different source ages and, as reported by Oey & Clarke (1998), older H II regions tend to have steeper LF slopes, mainly due to the short main-sequence lifetimes of the more massive stars constituting the brighter H II regions. This is the reason why, for example, FUV observations, probing H II regions with ages less than 100 Myr, are expected to deliver a steeper LF compared to Hα observations, typically probing H II regions younger than 10 Myr, and our comparison remains qualitative.


A growing body of work suggests that planet formation is strongly dependent on the birth environment of the host star. Stars preferentially form in groups (Lada & Lada 2003), and in sufficiently dense environments the evolution of a PPD can be significantly influenced by neighbours (de Juan Ovelar et al. 2012). Close star–disc encounters are one such environmental influence on PPDs that can result in enhanced accretion and hasten disc depletion (Clarke & Pringle 1993; Ostriker 1994; Pfalzner et al. 2005; Olczak, Pfalzner & Spurzem 2006; Bate 2018; Winter et al. 2018a; Cuello et al. 2019). However, the stellar number densities required for tidal truncation are high, and in practice few observed regions satisfy this condition (Winter et al. 2018b, 2019a). The influence of tidal truncation is therefore limited to stellar multiples, either in bound systems (Dai et al. 2015; Kurtovic et al. 2018) or during the decay of higher order multiplicity (Winter, Booth & Clarke 2018c). Since stellar multiplicity does not appear to be strongly dependent on environment (see Duchêne & Kraus 2013, for a review), this suggests that encounters are not an environmental influence, but may set disc initial conditions during the early phases of cluster evolution (Bate 2018). Discs can also be externally depleted via thermal winds driven by far-ultraviolet (FUV) and extreme ultraviolet (EUV) photons from neighbouring massive stars (Johnstone, Fabian & Taylor 1998; Störzer & Hollenbach 1999; Adams et al. 2004; Facchini, Clarke & Bisbas 2016; Haworth et al. 2018; Haworth & Clarke 2019). This process of external photoevaporation dominates over dynamical encounters in observed environments, and can deplete PPDs rapidly for many stars that are born in massive and dense clustered environments (Scally & Clarke 2001; Winter et al. 2018b). Many stars in the solar neighbourhood are born in regions where UV fields are sufficient to significantly shorten disc lifetimes (Fatuzzo & Adams 2008; Winter et al. 2018b), and the fraction of stars born in such environments may be much greater outside of this region, dependent on galactic environment (Winter et al. 2019a). From an observational perspective, Guarcello et al. (2016) report disc survival fractions that decrease with increasing FUV flux in Cygnus OB2 (see also Winter, Clarke & Rosotti 2019b), and Ansdell et al. 2017 find a correlation between the dust mass in PPDs and separation from σ Ori. However, Richert et al. (2015) find no correlation of disc fraction with distance from OB stars. Reconciling these contradictory findings may require appealing to the inefficiency of external photoevaporation at small radii within the disc, dynamical and projection effects, or the stellar age gradient apparent in many star forming regions (Getman et al. 2018).


Since long cosmologists have felt motivated to look for alternative explanations for the DE beyond a rigid cosmological constant Λ. The scalar field paradigm was then profusely used also to make the cosmic vacuum dynamical: Λ = Λ(ϕ). In the old days, the main aim was to adjust the large value of Λ typically predicted in QFT to be zero. There were many early proposals (see e.g. Endo & Fukui 1977, 1982; Fujii 1982; Dolgov 1983; Abbott 1985; Zee 1985; Barr 1987; Ford 1987; Peccei, Solà & Wetterich 1987; Weiss 1987; Barr & Hochberg 1988). In spite of the hopes raised by these works at solving the ‘old CC Problem’, it was later shown in Weinberg (1989) through the so-called no-go theorem that most if not all the dynamical adjustment mechanisms existing in the literature to date were plagued by more or less obvious forms of subtly hidden fine tuning. For this reason, the subsequent use of scalar fields in cosmology was mostly focused on trying to explain another aspect of the CCP: the cosmic coincidence problem (viz. the fact that $\rho _\Lambda$ happens to be so close to the matter density ρm right now; see e.g. Peebles & Ratra 2003). The new wave of dynamical scalar fields in cosmology crystalized in the notions of quintessence, phantom fields and the like, which have had a tremendous influence in cosmology till our days (see e.g. Peebles & Ratra 1988; Ratra & Peebles 1988; Wetterich 1988; Wetterich 1995; Caldwell, Dave & Steinhardt 1998; Zlatev, Wang & Steinhardt 1999; Amendola 2000; Caldwell, Kamionkowski & Weinberg 2003), the reviews (Sahni & Starobinsky 2000; Padmanabhan 2003; Peebles & Ratra 2003; Copeland, Sami & Tsujikawa 2006), and the many references therein. At the same time a blooming crest of models based on ascribing a direct phenomenological time-dependence to the CC term, Λ = Λ(t), broke with impetus into the market. For an account of some of the old attempts, see Overduin & Cooperstock (1998, and references therein).


Horizon scale imaging promises to test basic predictions of GR and improves our understanding of the physics responsible for accretion and emission in a strong gravitational field. In particular, imaging a black hole shadow has been a long-standing goal of black hole astronomy. However, imaging the black hole shadow feature in Sgr A* has been inherently challenged by two known effects. First, the scattering by interstellar medium blurs the strong GR features near the black hole. In a recent work, it has been shown that this effect can be mitigated based on the fact that the scattering is well understood over the relative range of baseline lengths provided by the EHT (Fish et al. 2014). Second, while the predicted shadow feature is nearly independent of the spin or orientation of the black hole to within 10% (Bardeen 1973; Takahashi 2004), the emission region surrounding the black hole depends on the details of the underlying accretion process and is intrinsically time variable primarily due to the stochastic nature of magnetorotational-instability-driven turbulence and magnetic reconnection in the accretion flow. Magnetorotational instability (MRI, Balbus & Hawley 1991, 1998) is believed to be the leading mechanism driving turbulence in accretion disks and develops on orbital timescales. The timescale for the Keplerian motion at the innermost stable circular orbit around the black hole in Sgr A* ranges from 30 minutes for a non-rotating black hole to 4 minutes for prograde orbits around a maximally rotating black hole (Doeleman et al. 2009b). These timescales are much less than the typical duration of a Very Long Baseline Interferometry (VLBI) experiment, which violates one of the basic requirements for VLBI Earth-rotation aperture synthesis imaging. In contrast, the corresponding timescales in the nearby giant elliptical galaxy M87, which has the second largest apparent event horizon, are much larger (a minimal timescale of a few days).


The main goal of this paper was to further expand the recent transport theory of Zank etÂ al. (2014) and thus, by default, earlier attempts by Drake etÂ al. (2006, 2013) and Bian & Kontar (2013). In our approach, similar to Zank etÂ al. (2014), the focus was on inertial-scale flux ropes that were modeled as quasi-2D magnetic islands superposed transversely on a strong large-scale magnetic field imbedded in the large-scale plasma flow, as suggested by the 3D MHD turbulence simulations with a strong guide field of Dmitruk etÂ al. (2004). We adopt a different perspective in proceeding from the basic guiding center kinetic equation (e.g., Kulsrud 1983) instead of the transformed Vlasov equation (Skilling 1975) used by Zank etÂ al. (2014). This offers the advantage of explicitly identifying drift acceleration for various guiding center drift mechanisms and the betatron acceleration that energetic particles would be subject to in both the large-scale plasma flow and magnetic field, and in the inertial-scale plasma flow and magnetic fields of contracting and merging flux ropes. Our approach allows us to distinguish between particle drift and betatron energization when magnetic flux ropes behave in an incompressible fashion (later stage contraction or during merging) or when they are compressible (early stage contraction and during island collisions). The transformation of the guiding center kinetic equation for nearly gyrotropic particle distributions into a focused transport equation clarifies the role of drift and betatron acceleration in focused transport. In the process, a more general focused transport formalism of particle transport and momentum change in contracting and merging flux ropes was derived, whereas Zank etÂ al. (2014) followed a more targeted focused transport approach based on specific conservation laws (magnetic moment conservation, conservation of parallel action, and conservation of magnetic flux) that are thought to apply to the above-mentioned three acceleration mechanisms (see also Drake etÂ al. 2006, 2013).


An EM counterpart is not strictly necessary to use compact binary mergers such as BBHs and BNSs as standard sirens. By matching the sky localization region of GW sources – which can be inferred from the GW measurements – with galaxy catalogues, one might in fact be able to extract complementary information on the redshift of the sources, without the need of spotting an EM counterpart. The idea was originally proposed by Schutz (1986) and it has subsequently been used and developed in different analyses (Holz & Hughes 2005; MacLeod & Hogan 2008; Petiteau, Babak & Sesana 2011; Del Pozzo 2012; Chen et al. 2018; Gray et al. 2020). It has already been tested with real data collected by the LIGO and Virgo detectors (Fishbach et al. 2019; Soares-Santos et al. 2019; Palmese et al. 2020; Abbott et al. 2020d; Finke et al. 2021), though the constraints obtained so far with this ‘statistical’ method are not competitive with the ones derived from GW170817 and its EM counterpart, mainly because of the poor spatial resolution of the current network of ground-based interferometers. Future observations, taken with an enlarged network of ground-based GW detectors, will allow for better cosmological measurements (Chen et al. 2018), mainly thanks to the improved sky localization accuracy. Other complementary methods, which analogously do not require the identification of an EM counterpart, might yield interesting results as well (Taylor & Gair 2012; Oguri 2016; Del Pozzo, Li & Messenger 2017; Mukherjee & Wandelt 2018; Farr et al. 2019; Mukherjee et al. 2020a; Mukherjee, Wandelt & Silk 2020b, c, d; Ezquiaga & Holz 2021). The era of precise cosmological measurements with GWs will however start only with next-generation interferometers, such as the Einstein Telescope (ET) (Punturo et al. 2010; Sathyaprakash, Schutz & Van Den Broeck 2010; Belgacem et al. 2019a; Maggiore et al. 2020) and the Cosmic Explorer (Abbott et al. 2017a; Reitze et al. 2019a, b) on the Earth, or TianQin (Mei et al. 2020), Taiji (Luo et al. 2020), and the Laser Interferometer Space Antenna (LISA) (Amaro-Seoane et al. 2017) in space. The latter instrument is the focus of the present investigation. In what follows, we will briefly introduce LISA and review previous studies of LISA’s capability to do cosmological analyses using standard sirens. More details on how to extract cosmology from GWs by statistically matching with galaxy catalogues will be given in Section 2.


Driven by the influx of spatially resolved observations coming from integral field units (IFU), more recent investigations have focused on attempting to infer structural, dynamical, and/or chemical properties for localized regions of galaxies, by decomposing them into physically motivated components. In fact, this concept pre-dates the large-scale use of IFU with works dealing with, for instance, photometric disc/bulge decompositions of surface brightness profiles (e.g. see Kent 1985; Cinzano & van der Marel 1993; Scorza & Bender 1995; Moriondo, Giovanardi & Hunt 1998; Krajnović et al. 2013), including using multiple filters (Dimauro et al. 2018). Aside from surface brightness, radial profiles of other parameters have also been subject to analogous decompositions. For instance, the decomposition of gas (usually H i) circular velocity profiles into contributions from different galaxy sub-components is a well-established practise (as in van Albada et al. 1985; Carignan, Sancisi & van Albada 1988; Battaglia et al. 2006; Noordermeer et al. 2007; Swaters et al. 2012; Aniyan et al. 2016, 2018; Sofue 2017), whilst decompositions of mass profiles have attempted to infer the contributions from dark matter (DM) and baryons (stars and globular clusters, gas, et cetera; Annunziatella et al. 2017; Poci, Cappellari & McDermid 2017; Bellstedt et al. 2018). These concepts have been extended to two dimensions, including multiband photometric disc/bulge decompositions of images, rather than profiles (for instance, see Scorza et al. 1998; de Souza, Gadotti & dos Anjos 2004; Norris, Sharples & Kuntschner 2006; Simard et al. 2011; Méndez-Abreu et al. 2017; Dalla Bontà et al. 2018). Moreover, there have been recent efforts to conduct the decomposition directly on an observed spectrum (Johnston et al. 2012; Coccato et al. 2015; Tabor et al. 2017; Coccato et al. 2018), to similarly determine the contributions to various spectral features coming from ‘distinct’ galaxy sub-components. This type of component-based approach attempts to isolate the distinct contributions to observed galaxies from regions that may or may not have had different origins and/or formation paths; however, they have thus far dealt with the problem from only one perspective – dynamics or stellar populations.