With the results from Gaia and the large number of stars collected from dedicated surveys, a plethora of Galactic mass estimates have recently been made using using different methods and data samples. We summarize these most recent results in Fig. 8. Grouping together the works applying a distribution function method (Callingham et al. 2019; Eadie & Jurić 2019; Posti & Helmi 2019; Vasiliev 2019; Li et al. 2020; Deason et al. 2021; Hattori et al. 2021; Correa Magnus & Vasiliev 2022; Shen et al. 2022; Slizewski et al. 2022; Wang et al. 2022) the weighted mean mass estimate is ∼0.93 ± 0.047 × 1012 M⊙. The methods using high velocity stars with full 6D phase-space information have been used to estimate the mass of the Milky Way (Monari et al. 2018; Deason et al. 2019; Grand et al. 2019; Koppelman & Helmi 2021; Necib & Lin 2022) have a weighted mean mass of ∼0.93 ± 0.099 × 1012 M⊙. Two recent works using either the Sagittarius or Magellanic Steams (Craig et al. 2021; Vasiliev et al. 2021) give a weighted mean mass of ∼0.98 ± 0.15 × 1012 M⊙. The lightest mass measurements have come from rotation curve based methods (de Salas et al. 2019; Eilers et al. 2019; Ablimit et al. 2020; Cautun et al. 2020; Karukes et al. 2020; Jiao et al. 2021) with a weighted mean of ∼0.76 ± 0.023 × 1012 M⊙. The works which use 6D satellite phenomenology compared to Milky Way-type simulations (Patel et al. 2018; Villanueva-Domingo et al. 2021) infer a weighted mean Galactic mass of ∼0.97 ± 0.0091 × 1012 M⊙ and Rodriguez Wimberly et al. (2022) find their results are consistent with a Galactic mass in the range of 1–1.2 × 1012 M⊙. Zaritsky et al. (2020) apply the timing argument to distant Milky Way halo stars to derive a lower limit to the Milky Way mass of 0.91 × 1012 M⊙. Within the uncertainty, our BHB mass estimates are in agreement with Zaritsky et al. (2020), although our KG mass estimates and a few of the recent mass estimates which we plot in Fig. 8 are lower than this limit.


Detailed IBEX results also showed that (1) the ∼0.5–6 keV ENA spectral indices in the GDF are ordered in latitude, with those observed near mid- and low latitudes between ±45° being significantly steeper compared with those observed at higher latitudes (Funsten et al. 2009b; McComas et al. 2009b), and (2) the corresponding ENA fluxes exhibit temporal variations on an annual scale that reflect the decreasing output of the SW, which resulted in a general decrease and flattening of the SW dynamic pressure during 2007–2010 (McComas et al. 2012, 2014). Desai et al. (2015, 2016; see also Dayeh et al. 2012) studied the energy dependence and latitudinal ordering of the ∼0.5–6 keV ENA spectral indices γ in the GDF between 2009 and 2013 and showed that the latitudinal (θ) dependence of γ is energy dependent and well represented by the cosine function
1

with different offsets, amplitudes, and phase angles. Desai et al. (2016) further reported that the general decrease in the >1 keV ena fluxes from 2009–2011 to 2012–2013 occurred at all latitudes and that this decrease was not accompanied by corresponding changes in the spectral indices. Indeed, over the first five years of the IBEX mission, the ENA spectral indices in the GDF exhibited a strong and persistent energy-dependent, latitudinal ordering that reflected the solar minimum latitudinal profile of the fast and slow SW speeds in the inner heliosphere (e.g., Funsten et al. 2009b; Dayeh et al. 2011; Livadiotis et al. 2011; Schwadron et al. 2014; Desai et al. 2015, 2016; Zirnstein et al. 2017). Based on the reconstructed latitudinal and temporal profiles of SW parameters from 2011 to 2014 (Sokół et al. 2013, 2015), i.e., during the ascending phase of solar cycle 24 and following the predictions of McComas et al. (2012, 2014), Desai et al. (2016) further suggested that the GDF in 2014–2017 would either stabilize or increase, and that the latitudinal ordering of the corresponding spectral indices would most likely be disrupted.


Several physical processes affect galaxies inside clusters in a simultaneous way. One of these mechanisms is the ram pressure stripping (e.g. Gunn & Gott 1972; Abadi, Moore & Bower 1999; Book & Benson 2010; Steinhauser, Schindler & Springel 2016). This process can remove an important fraction of the cold gas from galaxies, resulting in the inhibition of star formation. Although this mechanism is more effective at the central regions of massive clusters, it has been reported in less massive systems (e.g. Rasmussen, Ponman & Mulchaey 2006; Jaffé et al. 2012; Hess & Wilcots 2013). Ram pressure stripping occurs as galaxies move at high speeds through the hot ionized gas of the intracluster medium, which collides with the cold gas of the galaxies and removes it. The warm gas from the galactic halo can also be removed by the gas of the intracluster medium, a process known as starvation (e.g. Larson, Tinsley & Caldwell 1980; Balogh, Navarro & Morris 2000; McCarthy et al. 2008; Bekki 2009; Bahé et al. 2013; Vijayaraghavan & Ricker 2015). This process can cut-off further gas cooling from the galaxy’s halo gas that fuels future star formation. Kawata & Mulchaey (2008) predicted that starvation can act in galaxy groups as well. Another physical process that works on galaxies in their passage through the deep potential well of the cluster is tidal stripping (e.g. Zwicky 1951; Gnedin 2003a; Villalobos, De Lucia & Murante 2014). It can induce a central star formation burst (Byrd & Valtonen 2001), bar instabilities (Łokas et al. 2016), changes in the pattern of the spiral arms (Semczuk, Łokas & del Pino 2017), and truncate dark matter haloes (e.g. Gao et al. 2004; Limousin et al. 2009). In the outskirts of clusters, mechanisms like galaxy–galaxy interaction, known as harassment, are more effective (e.g. Moore et al. 1996; Moore, Lake & Katz 1998; Gnedin 2003b; Smith et al. 2015). Most of the processes mentioned above tend to decrease or to completely suppress the star formation in galaxies. As a consequence, galaxies in clusters are typically red, early-type, with an old stellar population, and have little or none star formation at all.


Within the framework of the fireball shock model, Pe'er etÂ al. (2007) proposed a method to infer central engine parameters using observed data. With the measured temperature and flux of an identified thermal component in the spectrum, along with a flux ratio between thermal and non-thermal components, one may infer the size of the jet at the base of the outflow, r0, and the dimensionless entropy of the outflow,  (which is also the bulk Lorentz factor of the outflow, if the photosphere radius is greater than the fireball coasting radius). Some authors have applied this method to some Fermi GRBs (Iyyani etÂ al. 2013; Preece etÂ al. 2014; Ghirlanda etÂ al. 2013). The derived central engine parameters are sometimes ad hoc or inconsistent. For instance, the analyses for GRB 110721A (Iyyani etÂ al. 2013) and for GRB 130427A (Preece etÂ al. 2014) led to a curious conclusion that the bulk Lorentz factor of the outflow of different layers are decreasing with time. This would lead to no, or at most very inefficient, internal shock emission. Yet both bursts have dominant non-thermal emission. More curiously, the data of GRB 110721A (Iyyani etÂ al. 2013) require that r0 is rapidly varying with time by 2â3 orders of magnitudes. This is hard to imagine given the well-believed paradigm of the GRB central engine: If the engine is naked, the size of the engine (a hyper-accreting black hole or a millisecond magnetar) is around r0 â¼ 107âcm; if an extended envelope of a collapsar progenitor is considered, the fireball may be âre-born,â with r0 â¼ R*Î¸j â¼ 109R*, 10Î¸j, â1âcm (where R* is the size of the progenitor star, and Î¸j is the jet opening angle). If one considers the depletion of the envelope, r0 should decrease with time. However, Iyyani etÂ al. (2013) showed that r0 increases from 106âcm to 108âcm early on, and then decreases mildly after 2Â s. These absurd conclusions suggest that the starting point of the analysis, i.e., the assumption of a pure fireball model, might not be valid. It is interesting to see whether a hybrid ejecta photosphere model may solve the problem. Incidentally, Ghirlanda etÂ al. (2013) analyzed another burst, GRB 100507, using the fireball framework (Pe'er etÂ al. 2007), but found that the derived r0 remains constant and reasonable. The jet composition of that burst may be more close to a fireball. It would be interesting to see whether a general theoretical framework can be established, which may be reduced to the standard fireball framework when Ï0  1.


Guillochon et al. (2014) suggest that the broad lines seen in TDEs are produced in a BLR structure (analogous to the one seen in AGNs) which lies above and below the forming accretion disk. Furthermore, they comment that if this is true, it would be reasonable to expect that these two astrophysical phenomena (i.e., AGNs and TDEs) should have many similarities in terms of velocity structures, as well as the components of the structure that play a key role in the production of the radiated light and the emergent emission lines. If their prediction is valid, it is not surprising that TDEs show the observed time lags pointed out in this work, as time lags (caused by the response of line luminosities to variations in the continuum) are commonly observed in AGNs. It has been suggested that the line emitting region must be stratified, where Helium is closer to the black hole than Hydrogen (Guillochon et al. 2014; Roth et al. 2016). Regular AGNs are well known to be stratified as well with He II, He I, Hβ and Hα being emitted from closest to furthest from the black hole (e.g., see Clavel et al. 1991; Peterson & Wandel 1999). To test this, we investigated how lagged the Helium lines are compared to Hydrogen (see Sects. 5.1.1 and 5.1.2). We chose He I 5876 Å as this line is more isolated and easier to measure than He II. We find a difference, depending on the spectroscopic type: H TDEs show larger lags in Hα than He I. On the other hand, for N III Bowen TDEs, He I has similar lag values to Hα. The average (lower-limit) lag value for Hα is 40 days for the H TDEs and 12 days for the N III Bowen TDEs (without including ASASSN-15oi because it does not belong in either of these categories as it is a He TDE with weak Balmer lines in some epochs). The average (lower-limit) lag value for He I is 15.48 light days for N III Bowen TDEs. For the H TDEs, only AT2018zr shows a clear lag in He I since for ASASSN-14ae and LSQ12dyw we can only place upper-limits). These results are visualized in Fig. 18 where we plot the time lags against the blackbody radii values at peak for each TDE. The Hα lags (filled symbols) increase with increasing RBB (the dashed line is a fit to Hα and the dot-dashed one is the same without fitting the three lower-limit points). On the other hand, He I (empty symbols) does not show such a correlation and the lags remain small (mostly upper-limits) even for the larger radii. This picture can be understood by a combination of two factors: (i) N III Bowen TDEs have smaller radii than H TDEs (van Velzen et al. 2021; ii) Helium lies deeper in the photosphere than Hydrogen (Roth et al. 2016). The ionization energy of neutral Hydrogen is 13.6 eV while the one of neutral Helium is 24.6 eV hence Helium would need a larger temperature in order to get ionized, hinting that it is indeed lying closer to the black hole than Hydrogen – consistent with a stratified photosphere. We find here, however, that these differences are minimized in the more compact Bowen TDEs. Guillochon et al. (2014) focus their study on PS1-10jh, the only TDE in our sample that shows no Hydrogen at all, but only strong He II. They suggest that the absence of Hydrogen lines indicates that the accretion disk had not yet extended to the distances required to produce the Hydrogen lines. Their calculations imply that He II 4686 Å should be produced at a distance of ∼2.1 light days from the SMBH (see their Fig. 7). Such small lags are beyond the precision that can be attained with the present data, as daily spectroscopic observations would be required.


In Sifón et al. (2013), we used the σ–M200 scaling relation of Evrard et al. (2008) to estimate dynamical masses. As discussed in Section 1, the scaling relation of Evrard et al. (2008) was calibrated from a suite of N-body simulations using DM particles to estimate velocity dispersions. However, the galaxies, from which velocity measurements are made in reality do not sample the same velocity distribution as the DM particles. They feel dynamical friction and some are tidally disrupted, which distorts their velocity distribution and biases their dispersion (e.g. Carlberg 1994; Colín et al. 2000). Recent high-resolution hydrodynamical simulations of ‘zoomed’ cosmological haloes have shown that there is a significant difference between the velocity distributions of DM particles and galaxies themselves; whether galaxies (i.e. overdensities of stars in hydrodynamical simulations) or DM subhaloes are used makes comparatively little difference (Munari et al. 2013). Results from state-of-the art numerical simulations depend on the exact definition of a galaxy and the member selection applied, but the current consensus is that galaxies are biased high (i.e. at a given mass the velocity dispersion of galaxies or subhaloes is larger than that of DM particles) by 5–10 per cent with respect to DM particles (Lau et al. 2010; Munari et al. 2013; Wu et al. 2013), translating into a positive 15–20 per cent bias in dynamical masses when using DM particles. This is illustrated in Fig. 5: DM particles are not significantly impacted by either dynamical friction or baryonic physics; therefore, the scaling relations for DM particles are essentially the same for all simulations. In contrast, DM subhaloes are affected by baryons in such a way that including baryonic feedback (most importantly feedback from active galactic nuclei – AGN, but also from cooling and star formation) makes their velocity dispersions much more similar to those of simulated galaxies. This means we can rely on our analysis of the previous section, based on DM subhaloes, to correct the velocity dispersions measured for ACT clusters, and then estimate dynamical masses using predictions obtained either from galaxies or subhaloes. The difference between the Saro et al. (2013) and Munari et al. (2013) galaxy scaling relations depends on the details of the semi-analytic and hydrodynamical implementations used in Saro et al. (2013) and Munari et al. (2013), respectively. The different cosmologies used in the Millenium simulation (in particular, σ8 = 0.9; Springel et al. 2005) by Saro et al. (2013) and the simulations by (Munari et al. 2013, σ8 = 0.8) may also play a role.


The C/O ratio varies across exoplanets’ host star populations (Delgado Mena et al. 2010; Brewer & Fischer 2016; Brewer et al. 2017), and this variation is likely to be reflected in the composition of exoplanet atmospheres, assuming that they are formed with the same materials as their stars. Moreover, various processes in the protoplanetary disks and the planet formation process can affect the exoplanet compositions and have a significant impact on the final C/O ratio (Öberg et al. 2011; Mordasini et al. 2016; Espinoza et al. 2017; Madhusudhan et al. 2017). For these reasons, it is necessary to consider the effects of the C/O ratio on the atmospheric chemistry and the formation of aerosols. Numerous studies have been performed using chemical models (Madhusudhan 2012; Moses et al. 2013; Venot et al. 2015; Tsai et al. 2017; Heng & Lyons 2016; Goyal et al. 2018; Drummond et al. 2019), but corresponding laboratory experiments are still largely nonexistent. Laboratory investigations can provide essential insight into the effects of the C/O ratio on the atmospheric photochemistry and the formation of aerosols. In a previous work, we performed the first laboratory experiments dedicated to the study of the chemistry in hot Jupiter atmospheres (Fleury et al. 2019). This work focused on the chemistry in atmospheres with T > 1000 K and a C/O ratio of 1 (representing C enhancement compared to the solar value of 0.54), because chemical models predict that the abundances of hydrocarbon and nitrile species increase by several orders of magnitude in these atmospheres compared to atmospheres with a low C/O ratio (Venot et al. 2015). Therefore, they can be considered as better candidates for the formation of complex organic molecules with longer carbon chains. This first study revealed that photochemical aerosols could be produced at temperatures as high as 1500 K and that water could be efficiently formed through photochemical channels. In the present work, we performed new experiments to study the chemistry in hot Jupiter atmospheres at similar temperatures (1173–1473 K) but with lower C/O ratios. We used a gas mixture of H2, H2O, and CO that represents the simplest plausible atmosphere for a hot Jupiter with a C/O ratio  1. This new study, compared with our previous work, allows us to assess the evolution of the chemistry in hot Jupiter atmospheres as a function of the C/O ratio and atmospheric composition.


Also, by studying different ratios we can get information about the masses of the progenitors enriching the ISM at the formation time of our stars. The work by Travaglio et al. (1999) showed that the best progenitors for reproducing the r-process contribution to the enrichment of the Galaxy are SNe II from stars with masses 8–10 M⊙. On the other hand, more massive SNe II of M > 15 M⊙ enriched the ISM with oxygen at earlier times since those massive stars evolve faster. As a consequence we can observe that the ratios of r-process elements with respect to oxygen are negative for low metallicities. In Fig. 14 we show the ratios between Eu-Y-Ba and O using the abundances of the oxygen line at 6158 Å derived for the same sample by Bertran de Lis et al. (2015). Since we do not have very metal-poor stars we cannot observe the behaviour of Y and Ba at very low metallicities, where they are thought to be mainly produced by the r- and not the s-process. We can see how [Eu/O] has a less steep decline towards lower metallicities when compared to Ba and Y. This occurs because Eu is a pure r-process, whereas Y and Ba at [Fe/H] ~ –1 dex are mainly produced by AGB stars, which evolve more slowly than the progenitors of Eu and present an even longer delay with respect to the more massive progenitors of oxygen. At this point it is also interesting to compare our heavy elements with Mg, another α element, using the rederived abundances in this work. In Fig. 15 we can see the same decreasing trends towards lower metallicities for Y and Ba but less steep than when comparing oxygen, while [Eu/Mg] is mostly flat. This might be explained by increasing O/Mg yields for higher mass SNe progenitors (e.g. Woosley & Weaver 1995; McWilliam et al. 2008, and references therein). Thus, the production of oxygen would start earlier in the Galaxy producing higher [O/Mg] at lower [Fe/H]. Moreover, the [Eu/Mg] is mostly flat suggesting that these two elements receive an important contribution from SNe progenitors of similar masses but less massive than oxygen progenitors, as explained above. However, the study of McWilliam et al. (2008) discarded the possibility of increasing O/Mg yields for higher mass SNe progenitors since it would imply a metallicity-dependent initial mass function (IMF), that is, an increase in the fraction of low-mass SNe at higher [Fe/H]. Instead, they proposed that a metallicity-dependent modulation of the SNe O/Mg ratio can perfectly explain the behaviour of this ratio in the disc and in the bulge. In Fig. 15 it is also interesting to see the well-defined separation of thick disc and hαmr stars with respect to the thin disc group for [Y/Mg] and [Ba/Mg].


Since our review paper 36 years ago (Allard & Kielkopf 1982), considerable progress in unified line broadening theory and in computational technology now enables us to calculate neutral atom spectra given the potential energies and radiative transition moments for relevant states of the radiating atom interacting with other atoms in its environment. Although our unified theory has been developed in Allard et al. (1999), and a detailed discussion is presented there, we provide an overview Sect. 2 for its use in this context. Because the underpinning atomic physics is understood, theoretical models may be drastically improved compared to previous work such as Koester & Wolff (2000) and Wolff et al. (2002) by including a more complete representation of the interactions, especially in the region of atomic separations that determine the line wings. Nevertheless, the main limitation remains a lack of precision in theoretical fundamental atomic interaction data suitable for such spectroscopic calculations. In a field where most work focuses on lower precision for use in chemistry and reaction kinetics, it is fortunate that Mg–He and Mg+–He molecular data are now very well studied and have accurate asymptotic energies available. The potentials we use are described in detail in Sect. 3. In Sect. 4.1 we examine the far wings quantitatively for the MgHe and Mg+He lines, which both contribute to the ultraviolet spectra. We present line profiles obtained over the full range of temperatures from 4000 to 12 000 K for helium densities varying from 1021 to 1022 cm−3. In Sect. 4.2 we study the relative contribution of the two resonance lines in their far wings and how they can contribute to the line blanketing. At sufficiently low densities of perturbers, the symmetric center of a spectral line is Lorentzian and can be defined by two line parameters, the width and the shift of the main line. The impact approximation determines the asymptotic behavior of the unified line shape autocorrelation function. The Lorentzian width can be readily extracted, and is presented in Sect. 4.3. Finally, we report the study of WD 2216–657 in Sect. 5.


The CE has been followed by many analytical (Rasio & Shapiro 1991; Iben & Livio 1993; Han, Podsiadlowski & Eggleton 1994; Terman, Taam & Hernquist 1994; Regős & Tout 1995; Armitage & Livio 2000; Sandquist, Taam & Burkert 2000; Papish, Soker & Bukay 2015; MacLeod et al. 2017b), as well as numerical studies (Taam, Bodenheimer & Ostriker 1978; Meyer & Meyer-Hofmeister 1979; Bodenheimer & Taam 1984; Livio & Soker 1988; Rasio & Livio 1996; Sandquist et al. 1998; De Marco et al. 2003; Lombardi et al. 2006; Ricker & Taam 2008; Taam & Ricker 2010; De Marco et al. 2011; Passy et al. 2011, 2012; Ricker & Taam 2012; Nandez, Ivanova & Lombardi 2014; MacLeod & Ramirez-Ruiz 2015a,b; Ivanova & Nandez 2016; Kuruwita, Staff & De Marco 2016; Nandez & Ivanova 2016; Pejcha, Metzger & Tomida 2016; Staff et al. 2016; Ohlmann et al. 2016a,b; Hillel, Schreier & Soker 2017; Iaconi et al. 2017; Murguia-Berthier et al. 2017; Ohlmann et al. 2017; MacLeod et al. 2017a; Chamandy et al. 2018; Grichener, Sabach & Soker 2018; Fragos et al. 2019; Grichener & Soker 2019; Iaconi & De Marco 2019; Iaconi et al. 2019; Prust & Chang 2019; Chamandy et al. 2019a, b; Reichardt et al. 2019, 2020; Glanz & Perets 2020; Prust 2020), nevertheless, many open questions remain unanswered. The dominant processes in the evolution and termination of the CE, for example, are not yet fully understood, and many mechanisms have been proposed [e.g. the αCE − λ formalism (van den Heuvel 1976), gamma formalism (Nelemans et al. 2000), recombination energy (Nandez, Ivanova & Lombardi 2015), binding energy (Iaconi et al. 2018), tidal forces (Iben & Livio 1993), internal energy (Han et al. 1994), magnetic fields (Regős & Tout 1995), accretion (Voss & Tauris 2003; Soker 2004), nuclear energy (Ivanova & Podsiadlowski 2003) dust-driven winds, Glanz & Perets (2018), and enthalpy (Ivanova & Chaichenets 2011) amongst others], none of which have been able to fully describe the evolution and termination of the CE phase (see for example Soker 2013; Iaconi et al. 2018). The launching of a jet from a compact object (CO) within the CE is also a possible alternative mechanism in the evolution and termination of this phase (Armitage & Livio 2000; Soker 2004; Chevalier 2012; Shiber, Schreier & Soker 2016; Soker & Gilkis 2018; Gilkis, Soker & Kashi 2019; Schreier, Hillel & Soker 2019; Soker, Grichener & Gilkis 2019; Jones 2020).


It is difficult to isolate the impact of mass and environment on the rate and timing of quenching. Mass quenching is more important at earlier times in the evolution of galaxies and may be more important in denser regions (e.g., Peng et al. 2010; Muzzin et al. 2012; Lee et al. 2015; Darvish et al. 2016, 2018; Kawinwanichakij et al. 2017). And in the case of powerful radio galaxies, which lie in over-dense environments, both gas-rich and gas-poor mergers likely play an important role in both the growth of the stellar mass and the black holes. Volonteri et al. (2015b) suggest that in the merger phase, the AGN dominates the bolometric luminosity but the accretion can be very stochastic (see also Gabor & Bournaud 2013; DeGraf et al. 2017). It appears that the galaxies in our sample with the highest star-formation rates all host very powerful AGN, and are potentially all advanced mergers, consistent with this picture. In fact, PKS 0529−549, which has one of the highest SFRs of all the galaxies in our sample, has a modest gas fraction of about 15%, a high star-formation efficiency (SFR/molecular gas mass), and has been transforming its gas into stars rapidly (Man et al., in prep.). The star formation efficiencies in the other radio galaxies with high SFRs also appear extreme (10–100 Gyr−1; Man et al., in prep.). But of course, that does not explain our results in themselves. Dubois et al. (2015), in a study using numerical simulations of the relative growth of SMBHs and their host galaxies, found that star formation may regulate the black hole accretion rate. During the most rapid, gas-rich phase of the growth of massive galaxies, it may be that a larger fraction of the gas in the ISM is not available to fuel the SMBHs, but is consumed via star formation (see DeGraf et al. 2017). As the gas fractions decline, the relative power of the AGN compared to that of the star formation increases, resulting in an increased star formation efficiency. Concomitantly, the increased star formation rate can then disperse the dense gas making it easier for the jets to drive vigorous and efficient outflows (Nesvadba et al. 2006, 2017).


Energy flows induced into magnetically dominated relativistic magnetospheres of compact objects are commonly modelled by numerical simulations in the force-free electrodynamics (FFE) limit. Fueled by the track record of observations in the era of multimessenger astrophysics, current targets for such simulations include the magnetospheres of rapidly spinning black holes, spiraling neutron stars, magnetars, and pulsars. The tenuous, magnetically dominated atmosphere (magnetosphere) of pulsars is an active field of scientific interest. They fascinate both observers (e.g. Lorimer et al. 1995; Ransom et al. 2005; Abdo et al. 2013; Jankowski et al. 2018) and theorists (e.g. Kennel & Coroniti 1984; Lyubarskii 1996; Contopoulos, Kazanas & Fendt 1999; Goodwin et al. 2004; Timokhin 2006; Timokhin & Arons 2013; Contopoulos 2019; Pétri 2020). With the remarkable progress in scientific computing, their rotating magnetosphere has captured designers of numerical methods that integrate FFE and magnetohydrodynamics (MHD) with ever-improving accuracy (e.g. Komissarov 2006; Spitkovsky 2006; Tchekhovskoy, Spitkovsky & Li 2013; Parfrey, Spitkovsky & Beloborodov 2017; Carrasco & Shibata 2020). Recently, particle-in-cell (PIC) simulations were able to resolve a broad range of scale separations and allow for unprecedented insight into the microphysics of pulsar magnetospheres across the global scale (Cerutti et al. 2015; Philippov, Spitkovsky & Cerutti 2015a; Kalapotharakos et al. 2018; Philippov & Spitkovsky 2018; Guépin, Cerutti & Kotera 2020). In this fascinating flurry of outcomes, only few references scrutinized whether the results from ideal plasma simulations are the best possible model for the pulsar magnetosphere that contains an inherently non-ideal region, namely the equatorial current sheet (ECS) beyond the closed zone (Contopoulos 2016; Contopoulos 2019; Contopoulos, Pétri & Stefanou 2020). Here, we study with rigorous technical depth how this non-ideal region can affect the global dynamics of the force-free aligned rotator magnetosphere – effectively serving as a blueprint for force-free magnetospheres of other compact objects.


Using moving meshes helps reduce the angular momentum errors from advection in grid codes. We have run >200 iterations of this test problem using the public version of fvmhd3d, systematically varying choices like the mesh regularization scheme, mesh ‘drifting’ (whether to use a strictly Lagrangian drift, or locally smoothed velocity, or regularized drift), initial mesh geometry, and boundary conditions. In both fvmhd3d and more limited tests with arepo, we find that running in the ‘simplest’ initial configuration (an initial Cartesian mesh with outflow boundary conditions, with the default mesh regularization scheme used for all other test problems shown here), the disc goes unstable and the angular momentum evolution tends to be corrupted within a few orbits (similar to the fixed-grid cases). Unfortunately, some significant errors in angular momentum evolution are difficult to avoid in moving-mesh codes, as has been discussed extensively in e.g. Duffell & MacFadyen (2012), Ivanova et al. (2013), Mocz et al. (2014) and Muñoz et al. (2014). In a shearing disc, if the cells adapt in a truly Lagrangian manner, then they are inevitably deformed into a highly sheared/irregular shape (Muñoz et al. 2014). This leads to other errors. As soon as they become non-spherical (or more accurately fail to be radially symmetric about their own cell centre of mass), then mass advection between cells necessarily leads to additional angular momentum errors (indeed, the angular momentum of an irregular cell cannot be defined exactly but only to the same order of integration accuracy as the local velocity gradient estimator). This is akin to the errors in our MFV method. More importantly, if some regularization procedure is used to keep the cell shapes ‘regular’ (as is necessary in any moving-mesh code used for this problem), then the regularization means the cells cannot move entirely with the fluid and the gas must be advected over the cells. This re-introduces some of the same (more serious) errors we saw with stationary-grid methods (specifically, see Ivanova et al. 2013, equation 53). This means that the results for moving meshes are quite sensitive to choices like the mesh ‘stiffness’, regularization procedure, and in particular the choice of boundary conditions for the mesh-generating points (since the rigid Voronoi volume partition can lead to a ‘mesh tension’ effect, whereby regularization-induced distortions in the central regions propagate outwards ‘through’ the mesh; Springel 2010). So there are ways to improve the situation on this problem – for this reason, we do not show a single ‘standard’ moving-mesh result, because significantly different results are obtained if we make just small changes to the mesh-regularization procedure in each code. However, like with AMR codes, the most effective methods for eliminating angular momentum errors in moving meshes generally depend on knowing the problem geometry ahead of time. For example, Duffell & MacFadyen (2012) design a moving grid which is a series of cylindrical shells free to rotate independently about a shared axis (the disco code); Muñoz et al. (2013) use a carefully chosen initial grid configuration with a specially designed boundary condition designed to prevent inward propagation of ‘mesh deformation’; these help considerably, but must be fine-tuned to the exact disc configuration.


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).


So far, these surveys have mostly relied on two-point estimators for their cosmological analysis, for example the shear two-point correlation functions (γ-2PCF, e.g., Kilbinger et al. 2013; Troxel et al. 2018; Hikage et al. 2019; Asgari et al. 2021). These estimators are inherited from cosmic microwave background (CMB) analyses, which probe the matter distribution of the early Universe. However, cosmic shear probes the recent Universe, where the matter distribution is more complex due to the nonlinear accretion of structures that creates non-Gaussian features in the matter field on small scales (e.g., Codis et al. 2015; Barthelemy et al. 2020). Two-point statistics fail to capture this non-Gaussian information and thus yield an incomplete description of the matter distribution at low redshift. To close this gap, the community has recently started to explore non-Gaussian cosmic shear estimators: for example weak-lensing peaks (e.g., Kruse & Schneider 1999, 2000; Dietrich & Hartlap 2010; Kratochvil et al. 2010; Fan et al. 2010; Yang et al. 2011; Maturi et al. 2011; Hamana et al. 2012; Hilbert et al. 2012; Marian et al. 2012, 2013; Shan et al. 2014, 2018; Lin & Kilbinger 2015; Martinet et al. 2015, 2018; Liu et al. 2015a,b; Kacprzak et al. 2016; Petri et al. 2016; Zorrilla Matilla et al. 2016; Giocoli et al. 2018; Peel et al. 2018; Davies et al. 2019; Fong et al. 2019; Li et al. 2019; Weiss et al. 2019; Yuan et al. 2019; Coulton et al. 2020; Ajani et al. 2020; Zürcher et al. 2021), Minkowski functionals (e.g., Kratochvil et al. 2012; Petri et al. 2015; Vicinanza et al. 2019; Parroni et al. 2020; Zürcher et al. 2021), higher-order moments (e.g., Van Waerbeke et al. 2013; Petri et al. 2015; Peel et al. 2018; Vicinanza et al. 2018; Chang et al. 2018; Gatti et al. 2020), three-point statistics (e.g., Schneider & Lombardi 2003; Takada & Jain 2003, 2004; Semboloni et al. 2011; Fu et al. 2014), density split statistics (e.g., Friedrich et al. 2018; Gruen et al. 2018; Burger et al. 2020), persistent homology (e.g., Heydenreich et al. 2021), scattering transform (e.g., Cheng et al. 2020), and machine learning (e.g., Merten et al. 2019; Ribli et al. 2019; Peel et al. 2019; Shirasaki et al. 2019; Fluri et al. 2019). Although these new statistics have shown a great potential, they have not yet been fully generalized to data analyses, mostly because they need a large number of computationally expensive N-body simulations to calibrate their dependence on cosmology, while this dependence is accurately predicted by theoretical models in the case of two-point estimators.


As described in Sect. 4.1.1, the TTV inversion code includes a Hill stability criterion for two-planet systems. Although this initial check filters out the least stable systems, it cannot guarantee the long-term stability of the derived orbital architecture of a four-planet system. On one hand, there is no analytical criterion for assessing the long-term stability of multi-planet systems (>2 planets) like that for two-planet systems (Gladman 1993; Chambers et al. 1996). Chambers et al. (1996), Smith & Lissauer (2009), Lissauer et al. (2011b), and similar numerical studies have found that long-term stability of multi-planet systems typically requires the mutual separations between planets to be at least ten mutual Hill radii, which is much larger than the cautious limit of

$2\sqrt{3}$

2
3

 mutual Hill radii required by the Hill stability criterion that is implemented in our TTV inversion code (Gladman 1993; Chambers et al. 1996). Meanwhile, these criteria are only valid under the assumptions of low mutual inclinations and small eccentricities. These two restrictions are usually not well-defined; limiting values of 1°–2° and e = 0.1–0.2, respectively, are often adopted (Petrovich 2015; MacDonald et al. 2016). Apparently, these restrictions and stability criteria are well satisfied by the nominal orbital architecture of the Kepler-411 system inverted from the TTV data. On the other hand, the Hill criterion provides no information about the long-term behavior of the system, and repeated weak interactions between planets in Hill stable orbits may still lead to ejections and/or physical collisions; these are referred to as Lagrange unstable (Petrovich 2015). The chaotic orbits that are generated primarily by first-order (or higher-order) resonance overlap are eventually subjected to large-scale variation of the semi-major axes and hence become Lagrange unstable. Based on previous studies on the chaotic behavior induced by the first-order resonance overlap (e.g. Wisdom 1980; Duncan et al. 1989), Deck et al. 2013 supply the condition that leads to chaotic behavior in a two-planet system (see Eq. (50) in Deck et al. 2013). We apply this criterion to estimate the nominal orbital architecture extracted from the TTV data of the Kepler-411 system, and find that the orbital configuration is far away from the chaotic motion. Therefore, we conclude that the nominal orbital architecture of the Kepler-411 system extracted from measured TTVs satisfies both the Hill and Lagrange stability criteria.


In Fig. 10, we plot the variation of the ratio of the outflow contribution to the FWHM and turbulent energy. The ratio of the outflow contribution  = 1 – ‘non-outflow contribution’/‘all contributions’. We observe that the outflow has a contribution in the FWHM: about 20 per cent in the local region at the H ii region (non-outflow contribution is about 81 per cent) and about 10 per cent even in the clumps. According to Eturb  = (3/16 ln 2)Mcloud × FWHM2, outflow has a contribution in the turbulent energy up to 35 per cent in the local region at the H ii region (1 − 0.812). It has a contribution of at least 15 per cent in the clump at early stages of massive star formation, which is lower than that reported in previous studies (e.g. Bally 2016; Drabek-Maunder et al. 2016). The outflow contribution decreases with time once the outflow action stops. This indicates that the outflows do not have a significant cumulative impact on the turbulent levels during the occurrence of several outflow actions. Thus, the outflow energy contribution to turbulent energy increases insignificantly with the evolutionary stages. Our results suggest that the outflow energy is large enough to maintain the turbulent energy in the clumps and that the outflow has some (not significant) effect on the turbulent energy. However, there is a better correlation between the outflow energy and turbulent energy (see Fig. 5). Therefore, we could not determine if the outflow significantly contributes to the turbulent energy in the clumps. This is consistent with the study conducted by Maud et al. (2015). They also reported that there is a better correlation between the outflow energy and turbulent energy, but the core turbulence is not driven by the local input from the outflows. However, Drabek-Maunder et al. (2016) and Yang et al. (2018) reported that there is no correlation between the turbulent and outflow energies. Urquhart et al. (2018) found that the clump mass and evolutionary stage are uncorrelated. For similar mass of massive star, it is likely that we can observe the obvious difference of turbulent energy between clump without and with outflow. However, for statistics, the mass parameter of turbulent energy is less constrained for each evolutionary stage. All these findings imply that the outflow action has some impact on the local environment and cloud itself, but the contribution from outflow does not mainly drive turbulence. This observation is consistent with several other studies that suggest that turbulence is mostly driven by large-scale mechanisms (Ossenkopf & Mac Low 2002; Brunt, Heyer & Mac Low 2009; Padoan et al. 2009; Arce et al. 2010; Mottram & Brunt 2012; Plunkett et al. 2015; Drabek-Maunder et al. 2016).


The formation of dark matter haloes has been studied extensively using numerical dark matter only simulations (e.g. Springel et al. 2005b; Fosalba et al. 2008; Boylan-Kolchin et al. 2009; Teyssier et al. 2009; Klypin, Trujillo-Gomez & Primack 2011).1 Extending the insight from dark matter only simulations to include a theory of galaxy formation requires a method to link the formation of dark matter haloes to observable galaxy properties. The most direct method available is hydrodynamical simulations, which model the co-evolution of dark matter and baryons (e.g. Katz, Hernquist & Weinberg 1992; Katz, Weinberg & Hernquist 1996; Weinberg, Hernquist & Katz 1997; Murali et al. 2002; Springel & Hernquist 2003b; Kereš et al. 2005; Ocvirk, Pichon & Teyssier 2008; Crain et al. 2009; Croft et al. 2009; Oppenheimer et al. 2010; Schaye et al. 2010; Vogelsberger et al. 2012). By directly including hydrodynamics in structure formation simulations, one can probe the thermal state and column density distribution of the intergalactic medium (IGM) via the Lyman α forest (Cen et al. 1994; Zhang, Anninos & Norman 1995; Hernquist et al. 1996; Theuns et al. 1998), the phase structure and heavy element composition of the circumgalactic medium and IGM (Aguirre et al. 2001; Cen & Fang 2006; van de Voort & Schaye 2012; Shen et al. 2013), and the nature and rates of accretion of dark matter and baryons into galaxies (Kereš et al. 2005; van de Voort et al. 2011; Nelson et al. 2013). Since these simulations can follow the dynamics of both the dark matter and baryons down to small spatial scales, predictions can be made about their internal structure including the distribution of gas (Kereš et al. 2012; Torrey et al. 2012) and the formation of stellar discs and bulges (Abadi et al. 2003; Governato et al. 2004; Agertz, Teyssier & Moore 2011; Sales et al. 2012; Marinacci, Pakmor & Springel 2014). As a result of this detailed information, simulations are a valuable tool for interpreting observational data and placing observed galaxies into a more complete evolution based cosmological context.


The direct detection of the first gravitational waves from the merger of two heavy black holes (BHs) in GW 150914 confirmed one of the toughest predictions of Einstein’s theory of general relativity. But while satisfying the world of physics in general, for astrophysics this was only the beginning: many were surprised by the large BH masses of, respectively, 36 and 29  M⊙ (Abbott et al. 2016), showcasing how the new field of multimessenger astrophysics had just re-opened the field of stellar evolution in a spectacular fashion. Stellar mass BHs had previously been revealed by their interaction in binary systems (Orosz et al. 2011), but the maximum stellar BH mass in our Milky Way is not higher than roughly 15–20  M⊙ (Belczynski et al. 2010). While we know that very massive stars (VMS) above 100  M⊙ exist (Crowther et al. 2010; Vink et al. 2015), this mass is significantly diminished via stellar winds already during core hydrogen (H) burning (Vink & Gräfener 2012). The heavy nature of the BH, as measured by LIGO/VIRGO therefore supported the assumption that the gravitational wave event occurred in a part of the Universe still pristine in its enrichment with heavy elements (‘metallicity (Z)’), lowering stellar wind mass-loss (Vink, de Koter & Lamers 2001; Vink & de Koter 2005). A low-Z solution was widely accepted until the announcement of a 70  M⊙ BH in LB-1 (Liu et al. 2019), spurring stellar evolution theorists to avoid heavy mass-loss in the Milky Way (Belczynski et al. 2020; Groh et al. 2020), either by arbitrarily lowering the mass-loss rates of VMS – seemingly contradicting VMS mass-loss calibrations (Vink & Gräfener 2012) – or by invoking the presence of a strong dipolar surface magnetic field that could quench the wind (Petit et al. 2017). While such magnetic fields in some 5–10 per cent of massive OB stars do indeed exist, no B-fields have yet been detected in VMS (Bagnulo et al. 2020). The problem of the formation of a $70\, \mathrm{ M}_\odot$ BH in a solar metallicity environment apparently resolved itself when the spectral signatures of LB-1 were re-interpreted (Abdul-Masih et al. 2020; El-Badry & Quataert 2020).


To perform a statistical analysis of the average quiescent fraction of satellites around our sample of massive galaxies, we use a statistical background subtraction technique (e.g., Kauffmann et al. 2010; Tal et al. 2012; Wang & White 2012; Kawinwanichakij et al. 2014). We detect objects within fixed apertures centered on our central galaxies and satisfying Equation (2). These apertures include physically associated galaxies as well as chance alignments of foreground and background galaxies. We estimate and correct for the contamination due to chance alignments by placing random apertures across the field. We adapt this procedure by restricting the placement of the random apertures to regions near the centrals, as demonstrated by Chen et al. (2006). This accounts for the bias due to contaminating galaxies that are physically associated with the centrals but are not satellites (i.e., the 2-halo term of the correlation function; see Chen et al. 2006).15

15
The contaminating galaxies that are physically associated with the central galaxies in our sample are expected to have marginally different properties than truly random field galaxies due to the fact that they exist in biased regions of the universe. There may be an additional effect due to large-scale 2-halo conformity. If 2-halo conformity exists, our procedure effectively corrects for it.
 We therefore place the random apertures within annuli with inner and outer radii equal to 1 and 3 cMpc from each central galaxy for the UDS and UltraVISTA. Parenthetically, our tests showed that the restriction on the location of the background apertures has only a small effect on the conformity signal. Relative to apertures that are placed randomly through the field, this correction increases the quiescent fractions of background galaxies by 0.4%–10%. For the smaller ZFOURGE fields, placing the random apertures within annuli is too restrictive, and for this survey we randomly place the apertures across the fields. We do note that the ZFOURGE fields are small enough that even these randomly placed apertures trace the same large-scale environment as the centrals. Additionally, we find that when we restrict the background apertures to be

 cMpc from the centrals, it changes the measured quenching efficiencies (see Section 4 below) by 10%, and none of our conclusions would be changed.


Studying the dynamical properties of rotating neutron stars is a domain which brings out various interesting features when one assumes a perfect fluid. It is known that the centrifugal force of a rotating star counters gravitational force and hence one can expect massive stars to be fast rotors, at least in the initial stages of the stellar evolution. As a result of rotation a star may experience damping due to unstable oscillations such as the r-modes. The r-modes are one of many pulsating modes that exist in neutron stars and are characterized by the Coriolis force acting as the restoring force (Andersson 1998). The r-modes are unstable to emission of gravitational radiation (GR) by the Chandrashekhar-Friedman-Schutz (CFS) mechanism (Chandrasekhar 1970; Friedman & Schutz 1978). It was shown in Andersson (1998) that the r-modes are unstable for all rotating perfect fluid stars irrespective of their frequency. Dissipative effects such as shear and bulk viscosities work towards suppressing GR driven instabilities and has been studied by various authors over the past few years (Lindblom, Owen & Morsink 1998; Jones 2001; Lindblom & Owen 2002; van Dalen & Dieperink 2004; Drago, Lavagno & Pagliara 2005; Nayyar & Owen 2006; Jaikumar, Rupak & Steiner 2008; Jha, Mishra & Sreekanth 2010; Ofengeim et al. 2019) under various considerations. If the GR time-scale is shorter than the damping time-scale due to such dissipative processes, then the r-mode will be unstable and a rapidly rotating neutron star could lose a significant fraction of its rotational energy through GR. At higher temperatures (T > 109 K), the dominant dissipation is due to bulk viscosity, which arises due to density and pressure perturbations, a consequence of the star being driven out of equilibrium by oscillations. The system tries to restore equilibrium through various internal processes. In the case of r-modes, since the typical frequencies are of the order of the rotational frequencies of the stars, the reactions that dominate are the weak processes. Within these weak processes, although the modified Urca processes involving leptons are important, it has been shown that non-leptonic processes involving hyperons contribute more significantly towards bulk viscosity at temperatures lower than a few times 109 K (Lindblom & Owen 2002). Our goal here is to investigate the same using a chiral model calibrated to reproduce the desired nuclear matter properties, in particular the density content of the nuclear symmetry energy at both low and high densities.


Using the whole sample (\hbox{$\bar{z}=0.40$}z̅ = 0.40), we find a decreasing faint end for both datasets with consistent values between HST (α =  − 0.76 ± 0.07) and Subaru (α =  − 0.78 ± 0.06). Separating between low-redshift (\hbox{$\bar{z}=0.29$}z̅ = 0.29) and high-redshift (\hbox{$\bar{z}=0.51$}z̅ = 0.51) samples, we find an evolution of the faint end slope of 1.7σ with HST and 2.6σ with Subaru. There is thus a mild decrease of the faint end slope (less negative α) with increasing redshift over the range (0.187 z 0.686). This evolution is in good agreement with recent papers in the literature: in particular Zenteno et al. (2016) found a decrease of the RS faint end at 2.1σ for a wider range of redshifts (0.1 z 1.13), but with ~ 80% of their clusters being in the same redshift range as ours. De Propris et al. (2013) claim that the evolution in the faint end slope has a significant contribution from surface brightness selection effects. They used HST data of differing depths on a single cluster (MS 1358.4+6254) to show that surface brightness selection effects become important above the formal magnitude limit of their data and that they affect the RS GLF at magnitudes z ≥ 24.5 for 2.7 ks HST exposures (see their Fig. 18). The faint RS for their cluster has F814W − z = 0.25, implying that the SB selection effects in their sample become important at F814W> 24.75. On the other hand, our CLASH data are significantly deeper than theirs (4.1 ks) and we limit our GLFs at F814W 24.5. Therefore, the real SB selection effects noticed in De Propris et al. (2013) should not be playing a role in our space-based results. In addition, De Propris et al. (2013) claim that previous estimates of the evolution in the RS GLF (e.g.,  De Lucia et al. 2007; Rudnick et al. 2009) were also due to SB effects. Both of those works were based on the same ground-based data with a formal magnitude limit of I = 24 or 24.5 (for the low- and high-redshift clusters, respectively) and the evolution in the GLF was seen over the faintest 2 mag. We cannot directly address the role of SB effects in the EDisCS results without detailed simulations on those data (see below for such simulations for our clusters) but the similarity between our HST and Subaru GLFs imply that the EDisCS evolution in the GLF is not dominated by SB effects.


To measure the emission lines’ flux within a spectrum, it is essential to fit the lines using the proper model with parameters that allow us to represent the intensities in all spectral elements. Estimating the number of components of each underlying emission line (i.e., multiple lines with multiple velocity components as would be expected from merging galaxy systems) is also crucial to extract meaningful information from the lines. Standard methodologies require fitting both single and double component models and computing their Bayes factors, or approximating it using a proxy such as the Akaike (or Bayesian) information criterion (AIC; Rhea et al. 2020b). However, these methods are highly reliant on the accuracy of the fits (e.g., Kieseppä 1997; Pooley & Marion 2018). Several promising new methods have been proposed utilizing machine-learning algorithms to solve this problem (Hampton et al. 2017; Keown et al. 2019; Rhea et al. 2020a). In particular, CLOVER, developed in Keown et al. (2019), uses a convolutional neural network (CNN) to classify high-resolution radio emission lines as having either single or double underlying components. In this paper, we expand upon this methodology for medium resolution, Fourier Transform IFU spectra taken by the Spectromètre Imageur à Transformée de Fourier pour l’Etude en Long et en Large de raies d’Emission (SITELLE) instrument at the Canada–France–Hawai’i Telescope (Baril et al. 2016). Each SITELLE observation contains approximately 4 million pixels and, thus, produces 4 million spectra of a given resolution set by the principal investigator (1  R  10, 000; Drissen et al. 2014; Martin & Drissen 2017; Drissen et al. 2019). The instrumental line function of SITELLE is described as a sinc model convolved with a Gaussian to represent intrinsic line broadening, which requires special care during the fitting process (Martin et al. 2016). Therefore, the development of machine-learning applications for SITELLE demands special treatment of the underlying emission profiles.


Similarly, there is general agreement about the astrophysical effects responsible for velocity segregation between more and less luminous galaxies. This effect can be explained by physical processes such as dynamical friction (also called dynamical breaking) that cause transfers of kinetic energy from larger galaxies to smaller galaxies, as well as gravitational interactions that can convert bulk kinetic energy into internal kinetic energy via, for example, accelerating and ejecting individual stars during galaxy mergers (Sarazin 1986; Kashlinsky 1987; Biviano et al. 1992; Mahajan et al. 2011). It is mildly puzzling that the velocity segregation effect that we see in our data for the brightest and faintest galaxies does not appear in some recent simulations; we are not the first to detect this signal in bright cluster member galaxies, (Chincarini & Rood 1977; Biviano et al. 1992; Mohr et al. 1996; Goto 2005; Ribeiro et al. 2010; Old et al. 2013; Barsanti et al. 2016), and the effect is seen in some simulations (e.g., Lau et al. 2010; Saro et al. 2013). We are wary of over-interpreting this discrepancy, because of the difference in our bright galaxy sample and the 50 brightest members approach used by Gifford et al. (2013), but it is possible that the discrepancy is related to the effects of missing baryonic/gas physics that are not captured in dark matter only simulations. We elect not to speculate too much about the pros and cons of various methods for the treatment of halos in simulated clusters, and how mock galaxies are placed into those halos, though it is not unreasonable to suppose that different prescriptions could generate significantly different results. Certainly the measurement we present here could represent a useful benchmark test to be reproduced in future simulations. Looking forward, we believe it is important that both observers and simulators strive to find useful quantities that can be measured in both data and simulations; it is with this in mind that we analyze galaxies in our sample in terms of relative luminosity, scaled by the characteristic magnitude, m*.


Several models have been advanced to explain the obliquity dichotomy, but so far none can account for all the relevant observations. Interpretations based solely on differences in the stellar properties (e.g., Rogers et al. 2012) cannot address the inferred dependence of the obliquity on Mp and the detection of highly misaligned planets around cool stars. In view of the fact that

 corresponds to the temperature above which the size of the outer convective zone of a main-sequence (MS) F star shrinks rapidly, it was suggested that close-in planets in both cool and hot stars are initially distributed over the entire angular range (0°–180°), but that only in cool stars where a substantial convective envelope is present can a sufficiently massive close-in planet (

) realign the star through tidal interaction (e.g., Winn et al. 2010; Albrecht et al. 2012). The host stars are also subject to magnetic braking, which declines strongly above the same transition temperature (corresponding to the break in the Kraft curve; Kraft 1967), and it was argued (Dawson 2014) that this, rather than the tidal dissipation efficiency, is the main factor underlying the difference in obliquity properties between cool and hot stars. Both variants of this scenario, however, face the conundrum that an HJ undergoing equilibrium tidal interaction with its host star would spiral in and be ingested on a timescale that is comparable to the realignment time. A possible way out of this difficulty is to appeal to the {10} component of the dynamical tide, which could in principle significantly reduce the alignment time without affecting the ingestion time (Lai 2012).1

1
An alternative possibility, that only the outer convective layer (Winn et al. 2010)—or even just a part of it (Dawson 2014)—partakes in the realignment process, is hard to justify on either theoretical or observational grounds.
 However, even though this model can be used to account for individual systems (Valsecchi & Rasio 2014), it remains unclear whether it can explain the overall λ distribution of HJs and the manifested difference between cool and hot stars (Rogers & Lin 2013; Xue et al. 2014). Furthermore, even the basic tidal interaction interpretation of the obliquity dichotomy has now been called into question by the results of Mazeh et al. (2015), who analyzed the rotational photometric modulations of a large sample of Kepler sources and inferred that (1) the conclusion that planets around cool stars are well aligned, and those around hot stars are not, is general and not restricted just to HJs; and (2) the low obliquity of planets around cool stars extends to orbital periods Porb that are a factor of ∼10 larger than the maximum value (

 days) for robust tidal interaction between an HJ and a

 Gyr old G or F star.


As in Flowers et al. (2019), to compare our model transmission spectra directly against the Ehrenreich et al. (2020) results, we must calculate the transmission spectra as a function of orbital phase throughout the duration of transit. To account for orbital phase dependencies, we apply the following procedure:1.Account for phase-dependent backlighting of the planet (i.e., stellar limb-darkening effects). At different points of its transit, the planet will occult regions of its host star of varying brightness. Furthermore, at a fixed orbital phase, different regions of the planet’s limb will be backlit by varying intensities of stellar light. Similar to Flowers et al. (2019), we calculate the normalized stellar intensity at the center of each cell of the 2D projected planetary grid produced by our GCM at each modeled orbital phase of the planet. We use the quadratic limb-darkening coefficients reported by Ehrenreich et al. (2020) to establish the stellar center-to-limb intensity profile, and we take into account the 89.°623 orbital inclination of WASP-76b (Ehrenreich et al. 2020) to determine where the planet resides on the stellar disk as a function of its orbital phase. We make the assumption of constant impact parameter b over the course of transit.
9

9
In reality, a planet on an inclined orbit will not have a constant b over the entire duration of transit; rather, the planet’s distance from the stellar equator will be decreased at ingress and egress, reaching its maximum at center of transit. Our tests reveal that, for WASP-76b, the relative error induced by the constant b assumption is on the order of 4% in distance, which results in a change on the order of 1 m s−1 at the blueshift level (see Section 3.1). Hence, our b treatment is justified. This procedure allows us to calculate a backlighting factor f, which ranges from 0 to 1, effectively replacing the constant I

λ,0 from Equation (3) with a variable

Iλ,0×f(θ′,z,φ)

, for a given orbital phase φ and 2D projected polar angle

θ′

.2.Account for the decreasing of the continuum by interpolating a light curve produced by the batman code (Kreidberg 2015). Step 1 ensures that less light is transmitted through the planet’s atmosphere than a uniform stellar disk would emit. Step 2 further enforces that the inner, optically thick core of the planet is simulated crossing a limb-darkened star, as opposed to a star of uniform brightness.3.Account for the planet’s rotation over the course of transit. Because the planet is continually rotating as it travels across the face of its host star, we must transform the GCM coordinate system so that the correct observer-facing hemisphere is modeled at each instance during transit. For simplicity, we assume zero obliquity, which allows us to calculate the coordinate transform simply by assigning a linear offset to each planetary longitude; i.e., ϕ
rotated = ϕ + φ.


The above analysis addresses a number of open questions. Firstly, it is necessary to ask whether impulsive heating events, such as Ohmic dissipation associated with magnetic field braiding can trigger coronal rain formation in the first place. The evolution of loop L1 shows that this is indeed possible, as the duration of the impulsive heating events occuring in the loop is 100−200 s, similar to the loop radiative cooling timescale of ∼100 s. An impulsive heating event of significant amplitude and with duration that is comparable to the radiative cooling timescale is sufficient to cause sufficient chromospheric evaporation into the loop for the loop to become thermally unstable (Johnston et al. 2019). Previous studies that addressed prominence formation with using a time-variable coronal heating term found that formation of condensations still occurs if 1. the heating is intermittent, but the frequency of the individual heating events exceeds the inverse of the radiative cooling timescale (Karpen & Antiochos 2008) and 2. if the heating ceases during the condensation formation, the condensation still continues to grow (Xia et al. 2011). It should also be noted that such impulsive events can also act as a perturbation that trigger the catastrophic cooling in a marginally stable plasma. We noted differences between condensations formed in loops L1 and L2, in particular that the heating driving the condensation formation in L1 has an impulsive character compared to the gradual heating of L2. Also, the cooling timescale of the condensation formed in L1 is much shorter than that of the condensation formed along L2, suggesting different conditions at coronal heights. Secondly, we also addressed the issue of the apparent coronal rain formation along open field lines and shown that flows of evaporated plasma can lead to sufficient density increase to trigger radiative instability in both closed and open magnetic field configurations. Finally, our work also addresses a possible mechanism responsible for destruction of coronal rain condensations before they reach the solar surface. A reconnection event occurring in the upper part of the leg of loop 3 leads to the condensation being heated to very high temperatures and subsequently destroyed as a result. This suggests that the lifetime of the condensations can be dependent on the frequency of such reconnection events in shorter loops. Also, it might possibly explain why coronal rain is not observed in short low-lying loops close to the active region core that are heated to very high temperatures. Even if the condensations do form in such loops (which is significantly less likely as it is easier to trigger thermal instability in longer loops; see e.g. Müller et al. 2004, 2005), they are most likely short-lived.


This work focuses on the formation of systems with high mass ratios and component masses in the LMG through canonical isolated binary evolution. Many other channels have been proposed for producing the compact binary mergers observed by LIGO–Virgo. Dynamical formation in dense stellar clusters such as globular clusters preferentially produces compact binaries with similar masses (e.g., Sigurdsson & Hernquist 1993), and thus the formation of NSBHs and other compact binaries with highly asymmetric masses is predicted to be rare (Clausen et al. 2013; Arca Sedda et al. 2020; Ye et al. 2020). While hierarchical mergers of NSs have been proposed as a means of populating the LMG (Gupta et al. 2020), this scenario is unlikely since heavier BHs dominate the dynamical interactions in clusters (e.g., Samsing & Hotokezaka 2020; Ye et al. 2020). The formation of compact binaries with highly asymmetric masses may be more prevalent in young star clusters (e.g., di Carlo et al. 2019; Rastello et al. 2020; Santoliquido et al. 2020), but Fragione & Banerjee (2020) finds the merger rate of NSBH systems in young massive and open clusters to be three orders of magnitude lower, similar to the predictions from old globular clusters. Other formation mechanisms have been explored for forming highly asymmetric compact binary mergers and mergers with components in the LMG, such as hierarchical systems in the galactic field (e.g., Antonini et al. 2017; Silsbee & Tremaine 2017; Fragione & Kocsis 2019; Safarzadeh et al. 2019; Fragione et al. 2020), hierarchical systems in galactic nuclei with a supermassive BH as the outer perturber (e.g., Antonini & Perets 2012; Petrovich & Antonini 2017; Hoang et al. 2018; Fragione et al. 2019; Stephan et al. 2019), and in disks around supermassive BHs in active galactic nuclei (e.g., McKernan et al. 2019; Yang et al. 2019). However, the rates and formation properties from these channels are uncertain. Nevertheless, a full picture of compact-binary mergers will require consideration of all these channels and investigation of how physical prescriptions (such as the connection between the underlying SN mechanism and remnant mass) jointly affect population properties, rates, and branching ratios across these channels (e.g., Stevenson et al. 2017; Talbot & Thrane 2017; Vitale et al. 2017; Zevin et al. 2017; Arca Sedda et al. 2020). The identification of bona fide NSBH systems and other compact-binary mergers with highly asymmetric masses will further constrain the relative contribution of various formation channels and the underlying physics of these formation pathways.


Recent years have seen a burgeoning in the volume of spatially resolved spectroscopic data from large surveys such as CALIFA (Sánchez et al. 2012), SAMI (Croom et al. 2012), and MaNGA (Bundy et al. 2015). These data have stimulated interest in the relationship between the gas-phase oxygen abundances, stellar mass, star formation rate (SFR), and gas content of galaxies on kiloparsec scales (e.g., Barrera-Ballesteros et al. 2016, 2018; Mingozzi et al. 2020; Teklu et al. 2020; Wang & Lilly 2021). By analogy to the global mass–metallicity relation (Tremonti et al. 2004), the oxygen abundance has been shown to be sensitive to the local stellar mass surface density (Σ*), tracing the integrated star formation history on local scales in a galaxy, as well as the presence of outflows (e.g., Barrera-Ballesteros et al. 2018) and inflows (Lian et al. 2019; Schaefer et al. 2019). Since early observations of this local relationship between Σ* and 12+log(O/H) (Moran et al. 2012; Rosales-Ortega et al. 2012), there has been a growing consensus that the global mass–metallicity relation can be explained as arising on local scales. That is, the accumulation of chemical elements on kiloparsec scales can be seen as a reflection of the buildup of stellar mass locally within galaxies over their evolutionary history rather than on global scales (see, e.g., Sánchez 2020; Sánchez et al. 2021). This is reinforced by recent observations that gas-phase chemical abundances in galaxies are correlated on ∼kiloparsec scales (Sánchez et al. 2015; Kreckel et al. 2020; Li et al. 2021), implying that their chemical enrichment proceeds by the local injection and diffusion of metals into the interstellar medium (ISM) of galaxies. Nevertheless, some observations have shown that the local gas-phase metallicity is also related to the total stellar mass of galaxies (Gao et al. 2018). This is likely due to the greater depth of the gravitational potential well of more massive galaxies, which makes the expulsion of metals through feedback-driven outflows more difficult.


It is to be mentioned here that most of the imaging techniques in RI literature work under the assumption of absence of any calibration errors or availability of pre-calibrated data. In the more practical scenario of working in the presence of DDE calibration errors, these terms need to be accounted for within the measurement model, such as done in Bhatnagar et al. (2013) in the case when these terms are known. Particularly for joint full polarization imaging, we can generalize the model proposed in Birdi et al. (2018b) and employ it to solve inverse problem (7). The corresponding imaging strategy leverages the CS theory. The main idea is to obtain an estimation of the sought images by solving a minimization problem of the form (Birdi et al. 2018a, b)
(9)$$\begin{eqnarray}
\underset{^{{{\boldsymbol{\sf {S}}}}}}{\mathrm{minimize}}\,\,\,\,r ({\boldsymbol{\sf {S}}}) \, \, \text{subject to} \, \, \Vert \Phi ({\boldsymbol{\sf {S}}}) - \boldsymbol {y} \Vert _2 \leqslant \epsilon ,
\end{eqnarray}$$where ϵ is related to the norm of the additive noise, ‖ · ‖2 denotes the ℓ2 norm of its argument vector. The term $r({\boldsymbol{\sf {S}}})$ is the regularization term, injecting prior information in the reconstruction process, whereas the data fidelity is ensured by the constraint $\Vert \Phi ({\boldsymbol{\sf {S}}}) - \boldsymbol {y} \Vert _2 \leqslant \epsilon$, implying that the residual is situated within an ℓ2 ball whose radius is determined by ϵ. In the current work, due to technical assumptions related to the proposed joint imaging and calibration algorithm (Chouzenoux et al. 2016), we propose to solve an unconstrained version of problem (9), given by
(10)$$\begin{eqnarray}
\underset{^{{{\boldsymbol{\sf {S}}}}}}{\mathrm{minimize}}\,\,\,\,\bar{h} \big ({\boldsymbol{\sf {S}}} \big) + r({\boldsymbol{\sf {S}}}),
\end{eqnarray}$$where $\bar{h}({\boldsymbol{\sf {S}}})$ is the data fidelity term. Using this formulation, and under the assumption that the additive noise is i.i.d. Gaussian, $\bar{h}({\boldsymbol{\sf {S}}})$ is given by a least-squares criterion
(11)$$\begin{eqnarray}
(\forall {\boldsymbol{\sf {S}}} \in {\mathbb {R}} ^{2 \times 2 N}) \, \, \bar{h}({\boldsymbol{\sf {S}}}) = \frac{1}{2}\Vert \Phi ({\boldsymbol{\sf {S}}}) - \boldsymbol {y} \Vert _2^2.
\end{eqnarray}$$This formulation has been introduced in Repetti et al. (2017) in the particular case of joint Stokes I imaging and calibration. In order to incorporate various polarimetric imaging specific prior informations in the regularization function, Birdi et al. (2018b) proposed to use a hybrid regularization term of the form
(12)$$\begin{eqnarray}
r({\boldsymbol{\sf {S}}}) = g({\boldsymbol{\sf {S}}}) + r^\prime ({\boldsymbol{\sf {S}}}),
\end{eqnarray}$$where the function $g:{\mathbb {R}} ^{2 \times 2N} \rightarrow ]-\infty , +\infty ]$ imposes sparsity of the underlying Stokes images and the function $r^\prime :{\mathbb {R}} ^{2 \times 2N} \rightarrow ]-\infty , +\infty ]$ constrains the domains of the argument images as per some physical constraints. In particular, the first term is inspired by the CS framework which proposes to exploit the sparsity of the target images in some dictionary ${\boldsymbol{\Psi }} \in {\mathbb {C}} ^{N \times J}$ (Candès et al. 2006; Donoho 2006). The choice of this dictionary is dependent on the images under scrutiny. To give an intuitive idea, images which are already sparse, for instance point sources images, are well represented by dirac basis taking ${\boldsymbol{\Psi }}$ to be identity. Otherwise, sparsity can be imposed in some other domain, such as TV regularization for piece-wise constant images (Rudin et al. 1992; Wiaux, Puy & Vandergheynst 2010; Akiyama et al. 2017), wavelet basis for smooth images (Mallat 2009), etc. In particular for astronomical images, a collection of wavelet bases is shown to be a good candidate for sparsifying dictionary ${\boldsymbol{\Psi }}$ (Carrillo et al. 2012, 2014), both for Stokes I imaging (Onose et al. 2016, 2017) and specifically for polarization imaging in Birdi et al. (2018a, b). Formally, for any matrix $\widetilde{{\boldsymbol{{{\sf S}}}}} \in {\mathbb {R}} ^{N \times 4}$, the sparse representation of the sought images in a chosen dictionary ${\boldsymbol{\Psi }}$ is given by ${\boldsymbol{\Psi }} ^\dagger \widetilde{{\boldsymbol{{{\sf S}}}}}$. The regularization function is then defined to impose sparsity of this term. This can be achieved by using the ℓ0 pseudo-norm, counting the number of non-zero components of its argument (Donoho et al. 1995). A more common approach is to use ℓ1 norm which overcomes the problem of non-convexity of the ℓ0 norm (Chen, Donoho & Saunders 2001). An even better approximation of the ℓ0 norm is provided by the (re)weighted ℓ1 norm, which tends to diminish the magnitude dependence of the ℓ1 norm (Candès et al. 2008; Carrillo et al. 2012). The (re)weighted ℓ1 norm is given by
(13)$$\begin{eqnarray}
g({\boldsymbol{\sf {S}}}) = \Vert {\boldsymbol{\Psi }} ^\dagger \mathcal {R} \big ({\boldsymbol{\sf {S}}} \big) \Vert _{{\boldsymbol{\sf {W}}},1} = \displaystyle \sum _{i=1}^4 \sum _{j=1}^J {\mathsf {W}} _{j,i} \big |[{\boldsymbol{\Psi }} ^\dagger \mathcal {R} \big ({\boldsymbol{\sf {S}}} \big) ]_{j,i} \big | \, ,
\end{eqnarray}$$where the subscripts j and i in the notation [ · ]j,i stand respectively for the row and column indices of the argument matrix, and $\mathcal {R}:{\mathbb {R}} ^{2 \times 2 N} \rightarrow {\mathbb {R}} ^{N \times 4}$ is the operator consisting in placing the four Stokes images contained in the matrix ${\boldsymbol{\sf {S}}}$ in four columns, whereas its adjoint $\mathcal {R}^\dagger :{\mathbb {R}} ^{N \times 4} \rightarrow {\mathbb {R}} ^{2 \times 2 N}$ does the contrary, i.e. stores the four images in the rows of a 2 × 2 block matrix. In equation (13), ${\boldsymbol{\sf {W}}} \in {\mathbb {R}} _+^{J \times 4}$ is the weighting matrix. In the case when this matrix is chosen to be identity, the ℓ1 regularization term is obtained. Another useful piece of information, which can be used to regularize the problem is the polarization constraint on the recovered Stokes images (Birdi et al. 2018b). This constraint comes from a physical point of view, that the polarized intensity should not exceed the total intensity and mathematically, can be described by the following set:
(14)$$\begin{eqnarray}
\mathbb {P} = \big \lbrace \widetilde{{\boldsymbol{{{\sf S}}}}} = \mathcal {R}\big ({\boldsymbol{\sf {S}}} \big) \in {\mathbb {R}} ^{N \times 4} \, \big | \, (\forall n \in \lbrace 1,\!\!\!&&\ldots ,N\rbrace) \nonumber \\
&& - \, \widetilde{{\mathsf {S}}}_{n,1} + \Vert \widetilde{{\boldsymbol{{{\sf S}}}}}_{n, 2:4} \Vert _2 \leqslant 0 \big \rbrace ,
\end{eqnarray}$$where, for every n ∈ {1, …, N}, $\widetilde{{\mathsf {S}}}_{n,1}$ and $\Vert \widetilde{{\boldsymbol{{{\sf S}}}}}_{n, 2:4} \Vert _2$ respectively represent the total intensity and the polarized intensity. As can be noticed, this constraint also imposes implicitly the positivity of the total intensity image (Stokes I). The enforcement of this constraint amounts to incorporation of the indicator function of the set $\mathbb {P}$ in the regularization function, i.e.
(15)$$\begin{eqnarray}
r^\prime ({\boldsymbol{\sf {S}}}) = \iota _{\mathbb {P}} ({\boldsymbol{\sf {S}}}).
\end{eqnarray}$$The indicator function of any such set $\mathbb {P}$ is defined as
(16)$$\begin{eqnarray}
\iota _{\mathbb {P}}({\boldsymbol{\sf {S}}}) = \left\lbrace \begin{array}{@{}l@{\quad }l@{}}0, \quad \quad \text{if} \, {\boldsymbol{\sf {S}}} \in \mathbb {P} \, , \\
+\infty , \quad \text{otherwise}. \end{array}\right.
\end{eqnarray}$$


In the study presented here, two solid-phase experiments were run for 3 hours each, to produce cosmic grain analogs from methane (5%) and acetylene (5%) precursors, respectively, seeded in a cold supersonic expansion of argon. Different concentrations of methane were tested in COSmIC, and the 5% concentration was chosen to produce sufficient solid material for analysis in our experimental setup. Methane is a one carbon-atom alkane known to be present in the CSE of carbon-rich stars (Van de Sande & Millar 2019). Acetylene is a two-carbon alkene and the most abundant molecule in the inner region of the CSE where cosmic grains are formed, after H2 and CO (Fonfria et al. 2008), and is a known precursor of aromatic compounds (Frenklach & Feigelson 1989). For each experiment, chemistry was induced by the plasma discharge through fragmentation and ionization of the molecular precursor and plasma-generated chemical reactions between the precursor, its atomic and molecular fragments, radicals, and ions, resulting in the production of larger molecules and eventually solid particles. The resulting carbon grains, analogs of cosmic dust, were deposited on 3 mm diameter transmission electron microscopy (TEM) copper grids with Ultrathin Carbon Film on Lacey Carbon Support Film (Ted Pella, 400 mesh) placed 3 cm away from the slit, far enough away to avoid strong disturbances of the expansion. Ultra-high purity (UHP; 99.9998%) Ar and CH4 gas cylinders were used. The protocol for the addition of C2H2 to the gas mixture using a cold trap has been described in Sciamma-O’Brien et al. (2014). After deposition, the samples were collected under inert argon atmosphere using a custom-made glove box connected to the chamber (see Figure 1), and placed in plastic containers sealed with parafilm to minimize exposure to air before the ex situ analysis of the sample at the SEM facility located at the NASA Ames Advanced Studies Laboratories (Sciamma-O’Brien et al. 2017). The SEM technique was used to characterize the cosmic grain analogs produced in COSmIC. By using the same relative concentration for methane and acetylene (5%), only one experimental parameter (the nature of the precursor) was changed while maintaining all other experimental parameters (energy, temperature, precursor density, and reaction time) identical, thus allowing us to investigate the effect of the molecular precursors (CH4 versus C2H2) on the grain size and morphology under controlled conditions.


We find that it is possible to infer

 and

, at the precision of spectroscopy and relatively imprecise

 and

 for red-giant stars. We attempted to infer the [Fe/H]; this label is available from the apogee spectroscopy for our stars. However, this label failed and, on inspection, no pixels correlated with [Fe/H]. Therefore, contrary to the findings by Corsaro et al. (2017), we find that there is no information with respect to [Fe/H] in the granulation signal from the Kepler multiepoch photometry. We note that corrections to scaling relations between

 and fundamental stellar parameters include both

 and [Fe/H] (White et al. 2011; Guggenberger et al. 2016; Sharma et al. 2016). Furthermore, Viani et al. (2017) showed, in the case of

, a dependence on mean molecular weight. While we do not find the signature in the ACF amplitude, this does indicate that a [Fe/H] dependence might be expected, as was also suggested by 3D hydrodynamical simulations of convection (Collet et al. 2007; Ludwig & Steffen 2016). For our proposed methodology, the model should be applied to test data that is assumed to be derived from the underlying population as the training data. Nevertheless, to assess the impact of stellar metallicity on the inference of our labels, we performed a test where we divided stars into two groups around the mean metallicity of the sample. We created a training set of stars with [Fe/H] > 0 and a test set with [Fe/H]  0 dex. These stars broadly cover the same

,

, and

 and

 ranges, although the means of these labels are shifted. We find that the

 label is impacted at test time when training on a sample of stars with metallicities not covered in the test sample. The inferred

 is biased to be about 85 K too hot, for training on the metal-rich stars and testing on the more metal-poor stars and 85 K too cold, for the reverse (although with a similar precision as before). This indicates that the [Fe/H] of the star is constraining as to the scale of the

, even if we cannot learn this information from the data. The inference of the other three labels is not similarly affected by drawing the test and training set from different metallicity distributions. It is interesting that metallicity affects the

 and not the other labels. This means that temperature manifests itself differently in the spectra of stars with low and high metallicities. When we do not include stars with low metallicity in the training sample, we cannot accurately predict the temperatures of low metallicity stars during test, and vice versa, as temperature-induced variations in the spectrum must depend on metallicity. The fact that this is not true for other parameters implies that variations in seismic parameters produce variations in the ACF that are independent of metallicity; we therefore do not need to know the metallicity of our stars to infer these parameters to the precision captured using this technique. There is a theoretical expectation that the asteroseismic observables will vary with stellar metallicity (e.g., White et al. 2011; Guggenberger et al. 2016; Kallinger et al. 2018; Viani et al. 2017). Following on from this, there is also opportunity to investigate this in more detail with a data-driven approach.


Radial velocity measurements (Anglada-Escudé et al. 2016) can only give us a minimum planetary mass, as long as no additional information is available to constrain the inclination of the star–planet system with respect to our observational plane. No transit of the planet has been observed so far, leading to the conclusion that the inclination is likely below 90°, and therefore the actual mass of the planet should be larger than 1.27 M⊕. Anglada et al. (2017) proposed the existence of a dust belt at an orbit of about 30 AU from the star, which, if confirmed, would suggest an inclination of the system of 45° with respectto the plane of the sky. Since confirmation has not been possible to date, we assumed four different inclinations spanning the wide range of likely inclinations and hence actual planet masses: 90, 60, 45, and 30°. The corresponding planet masses would then be 1.27, 1.47, 1.8, and 2.54 M⊕ (see also Table 2). The table lists in addition the predicted planet and core radii determined with our interior structure model (Noack et al. 2017) as well as the assumed initial temperature at the core–mantle boundary after planet accretion and solidification based on Stixrude (2014) and Noack & Lasbleis (2020). Both the iron content and the planet mass have a strong effect on the planetary structure and temperature profile. The resulting initial temperature profile in mantle and core, as well as the density, gravitational acceleration, pressure, and electrical conductivity profiles are shown in Fig. 1 for all investigated planet cases. The thermodynamic parameters (density as well as heat capacity and thermal expansivity of the material) were calculated following Noack et al. (2017) and using equations ofstate from Stixrude & Lithgow-Bertelloni (2011) for the mantle and Bouchet et al. (2013) for the metal core (here composed only of pure iron). The electrical conductivity profile is taken to be Earth-like from Xu et al. (2000). Thermal conductivity was calculated with the parametrisations derived in Tosi et al. (2013). For simplicity, the profiles for the different mantle properties were fixed during the evolution and did not take into account the influence of local melting or evolving chemical heterogeneity. The initial temperature profile, which is used in our interior evolution studies (described in Sect. 2.4), resembles the temperature profile depicted in Fig. 1. The temperature at the core–mantle boundary, however, and therefore the adiabatic temperature in the core, was scaled with the core–mantle boundary (CMB) temperature jump, which was varied in our study to investigate its effect on outgassing efficiency. Furthermore, we did not assume the existence of a primary atmosphere (see discussion in Sect. 4.1). During the evolution of Proxima Cen b, changes in atmospheric composition and mass can affect the surface temperature. However, since we did not couple our outgassing model to an atmospheric evolution model, surface temperatures remain constant throughout the evolution.


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).


Before the detection of GW170817, many associated EM counterparts had already been proposed for NS–NS/BH mergers, and their relative brightness is essentially determined by the properties of the post-merger central remnant object. In general, the merger remnant for an NS–BH merger would be a BH. But an NS–NS merger could lead to a BH or a supramassive NS, depending on the total mass of the NS–NS system and the NS equation of state (Dai et al. 2006; Gao & Fan 2006; Zhang 2013; Lasky et al. 2014; Gao et al. 2016). It is generally believed that, for both cases, sGRBs and their afterglow emission are expected as one of the major EM counterparts of NS–NS/BH mergers (Eichler et al. 1989; Narayan et al. 1992; Berger 2014). On the other hand, for both cases, the merger remnant would be surrounded by a mildly isotropic, sub-relativistic ejecta (which is composed of the tidally ripped and dynamically launched materials during the merger and the matter launched from the neutrino-driven wind from the accretion disk or neutron star surface; Rezzolla et al. 2011; Bauswein et al. 2013; Hotokezaka et al. 2013; Lei et al. 2013; Rosswog et al. 2013; Fernández et al. 2015; Song & Liu 2017). These ejecta are mostly composed of neutron-rich materials, and the radioactivity of these materials and the decay of r-process nuclei would heat the ejecta and then power an optical/IR transient (Li & Paczyński 1998; Metzger et al. 2010). When the merger remnant is a BH, r-process related radioactivity would be the only heating source, so that the luminosity of the optical/IR transient would be roughly ∼103 times that of the nova luminosity (Metzger et al. 2010). But if the merger remnant is a supramassive NS, its magnetic dipole radiation could serve as an additional heating source to the ejecta (Gao et al. 2013; Zhang 2013), which could easily exceed the r-process power, so that the thermal emission from the ejecta would be significantly enhanced (Yu et al. 2013; Metzger & Piro 2014). The luminosity of the optical transient, in this case, would be systematically brighter by more than one order of magnitude than the r-process dominating cases (Gao et al. 2017). Since the thermal emissions from the ejecta are essentially isotropic and also non-relativistic or mildly relativistic (due to the heavy mass loading), they therefore can be detected from any direction if the flux is high enough (see Metzger 2017a for a review).


The basic idea, summarized in Dekel et al. (2009), is that during VDI, the high surface density of gas and ‘cold’ young stars, Σ, drives the Toomre Q parameter below unity, Q ∼ σΩ/(πGΣ) ≲ 1, where σ is the 1D velocity dispersion and Ω is the angular frequency, a proxy to the epicyclic frequency κ, which is related to the potential well (Toomre 1964). It has been established that under such conditions, the disc will fragment and produce large star-forming clumps. This has been shown using idealized simulations of isolated galaxies (Noguchi 1999; Gammie 2001; Immeli et al. 2004a,b; Bournaud, Elmegreen & Elmegreen 2007; Elmegreen, Bournaud & Elmegreen 2008; Bournaud & Elmegreen 2009; Hopkins et al. 2012b), as well as cosmological simulations (Agertz, Teyssier & Moore 2009; Ceverino et al. 2010; Ceverino et al. 2012; Genel et al. 2012; Mandelker et al. 2014; Oklopcic et al. 2016). The ratio of clump mass to the mass of the cold disc scales as Mc/Md ∝ δ2, where δ = Md/Mtot is the ratio of the cold disc mass to the total mass within the disc radius, which includes the bulge and dark matter halo (e.g. Dekel et al. 2009). This leads to much larger clumps at z ∼ 2 than the low-redshift giant molecular clouds (GMCs). Gravitational interactions in the perturbed disc drive turbulence causing the disc to self-regulate in a marginally stable state with Q ≲ 1 (Dekel et al. 2009; Ceverino et al. 2010; Krumholz & Burkert 2010; Cacciato, Dekel & Genel 2012; Forbes, Krumholz & Burkert 2012; Forbes et al. 2014) that can last for more than a Gyr so long as the accretion is not interrupted. Some recent works have called into question the validity of linear Toomre analysis in the context of these highly non-linear galaxies (Behrendt, Burkert & Schartmann 2015; Tamburello et al. 2015; Inoue et al. 2016) and others have suggested alternate fragmentation mechanisms related to turbulence (e.g. Hopkins 2013). However, since clump formation is largely determined by the balance between self-gravity, turbulent pressure and the centrifugal force, the largest clumps are always roughly at the Toomre scale. Larger clumps would be disrupted due to the shear and/or tidal forces within the disc, or would not collapse in the first place due to the centrifugal force. Therefore, regardless of the full validity of linear Toomre analysis, it is plausible that the Toomre Q parameter can serve as a crude criterion for instability, possibly with a critical value that is larger than unity.


The EWs were measured with the methods described in Vásquez et al. (2015). As in Paper I, we used the sum of the EWs of the two strongest CaT lines (λ8542, λ8662) as a metallicity estimator, following the Ca II triplet method of Armandroff & Da Costa (1991). Different functions have been tested in the literature to measure the EWs of the CaT lines, depending on the metallicity regime. For metal-poor stars ([Fe/H] ≲ −0.7 dex) a Gaussian function was used with excellent results (Armandroff & Da Costa 1991), while a more general function (such as a Moffat function or the sum of a Gaussian and Lorentzian, G + L) is needed to fit the strong wings of the CaT lines observed in metal-rich stars (Rutledge et al. 1997; Cole et al. 2004). Following our previous work (Gullieuszik et al. 2009; Saviane et al. 2012) we have adopted here a G+L profile fit. To measure the EWs, each spectrum was normalised with a low-order polynomial using the IRAF continuum task, and set to the rest frame by correcting for the observed radial velocity. The two strongest CaT lines were fitted by a G+L profile using a non-linear least squares fitting routine part of the R programming language. Five clusters from the sample of Saviane et al. (2012) covering a wide metallicity range were re-reduced and analysed with our code to ensure that our EWs measurements are on the same scale as the template clusters used to define the metallicity calibration. Figure 5 shows the comparison between our EWs measurements and the line strengths measured by Saviane et al. (2012) (in both cases the sum of the two strongest lines) for the five calibration clusters. The observed scatter is consistent with the internal errors of the EW measurements, computed as in Vásquez et al. (2015). The measurements show a small deviation from the unity relation, which is more evident at low metallicity. A linear fit to this trend gives the relation: ΣEW(S12) = 0.97 ΣEW(this work) + 0.21, with an rms about the fit of 0.13 Å. This fit is shown in Fig. 5 as a dashed black line. For internal consistency, all EWs in this work have been adjusted to the measurement scale of Saviane et al. (2012) by using this relation. In Table 3 we provide the coordinates, radial velocities, and the sum of the equivalent widths for the cluster member stars, both measured (“m”) and corrected (“c”) to the system of Saviane et al. 2012.


The relationship established in our study between the occurrence rates of major flares and FHCMEs and the annual average latitude of sunspot groups may indicate the role of long-distance magnetic connectivity in the dependence of occurrence rates on the SC phase. In particular, the annual average latitude of sunspot groups determines the average length of trans-equatorial loops (TLs). A TL is a coronal loop connecting two separate ARs located in the opposite hemispheres (e.g., Tsuneta 1996; Pevtsov 2000). It has been found to be a common phenomenon, with up to one-third of all ARs exhibiting TLs in soft X-ray images (Pevtsov 2000). Therefore, our results may be a statistical indication that large-scale magnetic connectivities highlighted by TLs are important for producing solar activity such as major flares and FHCMEs. There have been many studies on the topology of the large-scale solar magnetic field structure (e.g., Babcock 1961; Hansen & Hansen 1975) and the relationship between the occurrence of solar flares / CMEs and large-scale magnetic connectivity (e.g., Antiochos et al. 1999; Khan & Hudson 2000; Wang & Sheeley 2003; Wang et al. 2007; Zhou et al. 2007; Fu & Welsch 2016). In particular, Dalla et al. (2007) established that the flaring rate (weakly) increases with the appearance of a new AR within 12° of the pre-existing flaring AR. Also, it has been reported that the interaction of ARs increases as sunspots move toward the equator (McIntosh & Leamon 2014; McIntosh et al. 2014). Such interactions may be related to the reconnection of magnetic fields that belong to different ARs, and the subsequent formation of large-scale structures such as TLs, which play an important role in triggering flares and CMEs (Khan & Hudson 2000). Moon et al. (2002) showed that sympathetic flares are more frequent in TLs than in loops connecting two ARs in the same hemisphere. Chen et al. (2006) examined the relation between the number of soft X-ray TLs and that of ARs each year from 1991 to 2001. They found good correlations of the TL numbers with SC indices, with the increase in TL number during the descending phase of SC 22 in comparison to other phases of SC 22. The effect of the dependence of flaring activity on AR separation and connectivity may be understood in terms of the interaction of magnetic energy between these ARs (Fu & Welsch 2016).