The origin of the observed colour bimodality must be explained by successful models of galaxy formation. Considerable efforts have been directed towards reproducing the observed distribution of galaxy colours using different semi-analytic models of galaxy formation (Menci et al. 2005; Cattaneo et al. 2006, 2007; Driver et al. 2006; Cameron et al. 2009; Trayford et al. 2016; Nelson et al. 2018; Correa, Schaye & Trayford 2019). A significant number of studies have also been devoted to understand the spatial distribution of red and blue galaxies using various clustering measures like two-point correlation function (Zehavi et al. 2011), three-point correlation function (Kayo et al. 2004), genus (Hoyle et al. 2002), filamentarity (Pandey & Bharadwaj 2006), and local dimension (Pandey & Sarkar 2020). The studies of mass function of red and blue galaxies (Drory et al. 2009; Taylor et al. 2015) play a crucial role in guiding the theories of galaxy formation and evolution. Any such analysis requires one to classify the red and blue galaxies using some operational definition. But colour is a subjective judgment and it is difficult to classify galaxies according to their colours in an objective manner. Also, one should remember that it is the observed bimodal distribution of galaxy colours that motivates us to classify the galaxies according to their colours. In reality, no galaxies can be regarded as truly either ‘red’ or ‘blue’ based on their colours. Strateva et al. (2001) prescribed that the red and blue galaxies can be separated by using an optimal colour separator (u − r) = 2.22. However, a substantial overlap between the two populations prohibit us to objectively define galaxies as ‘red’ and ‘blue’ based on their colours. The boundary separating the two populations remains arbitrary and currently there are no meaningful theoretical arguments favouring any specific cut over others. Applying a hard cut to define samples of red and blue galaxies is expected to introduce significant contamination in these samples. Previously, Coppa et al. (2011) used an unsupervised fuzzy partition clustering algorithm applied on the principal components of a PCA analysis to study the bimodality in galaxy colours. Another study by Norman et al. (2004) use Bayesian statistical methods instead of sharp cuts in parameter space for such classification problems.


Recently, dust-obscured galaxies (DOGs, Dey et al. 2008) shed light on this issue, because SMBHs in DOGs are expected to be rapidly growing during the coevolution. DOGs are originally defined as galaxies that are bright in mid-infrared (MIR), while faint in optical. Specifically,

 (i.e.,

; Dey et al. 2008; Fiore et al. 2008). In the context of the gas-rich major-merger scenario, it is expected that the SF phase evolves into the AGN phase because the merging event leads to the active SF, while the gas accretion onto the nucleus caused by such a merger requires some time (see, e.g., Davies et al. 2007; Hopkins 2012; Matsuoka et al. 2017). Because such active galaxies are expected to be heavily surrounded by dust, DOGs potentially correspond to galaxies in the SF phase or AGN phase (Dey et al. 2008; Hopkins et al. 2008). DOGs are classified into two subclasses according to their spectral energy distribution (SED): “bump DOGs” and “power-law (PL) DOGs” (Dey et al. 2008). The bump DOGs show a rest-frame 1.6 μm stellar bump in their SEDs, while the PL DOGs show a power-law feature on their SEDs. Therefore, it is considered that the bump DOGs correspond to galaxies in SF mode (Desai et al. 2009; Bussmann et al. 2011), while the PL DOGs correspond to galaxies in the AGN phase (Fiore et al. 2008; Bussmann et al. 2009; Melbourne et al. 2012). The fraction of PL DOGs among all DOGs increases with increasing MIR flux density (e.g., Dey et al. 2008; Toba et al. 2015), which is similar to the behavior of the luminosity dependence of the AGN fraction in ultraluminous infrared (IR) galaxies (ULIRGs; see Sanders & Mirabel 1996 for a review). The comoving number density of DOGs shows its peak at z ∼ 1–2 (e.g., Dey et al. 2008; Toba et al. 2017), which corresponds to the peak of SF rate density and the growth rate of SMBHs (e.g., Richards et al. 2006; Madau & Dickinson 2014). This strongly suggests that DOGs are related to the most active objects in terms of the coevolution between galaxies and SMBHs. In this sense, DOGs with a high IR luminosity potentially harbor a rapidly growing SMBH and are, therefore, important for understanding the coevolution of galaxies and SMBHs.


However, using the well-assessed new post-AGB evolutionary models, we confined the main-sequence ages of our halo sample to be mostly ∼2–5 Gyr, with the oldest being ∼6–8 Gyr, while the outer-disk sample are mostly ≲1–4 Gyr. We thus conjecture that our targets probably formed prior to the encounter with M33. Obviously, our sample represents the population that is different from the underlying, smooth, extended (and mostly metal-poor) halo component of M31 (Ibata et al. 2007, 2014), which was formed through the repeated accretion of smaller galaxies in the distant past. These bright PNe seem to resemble the younger, metal-rich population in the outer stream of M31, as revealed by HST pencil-beam pointings on the Giant Stream (Brown et al. 2006a; Bernard et al. 2015b). The metallicity of the stream fields was enriched continuously from [Fe/H] ∼ −1.5 to at least solar level about 5 Gyr ago (Bernard et al. 2015b). This timeline of metal enrichment is generally consistent with the stellar ages of our metal-rich sample. N-body simulations suggested that the Giant Stream and other stream-like features in the halo are debris of a massive (≳109–

) progenitor that was recently disrupted during the course of a merger (e.g., Ibata et al. 2004; Fardal et al. 2006, 2007, 2008, 2013; Font et al. 2006; Geehan et al. 2006; Mori & Rich 2008; Sadoun et al. 2014). The extended star formation history and the broad range of metallicity (−1.5 ≲ [Fe/H] ≲ 0.2) discovered in the stream fields can be explained by a disk galaxy progenitor (Brown et al. 2006a, 2006b; Bernard et al. 2015b). If the stellar streams in M31's halo indeed have a common origin, our sample of halo PNe then probably formed through extended star formation in this possibly massive, disk-like progenitor. Moreover, some simulations predict that the remnant of the disrupted satellite resides in the NE Shelf (e.g., Fardal et al. 2008, 2013; Sadoun et al. 2014); PN17 in our sample is located in this region and might be associated with this substructure (see Section 4.4).


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.


The first investigations of the rotational spectra of ethyl isocyanide were carried out in 1966 by Bolton et al. (1966). The spectra of the first vibrational and torsional excited states were measured in the centimeter wave domain (Anderson & Gwinn 1968). In this initial study, the dipole moment was determined to be μa = 3.79 D and μb = 1.31 D; this value is usually large for a molecule that includes a CN group. This causes dense and intense rotational spectra in the millimeter wave range and also in the submillimeter wave range up to 900 GHz (bQ lines). Anderson & Gwinn (1968) also observed some A–E splittings due to the internal rotation motion of the methyl group. The most recent spectroscopic study is from Krüger & Dreizler (1992) who reinvestigated the internal rotation measurements and also determined hyperfine coupling parameters due to the nitrogen quadrupole. As in our previous studies of ethyl cyanide isotopologs, it was not possible to observe internal rotation and hyperfine splittings due to our Doppler limited resolution. Our analysis was rather easy, starting from a prediction based on Krüger & Dreizler (1992) parameters. First, we analyzed and fit the most intense transitions, the aRh transitions, up to 330 GHz. These transitions were shifted only a few MHz from the initial predictions. Then bR and bQ lines were searched and included in the fit up to 330 GHz. Next, all the spectra were analyzed up to 990 GHz without difficulty. For the fitting, we employed ASFIT (Kisiel 2001) and predictions were made with SPCAT (Pickett 1991). The global fits included 6 transitions from Anderson & Gwinn (1968), 29 lines from Krüger & Dreizler (1992), and 2906 from this work. The maximal quantum numbers are J = 103 and Ka = 30. Both reductions A and S were tested. A reduction permits us to check theagreement of our new parameters set with those from Krüger & Dreizler (1992) (Table 1). Using S reduction slightly decreases root mean square from 30.3 to28.7 kHz. The condition numbers are nearly the same: 295 and 310 for the A and S reductions, respectively.The A reduction requires 23 parameters, but 5 additional parameters are required for the S reduction (Table 2). For this reason we used the A reduction even if this molecule is close to the prolate limit with kappa = −0.9521. Part of the new measurements are in Table 3. Owing to its large size, the complete version of the global fit Table S1 is supplied at the CDS. The fitting files .lin (S2), .par (S3), and the prediction .cat (S4) are also available at CDS.


Fast radio bursts (FRBs) are bright, cosmological origin, and millisecond-duration bursts in radio wavelengths (Lorimer et al. 2007; Thornton et al. 2013; Bassa et al. 2017; Macquart et al. 2020). After the discovery of the first FRB (Lorimer et al. 2007), a number of dedicated facilities have been conducted to search FRBs, such as the Parkes telescope (e.g., Bhandari et al. 2018), the updated Molonglo Observatory Synthesis Telescope (e.g., Farah et al. 2018), the Australian Square Kilometre Array Pathfinder (e.g., Shannon et al. 2018), the Canadian Hydrogen Intensity Mapping Experiment (CHIME; The CHIME/FRB Collaboration et al. 2018), the Deep Synoptic Array (Kocz et al. 2019; Ravi et al. 2019), the Green Bank Telescope (Masui et al. 2019), Arecibo (Spitler et al. 2014; Patel et al. 2018), and the Five-hundred-meter Aperture Spherical radio Telescope (FAST; Nan et al. 2011; Li et al. 2019). All these efforts result in an increasing rate of new FRB detections. Among them, more than 20 repeating FRBs have been reported. Particularly, the physical origin of the repeating FRB 20121102A was identified to be with a low-metallicity star-forming dwarf galaxy at a redshift 0.19273 (Bassa et al. 2017; Tendulkar et al. 2017). Another repeating FRB 20190523A was found to be associated with a more massive but low specific star formation rate (Ravi et al. 2019). The identification of the counterpart of the brightest radio bursts from SGR 1935+2154 as a magnetar in our Galaxy by HXMT (Li et al. 2021) and INTEGRAL (Mereghetti et al. 2020) with short-duration X-ray bursts suggests that at least a fraction of FRBs are connected with newborn magnetized neutron stars (e.g., Weltman & Walters 2020; Zhang 2021). More bursts with similar characteristics need to be detected in the future to confirm this conclusion. Recently, a new large sample with 535 FRBs was presented by CHIME/FRB Collaboration et al. (2021) that were detected by the CHIME survey, including 61 bursts from 18 previously reported repeating sources and 474 one-off bursts. Though an increasing catalog of theories and models is developing to explain the physical nature of FRBs (e.g., see the review of Platts et al. 2019; Xiao et al. 2021), the origin of FRBs remains a mystery.


It is now well established that intrinsic alignments exist in the Universe, and must be accounted for at some level to avoid biasing cosmological analyses based on cosmic shear and galaxy–galaxy lensing. IAs have been included in cosmic shear analyses for as long as shear has been a competitive cosmological probe (Heymans et al. 2013; Dark Energy Survey Collaboration 2016; Jee et al. 2016; Troxel et al. 2018; Chang et al. 2019; Hikage et al. 2019; Hamana et al. 2020; Hildebrandt et al. 2020; Asgari et al. 2021). Only recently, however, have the lensing data been of sufficient volume to potentially incur biases due to model insufficiency (see Krause et al. 2016, and the Stage IV forecasts of Fortuna et al. 2021 and the tests in the context of DES Y3 Secco, Samuroff et al. 2021; see also Joachimi et al. 2020 for an interesting counter discussion). Developing a fuller understanding of intrinsic alignments, then, will be crucial for, arguably, the current generation of cosmological surveys, and certainly the next. This paper is one small step in this direction, providing the first detailed analysis at the level of model constraints on the best available cosmological hydrodynamic simulations. Our results, of course, come with a number of caveats. Most notably, our selection function is not intended to accurately match current or future lensing surveys. This is in part because recreating the complex redshift-dependent selection function in a real lensing sample, which would typically be based on a number of correlated observables, is a difficult task; it is also, however, a function of our aim in this study. We wish to understand the behaviour of IAs at a physical level, in order to feed into understanding IAs and model building efforts, rather than make a detailed prediction or robustness test for a particular survey. The behaviour of intrinsic alignments on small physical scales is an important topic for future investigation, and one that could conceivably be addressed using hydrodynamic simulations; indeed, due to the larger number of measureable modes, the signal to noise on small scales is relatively high. The TATT approach allows some hope of pushing to smaller scales (though not into the regime of ∼1 h−1 Mpc, where one would need an explicit model for 1h alignment contributions). Unfortunately, a number of other poorly understood effects enter on small scales, particularly non-linear galaxy bias and baryonic physics. In order to pursue IA constraints on such scales, it is likely that one would need to consider both higher order bias terms and the interplay with the higher order IA terms.


Among the existing IACT systems, HESS has the largest FoV and hence provides the highest sensitivity for the diffuse γ-ray flux. Its electron spectrum analysis technique could be directly used to obtain a measurement of the diffuse Galactic γ-ray flux above energies of several TeV in the Galactic Ridge (|l|  30°, |b|  2°) region; see Figs. 3 and 4. A multi-year exposure of HESS could be sufficient for detection of the diffuse emission even from regions of higher Galactic latitude. This is illustrated in Fig. 5, where thick blue and red data points show mild high-energy excesses of the electron spectra derived by Kraus (2018), Kerszberg et al. (2017), Kerszberg (2017) over broken power-law models derived from the fits to lower energy data. Comparing these excesses with the level of the IceCube astrophysical neutrino flux and with the Fermi/LAT diffuse sky flux from the region |b| > 7° (corresponding to the data selection criterium of HESS analysis Kerszberg et al. 2017; Kerszberg 2017) we find that the overall excess flux levels are comparable to expected diffuse γ-ray flux from the sky region covered by the HESS analysis (the quoted systematic error on the electron flux is Δlog(EFE) ≃ 0.4). The overall excesses within 805 and 1186 h of HESS exposures (Kraus 2018; Kerszberg 2017) are at the levels of >4σ for the analysis of Kraus (2018) and 1.7σ for the analysis of Kerszberg (2017). A factor-of-ten longer exposure (which is potentially already available with HESS) could reveal a higher significance excess at the level of up to 5σ. Such an excess is predicted in a range of theoretical models including interactions of cosmic rays injected by a nearby source (Andersen et al. 2018; Neronov et al. 2018; Bouyahiaoui et al. 2019) or decays of dark matter particles (Berezinsky et al. 1997; Feldstein et al. 2013; Esmaili & Serpico 2013; Neronov et al. 2018) or a large-scale cosmic ray halo around the Galaxy (Taylor et al. 2014; Blasi & Amato 2019).


This work improves the efficiency of component by component modelling that has been successful in recovering the physical conditions for various individual absorbers (e.g. Churchill & Charlton 1999; Charlton et al. 2000, 2003; Ding et al. 2003a, 2003b; Zonak et al. 2004; Ding, Charlton & Churchill 2005; Masiero et al. 2005; Lynch & Charlton 2007; Misawa et al. 2008; Jones et al. 2010; Lacki & Charlton 2010; Muzahid et al. 2015; Richter et al. 2018; Rosenwasser et al. 2018). Rather than averaging over components and phases, it is possible to determine how much of the H i is associated with these different phases in order to derive separate metallicities for various clouds. Resolving the individual clouds allows us to break the degeneracy for components on the flat part of the Lyα curve of growth, even with coverage of just saturated H i lines, and derive metallicity constraints for different parcels of gas along the line of sight. It is important to do so because different processes, e.g. outflows (Bouché et al. 2012; Bordoloi et al. 2014; Rubin et al. 2014; Schroetter et al. 2016), pristine accretion (Martin et al. 2012; Rubin et al. 2012; Danovich et al. 2015), recycled accretion (Ford et al. 2014), minor and major mergers (Martin et al. 2012; Anglés-Alcázar et al. 2017), are surely contributing to the same system, and it is expected that conditions will vary significantly along a line of sight which can span hundreds of kpc spatially (Churchill et al. 2015; Peeples et al. 2019). This will lead to a more meaningful comparison to galaxy properties. For example, Pointon et al. (2019) did not find a difference between the metallicities of absorbers found within an impact parameter of 200 kpc along the major and the minor axes of isolated galaxies. Based on cosmological hydrodynamic simulations, a larger metallicity is expected along the minor axis due to outflows and a lower metallicity along the major axis due to inflows (Peroux et al. 2020). However, an observational trend could exist, for example, for the minor axis to have some, but not all, high metallicity components, or for the minor axis to have one or more low metallicity components. Such results would be ‘washed out’ by deriving an average metallicity for all gas along a line of sight, which clearly often has multiple complex origins. For some data sets/projects, the new analysis could be transformative, however, to make it feasible to use for large statistical studies it is important that the analysis is semi-automated and robust.


Sulfur-bearing molecules constitute a fundamental branch of prebiotic chemistry due to the recently gained importance of cysteine C3H7NO2S as a catalyst in the assembly of complex peptides (Foden et al. 2020). In cold, interstellar environments, cysteine is far from being detected, but other complex organic molecules (COMs) of prebiotic importance bearing S have recently been detected, highlighting ethyl mercaptan C2H5SH or thioformic acid (HC(O)SH; Kolesniková et al. 2014; Rodríguez-Almeida et al. 2021). In turn, the family of compounds to which HC(O)SH belongs (thioacids) has also been pointed out as possible catalysts in prebiotic processes in a primordial Earth (Chandru et al. 2016). Particularly puzzling is the fact that the presence of these molecules on Earth could have a (at least partial) panspermic origin, owing to both a confirmed presence of sulfur-bearing species in comets (Korth et al. 1986; Krishna Swamy & Wallis 1987; Calmonte et al. 2016; Rubin et al. 2019) and the fact that the simplest thioacid (thioformic acid) has been recently identified in the interstellar medium (ISM; i.e., the giant molecular cloud G+0.693; see Rodríguez-Almeida et al. 2021). The chemical mechanism behind the formation of thioformic acid is unknown, but such a mechanism needs to explain the formation of HC(O)SH from simple, sulfur-bearing precursors. In Rodríguez-Almeida et al. (2021) several possible routes were postulated for the formation of HC(O)SH, namely,
1

CO+SH→HSCO→HHC(O)SH,

2

HCO+SH→HC(O)SH,

3

OCS+2H→HC(O)SH.

In this work, we have focused on reaction (3) on interstellar dust grains, having two main objectives in mind. First, we wish to check whether or not the reaction proceeds effectively, and, second, we wish to determine the stereoisomerism of the reaction. The study of reaction (3) sparked our interest for two main reasons. First, OCS is a moderately abundant molecule in the astronomical source where HC(O)SH was detected (Armijos-Abendaño et al. 2014; Rodríguez-Almeida et al. 2021); second OCS is the only sulfur-bearing species positively detected on interstellar ices (Palumbo et al. 1997).


One major issue we face with the ALMA dust polarization observations is spatial filtering by the interferometer, which removes the scales of emission that are not included in the uv -coverage of the dataset. In contrast to the statistical analysis of dust polarization performed with single dish instruments such as Planck (Planck Collaboration Int. XIX 2015; Planck Collaboration Int. XX 2015; Planck Collaboration XII 2020), BLASTPOL in Fissel et al. (2016), and SCUPOL (Poidevin et al. 2013), our analysis of interferometric data requires us to characterize how the filtering alters the polarization quantities we use in our statistics. With this aim, we use a set of synthetically observed non-ideal MHD simulations computed with RAMSES (Teyssier 2002; Fromang et al. 2006) that follow the gravitational collapse of cores whose range of initial mass and turbulence reproduce the main characteristics of the sources from our sample. The set consists of six simulations of collapsing cores (with total masses of 30, 60, and 100 M⊙). We perform radiative transfer on these models using the POLARIS code (Reissl et al. 2016), which produces the Stokes I, Q, and U maps and assumeseither that a constant fraction of the dust grains are perfectly aligned everywhere (perfect alignment, known as “PA” hereafter) or that paramagnetic grains are aligned via radiative torques, known as “RATs” hereafter (e.g., Lazarian 2007). We note that the hypothesis of perfect alignment is not physical, and we do not aim to reproduce or interpret the polarized dust emission from Class 0 envelopes as resulting from perfect alignment. However, while we recognize that an hypothesis of perfect dust alignment is not a physical model but a phenomenological one, it has been suggested that the properties of dust polarization at the larger scales of the diffuse ISM (especially the results of

${{\mathcal{S}}\times{\mathcal{P}_{\rm{frac}}}}$S×Pfrac
) can be explained and reproduced with perfect alignment (Planck Collaboration XII 2020; Seifried et al. 2020). In the first part of our discussion we aim to compare our results with those obtained at larger scales, and thus perfect alignment remains an interesting point of comparison with RATs, and is a useful benchmark to compare how different physical models of grain alignment affect the statistical properties of the polarized emission. In addition, a case where the grains are perfectly aligned is only taking into account the source-specific geometrical effects governing the resulting polarization maps, and thus is useful to understand where alignment drops or is suppressed. We present all the details of the simulations and the radiative transfer calculations in Appendix D. In order to produce realistic synthetic observations to compare with the ALMA datasets, we use the CASA simulator (with the typical ALMA uv -coverage of these observations) to implement the effects of interferometric filtering and atmospheric noise on the POLARIS synthetic emission maps.


Whistler precursors are a manifestation of dispersive radiation (Tidman & Northrop 1968; Fairfield 1974; Hoppe 1981; Mellott & Greenstadt 1984), one mechanism through which collisionless shocks may transform bulk flow kinetic energy into other forms of energy. Several other mechanisms have been proposed, including wave–particle interactions (Sagdeev 1966; Coroniti 1970a; Gary 1981), particle reflection (Edmiston & Kennel 1984; Kennel et al. 1985; Kennel 1987; Bale et al. 2005; Su et al. 2012), and macroscopic quasi-static field effects (Scudder et al. 1986a, 1986b, 1986c). At low Mf, theory suggests that dispersive radiation and wave–particle interactions dominate (Kennel et al. 1985). Because this study focuses on low Mach number shocks (Mf ≲ 3), particle reflection and macroscopic field effects are not investigated in detail. Whistler precursors (Tidman & Northrop 1968; Fairfield 1974) are often observed and can dissipate energy through several processes, including generation of higher frequency waves by creating electron temperature anisotropies or current-driven instabilities (Gary 1981; Hull et al. 2012), acceleration of halo electrons and thermal ions (Wilson III et al. 2012; Chen et al. 2018), and deflection and modulation of core particles (Goncharov et al. 2014). Wave–particle interactions dissipate energy through anomalous resistivity, shorthand for the energy and momentum exchange between the electromagnetic fields and particles (Sagdeev 1966; Coroniti 1970a; Gary 1981; Papadopoulos 1985; Wilson III et al. 2007, 2010, 2012, 2014a, 2014b; Breneman et al. 2013). Goodrich et al. (2018) showed that ion acoustic waves may be indicators or facilitators of momentum transfer between reflected and incident ion populations, thus linking these waves to the transformation of bulk flow kinetic energy. In addition, work by Wang et al. (2020) shows how reflected ions interacting with incident ions generate Debye-scale electrostatic fluctuations, starting as ion acoustic waves that trap ions and decay into electrostatic solitary waves. Krasnoselskikh et al. (2013) provides a review of the quasi-perpendicular bow shock and the inferred dissipation mechanisms based on Cluster observations. Some of the types of waves observed near shocks include magnetosonic whistler mode waves (Fairfield 1974; Coroniti et al. 1982), solitary waves (Bale et al. 1998), ion acoustic waves (Fredricks et al. 1968; Gary et al. 1975; Rodriguez & Gurnett 1975; Gurnett et al. 1979a, 1979b; Formisano & Torbert 1982; Fuselier & Gurnett 1984; Balikhin et al. 2005; Hull et al. 2006), Langmuir waves (Filbert & Kellogg 1979; Kellogg 2003, and references therein; Pulupa & Bale 2008), and electron cyclotron harmonic waves and waves associated with the electron cyclotron drift instability (ECDI) (Wilson III et al. 2010, 2014a, 2014b; Breneman et al. 2013; Goodrich et al. 2018).


The first direct proof of the existence of magnetic fields in large-scale extragalactic environments, i.e., galaxy clusters, dates back to the 1970s with the discovery of extended, diffuse, central synchrotron sources called radio halos (see, e.g., Feretti et al. 2012 for a review). Later, indirect evidence of the existence of intracluster magnetic fields has been given by several statistical studies on the effect of the Faraday rotation on the radio signal from background galaxies or galaxies embedded in galaxy clusters (Lawler & Dennison 1982; Vallée et al. 1986; Clarke et al. 2001; Johnston-Hollitt 2003; Clarke 2004; Johnston-Hollitt & Ekers 2004). On scales up to a few Mpc from the nearest galaxy cluster, possibly along filaments, only a few diffuse synchrotron sources have been reported (Harris et al. 1993; Bagchi et al. 2002; Kronberg et al. 2007; Giovannini et al. 2013, 2015). Magnetic fields with strengths on the order of 10-15 G in voids might be indicated by γ-ray observations (see Neronov & Vovk 2010; Tavecchio et al. 2010; Takahashi et al. 2012, 2013; but see Broderick et al. 2014a,b for alternative possibilities). Nevertheless, up to now, a robust confirmed detection of magnetic fields on scales that are much larger than clusters is not available. Stasyszyn et al. (2010) and Akahori et al. (2014a) investigated the possibility of statistically measuring Faraday rotation from intergalactic magnetic fields with present observations, showing that only the Square Kilometre Array (SKA) and its pathfinders are likely to succeed in this respect. By comparing the observations with single-scale magnetic field simulations, Pshirkov et al. (2015) infer an upper limit of 1.2 nG for extragalactic large-scale magnetic fields, while the Planck Collaboration XIX (2016) derived a more stringent upper limit for primordial large-scale magnetic fields of B 0.67 nG from the analysis of the Cosmic Microwave Background (CMB) power spectra and the effect on the ionization history (but see also Takahashi et al. 2005; Ichiki et al. 2006).


However, the determination of the faint side of the QLF at z ∼ 5 is important to understand the overall picture of SMBH growth in the early universe. Previous observations suggest that the number density of luminous quasars increased from the early universe to z ∼ 2 and then decreased to the current universe (e.g., Richards et al. 2006; Croom et al. 2009). It is of particular interest to study possible luminosity dependences of the quasar number-density evolution (luminosity-dependent density evolution; LDDE). Recent optical surveys of high-redshift quasars have reported that low-luminosity quasars show peak number density at lower redshifts than do high-luminosity quasars (e.g., Croom et al. 2009; Ikeda et al. 2011, 2012; Niida et al. 2016). Since the quasar luminosity at a given Eddington ratio corresponds to MBH, the reported LDDE trend is sometimes called the downsizing evolution. The same trend has been found by X-ray surveys for all AGN populations, including obscured (type-2) ones (e.g., Ueda et al. (2003, 2014), Hasinger et al. (2005), Aird et al. (2015), Miyaji et al. (2015); see also Enoki et al. (2014) and Shirakata et al. (2019) and references therein for theoretical works on the AGN downsizing evolution). Note that the downsizing evolution was originally proposed to describe the redshift evolution of the galaxy mass function (e.g., Cowie et al. 1996; Neistein et al. 2006; Fontanot et al. 2009). Therefore, the AGN downsizing evolution, if present, may provide a significant insight into the galaxy–SMBH coevolution. However, the number density of low-luminosity quasars at high redshifts has been quite uncertain, which has prevented us from understanding the whole picture of the quasar LDDE. Ueda et al. (2014) noted a possibility that the number ratio of total (type-1 and type-2) low-luminosity AGNs to high-luminosity ones may increase from z ∼ 3 to z ∼ 5, which is referred to as “up-down sizing” (see also Glikman et al. 2010, 2011; Giallongo et al. 2015). We need large samples of high-z low-luminosity AGNs to examine such scenarios.


C-statistic (e.g. Jang & Miller 1997) is the most commonly used and the one-way analysis of variance (ANOVA; de Diego 2010) the most powerful test for verifying the presence of variability in a DLC. However, we did not employ either of these tests because, de Diego (2010) has questioned the validity of the C-test by arguing that the C-statistics does not have a Gaussian distribution and the commonly used critical value of 2.567 is too conservative. On the other hand, the ANOVA test requires a rather large number of data points in the DLC, so as to have several points within each sub-group used for the analysis. This is not feasible for our DLCs which typically have no more than about 30–45 data points. Therefore, we have instead used the F-test which is based on the ratio of variances, F = variance(observed)/variance(expected) (de Diego 2010; Villforth, Koekemoer & Grogin 2010), with its two versions : (i) the standard F-test (hereafter Fη-test, Goyal et al. 2012) and (ii) scaled F-test (hereafter Fκ-test, Joshi et al. 2011). The Fκ-test is preferred when the magnitude difference between the object and comparison stars is large (Joshi et al. 2011). Onward Paper II, we have only been using the Fη-test because our objects are generally quite comparable in brightness to their available comparison stars. An additional gain from the use of the Fη-test is that we can directly compare our INOV results with those deduced for other major AGN classes (Goyal et al. 2013). An important point to keep in mind while applying the statistical tests is that the photometric errors on individual data points in a given DLC, as returned by the algorithms in the iraf and daophot softwares are normally underestimated by the factor η which ranges between 1.3 and 1.75, as estimated in independent studies (e.g. Gopal-Krishna, Sagar & Wiita 1995; Garcia et al. 1999; Sagar et al. 2004; Stalin et al. 2004a; Bachev, Strigachev & Semkov 2005). Recently, using a large sample, Goyal et al. (2013) estimated the best-fitting value of η to be 1.5, which is adopted here. Thus, the Fη statistics can be expressed as

\begin{equation*}
F_{1}^{\eta } = \frac{\sigma ^{2}_{({\rm q-s1})}}{ \eta ^2 \langle \sigma _{{\rm q-s1}}^2 \rangle }, \hspace{5.69046pt} F_{2}^{\eta } = \frac{\sigma ^{2}_{({\rm q-s2})}}{ \eta ^2 \langle \sigma _{{\rm q-s2}}^2 \rangle }, \hspace{5.69046pt} F_{{\rm s1-s2}}^{\eta } = \frac{\sigma ^{2}_{({\rm s1-s2})}}{ \eta ^2 \langle \sigma _{{\rm s1-s2}}^2 \rangle },\end{equation*}

 where $\sigma ^{2}_{({\rm q-s1})}$, $\sigma ^{2}_{({\rm q-s2})}$ and $\sigma ^{2}_{({\rm s1-s2})}$ are the variances of the ‘quasar–star1’, ‘quasar–star2’ and ‘star1–star2’ DLCs and $\langle \sigma _{{\rm q-s1}}^2 \rangle =\sum _{\boldsymbol {i}=0}^{N}\sigma ^2_{i,{\rm err}}({\rm q-s1})/N$, $\langle \sigma _{{\rm q-s2}}^2 \rangle$ and $\langle \sigma _{{\rm s1-s2}}^2 \rangle$ are the mean square (formal) rms errors of the individual data points in the ‘quasar–star1’, ‘quasar–star2’ and ‘star1–star2’ DLCs, respectively. η is the scaling factor (= 1.5) as mentioned above.


Asymptotic giant branch (AGB) stars are a major contributor to the global dust budget in galaxies (Höfner & Olofsson 2018). Owing to their refractory nature, alumina (stoichiometric formula Al2O3) is a promising candidate to represent the first dust condensate in oxygen-rich AGB stars. Related alumina clusters are thought to initiate dustformation in these environments and are often referred to as ‘seed particles’ (Gail & Sedlmayr 2013). However, the sizes and compositions of these aluminium oxide clusters are not well characterised. In this study, we investigate a range of Al:O stoichiometries in order to review these predictions and to construct realistic models of these initial dust seeds. The emergence of a specific condensate is predicted by its condensation temperature (Tielens 2005) and depends on the thermal stability of the solid, as well as on the gas density and its composition. Usually, the evaluation of the stability of the likely condensates is based on macroscopic bulk properties such as the vapour pressure, which is a measure of the volatility of a substance. Hence, the most refractory condensate is expected to have the lowest vapour pressure. Corundum (α-alumina), corresponding to the most stable crystalline bulk form of alumina, fulfils this condition (Gail et al. 2013). The growth and size distribution of dust grains is commonly described by classical nucleation theory (CNT). However, the applicabilityof CNT in an expanding circumstellar envelope has been questioned (Donn & Nuth 1985; Goumans & Bromley 2012; Bromley et al. 2016; Gobrecht et al. 2017). In particular, the concept of vapour pressures and the universal assumption of thermodynamic equilibrium (TE) are in contradiction with the synthesis and growth of dust grains in highly dynamical AGB atmospheres. Moreover, in CNT, the properties of small solids are derived from the (crystalline)bulk material. However, the properties of nano-sized clusters often differ significantly from those of bulk analogues. The constraints associated with extremely small sizes lead to clusters with non-crystalline structures, whose characteristics (e.g. energy, geometry, bond lengths and angles, atomic coordination) differ substantially from those of the bulk material (Bromley & Zwijnenburg 2016). In particular, the energetic stability of such nano-clusters is typically higher than that of clusters with structures directly obtained from ‘top-down’ cuts from the parent bulk crystalline material, which represent metastable, or even unstable, configurations (Lamiel-Garcia et al. 2017). In addition, the concept of surface free energy (or tension), which is fundamental in CNT, is not applicable to small clusters, where it is difficult to differentiate between surface and bulk. Surface energies can only be applied to clusters with fairly large sizes (e.g. facetted bulk cut clusters). We understand nucleation as the formation and growth of stable seed nuclei (i.e. clusters) from prevalent gas-phase molecules, whose abundance varies in time (i.e. is often not in equilibrium). Therefore, a cluster is intermediate in size between a molecule and a bulk solid.


One possible, conventional, explanation for an apparently accelerating rotational period may be the light-time effect due to the orbit of a binary companion. However, none of the magnetic B-type stars in which this phenomenon has been detected, including the present star, are known to be in binary systems (Shatsky & Tokovinin (2002) conducted an NIR search for visual companions, and found no evidence of a companion in the case of HD 142990). The change in period ΔP due to the light-time effect should correspond to a change in radial velocity ΔRV = cΔP/P, where c is speed of light (e.g. Pigulski & Boratyn 1992). Fig. 6 shows the least-squares deconvolution (LSD) profiles extracted from the ESPaDOnS data set with a line mask using all metallic lines in the spectrum (for details, see Shultz et al. 2018). No bulk RV variability is apparent. Measuring the RV is complicated by the spectroscopic variability introduced by chemical spots, which in addition to equivalent width changes also introduce RV variations coherent with the rotation phase due to changes in the star’s centre of gravity. As a result, only measurements performed on observations obtained close to the same rotation phase can be compared. The ESPaDOnS data contains two observations obtained close to phase 0.6, separated by about 3 yr (one on 14/06/2014, the second on 14/05/2017, with a difference in phase of 0.02 cycles when phased using the variable ephemeris). Measuring the centres of gravity of the LSD profiles extracted from these observations yields a difference in RV of 1 km s−1, comparable to the measurement uncertainty. The RV change expected over 3 yr if $\dot{P}$ is due to orbital motion is about 3 km s−1, so this test must be considered inconclusive. However, a change of −20 s over the 30 yr of observations should have led to ΔRV = 71 km s−1; it is unlikely that such a large change in RV would have been missed. The Pulkovo Compilation of Radial Velocities (Gontcharov 2006) give RV = −12 ± 3 km s−1, consistent with RVs measured from ESPaDOnS data (which have a mean and standard deviation of −4 and 5 km s−1), suggesting that the RV has been stable over a time span of at least a decade.


The H α studies of Umeda et al. (2004) and Stroe et al. (2014a, 2015) are tracing instantaneous (averaged over 10 Myr) SF and little is known about SF on longer time-scales and the reservoir of gas that would enable future SF. An excellent test case for studying the gas content of galaxies within merging clusters with shocks is CIZA J2242.8+5301 (Kocevski et al. 2007). For this particular cluster unfortunately, its location in the Galactic plane, prohibits studies of the rest-frame UV or FIR tracing SF on longer time-scales, as the emission is dominated by Milky Way dust. However, the rich multiwavelength data available for the cluster give us an unprecedented detailed view on the interaction of their shock systems with the member galaxies. CIZA J2242.8+5301 is an extremely massive (M200 ∼ 2 × 1015 M⊙; Dawson et al. 2015; Jee et al. 2015) and X-ray disturbed cluster (Akamatsu & Kawahara 2013; Ogrean et al. 2013, 2014) which most likely resulted from a head-on collision of two, equal-mass systems (van Weeren et al. 2011; Dawson et al. 2015). The cluster merger induced relatively strong shocks, which travelled through the ICM, accelerated particles to produce relics towards the north and south of the cluster (van Weeren et al. 2010; Stroe et al. 2013). There is evidence for a few additional smaller shock fronts throughout the cluster volume (Stroe et al. 2013; Ogrean et al. 2014). Of particular interest is the northern relic, which earned the cluster the nickname ‘Sausage’. The relic, tracing a shock of Mach number M ∼ 3 (Stroe et al. 2014c), is detected over a spatial extent of ∼1.5 Mpc in length and up to ∼150 kpc in width and over a wide radio frequency range (150 MHz–16 GHz; Stroe et al. 2013, 2014b). There is evidence that the merger and the shocks shape the evolution of cluster galaxies. The radio jets are bent into a head–tail morphology aligned with the merger axis of the cluster. This is probably ram pressure caused by the relative motion of galaxies with respect to the ICM (Stroe et al. 2013). The cluster was also found to host a high fraction of H α emitting galaxies (Stroe et al. 2014a, 2015). The cluster galaxies not only exhibit increased SF and AGN activity compared to their field counterparts, but are also more massive, more metal rich and show evidence for outflows likely driven by SNe (Sobral et al. 2015). Stroe et al. (2015) and Sobral et al. (2015) suggest that these relative massive galaxies (stellar masses of up to ∼1010.0–10.7 M⊙) retained the metal-rich gas, which was triggered to collapse into dense star-forming clouds by the passage of the shocks, travelling at speeds up to ∼2500 km s−1 (Stroe et al. 2014c), in line with simulations by Roediger et al. (2014).


Star formation and supermassive resblack hole (SMBH) growth are two important processes in galaxies that influence their evolution throughout cosmic history. However, we do not yet understand why the global rates of star formation (e.g. Hopkins & Beacom 2006; Madau & Dickinson 2014; Driver et al. 2018) and SMBH growth (e.g. Ueda et al. 2003; Shankar, Weinberg & Miralda-Escudé 2009) both peaked at z ≈ 2, and then declined by an order magnitude to this epoch. It is clear that a ready supply of cold (Tk ≪ 104 K) gas is important; in the nearby Universe the surface densities of star formation and neutral gas, particularly the molecular component, are strongly correlated (e.g. Schmidt 1959; Kennicutt 1998; Bigiel et al. 2008), and likewise radiatively efficient active galactic nuclei (AGNs) are predominantly hosted by star-forming galaxies with a central young stellar population and therefore ample cold gas reservoirs (e.g. Kauffmann et al. 2003, 2007; Kauffmann & Heckman 2009; LaMassa et al. 2013; Ellison et al. 2019). Determining how the neutral interstellar medium in galaxies has evolved over the history of the Universe is therefore a key component in understanding their evolution. Much of our knowledge of the global content of neutral gas in galaxies comes from observing hydrogen gas, the most common element in the Universe. In its neutral atomic (H i) phase, hydrogen is readily detectable in nearby galaxies via 21-cm emission at radio wavelengths (see Giovanelli & Haynes 2016 for a review) or, at cosmological distances, through Lyman α (n = 1–2) absorption in the ultraviolet and visible bands (see Wolfe, Gawiser & Prochaska 2005). The total H i mass density shows comparatively less evolution over cosmological time-scales than that of star formation, decreasing by at most two-fold since z ≈ 2 (e.g. Zwaan et al. 2005; Martin et al. 2010; Braun 2012; Noterdaeme et al. 2012; Zafar et al. 2013; Crighton et al. 2015; Sánchez-Ramírez et al. 2016; Bird, Garnett & Ho 2017; Rhee et al. 2018), suggesting that much of the neutral gas content of galaxies is replenished over these time-scales.


The observation of massive neutron stars Demorest et al. (2010), Antoniadis et al. (2013) indicates that the EoS of nuclear matter must be very stiff in the regime of high densities and low temperatures. The degree of stiffness in the nuclear matter EoS is directly related to the repulsive interaction among particles at high densities, as well as to the particle content in the core of the stars. In particular, it has been extensively discussed in the literature whether exotic degrees of freedom might populate the core of neutron stars. On the one hand, it is more energetically favorable for the system to populate new degrees of freedom, such as hyperons (Dexheimer & Schramm 2008; Ishizuka et al. 2008; Bednarek et al. 2012; Fukukawa et al. 2015; Gomes et al. 2015; Maslov et al. 2015; Oertel et al. 2015; Lonardoni et al. 2015, 2016); Biswal et al. 2016; Burgio & Zappalà 2016; Chatterjee & Vidana 2016; Mishra et al. 2016; Vidaña 2016; Yamamoto et al. 2016; Tolos et al. 2017); Torres et al. 2017), delta isobars (Fong et al. 2010;Schurhoff et al. 2010; Drago et al. 2014; 2016; Cai et al. 2015; Zhu et al. 2016), and meson condensates (Ellis et al. 1995; Menezes et al. 2005; Takahashi 2007; Ohnishi et al. 2009; Alford et al. 2010; Fernandez et al. 2010; Mesquita et al. 2010; Mishra et al. 2010; Lim et al. 2014; Muto et al. 2015), in order to lower its Fermi energy (starting at about two times the saturation density). On the other hand, the EoS softening due to the appearance of exotica might turn some nuclear models incompatible with observational data, in particular with the recently measured massive neutron stars. One possible way to overcome this puzzle is the introduction of an extra repulsion in the YY interaction Schaffner & Mishustin (1996), Bombaci (2016), allowing models with hyperons to be able to reproduce massive stars (Dexheimer & Schramm 2008; Bednarek et al. 2012; Weissenborn et al. 2012; Banik et al. 2014; Bhowmick et al. 2014; Gusakov et al. 2014; Lopes & Menezes 2014; van Dalen et al. 2014; Yamamoto et al. 2014; Gomes et al. 2015). Another possible solution is the introduction of a deconfinement phase transition at high densities Bombaci (2016), with a stiff EoS for quark matter, usually associated with quark vector interactions (see Klähn et al. 2013 and references therein).

Dexheimer & Schramm 2008
Dexheimer & Schramm 2008


Our models for the density distribution in the thin and thick stellar disks of the Galaxy are based on the structural disk parameters presented by PJL. These authors performed a star counts model of the Galaxy using near-infrared data of the 2MASS survey (Skrutskie et al. 2006) with lines of sight covering the entire sky and including the Galactic plane. The authors explored the parameter space and estimated its optimal values with statistical methods such as the Markov chain Monte Carlo (MCMC; Gilks et al. (1996)) and the nested sampling (NS) algorithm (Skilling 2004). Using a modified exponential law, PJL modelled the radial profile of the density of each subcomponent of the stellar disk based on the Galactic model of Lépine & Leroy (2000). Such profile is equivalent to the Freeman Type II disk brightness profile, which contains a depletion in the centre with respect to a pure exponential law (Freeman 1970; Kormendy 1977). The stellar surface densities Σd★ for the thin and thick disks can then be written as (1)\begin{equation} \label{eq:sigma_thin_thick} \Sigma_{\mathrm{d}_{\bigstar,\,i}}(R)=\Sigma_{0\mathrm{d}_{\bigstar,\,i}}\,\exp\left[-\,\frac{(R-R_{0})}{R_{\mathrm{d}_{\,i}}}-R_{\mathrm{ch}_{\,i}}\left(\frac{1}{R}-\frac{1}{R_{0}}\right)\right], \end{equation}Σd★, i(R)=Σ0d★, i exp− (R−R0)Rd i−Rch i1R−1R0,where Σ0d★ corresponds to the local disk stellar surface density (at R = R0), Rd is the radial scale length, and Rch is the radial length of the “central hole” in the density of each stellar disk i subcomponent (i = thin, thick). The hypothesis that the Galactic disk is hollow in its centre has been justified by some models that use observational data at infrared bands to describe the inner structure of the Galaxy (e.g. Freudenreich 1998; Lépine & Leroy 2000; López-Corredoira et al. 2004; Picaud & Robin 2004). In the particular case of the PJL model, only the thin disk needs a density depression in its inner part; in contrast, the thick disk can be described by a simple radial exponential decay, i.e.  Rch thick = 0.


The Bayesian approach is indeed robust and optimal, within the context mentioned above. It focuses on the reconstruction of the LSS within the framework of the standard model of cosmology and for a given data base. However, most previous studies have not addressed the question how consistent is the assumed cosmological model with the observed data. This is not a trivial issue – the model needs to agree with the data so as to provide a solid foundation for the WF/CRs construction. Ideally, one should have started with establishing the agreement of the model with the data and only then reconstruct the LSS in the manner described above. However, history does not always proceeds in a linear fashion. The aim of the paper is to amend that situation and establish the likelihood of peculiar velocities data bases given the standard model of cosmology. The relevant methodology is straightforward and well established. One needs to calculate the likelihood function of the data given the model – namely the probability of the occurrence of the data within the framework of the assumed model (Jaffe & Kaiser 1995; Zaroubi et al. 1995; Hoffman 2001; Press et al. 2007). The likelihood function establishes the goodness-of-fit (GoF) of the data by the model. In the cosmological case and under the assumption of the linear regime, where the velocity field constitutes a random Gaussian vector field and the observational errors are normally distributed, the likelihood analysis amounts to calculating a χ2 statistics. This approach was indeed applied to velocity data bases (Jaffe & Kaiser 1995; Zaroubi et al. 1997, 2001). The application of the likelihood analysis to actual velocity data bases suffers however from one major drawback. The gravitational dynamics of structure formation induces non-linear contributions to the velocities of galaxies. These non-linear corrections render the parameter estimation and GoF analysis to be rather uncertain. The remedy to the problem involves the filtering of small scales to give linearized data. The likelihood analysis can then be safely applied to the linearized data. Here, we suggest such a small-scales filtering procedure and study the extent by which Cosmicflows-2 (CF2; Tully et al. 2013) is compatible with the Λ cold dark matter (ΛCDM) standard model of cosmology.


Galactic winds have been ubiquitously observed in galaxies at both low and high redshifts, and they are critical to galaxy formation and evolution. Simulations calibrated to match these observations predict that a large amount of galactic material is ejected as a wind before reaccreting to either form stars or be ejected once again (Oppenheimer et al. 2010; Anglés-Alcázar et al. 2017). Current cosmological hydrodynamic simulations of galaxy formation employ a variety of subgrid models (e.g. Springel & Hernquist 2003; Oppenheimer & Davé 2006; Stinson et al. 2006; Dalla Vecchia & Schaye 2008; Agertz et al. 2013; Schaye et al. 2015; Davé, Thompson & Hopkins 2016; Tremmel et al. 2017; Pillepich et al. 2018; Davé et al. 2019; Huang et al. 2020a) that artificially launch galactic winds, but the results are sensitive to numerical resolution and the exact subgrid model employed (Huang et al. 2019, 2020a). Simulations without these subgrid wind models (e.g. Hopkins et al. 2018; Kim & Ostriker 2015; Martizzi et al. 2016) allow winds to occur ‘naturally’, but these simulations may not resolve the scales necessary to resolve the important known physical processes (Scannapieco & Brüggen 2015; Brüggen & Scannapieco 2016; Schneider & Robertson 2017; McCourt et al. 2018; Huang et al. 2020b). Hence, modelling galactic winds accurately remains a theoretical challenge for even the most refined high-resolution simulations of galaxies (see Naab & Ostriker 2017, for a review). Even if one were able to accurately model the formation of galactic winds, the subsequent propagation in galactic haloes depends on a complicated interplay of many physical processes that occur on a wide range of physical scales that cannot be simultaneously resolved in a single simulation. For example, to robustly model the propagation and disintegration of moving clouds in various situations requires cloud-crushing simulations with at least sub-parsec scale resolution (Schneider & Robertson 2017; McCourt et al. 2018), which is orders of magnitudes below the resolution limits of cosmological simulations. Furthermore, most cosmological hydrodynamic simulations concentrate their resolution in the dense, star-forming regions of galaxies and thus have lower resolution in the circumgalactic medium (CGM, but see Hummels et al. 2019; Mandelker et al. 2019; Peeples et al. 2019; Suresh et al. 2019; van de Voort et al. 2019). To date, cosmological simulations do not include physically motivated subgrid models for galactic wind evolution, which are required to capture these small-scale physical processes.


Some studies use HIPPARCOS or Gaia data to determine the evolutionary status of field LiRG and show that these objects tend to accumulate close to the RGB bump, the clump, and the early-AGB (e.g. Charbonnel & Balachandran 2000; Kumar et al. 2011; Smiljanic et al. 2018; Deepak 2019), which is in agreement with open cluster studies (e.g. Delgado Mena et al. 2016). Other works report, however, that LiRG can be randomly located in the HRD (Jasniewicz et al. 1999; Smith et al. 1999; Monaco et al. 2011; Lebzelter et al. 2012; Martell & Shetrone 2013; Casey et al. 2016). The distinction is crucial to understanding the processes that may provide an explanation for the phenomenon, such as fresh Li production by internal mixing processes (Sackmann & Boothroyd 1999; Palacios et al. 2001; Guandalini et al. 2009; Strassmeier et al. 2015; Cassisi et al. 2016), prompt mass loss events (de La Reza et al. 1996, 1997), Li accretion during engulfment of planets or planetesimals (Alexander 1967; Siess & Livio 1999; Carlberg et al. 2010; Aguilera-Gómez et al. 2016a,b; Delgado Mena et al. 2016), tidal interactions between binary stars (Casey et al. 2019), or a combination of these mechanisms (Denissenkov & Weiss 2000; Denissenkov & Herwig 2004). However, since the evolution tracks of evolved stars all converge to the same area of the CMD, the definitive determination of the actual evolution status of LiRG requires asteroseismology to probe their internal structure and disentangle RGB from clump stars. As of today, very few LiRG have been observed with CoRoT and Kepler. The majority seems to be located in the core-He burning clump (Silva Aguirre et al. 2014; Bharat Kumar et al. 2018; Casey et al. 2016; Smiljanic et al. 2018; Singh et al. 2019), with the others being at the RGB bump or higher on the first ascent giant branch (Jofré et al. 2015; Casey et al. 2019). In a recent study using LAMOST spectra to derive both the Li abundance and asteroseismic classification, Casey et al. (2019) showed that ∼80% of their large sample of low-mass LiRG (2330 objects) probably have helium burning cores. They find that LiRG are more frequent at higher metallicity.


Age–velocity dispersion relations have been found in many resolved (Nordström et al. 2004; Grieves et al. 2018) and simulated (Martig, Minchev & Flynn 2014) studies. They primarily conclude that stars born earlier have a higher velocity dispersion compared to those formed later. The underlying physical cause of this relation, however, has evaded a general consensus in the literature. Some scenarios broadly claim that the increase in velocity dispersion is a dynamical effect of internal interactions that build up over time, with a number of different specific mechanisms being proposed as the culprit. Since the older stars have been experiencing these interactions for a longer period of time, they should therefore show the largest increase in velocity dispersion. Evidence in favour of such internal mechanisms has come from both observations (Yu & Liu 2018) and simulations (Saha, Tseng & Taam 2010; Aumer, Binney & Schönrich 2016; Grand et al. 2016). An alternative explanation is that in the early Universe, conditions were generally more chaotic (Wisnioski et al. 2015), so that any stars born at that time were more likely to have higher velocity dispersion. As conditions gradually settled over cosmic time, stars were being born in progressively lower-dispersion conditions. A number of studies have identified the conditions at birth as the dominant effect in determining a population’s present-day velocity dispersion, again both from resolved observations (Leaman et al. 2017) and simulations (Bird et al. 2013; Ma et al. 2017). Finally, the comparison between observations and simulations in Pinna et al. (2018) has identified the underlying complexity and inherent degeneracy in discriminating between these scenarios. They claim that many of the effects described above likely play a role to a varying degree and that the imprint of some mechanisms fade over time, further complicating any attempt to constrain the physical cause of disc heating.


The stochastic accretion of gas and galaxy merger-driven gas inflows are both known triggers of supermassive black hole (SMBH) growth and nuclear activity, but the relative contributions of each is still unclear. Simulations of galaxy mergers show that they drive gas to the centers of merger-remnant galaxies (e.g., Springel et al. 2005; Hopkins & Hernquist 2009), predicting that merger-driven SMBH mass growth occurs when the black hole nears the center of the merger remnant. Observations have shown that the AGN fraction does increase with decreasing distance between two merging galaxies (Ellison et al. 2011; Koss et al. 2012; Ellison et al. 2013), but this has not been well tested at the very centers of merger-remnant galaxies because of the observational difficulty of detecting and resolving two AGNs with separations 10 kpc. This is known as the “dual AGN” phase.4

4
The separation scale expected for dual AGNs is between 0.1 and 10 kpc. The SMBHs in a merger stay at these separations for a few hundred megayears before evolving into a gravitationally bound, parsec-scale separation binary AGN system (Begelman et al. 1980).
 Hundreds of AGN pairs with >10 kpc separations have been discovered (Myers et al. 2008; Hennawi et al. 2010; Liu et al. 2011). However, there are only a few confirmed kiloparsec-scale dual AGNs (Junkkarinen et al. 2001; Komossa et al. 2003; Hudson et al. 2006; Rodriguez et al. 2006; Bianchi et al. 2008; Fu et al. 2011b; Koss et al. 2011, 2012; Mazzarella et al. 2012; Liu et al. 2013; Comerford et al. 2015). Dual AGNs are an intermediate evolutionary stage between first encounter and final coalescence of two merging gas-rich galaxies (e.g., Comerford et al. 2009; Liu et al. 2012), in which strong tidal interactions are more likely to influence the nuclear accretion and star formation in both galaxies (Barnes & Hernquist 1996). Indeed, galaxy merger simulations and observations clearly show that the dual AGN phase is the critical stage when SMBH growth and star formation activity are the most vigorous (e.g., Koss et al. 2012; Van Wassenhove et al. 2012; Blecha et al. 2013).


In this context, massive (ℳ>1011 M⊙) PGs (MPGs) deserve particular attention. These systems are expected to evolve mainly through (dry) mergers (e.g. Hopkins et al. 2009; De Lucia & Blaizot 2007). If this is the case, in this mass range we should detect a stronger signal of the size-growth with respect to a lower mass range. So far, because MPGs are extremely rare, there have been very few studies that have investigated the combined evolution of the number density and of the age of MPGs as a function of their compactness (Carollo et al. 2013; Fagioli et al. 2016). Carollo et al. (2013) found that the number density of massive quiescent and elliptical galaxies with Re 2.5 kpc decreases by about 30% from z~1 to z~0.2 and that their U−V colours are consistent with passive evolution. They concluded that the driving mechanism for the average size-growth of the whole population is the appearance at later epochs of larger quiescent galaxies. More recently, Fagioli et al. (2016, hereafter F16) analysed the spectroscopic properties of ~500 MPGs (defined as galaxies with absent or very weak emission lines and no MIPS detections) at 0.2 z 0.8 in the zCOSMOS-bright 20 K catalogue (Lilly et al. 2007). From the analysis of stacked spectra of small and large MPGs, they dated the stellar content of these groups and found that the two sub-populations have similar ages. The authors concluded that, in this mass regime, the size growth of individual galaxies through dry mergers is the most likely explanation for the increase in the mean effective radius of the whole population. A recent analysis by Zahid et al. (2016) on the physical properties of compact post starburst galaxies at 0.2z0.8 with ℳ>1011 M⊙ provides new insights. On the basis of both their number density and of their ages, which have been found to be 1 Gyr, the authors suggest that this class of objects are the progenitors of compact quiescent galaxies. They conclude that a substantial fraction of dense quiescent galaxies at z0.8 are newly formed.


Submillimetre galaxies (SMGs) are ultraluminous dusty star-forming galaxies (SFGs) with the vast majority of radiation energy in the far-infrared (FIR) and submillimetre bands (Smail, Ivison & Blain 1997; Barger et al. 1998; Hughes et al. 1998; Michałowski et al. 2012; Casey, Narayanan & Cooray 2014). They are extreme starbursts with high star formation rate (SFR) of $\sim 10^2\, -\, 10^3$ M⊙ yr−1 and high stellar mass of ∼1010–11 M⊙, located preferentially at z ∼ 2–3 (Chapman et al. 2005; Wardlow et al. 2011; Smolčić et al. 2012; Simpson et al. 2014; Brisbin et al. 2017; Danielson et al. 2017; Michałowski et al. 2017; Smith et al. 2017; Hodge & da Cunha 2020, and references therein). The physical properties of SMGs derived from detailed studies of individual sources and large sky area submillimetre surveys suggest that SMGs represent an early evolutionary phase of all local ellipticals (Smail et al. 2002; Swinbank et al. 2006; Fu et al. 2013; Toft et al. 2014; Ikarashi et al. 2015; Miettinen et al. 2017; An et al. 2019; Gullberg et al. 2019; Dudzevičiūtė et al. 2020; Rennehan et al. 2020). Although SMGs are a rare population (∼400 deg−2 down to S850 = 4 mJy; Simpson et al. 2019; Shim et al. 2020), they contribute a significant fraction (∼20 per cent) of the cosmic SFR density at z > 2 (Bourne et al. 2017; Koprowski et al. 2017; Zavala et al. 2021). Their extreme SFRs are correlated with higher gas fractions compared to normal SFGs at the same epoch (Bothwell et al. 2013; Scoville et al. 2016; Decarli et al. 2016; Tacconi et al. 2018). The large amount gas is thought to be supplied by gas infall via cold streams from surrounding gas reservoirs (Narayanan et al. 2015; Ginolfi et al. 2017). The extreme starbursts of this population are partially triggered by galaxy major mergers (Tacconi et al. 2008; Engel et al. 2010, but see Davé et al. 2010; Narayanan et al. 2015; McAlpine et al. 2019), while a diversity of morphologies unveiled from the rest-frame ultraviolet (UV) and optical imaging indicate galaxy interactions and disc instabilities to be important mechanisms for enhancing star formation in SMGs (Swinbank et al. 2010; Kartaltepe et al. 2012; Chen et al. 2015), as well as AGN activities (Chapman et al. 2005; Wang et al. 2013). Because the rarity and high SFR of SMGs are sensitive to the physical processes governing galaxy formation (e.g. star formation, stellar and AGN feedback, gas infall, metal enrichment, and galaxy merging/interactions), the SMG population is used to constrain cosmological models. It remains challenging to reproduce the SMG population with high SFRs matching observations at high z (Davé et al. 2010; McAlpine et al. 2019; Hayward et al. 2021; Lovell et al. 2021).


In addition to successful and failed eruptions, there are also partial filament eruptions (Gilbert et al. 2007; Liu et al. 2007). After examining 54 Hα prominence activities, Gilbert et al. (2000) found that a majority of the eruptive prominences show a separation of escaping material from the bulk of the prominence; the latter initially lifted away from and then fell back to the solar surface. To explain the partial filament eruptions, the authors proposed a cartoon model in which magnetic reconnection occurs inside an inverse-polarity flux rope, leading to the separation of the escaping portion of the prominence and the formation of a second X-type neutral line in the upper portion of the prominence. The inner splitting and subsequent partial prominence eruption was also observed by Shen et al. (2012). Gilbert et al. (2001) interpreted an active prominence with the process of vertical reconnection between an inverse-polarity flux rope and an underlying magnetic arcade. Liu et al. (2008) reported a partial filament eruption characterized by a quasi-static, slow phase and a rapid kinking phase showing a bifurcation of the filament. The separation of the filament, the extreme-ultraviolet (EUV) brightening at the separation location, and the surviving sigmoidal structure provide convincing evidence that magnetic reconnection occurs within the body of a filament (Tripathi et al. 2013). Gibson & Fan (2006a, 2006b) carried out three-dimensional (3D) numerical simulations to model the partial expulsion of an MFR. After multiple reconnections at current sheets that form during the eruption, the rope breaks in an upper, escaping rope and a lower, surviving rope. The “partially expelled flux rope” model has been justified observationally (Tripathi et al. 2009). Tripathi et al. (2006) observed a distinct coronal downflow following a curved path at the speed of 150 km s−1 during a CME-associated prominence eruption. Their observation provides support for the pinching off of field lines drawn-out by the erupting prominences, and the contraction of the arcade formed by the reconnection. Tripathi et al. (2007) reported similar multithermal downflow at the speed of ∼380 km s−1, starting at the cusp-shaped structures where magnetic reconnection occurred inside the erupting flux rope that led to its bifurcation. Liu et al. (2012) studied a flare-associated partial eruption of a double-decker filament. Cheng et al. (2014b) found that a stable double-decker MFR system existed for hours prior to the eruption on 12 July 2012. After entering the domain of instability, the high-lying MFR impulsively erupted to generate a fast CME and GOES X1.4 class flare, whereas the low-lying MFR remained behind and continuously maintained the sigmoidicity of the active region (AR). From previous literature, we can conclude that magnetic reconnection and the release of free energy is involved in most of the partial filament eruptions. However, the exact mechanism of partial eruptions, which is of great importance to understanding the origin of solar eruptions and forecasting space weather, remains unclear and controversial.


The electronic computations were performed using the molpro (Molpro 2015, http://www.molpro.net) package. In a preliminary work, we used the complete active space self-consistent field (Knowles & Werner 1985; Werner & Knowles 1985) to examine the electronic wavefunction of the HNCO–He complex. These computations showed that this wavefunction is dominantly described by a unique electron configuration (with a weight ≥0.93) over the grid used for the generation of this PES. This justifies hence the use of monoconfigurational ab initio methods. Accordingly, we applied the recently established methodology by Hochlaf and co-workers for mapping multidimensional PESs of weakly bound molecular systems with high accuracy and relatively low computational cost (Lique, Klos & Hochlaf 2010; Halvick et al. 2011; Ajili et al. 2013; Mathivon, Linguerri & Hochlaf 2013; Kalugina et al. 2014; Mogren Al Mogren et al. 2014). Briefly, these electronic computations were carried out using the explicitly correlated coupled cluster method with single, double and perturbative treatment of triple excitations (CCSD(T)-F12) (Adler, Knizia & Werner 2007; Knizia, Adler & Werner 2009) in connection with the augmented correlation-consistent aug-cc-pVTZ basis set of Dunning and co-workers (Dunning 1989; Kendall, Dunning & Harrison 1992). In addition, molpro default choices for the density fitting and resolution of identity basis sets have been applied (Yousaf & Peterson 2008). Benchmarks by Hochlaf and co-workers (Lique et al. 2010; Halvick et al. 2011; Ajili et al. 2013; Mathivon et al. 2013; Kalugina et al. 2014; Mogren Al Mogren et al. 2014) showed that results obtained from this highly correlated approach are close to those deduced using standard coupled cluster techniques extrapolated to the complete basis set (CBS) limit, whereas a strong reduction in CPU time and disc occupancy are observed. For illustration, we performed CCSD(T)/aug-cc-pVXZ calculations (X = D, T, Q, 5) on the HNCO—He cluster. Then the energies were extrapolated to the CBS limit. The comparison between CCSD(T)-F12/aug-cc-pVTZ and CBS calculations is given in Table 1. It shows that the CCSD(T)-F12/aug-cc-pVTZ results are off by 4 per cent (at the maximum) with those deduced from CBS extrapolation. We compare also our results with those done using the CCSD(T)/aug-cc-pV5Z approach. We can clearly see that the CCSD(T)-F12/aug-cc-pVTZ approach offers a good agreement with the CCSD(T)/aug-cc-pV5Z calculations with a very reduced computational cost.


Many factors can affect the prevalence of AGN activity. One important question is how gas is brought down to the galaxy center to fuel supermassive black holes (SMBHs). In the literature, two kinds of mechanisms are proposed. One is the internal secular evolution process. The torque induced by non-axisymmetric galactic structures can drive slow and significant inflow (Kormendy & Kennicutt 2004; Hopkins & Quataert 2011; Sellwood 2014; Fanali et al. 2015). The galactic bar is one of the most prominent non-axisymmetric structures and it exists in about 40% of spiral galaxies (Oh et al. 2012). In addition, there is evidence demonstrating that bars can enhance star formation in the central regions of galaxies (e.g. Oh et al. 2012; Chown et al. 2019). However, the question of whether galactic bars can significantly affect AGN activity is still under debate (Arsenault 1989; Mulchaey & Regan 1997; Oh et al. 2012; Galloway et al. 2015; Goulding et al. 2017; Alonso et al. 2018). Other mechanisms, such as galaxy merger and interaction, are also expected to displace the angular momentum of the gas and transport the gas inward (e.g. Hopkins et al. 2006; Di Matteo et al. 2008; Bhowmick et al. 2020). Similarly to studies of secular evolution, observational evidence for this scenario is also mixed. Some studies have found significant environmental dependence of AGN activity (e.g. Koulouridis et al. 2006; Koss et al. 2010; Ellison et al. 2011; Sabater et al. 2013; Khabiboulline et al. 2014; Lackner et al. 2014; Satyapal et al. 2014; Hong et al. 2015; Kocevski et al. 2015; Goulding et al. 2018; Gao et al. 2020), while others have found no or only weak environmental effects (e.g. Grogin et al. 2005; Li et al. 2006a, 2008; Pierce et al. 2007; Ellison et al. 2008; Gabor et al. 2009; Darg et al. 2010; Wang & Li 2019; Man et al. 2019). The contradictory results may be caused by the difference in AGN selection criterion, observational bias, control sample, and environmental indicator used. As we show below, understanding the environmental effects on AGNs also requires knowledge about the evolutionary status of their host galaxies, as it can help us to better understand how to construct control samples and to adopt appropriate environmental indicators.


The oldest and most metal-poor stars contain a fossil record of the star formation processes in the early Universe. These first stars would have been composed solely of hydrogen, helium, and trace amounts of lithium (Steigman 2007; Cyburt et al. 2016); without metals to efficiently cool the gas, large Jeans masses, and thereby very massive stars ($M_* \gtrsim 100 \, \mathrm{M}_{\odot }$) are predicted to have formed (Silk 1983; Tegmark et al. 1997; Bromm, Coppi & Larson 1999; Abel, Bryan & Norman 2002; Yoshida et al. 2006). In addition, improved gas fragmentation models (e.g. Clark et al. 2011; Schneider et al. 2012) and the discovery of very low-mass ultrametal-poor stars ([Fe/H]  −4; Keller et al. 2014; Starkenburg et al. 2017b; Schlaufman, Thompson & Casey 2018; Nordlander et al. 2019) have suggested that lower mass, long-lived stars may have also formed in these pristine environments (e.g. Nakamura & Umemura 2001; Wise et al. 2012). Notably, if ≤0.8 M⊙ stars were to form, they could still exist today on the main sequence, and are expected to have undergone very little surface chemical evolution over their lifetimes. Detailed studies could provide invaluable constraints on (1) the nucleosynthetic yields from the first stars and the earliest supernovae (e.g. Heger & Woosley 2010; Ishigaki et al. 2014; Tominaga, Iwamoto & Nomoto 2014; Clarkson, Herwig & Pignatari 2018; Nordlander et al. 2019), (2) the physical conditions in the high-redshift universe (where stars are too faint to be observed individually; Tegmark et al. 1997; Freeman & Bland-Hawthorn 2002; Cooke & Madau 2014; Hartwig et al. 2018; Salvadori et al. 2019), (3) the primordial initial mass function (e.g. Greif et al. 2012; Susa, Hasegawa & Tominaga 2014), and (4) early Galactic chemical evolution processes (see Sneden, Cowan & Gallino 2008; Tolstoy, Hill & Tosi 2009; Roederer et al. 2014; Yoon et al. 2016; Wanajo et al. 2018; Kobayashi, Karakas & Lugaro 2020, and references therein).


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


The photoevaporation model successfully explains the ‘two-time-scale’ nature of protoplanetary disc evolution, where the inner regions of protoplanetary discs appear to evolve slowly on Myr time-scales, before dispersing on a much more rapid time-scale (e.g. Kenyon & Hartmann 1995; Ercolano, Clarke & Hall 2011; Koepferl et al. 2013; Ercolano et al. 2014). Furthermore, slow-moving (∼5–10 km s−1) ionized winds are observed to be occurring in many nearby discs hosting young stars (e.g. Hartigan, Edwards & Ghandour 1995; Pascucci & Sterzik 2009; Rigliaco et al. 2013) and are consistent with the photoevaporation model (Alexander 2008; Ercolano & Owen 2010; Pascucci et al. 2011; Owen, Scaife & Ercolano 2013a; Ercolano & Owen 2016). The photoevaporation model can also explain a large fraction of observed ‘transition discs’ (e.g. Owen & Clarke 2012; Espaillat et al. 2014), specifically those with holes ≲10 au and accretion rates ≲10−9 M⊙ yr−1 (Owen et al. 2011b) and even those with larger holes and higher accretion rates in more recent models that incorporate CO depletion in the outer disc (Ercolano, Weber & Owen 2018). Transition discs are protoplanetary discs with evidence for a large hole or cavity in their discs (e.g. Espaillat et al. 2014), but they are known to be a heterogeneous class of objects (e.g. Owen & Clarke 2012; van der Marel et al. 2016) and their origins are not always clear. However, a specific prediction of the standard photoevaporation scenario is that there should be a large number of transition discs with hole sizes ≳10 au but that are no longer accreting. This final long-lived stage of disc dispersal gives rise to transition discs which have lifetimes between 105 and 106 yr, but remain optically thick – ‘relic discs’ (Owen et al. 2011b). The long disc lifetimes emerge from the simple fact that discs store most of their mass at large radii, but photoevaporative clearing proceeds from the inside out, so it will always take longer to remove the larger disc mass that resides at larger distance. While several discs satisfy this criterion (Dong et al. 2017), the number of observed non-accreting transition discs with large holes falls far below the theoretical expectations (Owen et al. 2011b; Owen & Clarke 2012). Studies by Cieza et al. (2013) and Hardy et al. (2015) showed that optically thick relic discs are rare and many non-accreting stars that show evidence for a circumstellar disc are more consistent with young, radially optically thin, debris discs.


The broad-band SED of blazars, in a log(νFν) versus log(ν) representation, shows two prominent broad components, one (low-energy component) peaking form far-infrared frequencies to X-ray energies and another (high energy component) peaking at MeV/GeV energies. The peak of the low-energy component (νs) is used to further classify blazars as high synchrotron peaked BL Lacs (HBL when νs > 1015 Hz), intermediate synchrotron peaked BL Lacs (IBL when 1014  νs  1015 Hz), or low synchrotron peaked BL Lacs (LBL when νs  1014 Hz) objects (Padovani & Giommi 1995; Abdo et al. 2010). Sometimes the synchrotron peak can reach energies as high as ∼1 keV, (∼2 × 1017 Hz) or beyond, showing what is considered to be extreme behaviour, even for these highly peculiar sources (e.g. Giommi, Menna & Padovani 1999; Costamante et al. 2001; Biteau et al. 2020). Such a high synchrotron peak was first observed during a flare of Mkn 501 (Pian et al. 1998), and subsequently in many other objects (e.g. Costamante et al. 2018; Sahakyan 2020a). Independently of the location of the peak, the low-energy part of the SED is generally interpreted as synchrotron emission from the relativistic electrons in the jet. A proton synchrotron origin of the high energy end of this component during X-ray flares has also been considered (Mastichiadis & Petropoulou 2021; Stathopoulos et al. 2021). The nature of the high energy (HE; >100 MeV) component is instead still under debate. Within one-zone leptonic scenarios, the second component originates from inverse Compton scattering of the synchrotron photons (SSC) by the electron population producing the low-energy component (Ghisellini, Maraschi & Treves 1985
; Maraschi, Ghisellini & Celotti 1992; Bloom & Marscher 1996). Depending on the location of the emission region, the photons external to the jet [e.g. photons from the disc, or those reprocessed from the broad-line region (BLR) or those from the infrared torus] can up-scatter, producing the second component [external inverse Compton (EIC); Sikora, Begelman & Rees 1994; Błażejowski et al. 2000; Ghisellini & Tavecchio 2009
]. On the other hand, the HE component can be also produced from the interaction of relativistic protons either from their synchrotron emission (Mücke & Protheroe 2001) or from the secondary particles from pion decay (Mannheim & Biermann 1989; Mannheim 1993; Mücke & Protheroe 2001; Mücke et al. 2003; Böttcher et al. 2013). Recently, after associating TXS 0506+056 with the IceCube-170922A neutrino event (IceCube Collaboration 2018a, b; Padovani et al. 2018) the lepto-hadronic scenarios, when both electrons and protons contribute to the HE emission, have become more attractive. These models also predict very high energy (VHE; >100 GeV) neutrinos observable by the IceCube detector (Ansoldi et al. 2018; Keivani et al. 2018; Murase, Oikonomou & Petropoulou 2018; Padovani et al. 2018; Sahakyan 2018; Cerruti et al. 2019; Gao et al. 2019; Righi, Tavecchio & Pacciani 2019; Sahakyan 2019; Gasparyan, Bégué & Sahakyan 2022).


To explain the observed evolution, the physical processes invoked have to result in a large growth in size but not in stellar mass, nor drastic increase in the star formation rate. Most plausible candidates are mass-loss driven adiabatic expansion (‘puffing-up’) (e.g. Fan et al. 2008, 2010; Ragone-Figueroa & Granato 2011) and dry mergers scenarios (e.g. Bezanson et al. 2009; Naab, Johansson & Ostriker 2009; Trujillo, Ferreras & de La Rosa 2011). In the former scenario, galaxies experience a mass-loss from wind driven by active galactic nuclei (AGNs) or supernovae feedback, which lead to an expansion in size due to a change in the gravitational potential. In the latter, mergers either major involving merging with another galaxy of comparable mass, or minor that involves accretion of low mass companions, have to be dry to keep the low star formation rate (Trujillo et al. 2011). Nevertheless, major mergers are not compatible with the observed growth in mass function in clusters as well as the observed major merger rates since z ∼ 1 (e.g. Nipoti, Londrillo & Ciotti 2003; Bundy et al. 2009). On the other hand, minor mergers are able to produce an efficient size growth (see e.g. Trujillo et al. 2011; Shankar et al. 2013). The rates of minor mergers are roughly enough to account for the size evolution only up to z ≲ 1 Newman et al. (2012), at z ∼ 2 additional mechanisms are required (e.g. AGN feedback-driven star formation Ishibashi, Fabian & Canning 2013). In addition, the effect of continual quenched galaxies on to the red sequence as well as morphological mixing (known as the ‘progenitor bias’) further complicates the situation (e.g van Dokkum & Franx 2001). Processes that are specific in clusters such as harassment, strangulation and ram-pressure stripping (e.g. Treu et al. 2003; Moran et al. 2007) might play an important role in quenching and morphologically transforming galaxies. Several studies have already shown that the progenitor bias has a non-negligible effect on the size evolution (e.g. Saglia et al. 2010; Valentinuzzi et al. 2010b; Carollo et al. 2013; Poggianti et al. 2013; Beifiori et al. 2014; Delaye et al. 2014; Belli, Newman & Ellis 2015; Shankar et al. 2015).


These two isotopes are made by the rapid neutron-capture (r) process, and typical estimates for the time interval at which r-process nucleosynthetic events that are believed to enrich a parcel of gas in the Galaxy range between 200 and 500 Myr (Hotokezaka et al. 2015; Tsujimoto et al. 2017; Bartos & Marka 2019; Côté et al. 2021). Therefore the case of 247Cm/129I is the best example of Regime 3 because τeq = 5085 Myr (Table 2) is much longer than γ, while each τ (≃22.5 and 22.6 Myr, respectively) is much shorter than γ. The ratios to the long-lived or stable references isotopes, 247Cm/235U and 129I/127I, allow us to derive a TLE, for example, for the specific γ value of 316 Myr considered in Table 3, and derive typical production ratios of 1.35 for 129I/127I and 0.3 for 247Cm/235U. While our TLE values are not perfectly compatible with each other, the more detailed analysis shown by Côté et al. (2021) demonstrates that there is compatibility for TLE in the range between 100–200 Myr, depending on the exact choice of the K parameter (Côté et al. 2019a), γ, and the production ratios. The short mean lives of 247Cm and 129I ensure that there is no memory from previous events, while the long τeq of 247Cm/129I instead ensures that this ratio did not change significantly during TLE and has a high probability to be within the 10% of the production ratio. Therefore the production ratio of the last r-process event that polluted the ESS material can be accurately determined directly from the ESS ratio. If we assume that the last event produced a 247Cm/232Th ratio similar to the average predicted by Goriely & Janka (2016) and assume a solar ratio for 127I/232Th, then we find an inconsistency between the numbers in the last two columns of Table 3. The back-decayed value is more than five times lower than the assumed production ratio, which indicates a weaker production of the actinides from this last event with respect to the production ratios that we are using here. The number in the last column therefore represents a unique constraint on the nature of the astrophysical sites of the r process in the Galaxy at the time of the formation of the Sun and needs to be compared directly to different possible astrophysical and nuclear models (Côté et al. 2021).


The source shows some preferred tracks in its movement along the HID. Dips occur as the source is in the SUL regime, either from SUL2 or from SUL3 regions; ingress and egress times populate the D3 and D2 spectra, whereas the D1 spectrum comes from the time segments characterized by the lowest count rate (deep dip). We noted that during the longest dips, the source occasionally switched to harder flaring episodes in D2 state. Most dips show the following pattern: SUL2/SUL3 → D3 → D2 → D1 → D2 → D3 → SUL2/SUL3. The passage from the SSUL to SUL state is only occasionally observed. We selected seven regions on the HID and extracted the corresponding spectra. For the normal branch spectra, the continuum emission is well fitted with two thermal components: a soft blackbody and a disc multicolour blackbody. The blackbody emission represents the bulk of the emitted power in each spectrum. It is likely due to strong reprocessing in an optically thick environment formed at Rsph, where disc inflow is mainly inflated by internal radiation pressure. This picture is consistent with the observed low temperature, large radius, and super-Eddington luminosity (see Shen et al. 2015; Soria & Kong 2016; Urquhart & Soria 2016; Guo et al. 2019). The hotter component, which we fitted using a diskbb, dominates the emission above 2 keV. Although its origin is still debated, it might come from internal hard X-ray emission, which has been inefficiently reprocessed, or simply scattered along our line of sight. Alternatively, it can be continuum emission (bremsshtrahlung and/or Comptonization) from an extended optically thin plasma where the emission lines are produced, or a tail of the blackbody emission which has been Compton upscattered in a coronal environment around the photosphere. In addition to the continuum, we added multiple emission and absorption lines derived by the combined averaged PN / RGS analysis to mimic the emitting and absorbing plasmas found in Paper I. Their shifts suggest different Doppler motions in several states as a consequence of a velocity field which changes depending on the launching site and on the geometry of the system. This seems supported by correlations among the parameters of the emission lines and the underneath hard X-ray flux (see Table 3). However, given the limited energy resolution of the EPIC we are not able to distinguish between a varying ionization state of the plasma, the effect of a different line broadening for the different ionized species, a complex absorption/emission pattern. A thorough study of the lines is left to a dedicated forthcoming study. For consistency the same spectral model has been applied also to the dipping branch spectra, although the physical conditions in and out of the dips might be different.


The basically linear correlation between L′CO[5–4] and LIR is different from findings for low-J CO, where considering all galaxies together yields a trend more consistent with a slope of 1.7 (e.g., see the classical work of Solomon & van der Bout 2005) or, when distinguishing SB and MS galaxies, separate relations with slopes of 1.2 and different normalizations (e.g., Sargent et al. 2014). This suggests that CO[5–4] could behave as a tracer of the star-forming gas, meaning that the gas is dense enough to be directly related to the amount of stars formed, in a way that is insensitive of whether the star formation occurs in a quiescent disk or inside a violent merger. If this is the case, then CO[5–4] could be used as a more efficient and accessible tracer of the dense gas than standard molecules such as HCN or HCO, which also scale basically linearly with LIR, but are intrinsically 10–20 times fainter and harder to observe (Gao & Solomon 2004a,b; Gao et al. 2007)5. At the same time, given its fairly high frequency, CO[5–4] can be observed with reasonably high, subarcsec spatial resolution with both ALMA and IRAM PdBI. We caution, however, that the critical density of CO[5–4] is an order of magnitude lower than that of HCN (Carilli & Walter 2013). Strictly speaking, these are not equivalent as tracers. In addition, CO[5–4] has an excitation temperature of ~83 K, which is much higher than low-J HCN transitions. As such, the low-J lines of these molecules are clearer tracers of density because they do not require the medium to be both warm and dense; we will still need HCN[1–0] or other dense gas tracers at [1–0] to obtain the total dense gas including the much colder component that will be missed by high-J CO lines. We do not know, moreover, whether Eq. (4) manifests a direct connection between CO[5–4] and LIR or if both CO[5–4] and LIR are driven in similar ways by some other parameter, in which case their spatial distribution inside galaxies might differ. Evidence from local galaxies suggests that CO[5–4] emission with Tkin> 50 K, as favored by our LVG modeling, might not be excited by the photodissociation region, but more likely by mechanical heating from shocks (e.g., Rosenberg et al. 2014; Meijerink et al. 2013), which most likely are driven by winds connected to the SF regions. Future comparisons of high spatial resolution maps of CO[5–4] with HCN, for example, are required to clarify whether this is a viable approach or not, that is, to clarify if CO[5–4] can be used as a high-fidelity tracer of the star-forming gas.


For LLAGNs, there are two competing components for the emission at optical/UV wavebands. One component is the thermal emission from the outer truncated SSD, which peaks in optical or UV bands, depending on the location of the truncated radius. The other component is the Compton scattering of synchrotron emission from the inner hot accretion flow (Manmoto et al. 1997; Yuan & Narayan 2014). Since our sample is limited to sources whose λ  10−3, we argue that the emission at 2500 Å mainly comes from the inner hot accretion flow.3 Interestingly, for hot accretion flows around supermassive BHs (the LLAGN case), the optical/UV emission usually is the first Compton up-scattered bump (Manmoto et al. 1997; Yuan & Narayan 2014). The emission from such a process has a positive correlation with $\dot{m}$, as $\dot{m}$ will mainly determine the optical depth (surface density), a quantity that controls the probability of Compton scattering (Sunyaev & Titarchuk 1980; Dermer, Liang & Canfield 1991). On the other hand, the first Compton bump is even more sensitive to the energy of electrons (a.k.a. the electron temperature), as it determines the location (in wavebands) of the peak. For a given $\dot{m}$, larger α means lower density, or equivalently lower radiative cooling to the electrons. Consequently, the electrons will be more energetic at higher temperatures (Xie & Yuan 2012). The dependence of emission at optical/UV band on the parameter α relies on detailed numerical calculations, where Manmoto et al. (1997) reported that the emission at 2500 Å has a positive correlation with α. For the above reasons, we simply write LUV as
(6)
\begin{equation}
L_{\rm UV}\sim (\dot{m} \alpha )^b,
\end{equation}
where b ∼ 2. The estimation of b comes from the fact that the first-order Compton scattering (responsible for the optical/UV emission) depends on the product of the seed photon flux (synchrotron emission, $\propto \dot{m}^{0.5-1}$; cf. Mahadevan 1997; Yuan et al. 2015; note that electron temperature also depends on $\dot{m}$ for the expression in Mahadevan 1997) and optical depth in a vertical direction ($\propto \dot{m}^{1-2}$).


It is obviously of fundamental importance in this process to provide a very accurate absolute calibration of the Cepheid PL relation. This can be achieved in different ways, using Cepheids in our own Galaxy that have accurate parallax measurements, or using extragalactic Cepheids for which the distances of their host galaxies have been very accurately determined with some Cepheid-independent method. A critical aspect of the calibration of the PL relation is a precise determination of its possible dependence on the metallicity of the Cepheid variables. Without an accurate knowledge of this “metallicity effect” a distance measurement to a galaxy accurate to 1% with a Cepheid PL relation is clearly not possible. In the past a lot of work was done with a variety of methods to determine the metallicity dependence of the Cepheid PL relation. Early work includes the studies of Gould (1994), Kennicutt et al. (1998), and Sakai et al. (2004). More recent studies on the metallicity effect are those of Shappee & Stanek (2011), Mager et al. (2013), and Fausnaugh et al. (2015), among others. A very detailed compilation of metallicity effect determinations prior to 2008 can be found in Table 1 of Romaniello et al. (2008). These studies seem to indicate that the metallicity effect in the near-infrared JHK bands is small, perhaps even vanishing, while there is a significant effect in optical and mid-infrared photometric bands (e.g., Freedman & Madore 2011). While most studies yielded a negative sign of the metallicity effect in optical bands meaning that more metal-rich Cepheids are intrinsically brighter than their more metal-poor counterparts of the same pulsation period, the work of Romaniello et al. (2008) has yielded the opposite sign for the effect in the V band, meaning that metal-poor Cepheids are intrinsically brighter than their more metal-rich counterparts of the same pulsation period. Theoretical studies (e.g., Caputo et al. 2000; Bono et al. 2008) appear to support Romaniello’s results, but the uncertainty on these determinations of the metallicity effect from pulsation theory still seems to be rather substantial. In the most recent work on the subject, Wielgórski et al. (2017), using the extremely well-established Cepheid PL relations in the Magellanic Clouds in optical and near-infrared bands combined with the accurate distance determinations to the LMC (Pietrzyński et al. 2013) and SMC (Graczyk et al. 2014) from late-type eclipsing binaries, found a metallicity effect compatible with zero in all bands. As a conclusion, there is still no consensus about the true effect of metallicity on Cepheid absolute magnitudes in different spectral regions. It is especially important to obtain a truly accurate determination of the metallicity effect in the near-infrared bands since these have been used, due to their much lower sensitivity to extinction, in the space-based work on H0 with the Hubble Space Telescope over the last two decades, and will be used in the near future with the James Webb Space Telescope.