PYU+ formed from HC3N and H2NCO+, having at least 88 kJ mol−1 of internal energy, can redissociate or be stabilized by radiative relaxation. Collisional stabilization in the ISM is not effective due to an extremely low gas density. To compare rates of redissociation and radiative relaxation, the microcanonical rate constant for PYU+ → HC3N + H2NCO+ was calculated using the statistical Rice–Ramsperger–Kassel–Marcus (RRKM) theory (Marcus & Rice 1951). The method has been described elsewhere (Baer & Hase 1996; Yim & Choe 2011; Choe et al. 2017; Choe & Kim 2019). At 10–50 K, energies in the range of 0.2–1 kJ mol−1 (5/2RT) of thermal translational and rotational energies of HC3N and H2NCO+ are transferred to an vibrational internal energy of PYU+, which are added to 88 (87.8, more precisely) kJ mol−1 of the energy of PYU+ for redissociation. RRKM rate constants calculated at this energy range were (3–7) × 103 s−1 (Table 1). On the other hand, rate constants for typical radiative relaxations of vibrationally excited ions have been found to be lie within the range 101–103 s−1 (Herbst 1985; Dunbar et al. 1996; Smith et al. 2001; Wakelam et al. 2010). This indicates that a considerable number of the excited PYU+ ions would be stabilized by comparing rate constants. At lower temperatures, stabilization would be more effective because rate constants for dissociation and radiative relaxation are expected to show positive and negative dependences on temperature, respectively (Wakelam et al. 2010). The stabilized PYU+ ions can undergo a further association reaction with NH3, H2O, or CH3OH. We will call this case A. These association reactions with NH3 and H2O, which finally lead to CyH+ and UrH+, respectively, can occur without activation barriers. The latter reaction is barrierless when assisted by a H2O molecule. On the other hand, the reaction of stabilized PYU+ ion with CH3OH to form ThH+ can hardly occur thermally at low temperatures due to its overall activation energy of 13 kJ mol−1.


The availability of two rotational transitions with different upper level energies allows us to constrain the rotational temperature of the propargyl radical in TMC-1. We built a rotation diagram using the velocity-integrated intensities given in Table 1, and we derive a rotational temperature of 9.9 ± 1.5 K (see Fig. 2). We therefore confirm the assumption made by Agúndez et al. (2021a) that the rotational levels of CH2CCH are thermalized at the gas kinetic temperature of TMC-1, ~10 K (Fehér et al. 2016). This fact is expected based on the low dipole moment of CH2CCH (0.150 D; Küpper et al. 2002), which implies low critical densities, probably a few 102 cm−3 (i.e., well below the volume density of H2 in TMC-1, afew 104 cm−3; Pratap et al. 1997; Cordiner et al. 2013). The column density derived from the rotation diagram for ortho CH2CCH is (8.2 ± 1.7) × 1013 cm−2. A more precise determination of the column density can be obtained by fitting the observed spectra with synthetic spectra calculated under local thermodynamic equilibrium. For this calculation we adopted a rotational temperature of 9.9 K, as derived from the rotation diagram, a full width at half maximum of 0.72 km s−1 for the 20,2–10,1 lines and 0.57 km s−1 for the 50,5–40,4 lines, which are the arithmetic mean of the values derived for the hyperfine components of each transition (see Table 1), and assumed that the emission is distributed in the sky as a circle with a radius of 40″, as observed for various hydrocarbons in TMC-1 (Fossé et al. 2001). The observed spectra at 37.5 GHz and 93.6 GHz are well reproduced when adopting a column density of 7.5 × 1013 cm−2 (see Fig. 1). Assuming an ortho-to-para ratio of three, the column density of CH2CCH (including ortho and para) in TMC-1 is (1.0 ± 0.2) × 1014 cm−2, which is slightly higher than the value derived previously by Agúndez et al. (2021a). The column density of the closed-shell counterpart CH3CCH in TMC-1 is (1.1–1.3) × 1014 cm−2 (Gratier et al. 2016; Cabezas et al. 2021). Therefore, in this study we confirm that the propargyl radical is thermalized to the gas kinetic temperature of TMC-1 and revise the abundance ratio CH2CCH/CH3CCH to nearly one.


Figure 24 shows that the median Re increases for increasing mass (from ~5 Kpc to ~20 Kpc) and, given a stellar mass, our passive ETGs have median sizes smaller than those of the parent sample even by ~15% (at the highest masses). Furthermore, the entire Re distribution is extended to smaller radii in the case of passive ETGs, especially for log (M/M⊙) ≳ 11.5. Remembering that small differences in galaxy size imply large differences in stellar mass density, the derived trends suggest that the ETGs analyzed in this work should have formed from higher density progenitors which, in the hypothesis of no coeval mergers, do not increase their mass during the evolution. On the other hand, we cannot exclude the possibility that galaxies in the parent sample have experienced more dry mergers than our massive and passive galaxies, which have increased their size across cosmic time (Naab et al. 2009; Johansson et al. 2012a). The observed trend is also in agreement with some literature studies at low redshift which also suggest that more compact galaxies contain older stellar populations than larger ones (e.g. Saracco et al. 2009; Shankar & Bernardi 2009; Williams et al. 2010; Poggianti et al. 2013; McDermid et al. 2015). In general, this is qualitatively consistent with the high zF inferred by our analysis (z> 5) since, according to the cosmological evolution of the baryonic matter density, gas was denser at these cosmic epochs. These findings also agree with recent observations of compact systems (with various level of SF) at z ~ 2−3, which could be identified as local massive ETGs progenitors (e.g. Daddi et al. 2004; Cattaneo et al. 2013; Finkelstein et al. 2013; Marchesini et al. 2014; Nelson et al. 2014; Williams et al. 2015). Moreover, recent models of elliptical galaxy formation also predict the formation of compact and dense progenitors at high redshifts (e.g. Johansson et al. 2012a; Naab et al. 2014 and references therein).


Over the last 15 yr, our understanding of how galaxies form and evolve has improved substantially. The combination of technological and theoretical progress has brought this field into a new era: advances in observational techniques (e.g. multi-object spectroscopy, efficient near-infrared CCDs) have enabled multiwavelength observations of large samples of galaxies out to the highest redshifts, while the steady rise of computational power and refinement of numerical techniques have fostered new approaches (e.g. semi-analytic models, hydro-dynamic simulations) to model the formation and evolution of galaxies. This progress has led to a general consensus about the main physical ingredients required to describe the evolution of the galaxy population (e.g. Gonzalez-Perez et al. 2014; Lu et al. 2014; Vogelsberger et al. 2014; Henriques et al. 2015; Schaye et al. 2015): collapse and hierarchical growth of dark matter haloes; accretion of baryons on to these haloes; conversion of baryons into stars; feedback of massive stars and active galactic nuclei (AGN) on star formation; supernova- and AGN-driven outflows of metal-enriched gas; infall of both pristine and metal-enriched gas on to galaxies. The large-scale environment can also affect galaxy properties, in particular, by providing quenching mechanisms (e.g. tidal or ram-pressure stripping, strangulation; e.g. Lagos et al. 2014; Rafieferantsoa et al. 2015), and through its influence on the merger rate (e.g. Lackner et al. 2012; Rafieferantsoa et al. 2015) and galactic spins (e.g. Hahn, Teyssier & Carollo 2010; Codis et al. 2012). Although these different ingredients are present in many galaxy formation models, we still lack a detailed quantification of their respective roles in shaping the properties of galaxies. This is because of the complexity inherent in galaxy physics, which combines gravity, radiation hydro-dynamics, magnetic fields and high-energy physics, acting on scales from less than a pc (e.g. for the formation of proto-stellar cores) to over a Mpc (e.g. for environmental effects). For this reason, ‘first-principles’ simulations of galaxy formation remain far beyond the reach of current computational capabilities. Instead, small-scale baryonic physics is generally subsumed into sub-grid prescriptions, which vary from model to model (e.g. Scannapieco et al. 2012; Haas et al. 2013a,b; Vogelsberger et al. 2013; Torrey et al. 2014; Crain et al. 2015). The appropriateness of such prescriptions, and hence, our ability to understand galaxy formation, must be assessed by comparing simulated and observed galaxy properties.


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


In the 2D density distribution (Fig. 5, upper panel) we can distinguish only the primary structure. Taking into account the measured mass according to the fitted shear profile for this component, we compute the corresponding projected density profile, Σ(r), assuming a NFW distribution according to the equations given by Wright & Brainerd (2000). All of the obtained values are below the 3σ detection level (250 h70 M⊙ pc−2) and only the inner region, corresponding to a radius of 60 kpc would present a density larger than the 2σ detection level (180 h70 M⊙ pc−2). Thus, we consider that the mass of this structure is near the detection threshold of the 2D density contrast distribution. Also, we do not detect significant X-ray emission in the secondary structure region above the threshold adopted to build the brightness contours. In order to establish if this is due to the observing detection limit, we consider the lowest detected flux of RASS-based catalogs according to Piffaretti et al. (2011), which contains the lowest X-ray emission clusters identified using this data. This corresponds to a flux Flim = 1.5 × 10−12 erg s−1 cm−2, in the 0.1–2.4 keV band of the SGP catalog (Cruddace et al. 2002). Considering this flux and the redshift of the secondary structure, we obtain a limiting luminosity of 1.5 × 1042

$h^{-2}_{70}$

h

70

−2

 erg s−1. Taking into account the obtained lensing mass, we compute the expected X-ray luminosity for the system according to Leauthaud et al. (2007) M_ LX relation, obtaining (3.7 ± 2.4) × 1043

$h^{-2}_{70}$

h

70

−2

 erg s−1, only 1.5σ above the detection limit. For this calculation we use the derived SIS mass since it has the lowest χ2 value and errors correspond to the propagation of the M_LX parameter errors. Therefore, according to the lensing estimated mass the secondary structure would be roughly at the detection limit of the X-ray observation. We considered using more sensitive X-ray data, therefore we checked in the available databases of Chandra and XMM; however this component is not present in the field-of-view of these surveys. Considering the X-ray luminosity emission upper limit (6.1 × 1043

$h^{-2}_{70}$

h

70

−2

 erg s−1) the emission is 2.5σ above the detection limit given by Flim (Piffaretti et al. 2011). Therefore, it is important to highlight that a low X-ray emissivity could be explained by a low density of the intracluster gas, which might be produced by a past interaction between the structures.


Since the ground-breaking observation of radio pulsars by Hewish et al. (1968), NSs remain one of the most studied astrophysical objects; they are assumed to be possible sources of high-energy emission. The typical values of the surface magnetic field as inferred from simple magnetic dipole models and spin-down rates are in the range 108–1013 G (Taylor et al. 1993; Alpar et al. 1982). Note that among radio pulsars, PSR J1847−0130 exhibits a strong magnetic field of B = 9.4 × 1413 G (McLaughlin et al. 2003). However, besides the X-ray luminosities observed from the anomalous X-ray pulsars (AXPs), the inferred periods of AXPs and soft-γ repeaters suggest that such NSs have even larger surface magnetic fields of 1014−1015 G (Duncan & Thompson 1992; Paczynski 1992; Thompson & Duncan 1996; Melatos 1999). NSs with such high surface magnetic fields are popularly known as magnetars. Several interesting studies (Usov 1992; Kluźniak & Ruderman 1998; Wheeler et al. 2000; Starling et al. 2009; Cenko et al. 2010) have predicted that magnetars are the probable source of γ-ray bursts, and they require a higher magnetic field such as 1016–1017 G to initiate Poynting-flux-dominated jets. Although until now only around 30 magnetars have been detected, researchers have speculated that these astrophysical objects may account for 10% of the NS population (Kouveliotou et al. 1998). For NSs, the effects of a strong magnetic field on the ultra-dense electron gases in their interiors have been studied in several papers (Canuto & Ventura 1977; Fushiki et al. 1989; Abrahams & Shapiro 1991; Fushiki et al. 1992; Roegnvaldsson et al. 1993). Studies of dense and strongly magnetized nuclear matter have also been carried out by Chakrabarty et al. (1997), Bandyopadhyay et al. (1998), Broderick et al. (2000), Suh & Mathews (2001), Harding & Lai (2006), Chen et al. (2007), Rabhi et al. (2008), and references therein. Finally, we mention that studies of NSs with different magnetic-field configurations, viz., toroidal, poloidal, or mixed were carried out by Bocquet et al. (1995), Cardall et al. (2001), and Pili et al. (2014).


The interaction of the pulsar wind with the surrounding environment gives rise to a pulsar wind nebula (PWN) (Gaensler & Slane 2006; Bucciantini 2008; Olmi et al. 2016). A bubble of relativistic pairs and magnetic field, that shines with a non-thermal broad-band spectrum, extending from radio to X-rays and γ-rays, via synchrotron and inverse Compton emission. The Crab nebula is the prototype of PWNe inside the parent supernova remnant (SNR) (Hester 2008). Given that the typical pulsar speed at birth, the so called kick velocity, is usually of the order of 100–400 km s−1 (Cordes & Chernoff 1998; Arzoumanian, Chernoff & Cordes 2002; Sartore et al. 2010; Verbunt, Igoshev & Cator 2017), much smaller than the expansion speed of young SNRs [typically a few thousands km s−1 (Truelove & McKee 1999; Hughes 1999, 2000; DeLaney & Rudnick 2003; Borkowski et al. 2013; Tsuji & Uchiyama 2016)], for the first few thousands of years, the PWN is going to remain confined within the parent SNR (van der Swaluw et al. 2003; van der Swaluw, Downes & Keegan 2004; Temim et al. 2015). However the SNR expansion speed will drop in time as the expansion proceeds (Cioffi, McKee & Bertschinger 1988; Leahy, Green & Tian 2014; Sánchez-Cruces et al. 2018), sweeping up more and more interstellar medium (ISM) material, such that on a typical time-scale of a few tens of thousands of years, the pulsar can escape from the SNR, and begin to interact directly with the ISM. Given the typical sound speed of the ISM, the pulsar motion is highly supersonic, and the ram pressure balance between the pulsar wind and the ISM flow gives rise to a cometary-like nebula (Wilkin 1996) known as bow-shock pulsar wind nebula (BSPWN), of shocked pulsar and ISM material (Bucciantini & Bandiera 2001; Bucciantini 2002b). If the ISM is cold and its neutral fraction is high, these nebulae can be observed in H α emission (Kulkarni & Hester 1988; Cordes, Romani & Lundgren 1993; Bell et al. 1995; van Kerkwijk & Kulkarni 2001; Jones, Stappers & Gaensler 2002; Brownsberger & Romani 2014; Romani, Slane & Green 2017), due to charge exchange and collisional excitation, taking place in the shocked ISM downstream of the forward bow shock (Chevalier, Kirshner & Raymond 1980; Hester, Raymond & Blair 1994; Bucciantini & Bandiera 2001; Ghavamian et al. 2001), or alternatively in the UV (Rangelov et al. 2016), and IR (Wang et al. 2013). On the other hand the shocked pulsar material is expected to emit non-thermal synchrotron radiation, and indeed many such systems have been identified in recent years either in radio or in X-rays (Arzoumanian et al. 2004; Gaensler et al. 2004; Chatterjee et al. 2005; Gaensler 2005; Li, Lu & Li 2005; Yusef-Zadeh & Gaensler 2005; Kargaltsev et al. 2008, 2017; Misanovic, Pavlov & Garmire 2008; Hales et al. 2009; Ng et al. 2009; Ng et al. 2010; De Luca et al. 2011; Ng et al. 2012; Marelli et al. 2013; Jakobsen et al. 2014; Klingler et al. 2016; Posselt et al. 2017). There is also an interesting dichotomy between H α emitting systems and synchrotron emitting ones, suggesting that energetic pulsars, more likely to drive bright synchrotron nebulae, might pre-ionize the incoming ISM suppressing line emission from neutral hydrogen.


As we discussed in the introduction, different choices of age anchors for the 26Al–26Mg decay system, CAIs versus the D’Orbigny angrite, result in different ages with a difference of 1–1.5 Ma. The differences can be interpreted as a reflection of different initial 26Al/27Al in the CAI accretion region, closest to the Sun (MacPherson, Wark & Armstrong 1988; Sossi et al. 2017) compared with the initial 26Al/27Al in the angrite formation region. In fact, CAIs also show large mass-independent isotopic anomalies for multiple elements, e.g. O, Cr, and Ti (Trinquier et al. 2009; Krot et al. 2020), which suggest that they formed in different nebula environments compared to achondrites like angrites and EC 002. In Fig. 3 and Table S6, we show U–Pb, 53Mn–53Cr, and 26Al–26Mg age comparisons for several achondrites. The data indicates that for all NC-like achondrites [ε54Cr values  0.3; Zhu et al. (2021a)], their U–Pb ages, and 53Mn–53Cr and 26Al–26Mg ages anchored to D’Orbigny are consistent. This consistency may indicate that the abundance of initial 26Al/27Al value of NC achondrites at 4567 Ma may have been lower in the non-carbonaceous region relative to the canonical initial Solar system value of 26Al/27Al derived from CAIs (Schiller et al. 2015). However, for NWA 6704, which has a CR chondrite-like ε54Cr, its 53Mn–53Cr ages are more consistent if its 26Al–26Mg age is anchored to CAIs, which suggests that the 26Al abundance of the CC bodies in the outer Solar system may follow that of CAIs. This conclusion is also consistent with the olivine grains (with Al/Mg ratio close to 0) in carbonaceous chondrites having the canonical initial μ26Mg (∼−35 ppm), indicating that the initial 26Al abundance in CCs at 4567 Ma was similar to that of CAIs (Gregory et al. 2020). Thus, the age difference of 26Al–26Mg ages relative to 53Mn–53Cr ages can be caused by a different initial abundance of 26Al in the inner relative to the outer Solar system. We note that the U–Pb age of NWA 2976 overlaps the Al–Mg ages anchored to both CAIs and D’Orbigny. This issue warrants more detailed assessment and discussion, e.g. the U–Pb dating (Krestianinov, Datta & Amelin 2021); however, mineral fractions used for dating should avoid xenocrystic material that may have formed at different times and from different sources.


The second problem is that of the angular momentum distribution. Even if angular momentum is assumed to be conserved, one cannot explain the exponential form of disc galaxies. Using cold dark matter (CDM) numerical simulations (Bullock et al. 2001), found that if discs are formed from gas with an angular momentum distribution similar to that of dark matter, this results in excess mass near the centre, in comparison with an exponential disc. Specifically, the models predict too much material with low angular momentum, and this makes it particularly difficult to explain the origin of bulgeless dwarf galaxies (van den Bosch, Burkert & Swaters 2001). Responding to this difficulty Maller & Dekel (2002) proposed a model in which the angular momentum is built up by a sequence of mergers. While the acquisition of angular momentum in dissipationless N-body simulations has been well studied (Bullock et al. 2001; Maller, Dekel & Somerville 2002; Vitvitska et al. 2002; Avila-Reese et al. 2005; Bett et al. 2007, 2010; D'Onghia & Navarro 2007), our understanding of the extent to which gas behaves similarly has only recently started to be explored via computations (Chen, Jing & Yoshikaw 2003; Sharma & Steinmetz 2005; Brook et al. 2011; Kimm et al. 2011; Pichon et al. 2011; Sharma & Nath 2012). In the last decade galaxy redshift surveys (see e.g. Colless et al. 2001) have enabled us to map the universe on increasingly large scales, and to study systematically the properties of large-scale structures. These surveys show that the galaxies are not distributed evenly, but develop within a pattern of filaments and sheets which are separated by immense voids. The latter are defined observationally as large regions with very low galaxy number density, which occupy some 40 per cent of the overall cosmic volume (Hoyle & Vogeley 2004). It is generally believed that the voids originate from the local minima of the primordial density fluctuations, and as their mean density is lower than that of their surroundings, they expand more quickly. If tidal shear plays a significant role in their development, it should not only cause them to depart from sphericity, but should entail their acquisition of spin angular momentum (Lee & Park 2006). The specific angular momentum of cold dark matter haloes in a ΛCDM universe depends strongly on their merging histories (D‘Onghia & Burkert 2004). Haloes with a quiet merging history, dominated until the present epoch by minor mergers and accretion, acquire by tidal torques an average of only 3 per cent of the angular momentum required for their rotational support. This is in direct conflict with the observational data for a sample of late-type bulgeless galaxies, which indicate that these galaxies reside in dark haloes with exceptionally high values of specific angular momentum. Although minor mergers and accretion preserve or slowly increase the specific angular momentum of dark haloes as a function of time, this mechanism is not efficient enough to explain the observed spin values, especially for late-type dwarf galaxies. Energetic feedback processes have been invoked to solve the problem implied by the loss of a large fraction of its specific angular momentum by the gas during infall. This is predicated on the assumption that dark haloes which host bulgeless galaxies acquire their mass via quiescent accretion. D‘Onghia & Burkert (2004) find an even more serious version of this problem: the specific angular momentum gained during the formation of these objects is not enough to provide rotational support even if no angular momentum is lost during gas infall.


The new sample of HSPs gave us an opportunity to see the optical IDVs of HSPs and compare its properties with optical IDVs of LSPs. We started a dedicated project to search for optical IDV in HSPs and after doing 62 nights of IDV observations of HSPs which gave us 144 LCs (41 in B band, 62 in R band, and 41 in B−R colour) of five HSPs (Mrk 421, 1ES 1426+428, 1ES 1553+113, 1ES 1959+650, and 1ES 2344+514). Interestingly, we found that, four HSPs did not show any IDV (Gaur, Gupta & Wiita 2012a; Gaur et al. 2012b,c), but only one HSP 1ES 1426+428 for which we have the least observations have shown IDV in six LCs out of eight LCs (Gaur et al. 2012c). Our this pilot project gave us 6 IDV LCs out of 144 LCs searched for IDV i.e ∼4 per cent LCs have shown IDV. We explained it by density inhomogeneities and bends in the bases of the jets by Kelvin–Helmholtz instabilities (Romero, Cellone & Combi 1999). We gave an alternative explanation i.e. since in HSPs, the optical band lies below the SED peak, hence, we should see changes in the efficiency of acceleration of, and/or in the rates at which energy is radiated by, the highest energy electrons available for synchrotron emission would have a more retarded effect on optical variability in HSPs (Gaur et al. 2012b). In LSPs, the optical band is dominated by highest energy electrons emitting synchrotron radiation and probably the X-ray emission is dominated by the comparatively lower energy electrons emitting the inverse Compton radiation, hence their X-ray variability is less pronounced than optical variability. If SED peak is really responsible for IDV properties, then we suspected that X-ray IDV LCs in LSPs should not show any IDV at all or show on rare occasions. With this motivation, here we present the X-ray IDV study of almost complete sample of 10 LSPs and 2 ISPs observed by XMM–Newton since its launch and we found that the LSPs show very less IDV 2 out of 50 LC i.e. 4 per cent in X-ray bands. We have reported above the similar finding for HSPs in optical bands.


Many classical theories are presented exploring the dynamics of various rotating plasma instabilities, such as those of Vedenov et al. (1961) and Rosenbluth & Simon (1965). Initially studied by Velikov (1959), work in this area starts with the nondissipative Couette flow of an ideal conducting fluid between two differentially rotating cylinders. It is observed that the fluid is destabilized by applying an axial magnetic field. This work was confirmed by Chandrasekhar (1960). By now, research on magnetorotational instability (MRI) is well understood and reported in both experimentally (liquid metals; Rüdiger et al. 2003; Ji et al. 2004) and theoretically based studies of astrophysical plasmas (Blaes & Balbus 1994; Hawley et al. 1995; Quataert et al. 2002). In astrophysical environments, MRI is now believed to be the main factor deriving plasma turbulence and also to account for the accretion process that feeds stars and black holes (Kotake et al. 2004). After its discovery, MRI remained outside the general theory of plasma instabilities for almost four decades, and was revisited with its application to astrophysical objects by considering the anomalous viscosity problem in the accretion disks surrounding astrophysical compact objects; see Balbus & Hawley (1991). MRI is supposed to be a destructive factor for the hydrodynamical Rayleigh’s stability criterion, making it magnetohydrodynamically unstable and leading directly to orbital angular momentum transport and disk turbulence (Hawley & Balbus 1991, 1992; Balbus & Hawley 1998). A two-fluid model for MRI in differentially rotating plasma was presented by Ren et al. (2011) to describe the dynamical behavior of ions and electrons in both low- and high-frequency regimes. They have demonstrated the instability criteria that differ significantly from the one derived in the single-fluid model (Balbus & Hawley 1991). Mikhailovskii et al. (2008a) studied MRI in dusty plasmas using a single-fluid MHD model. They derived a generalized relation by including the effect of dust particulates, and due to the induced electric field the rotation of equilibrium plasma was modified and gave rise to an instability called a dust-induced rotational instability. In their preceding work (Mikhailovskii et al. 2008b) with an immobile dust grain assumption, a comprehensive analysis was carried out for the collective phenomenon of instability which provides a more detailed theory about MRI. The MRI in differential rotating dusty plasmas with dissipative effects was investigated by using local linear analysis with effect of immobile dust grains (Ren et al. 2009).


To confirm the importance of VO, water and an inversion layer (Evans et al. 2018; Mikal-Evans et al. 2019, 2020) obtained repeated HST observations of the transmission spectrum and the secondary eclipse using the STIS and WFC 3 instruments. The optical transmission spectrum displays rich variation, with multiple features consistent with VO absorption that Evans et al. (2018) could reproduce by assuming an isothermal T-P profile at 1500 K and a metallicity equivalent to 10× to 30× solar. Absorption bands of TiO appeared to be muted in the transmission spectrum, which was explained by Evans et al. (2018) as evidence of condensation of Ti-bearing species, which commences at higher temperatures than condensation of V-bearing species, producing for example, calcium titanates (Lodders 2002) while VO remains in the gas phase. Mikal-Evans et al. (2019) observed the day side emission spectrum with the G102 grism of WFC3 (0.8–1.1 μm), augmenting their earlier observations with the G141 grism. The G102 spectrum does not show the VO bands expected to be present there, and this led Mikal-Evans et al. (2019) to question the interpretation that the 1.2 μm feature is caused by VO emission. The secondary eclipse was observed at 2 μm (Kovács & Kovács 2019) and at optical wavelengths with the TESS instrument. These were analysed together with the preceding Hubble, Spitzer, and ground-based observations to yield tighter constraints on the atmospheric structure, composition and overall system parameters (Bourrier et al. 2020a; Daylan et al. 2019). These studies found that the hottest point on the day side exceeds a temperature of 3000 K, that the atmosphere is inverted on the day side, and a metallicity that is consistent with solar (Bourrier et al. 2020a) or slightly elevated (Daylan et al. 2019). Although the chemical retrievals follow different strategies (equilibriumversus free-chemistry), both indicate that a depletion of TiO relative to VO is needed to explain the observed emission spectrum, supporting the earlier findings by Mikal-Evans et al. (2019). Recently, Mikal-Evans et al. (2020) obtained new secondary-eclipse observations using the G141 grism of WFC3. Although confirming the presence of emission by H2O, a joint analysis with their previous WFC3 observations did not reproduce the emission feature at 1.2 μm, prompting the authors to entirely discard their previous interpretation of emission caused by VO.


During the X-ray ‘hard’ state, the radio and X-ray behaviour of BHXBs is correlated and has been studied in depth for many sources using quasi-simultaneous observations (e.g. Corbel et al. 2003; Gallo, Fender & Pooley 2003; Coriat et al. 2011; Corbel et al. 2013), and is known as the radio:X-ray plane. It was thought that all XBs followed a relation in the form of $L_{\rm Radio} \propto L_{\rm X-ray}^{0.6}$, based upon early observations of GX 339−4 (Hannikainen et al. 1998; Gallo et al. 2003; Corbel et al. 2003, 2013). This relation extends down to very low luminosities, i.e. into quiescence (Corbel et al. 2003, 2013; Plotkin et al. 2017; Tremou et al. 2020), and has been observed in other sources such as V404 Cygni (e.g. Corbel, Koerding & Kaaret 2008) and XTE J1118+480 (Gallo et al. 2014). However, further observations revealed the presence of another population of BHXBs which are less radio luminous than this relation, a so-called ‘radio-quiet’ branch, which followed $L_{\rm R} \propto L_{\rm X}^{1.4}$, such as H 1743−322 (e.g. Coriat et al. 2011; Williams et al. 2020). In some of these ‘radio-quiet’ objects, they are then found to re-join the ‘radio-loud’ branch when they go back into quiescence (Coriat et al. 2011; Carotenuto et al. 2021). The underlying cause of the split tracks (see Gallo, Miller & Fender 2012; Gallo et al. 2014; Gallo, Degenaar & van den Eijnden 2018, for a clustering analysis into the statistical robustness of this split) for BHXBs is not known, but it may be due to differences in the radiative efficiency of the accretion flow (Coriat et al. 2011; Koljonen & Russell 2019), an inclination effect of the source (Motta, Casella & Fender 2018), differences in the accretion disc contribution (Meyer-Hofmeister & Meyer 2014) or changes in the magnetic field (Casella & Pe’er 2009). For the purposes of this paper, we will refer to the original $L_{\rm R} \propto L_{\rm X}^{0.6}$ correlation sources as ‘radio-loud’ objects, and those that diverge on to the $L_{\rm R} \propto L_{\rm X}^{1.4}$ track as ‘radio-quiet’ sources.


The difference in the early-type fractions of star-forming and quenched satellites may be taken to indicate that quenching is associated with structural changes in the galaxies, that is, changes affecting their underlying mass distribution, such as substantial growth of stellar mass in the bulge (or inner disk) components. It is well established that quenched galaxies have radial surface brightness profiles that are steeper than those of star-forming galaxies and are well described by high Sérsic indices (e.g., Kormendy et al. 2009 and references therein), reflecting high central mass densities (e.g., Fang et al. 2013 and references therein). Also, since the pioneering work of Mihos & Hernquist (1994), inward flows of gaseous material have long been recognized to take place during galaxy mergers and through disk instabilities. Such inward gas flows are likely to contribute to the growth of stellar mass in galactic bulges (see, e.g., Courteau et al. 1996; MacArthur et al. 2003; Immeli et al. 2004; our own work, i.e., Carollo et al. 1997, 1998, 2001, 2007 and Carollo 1999, 2004; the comprehensive review by Kormendy & Kennicutt 2004 and references therein; Bournaud et al. 2011, and many others). This idea has been further developed in more recent theoretical studies (e.g., Dekel & Burkert 2014) and is suggested to be observed at high redshifts (e.g., Genzel et al. 2006; Cameron et al. 2011) and, at least for low-mass bulges, certainly observed in the local universe, where small bulges show signs of “rejuvenation” of their stellar populations, with up to 10%–30% of their total mass consistent with having formed in the past few gigayears (Thomas & Davies 2006; Carollo et al. 2007). If mergers and disk instabilities were directly or indirectly connected with galactic quenching, it would not be implausible to draw a connection between quenching and the growth of bulges. Establishing the direction of causality in any such change would remain, however, very difficult. Quenching could be directly linked to the growth of the bulge (e.g., Martig et al. 2013; Genzel et al. 2014), or the quenching process itself could be associated with bulge growth, or the prominence of the bulge could be linked to a third property (e.g., galactic mass or the presence of an AGN) that itself controls the quenching of star formation.


Large-scale molecular outflows are also commonly associated with the earliest stages in the formation of massive (B- and O-type) stars. However, bipolar outflows observed in high-mass star-forming regions tend to be less collimated than those observed in low-mass regions (e.g., Arce et al. 2007). Recent radio observations have established that very young massive protostars are also commonly associated with compact free–free emission, being the signpost of mass ejected near the protostar (e.g., Moscadelli et al. 2016; Purser et al. 2016, 2021; Rosero et al. 2016, 2019; Sanna et al. 2018; Obonyo et al. 2019). However, it is not yet clear whether this emission traces the bases of jets as well collimated as those observed in low-mass star-forming regions. To date, we know of only a handful of highly collimated jets from massive protostars extending over tens of thousands of au (e.g., Cep A HW 2: Curiel et al. 2006; HH 80–81: Rodríguez-Kamenetzky et al. 2017; IRAS 16547−4247: Rodríguez et al. 2005; G035.02+0.35: Sanna et al. 2019b; IRAS 16562−3959: Guzmán et al. 2010; G016.59−0.05: Moscadelli et al. 2019), and, although evidence exists for magnetic fields playing an important role in their collimation (e.g., Carrasco-González et al. 2010; Surcis et al. 2014; Sanna et al. 2015; Maud et al. 2019), it is not yet clear whether collimation takes place at small distances from massive protostars. One possibility is that different mechanisms could be at work to produce jets around massive protostars, as they are expected to accrete at higher rates from much larger, massive and turbulent disks than those around low-mass protostars (e.g., Carrasco-González et al. 2012; Sanna et al. 2019a; Añez-López et al. 2020). Under these conditions, it could be very difficult to form strong and well-structured helical magnetic fields capable of highly collimate jets at au scales. Indeed, wide-angle or even spherical winds are also commonly found in high-mass star-forming regions (e.g., Torrelles et al. 1997, 2001, 2011; Moscadelli et al. 2007). Interestingly, it has been proposed that initially poorly collimated winds could be externally collimated at large (≳10–100 au) distances from the protostar by strong ambient medium pressure (e.g., Carrasco-González et al. 2015) or by a large-scale ordered magnetic field (e.g., Albertazzi et al. 2014). Therefore, there is the possibility that mass ejection from massive protostars could be mostly isotropic at au scales, and, under favorable conditions, it might become collimated at larger distances from the driving source.


Since the expected number density of high-z massive quiescent galaxies is low, large fields with deep photometric coverage are required to identify these systems and reliably assess their SEDs. For this reason, we exploited the 2 deg2 COSMOS field. Sources with Ktot  22.5 were extracted from the catalogue of McCracken et al. (2010), limiting the selection to those satisfying the observed-frame BzK colour criterion for passive systems (Daddi et al. 2004). Targets formally classified as star-forming BzK (sBzK) with a signal-to-noise ratio S/N  5 in the B and z bands were retained since these photometric candidates are degenerate with quiescent galaxies becoming fainter in these bands with increasing redshift and decreasing mass. Photometric redshifts specifically calibrated for high-z QGs were derived with EAZY (Brammer et al. 2008) as in Onodera et al. (2012) and Strazzullo et al. (2015). This calibration was based on the sample of 34 spectroscopically confirmed passive galaxies at 1.3  zspec  2.1 observed with VLT/VIMOS that later appeared in Gobat et al. (2017) and the sample of 18 passive galaxies at 1.4  zspec  1.9 of Onodera et al. (2012) observed with Subaru/MOIRCS. The calibrated zphot were used to select galaxies within 2.5 ≤ zphot ≤ 3.5 and to remove objects with UVJ rest-frame colours inconsistent with passive evolution (Pozzetti & Mannucci 2000; Labbé et al. 2005; Williams et al. 2009). SED fitting was performed using FAST (Kriek et al. 2009), allowing for constant and delayed exponentially declining SFHs. Optical dust attenuation was left free to vary up to AV = 5 mag assuming a Calzetti et al. (2000) attenuation law. Fits were repeated by adopting purely quiescent templates only. All passive UVJ candidates whose SED fits to optical-NIR photometry could not reject dusty star-forming solutions at high confidence were further discarded. Contamination from dusty star-forming galaxies was further minimised by removing objects with Spitzer/MIPS 24 μm S/N ≥ 4 detections in the Le Floc’h et al. (2009) catalogue, except for galaxies with high-confidence passive SEDs, which are indicative of mid-infrared (MIR) emission caused by a central dusty AGN torus. This selection provided a total of 174 passive candidates with UVJ-quiescent colours (47 of which were pBzK in the original selection, plus 67 and 60 uncertain sBzK with and without significant MIPS detections, respectively). The maximum required magnitude to obtain HST/G141 spectra with sufficient S/N in order to secure spectroscopic confirmation within one to two orbits was assessed by simulating their grism spectra based on their best-fitting SED templates. This yielded a magnitude cut of HAB  22, which narrowed the sample down to 23 objects. A total of 10 galaxies were targeted for HST WFC3/IR G141 near-IR observations: 9 randomly drawn galaxies with HAB  22 (M⋆ > 1.1 × 1011 M⊙) plus 1 robust candidate with HAB = 22.9 (M⋆ = 8 × 1010 M⊙) selected to be the highest-z candidate based on its high-confidence passive SED. More details about the selection are available in Lustig et al. (2021).


As a prediction of the Λ cold dark matter (ΛCDM) cosmological model (Springel, Frenk & White 2006), hierarchical clustering (White 1997; Steinmetz 2001) and major mergers (Toomre 1977) build elliptical galaxies and classical (elliptical-like) bulges of disc galaxies on a short time-scale through the complete and violent collapse of the protogalactic clouds. In this schema, mergers get less common through the expansion of the Universe and consequently the evolution of galaxies, which are getting now more and more isolated, gradually changing to a more secularly driven one under the influence of internal rather than external actors (Toomre 1977; Le Fèvre et al. 2000; Conselice, Chapman & Windhorst 2003; Kormendy et al. 2010; Athanassoula, Machado & Rodionov 2013; Knapen 2013). This slow evolution of galaxies has been introduced as ‘secular evolution’ (Kormendy & Illingworth 1982; Kormendy & Kennicutt 2004; Kormendy 2008). However, mergers and accretion must also occur along the life of galaxies, even in low-density environments, and such external processes are known to push disc galaxies along the Hubble sequence towards Sa/S0 (Aguerri, Balcells & Peletier 2001; Eliche-Moral et al. 2006, 2011). Much observational and numerical work has been devoted to discriminating between internal and external evolutionary mechanisms (for a review see Kormendy 2013). Bars in disc galaxies are considered as key drivers of the secular evolution by redistribution of the angular momentum, triggering of star formation, and the morphological transformation of galaxies. During the secular evolution phase, bars can significantly alter the structure and kinematics of disc galaxies and develop a complex rotation pattern within the central parts of galaxies, called ‘cylindrical rotation’ (Kormendy & Illingworth 1982). This feature is defined as almost constant stellar rotation speed within the bulge of a galaxy in the direction perpendicular to the disc plane, such that δ$v$/δ|$z$| ∼ 0, where $v$ is the line-of-sight velocity and $z$ is the distance from the disc plane in edge-on projection. These feature has been confirmed in several observational studies of nearby barred galaxies observed in the edge-on view (e.g. Pence 1981; Kormendy 1983; Bettoni & Galletta 1997; Emsellem et al. 2001; Márquez et al. 2003; Pérez, Sánchez-Blázquez & Zurita 2009; Williams et al. 2011; Molaeinezhad et al. 2016, 2017), including our Milky Way (see Barbuy, Chiappini & Gerhard 2018, and references therein). N-body simulations of barred galaxies confirm the link between the presence of a bar and a tendency to rotate on cylinders for stars within the bar, as a natural consequence of the bar buckling processes (see Combes & Sanders 1981; Athanassoula 2003, 2005; Martinez-Valpuesta & Shlosman 2004; Bureau & Athanassoula 2005). In this scenario, after the bar develops, it experiences a period of buckling instability that thickens it in the axial direction (e.g. Combes & Sanders 1981), giving birth to a boxy or peanut-shape bulgy structure in the central parts of the bar, termed boxy/peanut bulge (B/P, hereafter). From the galactic-dynamics point of view, bar formation makes the orbits in the bar more eccentric and more boxy and aligns their principal axes without greatly affecting the motion perpendicular to the plane; consequently, the cylindrical rotation follows naturally (Bureau & Freeman 1997). As demonstrated in numerous N-body simulation studies of barred galaxies, the resulting velocity field due to this orbital reconfiguration is compatible with the observed cylindrical rotation in B/P bulges (see Molaeinezhad et al. 2016, and references therein).


Also as noted in Mason et al. (2008), He/O, and to a lesser degree Ne/O, ratios show a downward slope with respect to Fe/C. This cannot by explained by variations of solar wind composition between fast and slow streams. The relative abundances of C and O are similar between slow and fast wind, and since the Fe, He, and Ne are more abundant in the slow than the fast solar wind, this would lead to a positive correlation (von Steiger et al. 2000). However, it is possible that the variations along the power-law slopes are, at least partially, due to a solar cycle effect on the solar wind composition, with the He/O ratios and Ne/O ratios varying throughout the solar cycle (see Desai et al. 2006; Mason et al. 2008). In order to investigate solar cycle phase dependencies in the abundance ratios, the right column of Figure 3 illustrates the ratios by solar cycle phase. To define the phase, the smoothed sunspot number was normalized to the maximum for each solar cycle and broken up into times when the normalized sunspot number was less than 1/3 (solar minimum, blue triangles), greater than 2/3 (solar maximum, red diamonds), or in between (ascending/descending phase, green rectangles). As would be expected from the Fe/O ratio in Figure 1, all of the times the Fe/C ratios were greater than approximately 0.3 occurred during solar maximum. However, the ratios during solar minimum and the declining/ascending phase are very similar. While the solar maximum Fe/C ratios extend to much higher values than for CIRs during either solar minimum or the declining/ascending phases, some of the solar maximum CIRs are also observed to have Fe/C ratios well within the range of values observed for the other phases. This seems to suggest that the process(es) that is/are energizing Fe preferential to C can be more efficient during solar maximum, but the process(es) does/do not require all CIR-associated Fe/C ratios during solar maximum to be necessarily elevated above that during the other phases. An example of this is the Fe/O enhancement during the declining phase (Figure 1).


The circumgalactic medium (CGM) is the interface between cold flows from the intergalactic medium on to a galaxy, and hosts hot halo gas and material ejected from galaxies (for reviews, see Putman, Peek & Joung 2012; Tumlinson, Peeples & Werk 2017). With various processes in galaxy evolution consuming (e.g. star formation) and removing (e.g. winds) gas, the CGM is shaped by the processes internal to the galaxy. Early progress in the study of the CGM came from connecting the absorption lines in quasar (QSO) spectra with galaxies imaged in the foreground, tracing the extent and properties of the CGM gas as a function of the host galaxy’s properties (e.g. Bergeron 1986; Bowen, Blades & Pettini 1995; Lanzetta et al. 1995; Adelberger et al. 2005; Chen et al. 2010; Steidel et al. 2010; Bordoloi et al. 2011; Prochaska et al. 2011; Turner et al. 2014). Building on these foundations, our understanding of the CGM has been significantly improved through the surveys with the Hubble Space Telescope (HST) Cosmic Origins Spectrograph (COS; Green et al. 2012). The first of several surveys of the CGM surrounding low-redshift galaxies was the COS-Halos survey (Tumlinson et al. 2013) which targetted the CGM around 44 ∼L⋆ galaxies, demonstrating that the properties of the CGM differ depending on whether the central galaxy is passive or star forming [defined using a specific star formation rate cut of specific star formation rate (sSFR) $\rm {=10^{-11} yr^{-1}}$; Tumlinson et al. 2011; Werk et al. 2013; Borthakur et al. 2016]. The COS-Halos team found a distinct lack of O vi around passive galaxies, while H i was found at the same strength around all galaxies (Tumlinson et al. 2011; Thom et al. 2012). Additionally, connections have been made between the CGM and properties of the host galaxy, including increased H i content of the CGM with larger interstellar medium (ISM) gas masses (COS-GASS; Borthakur et al. 2015), the presence of extended gas reservoirs around galaxies of all stellar mass (COS-Dwarfs; Bordoloi et al. 2014b), and enhanced metal content around starbursting hosts (COS-Burst; Borthakur et al. 2013; Heckman et al. 2017).


DSFGs in the z > 5 tail are thought to be rare, but their level of rarity is subject to debate (e.g., Béthermin et al. 2015, 2017; Asboth et al. 2016; Ivison et al. 2016; see also Simpson et al. 2014, 2020; Dudzevičiūtė et al. 2020). A significant challenge in determining the space density of such sources is the difficulty in finding them in the first place. Given their distance, classical techniques combining optical and radio identifications have been largely unsuccessful due to the faintess or lack of detection at these wavelengths, commonly leading to misidentifications given the significant positional uncertainties of the classical sub/millimeter single-dish surveys in which they are the most easily seen (e.g., Chapman et al. 2005; Cowie et al. 2009, and references therein). Also, due to the strong negative K correction at sub/millimeter wavelengths (e.g., Blain et al. 2002), it remained challenging to pick out the most distant DSFGs among the much more numerous specimens at z  3.5. Over the past decade, many of these challenges were overcome through new observational capabilities and selection techniques, such as direct identifications based on interferometric observations of the dust continuum emission (e.g., Younger et al. 2007; Smolčić et al. 2012; Simpson et al. 2014, 2015; Brisbin et al. 2017; Stach et al. 2018; see also earlier works by, e.g., Downes et al. 1999; Dannerbauer et al. 2002), redshift identifications through targeted molecular line scans (e.g., Weiß et al. 2009; Riechers 2011), and target selection based on sub/millimeter colors or flux limits (e.g., Cox et al. 2011; Riechers et al. 2013, 2017; Dowell et al. 2014; Vieira et al. 2010; Weiß et al. 2013 ). Nevertheless, all of the current studies only provide incomplete censuses of the z > 5 DSFG population due to biases in the selection, limited sensitivity in the parent sub/millimeter surveys, and incomplete redshift confirmations of existing samples.


PNe provide crucial information about the nucleosynthesis and chemical evolution of different elements. It is thought that PNe progenitors do not synthesize O and other α-elements as Ne, S, or Ar and, in principle, they can be considered as probes of the chemical composition of the ISM at the moment of the birth of the progenitors. Therefore, they can be used as tracers of the temporal evolution of the abundance gradients of the Galaxy. However, the recent results by Delgado-Inglada et al. (2015) indicate the production of O in C-rich PNe at near-solar metallicities that can increase the O/H ratio up to 0.3 dex. This result calls into question the suitability of O in PNe as tracer of the ISM composition. Other critical problems in the determination of the abundance gradients from PNe data is the large uncertainties in the distances of these objects (Frew, Parker & Bojičić 2016; Stanghellini & Haywood 2018; García-Rojas 2018; Peña & Flores-Durán 2019), the different range of ages of their progenitors and the radial migration along the lifetime of the progenitors. Most of the determinations of the Galactic O/H gradient based on data of young PNe – with ages between 1 and 4 Gyr – provide slopes which tend to be flatter than our value (Liu et al. 2004; Maciel, Costa & Cavichia 2015; Stanghellini & Haywood 2018; Peña & Flores-Durán 2019), with typical values in the range between −0.019 and −0.048 dex kpc−1 for RG between 0 and 16 kpc. This behaviour has led some authors to propose the steeping of the O gradient with time (e.g. Stanghellini & Haywood 2018). However, other authors as Henry et al. (2004) or Maciel & Costa (2013) claim that the time variation of the O/H gradient may be masked by the aforementioned uncertainties related to the abundance and gradient determination with PNe. As α-elements, Ne, S, and Ar should have abundance gradients similar to that of O/H, but as it has been discussed in Section 4.2, their value may be affected by the ICF scheme used. For Ne and Ar, Peña & Flores-Durán (2019) reported a slope of −0.026 ± 0.014 dex kpc−1 and −0.010 ± 0.006 dex kpc−1, respectively, for a sample of young PNe, which are flatter than our slopes for these elements in H ii regions. Henry et al. (2004) studied a large sample of PNe providing the radial gradients for the different elements studied here but for a sample of objects covering progenitors of a wide range of ages. Those authors reported values of the slope for the gradients of Ne, S, Cl, and Ar abundances fairly similar to ours, from −0.030 to −0.048 dex kpc−1. On the other hand, the results obtained by Stanghellini & Haywood (2018) for their compilation of PNe data from the literature show slopes of Ne and Ar which are somewhat flatter than ours, −0.018 to −0.030 dex kpc−1, respectively. As we can see, the comparison with available data from PNe does not give conclusive evidence of a time variation of the abundance gradients in the Milky Way.


The Chamaeleon I star-forming region, including CR Cha, was covered in Sectors 11 and 12 of the Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2015) in 2019. The observations started on 2019 April 22 and were completed on June 19, providing almost uninterrupted broadband optical photometric observations with a 30-min cadence. Details of the TESS data reduction and photometry can be found in Plachy et al. (2021) and Pál et al. (2020). We only summarize the main steps here. Photometry of the source was performed via differential image analysis using the ficonv and fiphot tools of the FITSH package (Pál 2012). This requires a reference frame, which we constructed as a median of 11 individual 64 × 64 subframes obtained close to the middle of the observing sequence. The convolution-based approach used here exploits all of the information in the images by minimizing the difference and simultaneously correct for the various temporal aberrations (e.g., differential velocity aberration, variations in the point spread function, PSF, and pointing jitter corrections). A more detailed description of these methods can be found in Plachy et al. (2021) or Pál et al. (2020). This method is therefore equivalent to an ensemble analysis and requires basically no further post-processing of the light curves such as cotrending or similar types of decorrelartion methods. The photometry process also requires a reference flux to correct for various instrumental and intrinsic differences between the target and the reference frames. For this, we used the median of our SMARTS I-band photometry (see below) taken over the same time period as the TESS data. We obtained aperture photometry in the TESS images using an aperture radius of 2 pixels and a sky annulus between 5 and 10 pixels (the pixel scale is about 20″). We note that we also inspected the most recent TESS observations, obtained between 2021 April 2 and June 24, and those data were reduced with the same procedure.


The second ingredient is the probability distribution of stellar mass at given SFR and redshift:
5

dpdlogM⋆(M⋆∣ψ,z)∝M⋆M⋆M⋆,MS(ψ,z)M⋆,MSexp−logM⋆−logM⋆,MSψ,z22σlogM⋆2M⋆≥M⋆,MS(ψ,z),

where M
⋆,MS(ψ, z) is the observed redshift-dependent galaxy main sequence with log-normal scatter

σlogM⋆≈0.2

 dex (we adopt the determination by Speagle et al. 2014 for an anlytic fit, see their Equation (28)). The main sequence is a relationship between SFR and stellar mass followed by the majority of star-forming galaxies, apart from some outliers located above the average SFR at given stellar mass (see Daddi et al. 2007; Rodighiero et al. 2011, 2015; Sargent et al. 2012; Speagle et al. 2014; Whitaker et al. 2014; Schreiber et al. 2015; Caputi et al. 2017; Bisigello et al. 2018; Boogaard et al. 2018). The expression in Equation (5) holds for an approximately constant SFR history, which is indicated both by in situ galaxy formation scenarios (see Mancuso et al. 2016b; Pantoni et al. 2019; Lapi et al. 2020) and by observations of ETG progenitors (that have on overage slowly rising star formation history with typical duration of ≲1 Gyr; see Papovich et al. 2011; Smit et al. 2012; Moustakas et al. 2013; Steinhardt et al. 2014; Cassará et al. 2016; Citro et al. 2016) and late-type galaxies (that have on the average slowly declining star formation history over a long timescale of several gigayears; e.g., see Chiappini et al. 1997; Courteau et al. 2014; Pezzulli & Fraternali 2016; Grisoni et al. 2017). In this vein, off-main-sequence objects can be simply viewed as galaxies caught in an early evolutionary stage that are still accumulating their stellar mass (which grows almost linearly with time for a constant SFR), and are thus found to be preferentially located above the main sequence or, better, to the left of it. As time goes by and the stellar mass increases, the galaxy moves toward the average main-sequence relationship, around which it will spend most of its lifetime before being quenched due to gas exhaustion or feedback processes.


In this paper, we will use a SAD map of the Large Magellanic Cloud (LMC) to derive the DTD of RR Lyrae stars—pulsating horizontal branch stars with periods between 0.2 and 1 day (Smith 2004). We chose to test the DTD method on RR Lyrae for several reasons. First, the sample size of RR Lyrae in the LMC is quite large (see Section 2.1), allowing us to measure a DTD with high significance. Second, there is strong evidence that RR Lyrae are mostly ancient stars, older than 10 Gyr, given their pulsational properties (Smith 2004; Marconi et al. 2015) and abundance in old globular clusters (Clement et al. 2001; Soszyński et al. 2014, 2016). Measuring an RR Lyrae DTD therefore provides a rigorous test of the DTD method for the recovery of progenitor age distributions as well as measurements of the star formation history of old resolved stellar populations. Lastly, a DTD analysis provides an opportunity to test stellar evolution models of RR Lyrae in a completely new way. While there is consensus on the interpretation of RR Lyrae as ancient stars, the lower limit on their ages has been somewhat unconstrained. For example, the absence of RR Lyrae in the SMC cluster Lindsey 1 (

t
≈
9

 Gyr), compared to their presence in NGC 121 (

t

≈

 10–11 Gyr), is generally cited as evidence of a lower limit of 10 Gyr for the progenitor age of RR Lyrae (Olszewski et al. 1996; Glatt et al. 2008). However, growing evidence of thin-disk RR Lyrae in the Milky Way raises questions about whether this limit might be lower, and whether an intermediate-age progenitor channel can exist (Layden 1995; Zinn et al. 2019; Prudil et al. 2020). Additionally uncertainties may exist in the evolutionary models of RR Lyrae stars themselves: since RR Lyrae are horizontal branch stars, their positions on the color–magnitude diagram depend on an unknown combination of factors (commonly known as the second-parameter phenomenon) such as metallicity, age, mass loss on the red giant branch, stellar rotation, core structure, and chemical abundance (see Fusi Pecci & Bellazzini 1997; Catelan 2009; Dotter 2013, for reviews).


Accretion disks around compact objects. Compact low-luminous massive objects are expected to lurk in the CGM of galaxies. From lone low-mass stars (e.g., Helmi 2020), to black holes (BHs) arising from stellar evolution (e.g., Fender et al. 2013), including remnants of Population III stars (e.g., Madau & Rees 2001; Filho & Sánchez Almeida 2018), and primordial BHs (e.g., Carr & Hawking 1974; Clesse & García-Bellido 2015). The number density of these objects is assumed to be high; for example, there are claims that primordial BHs account for all the dark matter in the universe (Clesse & García-Bellido 2015). Even if this is not the case (e.g., Carr & Kühnel 2020), the expectations clearly overwhelm the density required to account for all the emission signals that we observe, of the order of one clump per central galaxy (Section 4.1). When these compact objects are surrounded by accretion disks, they should emit in Hα, with the rotation of the disk giving rise to two-horn Hα profiles when observed with the appropriate viewing angle (Smak 1969). This kind of double-peak Hα emission is observed in X-ray binaries (Grundstrom et al. 2007; Zamanov et al. 2013; Casares & Torres 2018; Monageng et al. 2020) and cataclysmic variables (e.g., Zolotukhin & Chilingarian 2011), with peak separations of up to hundreds of km s−1 (Zamanov et al. 2013). At a completely different mass scale, double-peak Hα emission is sometimes observed in the broad-line region of AGN, where it is also supposed to trace a rotating disk (e.g., Eracleous & Halpern 1994; Ho 2008). The double-peak Hα emission observed around stellar-mass compact objects comes together with continuum emission (e.g., McSwain et al. 2010; Zamanov et al. 2019). There are hints of continuum emission in our stacks of observed spectra (Figure 8), but the question arises as to whether this very faint continuum is consistent or not with an accretion disk around a compact object. A number of arguments show that the observed lack of continuum emission does not discard the accretion disk scenario. First, large Hα equivalent widths (EWs) are sometimes observed in X-ray binaries. Hα EWs larger than 100 Å are not rare during quiescence (Fender et al. 2009; Casares & Torres 2018), with maxima reaching 2000 Å (Muñoz-Darias et al. 2016), which implies line to continuum flux ratios enough to account for our observations (Figure 8). Second, Hα photons are to be produced by recombination of H atoms photoionized by the accretion disk (e.g., Matthews et al. 2015). Under particular circumstances, the nebular emission produced by a photoionizing source can emit an Hα line with very little underlying continuum. For example, young starbursts produce Hα with an EW in excess of 103 Å (Leitherer et al. 1999), and galaxy-integrated spectra with EW of hundreds of angstrom are not uncommon (e.g., Morales-Luis et al. 2011). The main physical ingredient for the photoionization source to produce little continuum is presenting a hard spectrum with an ionization flux greatly exceeding the flux in the optical. Accretion disks can easily match this requirement since they can be extremely hot with spectra peaking in the far-UV and X-ray.


Some studies have used the 2.5D mean-field dynamo approach to do so, extending solar mean-field dynamo models to other stellar spectral types (Chabrier & Küker 2006; Jouve et al. 2010; Küker et al. 2011; Kitchatinov et al. 2018, and references therein). While these studies are very helpful, most of them lack the full nonlinearity and genuine parametric dependence of 3D magnetohydrodynamic (MHD) simulations. Recent developments by Pipin (2021) are starting to overcome these limits and have extended the work of Rempel (2006) on the Sun to solar-type stars with various rotation rates. Nevertheless, with the arrival of more powerful supercomputers, other authors have used instead global 3D MHD simulations to model DR and stellar magnetism in the convection zone of solar-like stars (Glatzmaier & Gilman 1982; Miesch et al. 2000, 2006; Brun et al. 2004, 2011; Brown et al. 2008, 2010; Ghizaru et al. 2010; Käpylä et al. 2011, 2014; Gastine et al. 2014; Augustson et al. 2015; Karak et al. 2015). These studies pointed out the large magnetic temporal variability and the critical effect of stellar rotation and mass on magnetic field generation through dynamo mechanism, leading in some parameter regimes to configurations with cyclic activity (Gilman & Miller 1981; Gilman 1983; Glatzmaier 1985a; Brown et al. 2011; Racine et al. 2011; Augustson et al. 2013, 2015; Käpylä et al. 2013; Nelson et al. 2013; Beaudoin et al. 2016; Guerrero et al. 2016, 2019; Strugarek et al. 2017, 2018; Viviani et al. 2018, 2019; Warnecke 2018; Matilsky & Toomre 2020). Several studies pointed out the positive effect of a stable region underneath the convection zone (Parker 1993) on the efficient storage of intense toroidal field and the lengthening of the stellar dynamo cycle period (Glatzmaier 1985b; Browning et al. 2006; Lawson et al. 2015; Beaudoin et al. 2016; Guerrero et al. 2016, 2019; Käpylä et al. 2019; Bice & Toomre 2020). Over the last decade, significant progress has been made in successfully simulating large-scale mean flows and stellar activity cycle using different numerical codes and methods (Jones et al. 2011). This is quite reassuring that a global consensus is growing on the nature of solar-like star dynamos. It is common knowledge that there are still key transitions in Rossby number (at low and high values of this parameter) that need to be understood further, as well as what is the exact type of convective dynamos realized in solar-like stars as their global parameters are varied. This study continues this effort by doing an even broader systematic parametric study of solar-like star dynamos coupled to a stably stratified layer below than what have been published so far. It extends the work published in Varela et al. (2016) and Brun et al. (2017) with the MHD anelastic spherical harmonic code (ASH) (Brun et al. 2004). In particular, we wish to better characterize energy transfers and how much of a star’s energy (luminosity) is converted into magnetic energy by nonlinear global convective dynamos over a wide range of Rossby numbers, generalizing to solar-like stars the work by Starr & Gilman (1966) and Rempel (2006).


For comparisons with the light curve YORP constraints, the YORP effect acting on Cuyo could be predicted by computing the total recoil forces and torques from reflected and thermally emitted photons from the asteroid surface using the ATPM. These calculations were made for both a smooth and rough surface, and were averaged over both the asteroid rotation and elliptical orbit (see Rozitis & Green 2012, 2013, for methodology). As demonstrated in Rozitis & Green (2012), the inclusion of rough-surface thermal-infrared beaming effects in the YORP predictions tends to dampen the YORP rotational acceleration on average but can add uncertainties of up to several tens of per cent if the roughness was varied across the surface. Since the light curve inversion produced convex shape models only, then shadowing and self-heating effects inside global-scale concavities (see Rozitis & Green 2013) were not possible to model. However, a study of non-convex shape models for fast two to four hour rotators in Rozitis & Green (2013) indicated that such asteroids have rather minimal levels of global-scale concavities, and the ~ 2.7 h rotation period of Cuyo implies that its shape could be similar. Furthermore, the Tangential-YORP effect, that is, a predicted rotational acceleration caused by temperature asymmetries within exposed rocks and boulders on the surface of an asteroid (Golubov & Krugly 2012), was also not included in the ATPM predictions. However, the very low thermal inertia value measured for Cuyo implies the absence of rocks and boulders on its surface of the quantity and size that are necessary to induce a significant Tangential-YORP component. As Cuyo is likely to be an S-type rubble-pile asteroid, a bulk density equivalent to that measured for the S-type rubble-pile asteroid (25143) Itokawa (Abe et al. 2006) of 2 g cm−3 was assumed for the YORP computations. Using the thermo-physical properties derived earlier, the ATPM predicts YORP rotational acceleration of (−6.39 ± 0.96) × 10−10 rad day−2 for the nominal shape model. The uncertainty given here corresponds to the standard deviation of results when the degree of surface roughness israndomly varied across the surface of Cuyo (see Lowry et al. 2014, for details of the Monte Carlo methodology used). These values lie well within the light curve rotational acceleration constraints determined previously.


As described in Sect. 1, cloudshine is observed in the near-IR, usually in the three photometric bands J, H, and K. For instance, using the Wide Field CAMera of the United Kingdom InfraRed Telescope (WFCAM of UKIRT), Malinen et al. (2013) observed a 1° × 1° field in the Taurus Molecular Complex (d ~ 140 pc). This field is centred on the dense TMC-1N cloud (RA (J2000) 4h39m36s and Dec (J2000) + 26°39′22′′) north of TMC-1. After smoothing the data to 40″ resolution on a 8″ pixel grid and removing background emission, Malinen et al. (2013) were able to extract J, H, and K coreshine median radial profiles across the TMC-1N filament (see their Fig. 12). This filament was previously observed with PACS and SPIRE instruments on board Herschel: using the colour temperature of the dust submm emission and assuming that the dust opacity varies as 0.1 cm2/g (ν/ 1000 GHz)β with β = 2, Malinen et al. (2012) found that the density distribution of the cloud is accurately described by a Plummer-like function with ρC = 4 × 104 cm-3, Rflat = 0.03 pc, and p = 3 (see Eq. (1)). To model this cloud, we start from this density distribution and the dust population mixtures presented in Sect. 4.1. The cloud is then illuminated by the ISRF+CM radiation field, extinguished or not by a layer of CM grains with \hbox{$A_V^{\rm ext} = 0.5$}AVext=0.5 to 3 (see Fig. 5). The resulting dust scattered emission maps4 are finally smoothed to the same resolution as the data presented by Malinen et al. (2013). The best fit is achieved for the CMM+AMMI populations illuminated by the ISRF+CM radiation field with \hbox{$A_{{V}}^{\rm ext} = 1.5^{{\rm mag}}$}AVext=1.5mag. The results are presented in Fig. 11. As Malinen et al. (2013) subtracted the cloud background, it is not surprising to find \hbox{$A_{{V}}^{\rm ext} \neq 0$}AVext≠0; it probably reflects the fact that the incident radiation field is extinguished by the removed envelope before reaching the dense cloud. The peak intensity and the profile shapes are reproduced well for the three bands, even if the modelled profiles for the J and K-bands are slightly broader than the observed values.


Lastly, we model the evolution of the ejecta discussed in Section 2.2 into circumstellar profiles discussed in Section 2.3. We use our cosmic-ray hydrodynamics code, hereafter called ChN to model the evolution of the ejecta to an age of

t

SNR

=
400

 yr. ChN is a Lagrangian hydrodynamics code that includes a prescription for diffusive shock acceleration (DSA; Ellison et al. 2007; Lee et al. 2012). We have modified the code to include the effects of DSA on non-equilibrium ionization (Patnaude et al. 2009, 2010) and have coupled the code to SN ejecta models (Lee et al. 2014; Patnaude et al. 2015). We have also included radiative losses via forbidden line cooling (Lee et al. 2015). This effect will be important in the evolution of the SN shock with a nearby CSM shell, or if we choose to model the radiative shock that could form in the ejecta during early SN evolution (Nymark et al. 2006). However, we begin our simulations at an age of 5 yr, and over the lifetime of the simulation the shocks remain adiabatic, so we do not consider the radiative shock model presented in our previous work here. Since ChN couples nonlinear particle acceleration to the SNR shock dynamics, we are able to reproduce the broadband thermal and nonthermal emission (Ellison et al. 2010, 2012; Castro et al. 2012; Slane et al. 2014; Lee et al. 2013). The diffusive shock acceleration process is an integral part of ChN, and some injection of thermal particles into the acceleration process is always assumed. Here we set the injection parameter to the test particle limit, though we note that the interaction of a strong shock with a massive CSM shell or cloud will lead to enhanced particle acceleration (e.g., Ellison et al. 2012; Lee et al. 2014), and the differing CSM configurations, combined with the differing ejecta profiles and compositions, may result in differences in the broadband nonthermal emission. The study of nonthermal emission in evolving SNe is sufficiently broad that we defer its study to future papers.


As the initial state of star-forming clouds, a critical Bonnor–Ebert (B.E.) density profile (Ebert 1955; Bonnor 1956) is adopted for each model. Note that the B.E. density profile or B.E. sphere is usually used as the initial condition of star-forming clouds (e.g. Matsumoto & Tomisaka 2004; Banerjee & Pudritz 2006; Machida et al. 2006a; Machida, Inutsuka & Matsumoto 2006b). The B.E. density profile is determined by the central density nc, 0 and isothermal temperature Tcl. The initial central density is set to $n_{\rm c,0}=10^4\, {\rm cm}^{-3}$ for all models. The temperature Tcl of each cloud is determined as the result of a one-zone calculation (for details, see Susa et al. 2015, and Paper I), and the results Tcl are given in Table 1. The cloud radius rcl, which depends on the initial cloud temperature, is also given in Table 1. To promote cloud contraction, the density is set to 1.8 times to the critical B.E. density profile (Machida & Hosokawa 2013). The initial cloud mass for each model is also listed in Table 1. Although the initial clouds have different radii and masses with different metallicities, the ratio α0 of thermal to gravitational energy, which significantly affects the cloud collapse (e.g. Miyama, Hayashi & Narita 1984; Tsuribe & Inutsuka 1999a,b), is the same for all models (α0 = 0.47). In addition, the ratio of rotational to gravitational energy in the initial cloud is set to β0 = 1.84 × 10−2 for all models (Goodman et al. 1993; Caselli et al. 2002). The initial magnetic field strength in each cloud is defined to satisfy μ0 = 3 (Troland & Crutcher 2008; Crutcher et al. 2010; Ching et al. 2017). The parameter μ0 is the mass-to-flux ratio of the initial cloud normalized by the critical value and is defined as
(1)
\begin{eqnarray*}
\mu _0 &=& \frac{\left(M/\Phi \right)}{\left(M/\Phi \right)_{\rm cri}},
\end{eqnarray*}
where M and Φ are the mass and magnetic flux of the initial cloud, respectively, and (M/Φ)cri is the ratio of the critical values of these parameters, which is (M/Φ)cri ≡ (2πG1/2)−1 (Nakano & Nakamura 1978). The direction of the magnetic field vector is parallel to the rotation vector (z-axis) in the initial cloud, in which a uniform magnetic field and rigid rotation are imposed.


While the Loison et al. (2015) CH3C3N model corroborates the upper atmospheric abundance of C4H3N inferred by Vuitton et al. (2007) from the T5 INMS measurements (a factor of 2 higher than those derived from T40 in Vuitton et al. 2019), a large disparity between the photochemical models (and within the ensemble of models produced by Loison et al. 2015) arises in the lower atmosphere due to the poorly constrained C4H3N branching ratios and reaction rate coefficients at temperatures appropriate for Titan. Aside from electron dissociative recombination of C4H3NH+ (Vuitton et al. 2007), neutral production of CH3C3N can occur in a few ways, as found through crossed beam experiments and theoretical and photochemical modeling studies (Huang et al. 1999; Balucani et al. 2000; Zhu et al. 2003; Wang et al. 2006; Loison et al. 2015). First, through the reactions of larger hydrocarbons with CN radicals,
1

2

Similarly, with CCN radicals following their formation through H + HCCN (Takayanagi et al. 1998; Osamura & Petrie 2004) and subsequent reactions with ethylene,
3

or through the chain beginning with acetylene,
4

While both reactions (3) and (4) are found to be equally likely by Loison et al. (2015), the production of CCN via H + HCCN is not well constrained, and the synthesis of CH3C3N through CN radicals (Equations (1) and (2)) are not included in their photochemical model. Additionally, cyanoallene may be produced through reactions (1)–(4) instead of (or in addition to) methylcyanoacetylene. CH3C3N itself may form the protonated species, C4H3NH+, through reactions with the HCNH+ and C2H5+ ions producing HCN and C2H4, respectively (Vuitton et al. 2007). The other mechanism for forming C4H3NH+ is through the combination of HCN and l-C3H3+, though the reaction rate coefficient for this reaction and the abundance of l-C3H3+ are unknown (Vuitton et al. 2007). As such, the production and loss pathways for both C4H3NH+ and CH3C3N require further investigation.


Although in the MIR, the dust models are more absorbant than the measured samples, the opposite is true in the FIR. Table 2 gives the value of the MAC of the measured samples and of the modeled MAC at selected wavelengths in the 100 μm−1 mm range. In this range, the experimental MAC at 300 K is more than five times greater than the modeled MAC for all samples. At 10 K, the experimental MAC is lower than at 300 K and the factor of enhancement compared to the models is smaller, depending on the sample and on the wavelength, however it is always higher than two and usually of the order of four to five. The MAC value of the ferromagnesium silicate analogues in this study is very close the MAC of the pure Mg-rich samples from Demyk et al. (2017) and from Coupeaud et al. (2011). This shows that the enhancement of the measured MAC compared to the modeled MAC is not related to the iron content of the grains, that is, to differences in composition between the studied samples and the analogues used in the cosmic dust models. As discussed in detail by Demyk et al. (2017), an enhancement factor greater than two cannot be explained by the effect of grain size, grain shape, or by grain coagulation within the pellets. Grain size and grain shape effects are illustrated in Fig. 10 and the increase of the MAC due to large (micronic) spherical grains is negligible in the FIR. Coagulation might happen during the process of fabrication of the pellets and it is taken into account during the analysis of the experimental data following the method explained in Mennella et al. (1998) and based on the Bruggeman theory. More detailed treatment of dust coagulation by methods such as DDA have shown that it may increase the MAC by a factor of two at most (Köhler et al. 2011; Mackowski 2006; Min et al. 2016), that is, not enough to fully account for the discrepancy of the cosmic dust models and the experimental data. The enhancement of the emissivity of iron-rich analogues compared to the MAC of cosmic dust models commonly used for interpreting FIR/submm dust emission observations is related to the disordered nature of the samples, to the number, distribution, and nature of defects in their structure at microscopic scale and to the existence of absorption processes added to the classical Debye model (we refer to Demyk et al. 2017, for more details). These additional absorption processes are more or less important depending on the structural state of the material at the microscopic scale.


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).


A number of candidate TDEs were discovered by UV and X-ray surveys (e.g. NGC5905; Komossa & Greiner 1999, RX J1624+75; Grupe et al. 1999, A1795; Donato et al. 2014, Swift J164449.3+573451; Bloom et al. 2011; Burrows et al. 2011; Levan et al. 2011; Zauderer et al. 2011, Swift J0258.4+0516; Cenko et al. 2012b, and GALEX candidates D1–9, D3–13, and D23H-1; Gezari et al. 2008, 2009). Many of these cases did not show correspondingly strong optical emission, and in some cases they were discovered in sparse archival data, limiting their usefulness as probes of TDE physics. In recent years, however, a number of candidates have been found by high-cadence optical surveys, including the ASASSN-14ae (Holoien et al. 2014a), the Palomar Transient Factory (PTF10iya, Cenko et al. 2012a; PTF09ge, PTF09axc, and PTF09djl, Arcavi et al. 2014), Pan-STARRS (PS1-10jh, Gezari et al. 2012; PS1-11af, Chornock et al. 2014), and the Sloan Digital Sky Survey (SDSS; TDE 1 and TDE 2; van Velzen et al. 2011). These transients typically showed strong UV and optical emission but no associated X-ray emission, and were often better-studied than previous candidates, as they were discovered and followed up by survey projects searching their data in real-time. Optically discovered candidates have provided new opportunities to study these rare transients in greater detail than previously possible, and recent estimates based on optical TDE discoveries put the TDE rate at $\dot{N}_{\text{TDE}}=$ (1.5–2.0)$^{+2.7}_{-1.3}\times 10^{-5}$ yr−1 per galaxy (van Velzen & Farrar 2014). However, there is still tension between this estimate and the rates predicted by modelling two-body scattering of stars in galactic nuclei (typically ∼10−4 yr−1 per galaxy), which may in part be due to the fact that only a small fraction of TDEs are optically luminous (Stone & Metzger 2014; Metzger & Stone 2015). Selection effects from optical surveys may also play a role in this discrepancy, and a careful determination of TDE detection efficiency and completeness is needed to determine the degree to which the actual TDE rate may be higher than the rates inferred from optical surveys.


AstroSat data enabled us to derive the X-ray spectrum in the 0.8–70 keV energy band as shown in Figure 7. The spectrum was fitted reasonably well using two models. The first model was defined as an absorbed Fermi–Dirac cutoff model along with a blackbody, an Fe emission line, and three Gaussian absorption lines introduced to model cyclotron scattering features and its two higher harmonics as observed in the spectrum. The CompTT model was used as the second model in combination with an Fe emission line and three Gaussian absorptions lines as defined in the first model. The CompTT model is generally used for neutron-star-based low-mass X-ray binaries such as Z-type and atoll sources with a relatively lower magnetic field (

 G) of the neutron star (Ferinelli et al. 2008). However, the model could also successfully define the spectrum of some of the pulsars in Be binaries, for example, Cep X-4 (Jaiswal & Naik 2015), 4U 1907+09 (Varun et al. 2019), and GRO J2058+42 (Molkov et al. 2019). The parameters derived from the two models are tabulated in Table 2. The first model estimated a blackbody temperature of 0.83 ± 0.04 keV and detected the presence of a cyclotron resonance scattering feature and its harmonics. The Comptonization model, on the other hand, enabled us to determine the input photon Wien temperature of 0.52 ± 0.02 keV, the plasma temperature of 8.22 ± 0.10 keV, and the plasma optical depth of 5.21 ± 0.12 for the phase-averaged spectra. The Wien temperature, per the CompTT model, originates far from the neutron star surface and closer to the inner accretion disk i.e., at the outer transition layer; hence, the Wien temperature is always found to be relatively lower than the neutron star blackbody temperature as it originates closer to the inner transition layer, i.e., near the surface of the neutron star (Ferinelli et al. 2008). For the CompTT model, bulk Comptonization occurs in the innermost part of the transition layer region, while thermal Comptonization is dominant in the outer transition layer and presumably within some extended region located above the accretion disk. Similar deviations were also observed in the case of Cep X-4 fitted with the CompTT model and a blackbody combined with the FDCUT model (Table 1 of Jaiswal & Naik 2015). However, the centroid energy of the cyclotron absorption features and its detected harmonics are found to be consistent within errors for the two models (Table 2).


We aim to measure the mass associated with each molecular structures described in the previous section. We defined spatial boundaries enclosing these structures and independently studied the spectral data corresponding to each subregion of the field. The spatial boxes defined for the cloudlet (A), ring-like structure (B), shocked clump (C), and shocked knot (D) are shown in Fig. 6, and the average spectra obtained in these boxes are presented in Figs. 8 and 7 for every line from CO and its isotopologs, which are available in our IRAM 30 m and APEX data cubes. The choice of the boundaries is based on our morphological classification, but we carefully checked that the brightest spectral features are coherent across the different boxes that we defined (coordinates of these boxes are given in Table A.1). We performed that selection manually, as the size of our sample is not large enough to apply statistical methods (e.g., clustering, see Bron et al. 2018). Based on the analysis of the emission of 12CO, 13CO and C18O lines, our description of these spectral features is the following:

1.Cloudlet: toward box A (Fig. 7, left-panel), the line profile of 12CO and 13CO lines are similarly double peaked and best modeled by the sum of two Gaussian functions centered on the systemic velocities vLSR = −5.7 ± 0.3 km s−1 (associated with the cloudlet) and vLSR = −3.3 ± 0.1 km s−1 (associated with the ambient cloud).
2.Ring-like structure: toward box B (Fig. 7, right-panel), the 12CO and 13CO lines are double peaked as well. The use of two Gaussian functions to model the line profile yields the systemic velocities vLSR = −5.6 ± 0.2 km s−1 (associated with the ring-like structure) and vLSR = −3.3 ± 0.1 km s−1 (associated with the ambient cloud). The Gaussian decomposition is very similar to that of the cloudlet, suggesting that the apparent ring-like structure might be incidental despite its remarkable features in the first moment map (Fig. 5).
3.Shocked clump: considering the geometry of the SNR and the locally perpendicular direction of propagation of the SNR shockwave (van Dishoeck et al. 1993), the high-velocity emission arises from at least two shock waves, if not a collection of transverse shocks propagating along the molecular shell. In other words, the projection along the line of sight of several distinct shocked knots with distinct systematic velocities could contribute to the broadening of the 12CO lines. We measure vs ≃ 27 km s−1 and vs ≃ 21 km s−1 for the blueshifted and redshifted transverse shocks, respectively. Except for the J = 1–0 spectrum for which the emission of the ambient gas contributes to the average spectra, all spectra of 12CO lines exhibit a significant absorption feature around the vLSR of IC443G, suggesting that there is strong self-absorption of the emission lines. Evidence of line absorption is found in the velocity range −6 km s−1 vLSR  −2 km s−1, which is where we detect the spatially extended features associated with the NW-SE complex of molecular gas described by Lee et al. (2012). Hence, it is possible that the foreground cold molecular cloud is at the origin of the absorption of the 12CO J = 1–0 and J = 2–1 lines. A faint and thin emission line is detected around v = 6.5 km s−1 both in the 12CO and 13CO spectra. This signal is associated with the NE–SW complex of molecular gas described in Sect. 3.2.
4.Shocked knot: the shock signature of this line is distinct from the shocked clump. As hinted by the moments map (Fig. 5), its fainter high-velocity wings are displaced toward negative velocities. A self-absorption feature is also observed in this structure. Between v = −5.5 km s−1 and v = −2 km s−1 a bright andthin feature traces the ambient gas shown on the channel maps in Fig. 2 (second row from bottom; first, second and third panels from left).


In our calculation, we introduce two dust components: small dust grains and large dust grains. The minimum and maximum sizes are 0.0025 and 0.2 μm for small dust grains and 0.01 μm and 1 mm for large dust grains, respectively. The size distribution of both dust components is n(a) ∝ a−3.5, where n(a) is the number density per unit radius and a is the radius of dust grains. The opacity models for both small and large dust grains are described in Hashimoto et al. (2015) (see also Kim et al. 1994; Wood et al. 2002; Dong et al. 2012). We adopt Equation (16) as the surface density distribution of large dust grains and assume that the surface density of the small dust grains is 10 times smaller than that of the large dust grains (Σsmall = 0.1Σlarge; e.g., D’Alessio et al. 2006). We note that the small-to-large dust mass ratio for the size distribution of n(a) ∝ a−3.5 is 1%. However, many practical calculations (e.g., Andrews et al. 2011; Dong et al. 2015b) use the size distribution and change the small-to-large dust mass ratio independently because the results are not very different even if the mass ratio is assumed as 10%. To obtain the density distributions of small and large dust grains, we set the scale height of them,
17

18

where Hl and Hs are the scale heights of large and small dust grains, respectively. We assume that the scale height of small dust grains is similar to the gas scale height. The scale height of the large dust grains is assumed to be about three times smaller than that of the small dust grains.15

15
If we assume that the gas surface density is 10 g cm−2 and turbulence strength α = 10−2 at 70 au, we obtain that the scale height of 1 mm dust, which is the maximum size of the large dust, is about three times smaller than the gas scale height. In reality, this ratio will depend on the radius, but here we assume the constant ratio for simplicity.
 Using these scale heights, we evaluate the density of small and large dust grains, whose density distributions in the z-direction are proportional to

. We note that the dependence of model parameters on the resulting disk structures is beyond the scope of this work and remains to be explored.


To infer starburst and AGN luminosities, we use the multicomponent SED fitting technique described in Hatziminaoglou et al. (2008) and Hatziminaoglou, Fritz & Jarrett (2009). In the most general case, the method fits fluxes and their errors with three separate models: stellar, AGN, and starburst. Our sample however consists entirely of luminous type 1 quasars with extremely high SFRs. This allows us to make two key simplifications to the general method. First, it is almost certain that the stellar emission will be outshone by the AGN and/or the starburst at all wavelengths, so we do not include a stellar template in the fit. Second, since our sources are type 1 quasars, it is reasonable to conclude that the optical to mid-infrared (MIR) coverage will be dominated by the AGN (Hatziminaoglou et al. 2005), and that the FIR coverage will be dominated by the starburst (e.g. Hatziminaoglou et al. 2010; Ma & Yan 2015; Harris et al. 2016). The infrared emission reprocessed by the AGN torus strongly depends on the dust geometry. In particular, the ratio between the outer and inner radius of the torus plays a major role in determining the AGN SED at longer wavelengths (in the models used in this paper the maximum value of this ratio is 150). As a result, the peak of the infrared emission of the AGN torus models lies at 10–30 μm (fig. 5 of Feltre et al. 2012) and the maximum width of the infrared bump (as defined in Feltre et al. 2012) for these models is ∼50 μm. We therefore do not expect any significant contribution from the AGN emission at wavelengths larger than ∼50 μm. Complementary, observationally motivated discussion on this point can be found in section 5.3 of Harris et al. (2016). We note the caveat though that, with our data, which do not cover the range between 22 and 250 μm, we cannot completely rule out significant FIR emission from the AGN. We thus use the shorter wavelength data to constrain the properties of the AGN, and, having done so, then use the SPIRE data to constrain the properties of the starburst. Two example SED fits are given in Fig. 3; one for a classical quasar and one for a BAL quasar.


The NLA analysis on these new satellite/central disaggregated data vectors are shown in Fig. 15. As expected, the galaxy bias is consistent between the two, and constrained primarily by wgg, which is the same in the two data vectors. By construction the large scale fits to these data are each sensitive to a particular combination of two halo IA power spectra. Specifically $\mathbf {D}^{c}$ is sensitive to ($P^{2h, s}_{\rm GI}$, $P^{2h, ss}_{\rm II}$), and $\mathbf {D}^{s}$ probes ($P^{2h, c}_{\rm GI}$, $P^{2h, cc}_{\rm II}$). Again, we assume that on two halo scales, the satellite/central composition of the density tracer is not relevant. Notably, the amplitude of large-scale central alignments in Fig. 15 is stronger than that of satellites by a factor of ∼2, at the level of a few σ. The subject of satellite alignments has been discussed quite extensively in the literature, and the overall picture fits with our results here. A number of theoretical studies point to satellite IAs being dominated by tidal torque induced radial alignments within their haloes (Faltenbacher et al. 2007; Knebe et al. 2008; Pereira, Bryan & Gill 2008), which scale rapidly with separation, and tend to wash out on very large scales. There is also now evidence from various observations on both cluster and galaxy scales supporting the same picture (Sifón et al. 2015; Singh et al. 2015; Huang et al. 2018). This, again, is consistent with Johnston et al. (2019) and Fortuna et al. (2021), who suggest satellite shapes are effectively random on sufficiently large scales. Centrals, on the other hand, tend to align with the host halo, and so trace the large scale correlations in the background large-scale structure (Catelan et al. 2001; Kiessling et al. 2015). Although not shown in Fig. 15, it is also worth noting that the central galaxies show a clear monotonic increase in IA amplitude with redshift, a trend which is not replicated in satellite galaxies. There is also some evidence to suggest not only that satellites are distributed in a significantly anisotropic way within their haloes (Zentner et al. 2005; Piscionere et al. 2015; Butsky et al. 2016), but also that this anisotropy can have a non-trivial impact on the IA signal, even on large scales (Huang et al. 2016; Samuroff, Mandelbaum & Di Matteo 2020).