The UK Chemistry and Aerosol (UKCA) model (Morgenstern et al. 2009; O’Connor et al. 2014; Archibald et al. 2020) is a framework that we use to describe the global atmospheric chemical composition of our simulated exoplanet. UKCA includes aerosol and gas-phase chemistry and is coupled to the UM dynamics. It uses the UM components for large-scale advection, convective transport, and boundary layer mixing of its aerosol and chemical tracers (O’Connor et al. 2014; Archibald et al. 2020). UKCA contains a large number of gas-phase and heterogeneous chemical reactions, some of which we have included in our chemical network. Furthermore, the chemistry schemes in UKCA describe wet and dry deposition (Giannakopoulos et al. 1999). In this study, we use the Stratospheric (Strat, Morgenstern et al. 2009) and Stratospheric-Tropospheric (StratTrop, Archibald et al. 2020) chemistry schemes. Originally, StratTrop includes 75 chemical species that are connected by 283 reactions (Archibald et al. 2020). We used a reduced version of the UKCA chemistry schemes (Table 2) to quantify the impact of the different chemical mechanisms on the atmospheric chemistry of a tidally-locked exoplanet. First, we use a simple network that describes the Chapman mechanism of ozone formation (Chapman 1930), following Yates et al. (2020). Second, we add the reactive hydrogen (HOx) catalytic cycle, where HOx denotes the ensemble of atomic hydrogen (H), the hydroxyl radical (OH) and the hydroperoxy radical (HO2). We include this cycle to account for ozone chemistry following the oxidation and photolysis of water vapour. Lastly, we add the nitrogen oxide (NOx) catalytic cycle, including NO and nitrogen dioxide (NO2) to the network. We also include other oxidized nitrogen species, such as nitrate (NO3), nitrous oxide (N2O), and the reservoirs nitric acid (HNO3), and dinitrogen pentoxide (N2O5). Collectively, these nitrogen species belong to the NOy family and can also influence ozone chemistry. In our simulations, lightning is the main source of NO that initiates further NOy chemistry, as described in Section 2.4. In the upper atmosphere, the slow termolecular reaction between N2 and O(1D) provides another source of NOy, but this does not impact the lightning-induced chemistry that occurs at altitudes below 20 km.

In this study, we use the Stratospheric
chemistry schemes.


From the observational side, the deep FDS data further confirm that the bulk of the gravitational interactions between galaxies happened on the W-NW sub-clump of the cluster. In fact, this is the only region of the cluster, inside the virial radius, where the intra-cluster baryons (diffuse light and GCs) are found, that is, the bridge between NGC 1399 and FCC 184 (Iodice et al. 2016), the intra-cluster light and GCs between FCC 184, FCC 170, and FCC 161 (Iodice et al. 2017b), and the new faint filaments between FCC 143 and FCC 147 (see Sect. 5.1 and Fig. 13). The gravitational interactions could have also modified the structure of the galaxy outskirts and produced the intra-cluster baryons. Compared with simulations by Rudick et al. (2009), the diffuse form observed for the ICL is consistent with the scenario where this component formed by stripped material from the outskirts of a galaxy in a close passage with the cD (Iodice et al. 2017b). In this area of the cluster, the stellar envelope of some ETGs is asymmetric, appearing more elongated and twisted in one direction, while the outskirts of galaxies at larger distances from the cluster centre have a more regular shape. Mastropietro et al. (2005) show how harassment can induce twists in the outer isophotes of dwarf galaxies. More massive and luminous galaxies, like the elliptical galaxies in this region of the Fornax cluster, have a deeper potential well, therefore the stripping of stars by harassment implies even stronger tidal forces. A disturbed morphology in galaxy outskirts could also result from the ongoing accretion of smaller satellites. Simulations on the mass accretion and stellar halo formation for different stellar masses (1010 − 1013 M⊙) show that the outskirts of galaxies (for μr ∼ 27 − 31 mag arcsec−2) appear with a quite disturbed morphology and with an overall elongated shape (Michel-Dansac et al. 2010; Cooper et al. 2015; Monachesi et al. 2018). The structure of the stellar envelope, as well as the shape of the SB profile, depends on the mass and number of the accreted progenitors. The ETGs showing asymmetric and diffuse envelopes (FCC 161, FCC 167, FCC 184, see Sect. 5.1 and Fig. 13) are in range of stellar mass (∼3 − 10 × 1010 M⊙) comparable with simulations and they could still build up their envelope. As noticed by Iodice et al. (2017b), a fraction of the ICL population in this region of the cluster could also come from lower mass dwarf galaxies that are tidally disrupted in the potential well of the massive galaxies, which are therefore contributing to the mass assembly in their halo. This is further supported by a recent study from Venhola et al. (2017), based on FDS data, that found a drop in the number density of LSB galaxies at cluster-centric distances smaller than ∼180 kpc.


At intermediate energies, Fig. 1 shows that non-thermal bremsstrahlung processes become more important. We find this dominates the keV X-ray emission during the first ∼2 Myr. While OY22 demonstrated this non-thermal emission would likely not be detectable in external galaxies, X-ray observations towards the Galactic Fermi bubbles reveal substantially higher emission than that computed with our model at a similar bubble age (see the comparison in OY22; also Snowden et al. 1997; Kataoka et al. 2013; Predehl et al. 2020). Although this may suggest better X-ray detection prospects for external galaxy bubbles than our results would imply, we note that these Galactic observations may include a very significant thermal bremsstrahlung contribution from all the gas in the Milky Way halo, which likely extends to a radius of ∼250 kpc (i.e. far larger than the size of our simulation box, see e.g. Blitz & Robishaw 2000; Grcevich & Putman 2009), the Galactic bulge, and gas heated by the shocks associated with the bubble (Yang et al. 2022; see also Zhang & Guo 2021), none of which is included in our model (and could evolve as the bubble ages). Moreover, features external to the Galactic bubbles (e.g. the North Polar Spur; Kataoka et al. 2013) are not included in our model, but may make a contribution to the observed X-ray emission. We thus consider a direct comparison between the X-ray emission from our model and that observed from the Galactic Fermi bubbles/halo to be complicated by substantial thermal emission and emission from structures not associated with the bubbles. Addressing these additional contributions is non-trivial, and is not necessarily informative to predict the observational prospects of bubbles around external galaxies where thermal emission contributions could differ greatly. After the first few Myr, non-thermal bremsstrahlung X-rays are surpassed by inverse Compton emission, which dominates the X-ray emission from the bubble by 7 Myr. At these later times, a significant non-thermal bremsstrahlung component can also be seen to emerge in TeV γ-rays. This is attributed to the concentration of gas and CR energy density near the top of the bubble (cf. Section 3.3), although we note that the physical strength of this emission may not be properly resolved.20 This will be explored in more detail in future work (see also Section 4.3).


In this paper, we are focusing on the association of the acceleration and release of SEPs with different types of CME–CME interaction. In fact, the particle acceleration process is a complex one involving many factors, e.g., (1) the CME (or shock) speeds (Richardson et al. 2015; Papaioannou et al. 2016; Kouloumvakos et al. 2019), (2) the shock parameters, e.g., Mach numbers, compression ratios, and shock geometry (Lee 1983; Kozarev et al. 2015; Kouloumvakos et al. 2019), (3) the magnetic connectivity between the spacecraft and the source (Richardson et al. 2014; Xie et al. 2019), (4) the level of seed particles, and (5) the level of turbulence (e.g., Wanner & Wibberenz 1993; Laitinen et al. 2018; Strauss & le Roux 2019). Figure 2 shows a relationship between the CME 3D speed and the SEP Ip in NP3D group, which is consistent with the results in Kouloumvakos et al. (2019). The penultimate point has been widely discussed (e.g., Gopalswamy et al. 2004; Kahler & Vourlidas 2014; Ding et al. 2015), involving the role of the flare material and the interacting CMEs on seed particles. In Ding et al. (2015), the authors used a Fe/O ratio of 2.0 as the threshold for the presence of flare material and found that all events except one with Fe/O > 2.0 are in the “twin-CME” scenario, indicating the presence of flare seed material that are possibly from pre-flares. In Kahler & Vourlidas (2014), they proposed that higher SEP Ip could be explained by increases in both CME rates and seed particles during times of high solar activity instead of being due to CME–CME interaction. In Figure 7, the higher Ip in the cases of (nearly) interacting CMEs gives a hint that more seed particles will be accelerated if the priCME eruption is close to the preCME eruption, but it is still necessary to figure out which factor, i.e., the solar activity, the flare, or the preCME, mainly controls the level of the seed populations. The launch of the Parker Solar Probe (PSP) can contribute to this investigation in the future, because the spacecraft will reach as close as 8.86 Rs from the solar surface by 2024. During its first two perihelion passages, a series of SEP events have been studied, focusing on the acceleration mechanisms and seed population preconditioning (see McComas et al. 2019; Schwadron et al. 2020).


We consider that the amplified hotspot magnetic field B is turbulent, and that the large-scale background field downstream of the reverse shock is Bjd, nearly perpendicular to the shock normal because the perpendicular component is compressed and enhanced by a factor of 4 to 7 (i.e. Bjd ∼ rBj). In such a case, to accelerate particles up to an energy Ec via a diffusive mechanism, the mean-free path λc ∼ rg(γc, B)2/s in the shock downstream region, where B is a small-scale field, has to be smaller than Larmor radius in Bjd (Lemoine & Pelletier 2010; Reville & Bell 2014).4 The condition λc ≲ rg(γc, Bjd) is satisfied when the magnetic-turbulence scalelength is

(23)

\begin{equation}
s \ge \frac{E_{\rm c}}{eB}\left(\frac{B_{\rm jd}}{B}\right) = r_{\rm g}(\gamma _{\rm s},B),
\end{equation}

where rg(γs, B) is the Larmor radius of protons with energy

(24)

\begin{eqnarray}
E_{\rm s} &=& E_{\rm c}\left(\frac{B_{\rm jd}}{B}\right) = 0.07 E_{\rm c}\left(\frac{r}{7}\right) \left(\frac{B_{\rm j}}{\rm \mu G}\right) \left(\frac{B}{100 \,\rm \mu G}\right)^{-1}\nonumber\\
&&\sim 10 \left(\frac{r}{7}\right) \left(\frac{\nu _{\rm c}}{10^{14}\,{\rm Hz}}\right)^{\frac{1}{2}} \left(\frac{B_{\rm jd}}{\rm \mu G}\right) \left(\frac{B}{\rm 100\,\mu G}\right)^{{-}\frac{5}{2}}\,\,{\rm GeV},
\end{eqnarray}

where we take B ∼ 100 μG and Bj ∼ μG as characteristic values. Note that

(25)

\begin{equation}
\frac{s}{\rm cm} > 5\times 10^{11}\left(\frac{r}{7}\right) \left(\frac{\nu _{\rm c}}{10^{14}\,{\rm Hz}}\right)^{\frac{1}{2}} \left(\frac{B_{\rm jd}}{\rm \mu G}\right) \left(\frac{B}{\rm 100\,\mu G}\right)^{{-}\frac{5}{2}}
\end{equation}

is greater than c/ωpi in equation (14), as required. Note however that this limit, s ≳ 500 c/ωpi for typical values considered in this paper, cannot be fulfilled by Weibel-generated turbulence with scale ∼c/ωpi. Therefore, the maximum energy achieved by electrons in the jet reverse shock, Ec, cannot be constrained by Weibel instabilities.


Note that the evolution scenario in Fig. 2 is qualitatively different from previous expectations that assumed standard viscous damping and a large saturation amplitude, see e.g. Levin (1999). There it was proposed that sources slowly spin-up at low temperatures outside of the instability region (where cooling becomes slow) followed by quick r-mode heating once the source enters the instability region and similarly fast spin-down and cooling segments which complete a cycle. There would then be no gravitational wave emission from known radio pulsars since sources would leave the instability region very quickly (Levin 1999). However, this scenario is not compatible with the well-established hypothesis that LMXBs are the progenitors of millisecond pulsars, because their observed large temperatures and frequencies (Haskell et al. 2012) place them firmly inside the instability region, as shown e.g. in fig. 1 of Alford & Schwenzer (2013). These astrophysical observations are furthermore theoretically explained by deep crustal heating due to pycnonuclear reactions (Brown, Bildsten & Rutledge 1998). For large r-mode saturation amplitudes LMXBs either could not spin-up to the high frequencies of observed radio pulsars or would be spun down very quickly, which should rule out this scenario. A modified scenario that might account for the observed spin limit of pulsars would be the presence of enhanced damping that does not increase with temperature, for instance due to a viscous boundary layer (Andersson et al. 2000) or mutual friction in a superfluid and superconducting core (Haskell, Andersson & Passamonti 2009; Haskell et al. 2012). In this case r-modes could be completely damped up to the frequencies of observed radio pulsars and it would be very unlikely that any of the known pulsars currently emits gravitational waves (Andersson et al. 2000). However, estimates on mutual friction are still rather uncertain (Haskell et al. 2009, 2012), and we have recently shown that even in the benevolent scenario of a thin viscous boundary layer the damping is very likely not sufficient to explain the fastest spinning sources (Alford & Schwenzer 2013). In Fig. 2 we show the case that crustal heating dominates r-mode heating whereby a source spins up along a vertical trajectory. If r-mode heating dominates, a source would spin-up along roughly the same trajectory along which it subsequently spins down. Another option is that the spin-up stalls since a steady state is reached where the accretion spin-up is balanced by r-mode spin-down (Wagoner 2002). However these different scenarios during the LMXB phase lead to the same qualitative evolution once the accretion ends.


Massive black holes (MBHs) are ubiquitous in the Universe, and inhabit all massive galaxies (e.g. Ferrarese & Merritt 2000). MBHs are typically observed via their accretion-powered radiation as active galactic nuclei (AGNs), whose impact on to the host galaxy is invoked to explain massive galaxy quenching (e.g. Silk & Rees 1998; Di Matteo, Springel & Hernquist 2005) and the emergence of the MBH–galaxy correlations (Gültekin et al. 2009; Kormendy & Ho 2013). However, the demographics of MBHs are not yet well constrained (see e.g. Reines & Comastri 2016; Greene, Strader & Ho 2019, for reviews) and the role of AGN feedback in dwarf galaxies is just starting to be explored (Penny et al. 2018; Mackay Dickey et al. 2019; Manzano-King, Canalizo & Sales 2019). In particular, theoretical studies have shown that the MBH–halo occupation fraction can be low in dwarf galaxies (e.g. Greene 2012; Miller et al. 2015; Habouzit, Volonteri & Dubois 2017), and even in systems hosting MBHs, their growth is strongly suppressed because of the typically low gas densities in the host (compared to more massive disc galaxies) and the strong impact of supernova explosions, both at low and high redshift (Dubois et al. 2014; Anglés-Alcázar et al. 2017; Prieto et al. 2017; Trebitsch et al. 2018). Observationally, this could be partially reflected in MBHs in dwarfs being inactive for most of their life, hence in the small number of low-luminosity AGNs found (Reines, Greene & Geha 2013; Baldassare et al. 2016, 2018, 2019; Mezcua et al. 2016, 2018; Reines et al. 2019), although there are also strong observational biases that could make these AGNs difficult to find. On the other hand, if MBHs were present in many dwarfs, and efficiently grew, their feedback could significantly affect their host (see e.g. Penny et al. 2018; Mackay Dickey et al. 2019; Manzano-King et al. 2019), could play a role in the reionization of the Universe (Volonteri & Gnedin 2009), could help removing gas from massive disc progenitors (e.g. Peirani et al. 2012), and also mitigate the ‘too-big-to-fail’ problem (Garrison-Kimmel et al. 2013). Recently, Kaviraj, Martin & Silk (2019; K19 hereafter) tried to better assess the role of AGN feedback in dwarfs by jointly analysing the Hyper-Supreme Cam Subaru Strategic Program (Aihara et al. 2018b) and the WISE (Wright et al. 2010) surveys, finding that AGNs in dwarfs could exhibit very large bolometric luminosities, hence they could play a significant role in their host evolution. However, a clear consensus on the identification of AGNs in dwarfs is still missing (see e.g. Satyapal et al. 2014; Sartori et al. 2015; Marleau et al. 2017), in particular because of the low resolution of WISE (∼6  arcsec) relative to current optical surveys, resulting in a strong source overlap, and the possible contamination of infrared emission by star formation activity that could mimic AGN activity (Hainline et al. 2016; Satyapal, Abel & Secrest 2018), especially in dwarf galaxies (Hainline et al. 2016). In this paper, we build-up on the K19 work by re-analysing their dwarf sample in more detail in the aim at better disentangling plausible AGNs in dwarf from star-forming galaxies by taking into account possible source overlapping in the sample, and also assess the MBH properties.


As discussed before, a fraction of PSRs is bound to emerge from the progenitor SNR before our fiducial final time tend = 105yr, due to the high average kick velocity that characterizes the pulsar population. The typical escape time can be estimated by matching the PSR displacement due to its kick velocity (Vpsr) with the size of the SNR in the Sedov–Taylor phase:
(14)$$\begin{eqnarray}
t_{\rm esc} \simeq 725\,\, \mbox{kyr} \left[\left(\frac{E_{\rm sn}}{10^{51} \, \mbox{erg}}\right)\! \left(\frac{\rho _0}{1\, \mbox{part/cm^{3}}}\right)^{-1}\! \left(\frac{V_{\rm psr}}{100\, \mbox{km/s}}\right)^{-5} \right]^{\, 1/3}\!\!\! . \\
\end{eqnarray}$$Considering the mean (median) value of the PSR velocity distribution of 380 (330) km s−1 and of the ISM number density of 0.7 (0.25) particles cm−3, we obtain a mean (median) escape time of tesc ≃ 88 (160) kyr. Even taking into account that transition of SNRs to the radiative phase is expected at 35 (60) kyr, the escape time only slightly reduces to tesc ≃ 77 (120) kyr. Since tend = 100 kyr, only a fraction of the sources will then escape the SNR by the end of the simulation. For those systems with tesc tend, the runaway PSR will give rise to the formation of a bow shock nebula. These nebulae, whose first examples were detected in Hα (Chevalier, Kirshner & Raymond 1980; Kulkarni & Hester 1988; Cordes, Romani & Lundgren 1993; Bell et al. 1995; van Kerkwijk & Kulkarni 2001; Jones, Stappers & Gaensler 2002; Brownsberger & Romani 2014; Dolch et al. 2016; Romani, Slane & Green 2017), more recently have been discovered and observed in X-rays and sometimes in radio (Gaensler et al. 2002, 2004; Arzoumanian et al. 2004; Chatterjee et al. 2005; Yusef-Zadeh & Gaensler 2005; Hui & Becker 2007; Hui & Becker 2008; Kargaltsev & Pavlov 2008; Misanovic, Pavlov & Garmire 2008; de Rosa et al. 2009; Ng et al. 2010; De Luca et al. 2011; Ng et al. 2012; Marelli et al. 2013; Jakobsen et al. 2014; Auchettl et al. 2015; Klingler et al. 2016; Kargaltsev et al. 2017; Posselt et al. 2017; Kim et al. 2020). They are characterized by a cometary shape, with a tiny head typically of the order of 1016 cm, whose size is set by ram pressure balance between the PSR wind and the incoming (in the PSR frame) ISM, followed by a long tail opposite to the PSR motion, which can extend for very long distances up to a few pc. Given their limited spatial extension and low residual luminosity (Kargaltsev et al. 2017), bow shock nebulae will not probably be statistically relevant in γ-rays and so far have not been detected (Abdalla et al. 2018c). Runaway PSRs, however, have recently been associated to extended TeV haloes (Abeysekara 2017; Sudoh et al. 2019), most likely due to escaping pairs (Bykov et al. 2017; Evoli, Linden & Morlino 2018; Olmi & Bucciantini 2019c; Di Mauro, Manconi & Donato 2020; Evoli et al. 2021). However, the formation and properties of γ-ray haloes are still poorly understood, and different interpretations lead to very different expectations in terms of the possible detection of these sources in the next future (Sudoh et al. 2019; Giacinti et al. 2020). The modelling of these complex sources is outside the scopes of the present work, so we simply keep trace of the position of escaped PSRs for possible future implementations. The fraction of PWNe escaped from their parent SNR at the end of the simulation is represented in the right-hand panel of Fig. 1, where evolved PWNe are shown on top of the initial distribution of PWNe + SNRs.


Finally in this paper, we restricted ourselves to a very limiting case when the ISM is at rest with respect to the star. This two-jet solution can, in principle, be generalized by adding the interstellar flow. Let us consider an arbitrary plane perpendicular to z-axis. This plane cuts a circle from the astropause. In the case of subsonic ISM flow, we can consider planar potential solutions around circles for each plane. According to the d'Alembert paradox, the force acting on each circle is zero. Therefore, the tube of the astropause should not be deflected into the tail, although the circle could be deformed to the ellipsoidal shape in the self-consistent solution. This scenario works, if we consider the interstellar flow to be ideal and incompressible. However, numerical results (e.g. Opher et al. 2015) show some bending of the jets towards the tail. This bending in numerical models (for slow incompressible ISM flows) is connected with the numerical dissipation inherent in the numerical schemes. Numerical viscosity may cause the boundary layer breakage on the surface of the astropause, which consequently causes the pressure asymmetry that deflects the astropause. This may be the explanation for the fact that the tube of the astropause is always deflected to the tail in the numerical models. The above-described numerical effects have nothing to do with physical dissipation phenomena responsible for the bending of real astrospheres. The physical dissipation mechanisms (e.g. magnetic reconnection, finite resistivity, Hall effects) should be explored as a possible cause of the astropause bending in the models with slow subsonic ISM flow. For the fast supersonic ISM flow, the BS is formed around the astropause. The post-shock ISM flow is vortical, and the d'Alembert paradox does not work in this case. Therefore, the bending of the astrospheric jets into the tail direction is easier to justify for the supersonic relative ISM/SW motion.

Compare/Contrast
Compare/Contrast
Future Work


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


Recently, rotationally supported disks have been found not only in Class I sources but also in some Class 0 sources (e.g., Murillo et al. 2013; Yen et al. 2013, 2017; Ohashi et al. 2014; Tobin et al. 2015, 2016b, 2016a; Seifried et al. 2016; Aso et al. 2017; Lee et al. 2017; Okoda et al. 2018). In spite of these extensive studies, there is still controversy regarding when and how a disk structure is formed around a newly born protostar. Moreover, the disk formation process has been revealed to be much more complicated for binary and multiple cases, both in observations (Dutrey et al. 2014; Tokuda et al. 2014; Takakuwa et al. 2014, 2017; Tobin et al. 2016b, 2016a; Boehler et al. 2017; Artur de la Villarmois et al. 2018; Alves et al. 2019) and in numerical simulations (e.g., Bate & Bonnell 1997; Kratter et al. 2008; Fateeva et al. 2011; Shi et al. 2012; Ragusa et al. 2017; Satsuka et al. 2017; Price et al. 2018; Matsumoto et al. 2019). For instance, circumbinary/circummultiple disk structures with a spiral structure as well as a circumstellar disk for each component are reported (e.g., Tobin et al. 2016a; Takakuwa et al. 2017; Artur de la Villarmois et al. 2018; Matsumoto et al. 2019; Alves et al. 2019). In addition, it is not clear how molecules are processed during the disk formation process and what kinds of molecules are finally inherited by protoplanetary disks and potentially by planets. Understanding these processes is crucial, as they will provide important constraints on the initial physical and chemical conditions for the planetary system formation study. In this context, physical and chemical structures and their mutual relation for disk-forming regions of low-mass protostellar sources have been investigated with the Atacama Large Millimeter/submillimeter Array (ALMA; e.g., Sakai et al. 2014b, 2014a; Oya et al. 2016, 2017, 2018, 2019; Imai et al. 2016, 2019; Jacobsen et al. 2019). These studies reveal that infalling envelopes and rotationally supported disks are not smoothly connected to each other either in physical structure or in chemical composition, unlike previous expectations.


As one of the previous studies on the atomic gas in the Perseus region, Stanimirović et al. (2014) calculated the

 optical depth toward 26 extra-Galactic radio continuum sources (such as quasars). They calculated

 as a function of velocity toward each radio source by using the method described in Heiles & Troland (2003). The calculated

 spectra were fitted with a sum of Gaussian functions, and the peak

 values and the Gaussian FWHMs (full width at half maximum) of each velocity component were derived. However, they found the optically thick

 gas only toward

 of lines of sight. We test the results in Stanimirović et al. (2014) and Fukui et al. (2014, 2015), which differ by several factors. To do this, we compare

 derived in Stanimirović et al. (2014) and that obtained in Section 3.5. Since our

 corresponds to the average value within given velocity width (

; see Section 3.4), we compare the following two values toward each radio source located in the region we analyzed: (1) the sum of the areas of each Gaussian component of the

 profiles calculated in Stanimirović et al. (2014), and (2) the products of our

 and

. The results are listed in columns 8 and 9 of Table 2. Note that 4C +30.04, 3C 092, and 3C 093.1 are located at the masked area; therefore

 cannot be calculated by our method toward them. Although there is a rough positive correlation between them, they differ

 times as a concrete numerical value. The correlation between them is plotted in Figure 16. The solid line indicates the one-to-one relationship (

), and the dashed line is the best-fit regression line through the origin (

). The results in Stanimirović et al. (2014) are systematically smaller than our results, and it is obvious that there is a discrepancy between these two results. This discrepancy can, however, be explained by characteristics of the data used to derive

 in the present study and Stanimirović et al. (2014).


We use the largest sample of FRB 121102, which is observed by GBT at 4–8 GHz (Zhang et al. 2018). This sample contains 21 pulses reported in Gajjar et al. (2018) and 72 pulses identified by machine learning. These pulses were observed within a 6 h observation. They share the same observation conditions and were observed by the same telescope. Therefore, we can put them together to analysis and ignore complex selection effects. Power-law distributions of energy αE = 1.63 ± 0.06 and distributions αT = 1.57 ± 0.13 for these 93 FRB 121102 bursts are shown in Fig. 5. Gourdji et al. (2019) discovered a low-energy sample with 41 bursts for FRB 121102 and found αE ∼ 1.7 if all bursts are included (see their fig. 5). However, if the low-energy bursts are discarded, a steeper αE ∼ 2.8 is found. Wang & Zhang (2019) also found that six samples of FRB 121102 bursts observed by different telescopes at different frequencies show a universal energy distribution with αE around 1.7. Meanwhile, a similar power-law index of energy distribution for non-repeating FRBs is also found (Lu & Piro 2019; Zhang & Wang 2019). The waiting time distribution of FRB 121102 can also be described by a non-stationary Poisson process with mean burst rates $\lambda _{0}=1.23^{+0.80}_{-0.38} \times 10^{-5} \,\rm ms^{-1}$. Zhang et al. (2018) found that the rate of detection is not stationary, and the distribution of waiting time cannot be well fitted using Poissonian distribution for the same sample. For a small sample of waiting times of FRB 121102, Oppermann, Yu & Pen (2018) modelled the distribution of waiting times as Weibull distribution, which can describe non-Poissonian distributions with clustering. It must be noted that the non-stationary Poissonian distribution used in this paper is similar to the Weibull distribution. Because the rate of bursts in a non-stationary Poisson process also varies with time (Wheatland et al. 1998), the mean burst rate is 1.23$^{+0.80}_{-0.38}\times 10^{-2}$ s−1. Using the same data, Zhang et al. (2018) found that the rate is 0.05 s−1 for Poissonian distribution. Using a sparse waiting time sample, Oppermann et al. (2018) derived a mean repetition rate of $5.7^{+3.0}_{-2.0}$ d−1. The large discrepancy between the two rates is that the waiting times used in this paper are derived from 93 bursts in 5 h observation, comparing to 17 bursts in about 74 h observation in Oppermann et al. (2018).


The results presented here are based on the assumptions that the CBPs do not interact with the material ejected from their binary star. However, numerical studies have indicated that this material is neither lost isotropically from the binary during the CE phase, nor does it all become unbound. Instead, 1–10% of the ejecta may fall back into a CB disk according to Kashi & Soker (2011), and Passy et al. (2012) suggest that ∼80% of the ejected material may remain gravitationally bound to the binary (also see Kuiper 1941; Shu et al. 1979; and Pejcha et al. 2016 for mass loss outflows through the L2 Lagrange point24

24
Mass loss through L2 results in several possible outcomes, e.g., isotropic or equatorial wind, CB disk; for details, see Table 1 and Figures 12 and 13 of Pejcha et al. (2016).
). Either of these scenarios would significantly complicate the dynamical evolution of the system as the CBP could accrete material and gain mass and also experience migration similar to that during planetary formation.25

25
There are, however, two potential benefits of the former in terms of detection: a more luminous planet would be more amenable to direct imaging efforts, and a more massive planet would cause stronger ETVs.
 Such accretion of material of a different specific angular momentum will change the orbital evolution of the planet, as will gravitational interaction with the bulk gas in an accretion-favorable environment such as a CB disk. Additionally, interactions between CBPs and the CE ejecta of close binary stars (including ejection or destruction of the planets) may also play an important role in the elusive mechanisms responsible for the shaping, morphology, and chemistry of planetary nebulae (see Bear & Soker 2016 for triple star origin of asymmetric planetary nebulae; for recent reviews see Zijlstra 2014 and Jones 2015, and references therein). We note that the CE-triggered dynamical disturbances discussed here occur on timescales of ∼1 year and are thus “instantaneous” compared to any subsequent planet migration, which occurs on much longer timescales.


In the framework of the hierarchical formation of structures, clusters of galaxies are continuously accreting galaxies. It has been suggested that in this process of falling, galaxies could undergo different physical processes that could affect the star formation even before they reach the cluster. Consequently, to fully understand what the cluster environment produces in galaxies, it is of key importance to have a throughout characterisation of the population of galaxies in the outskirts of clusters. Several observations have shown that properties of galaxies such as star formation, gas content, and colour are affected by the cluster environment at large clustercentric distances (e.g. Lewis et al. 2002; Solanes et al. 2002; Gómez et al. 2003; Braglia et al. 2009; Hansen et al. 2009; Park & Hwang 2009; von der Linden et al. 2010; Haines et al. 2015; Rhee et al. 2017). In particular, spiral galaxies with low star formation rates were found in the outskirts of clusters in early studies such as Couch et al. (1998) or Dressler et al. (1999). In recent years, a deficit of star-forming galaxies in the infalling region of clusters has been reported (e.g. Wetzel et al. 2013; Haines et al. 2015; Bianconi et al. 2018). This has been reproduced in simulations by Bahé et al. (2013). These results can be explained by the presence of environmental effects accelerating the consumption of the gas reservoir before galaxies enter in a cluster, a process known as pre-processing (e.g. Fujita 2004; Mihos 2004). An important fraction of the cluster galaxies has spent time in groups or filaments before they fall into the cluster (e.g. McGee et al. 2009; De Lucia et al. 2012; Wetzel et al. 2013; Hou, Parker & Harris 2014). The population of galaxies in the outskirts of clusters includes not only galaxies that have not yet entered the cluster but also backsplash galaxies, i.e. galaxies that have passed close to the centre of the cluster since their infall and are now beyond the virial radius (e.g. Mamon et al. 2004; Gill, Knebe & Gibson 2005; Mahajan, Mamon & Raychaudhury 2011). For an adequate characterisation of the properties of galaxies that are falling into clusters, it is important to take into account the contamination by backsplash galaxies, which, having orbited through the inner regions of a cluster, could have been affected by the physical processes present in that extreme environment. The backsplash scenario in the evolution of galaxies has also been explored in Rines & Diaferio (2005), Pimbblet et al. (2006), Aguerri & Sánchez-Janssen (2010), and Muriel & Coenda (2014).


We present these results with one very important caveat. Accurately determining metallicities at different redshifts is of key importance to studying the evolution of the MZR. In the local universe, relationships between strong emission line ratios and metallicity can be calibrated to âdirectâ electron temperature-determined metallicities from measuring auroral lines such as [Oâiii]Â Î»4363 (Pettini & Pagel 2004; Pilyugin & Thuan 2005) or photoionization models of star-forming regions (Zaritsky et al. 1994; Kewley & Dopita 2002; Kobulnicky & Kewley 2004; Tremonti et al. 2004). At redshifts above z â¼ 1, it is nearly impossible to detect weak auroral lines for directly determining metallicity (but see Yuan & Kewley 2009; Rigby et al. 2011; Brammer et al. 2012a; Christensen et al. 2012; Maseda et al. 2014). Creating photoionization models that suitably represent high-redshift star-forming regions requires knowledge of physical parameters which have been poorly constrained up to this point. Thus, it is unknown if local metallicity calibrations hold at high redshifts. Figure 6 shows a comparison between metallicities determined using the O3N2 indicator and the N2 indicator for both local SDSS galaxies (grey points) and MOSDEF z â¼ 2.3 galaxies (black points). The black dashed line indicates a one-to-one relationship. If local calibrations do indeed hold at high redshifts, then the relationship between metallicities determined from different indicators should not evolve with redshift. It is clear that the z â¼ 2.3 galaxies are offset below the local galaxies. The dotted line is the best-fit line of slope unity to the individual z â¼ 2.3 galaxies, yielding an offset of â0.1 dex from a one-to-one correspondence, over twice that displayed by the SDSS sample. Steidel et al. (2014) found an offset slightly larger than this at z â¼ 2.3. This offset demonstrates that the two metallicity indicators are not evolving in the same way with redshift, and shows the need of metallicity calibrations appropriate for high-redshift galaxies.


Finally, we attempted to estimate the total obscured star formation within the Mpc scale environments of ELAN, which can be achieved by assuming that the excess number of submillimeter sources are all associated with the respective ELAN. To compute the SFR densities we first seek a proper conversion from S850 to SFRs. We utilized a sample of ALMA-identified SMGs in the UKIDSS-UDS field, which has been studied in detail with proper SED fittings (Dudzevičiūtė et al. 2020). Similarly to our observations, the sample of Dudzevičiūtė et al. (2020) was drawn from a flux-limited sample produced by the SCUBA-2 Cosmology Legacy Survey (Geach et al. 2017). Their results should therefore be representative, on average, of SCUBA-2 sources uncovered in other fields. These authors found a linear correlation of log10[SFR(M⊙ yr−1)] = (0.42 ± 0.06) × log10[S870(mJy)] + (2.19 ± 0.03) for their SMGs, which span a flux range of ∼1 − 10 mJy, appropriate for the SCUBA-2 sources discovered in our target ELAN fields. We then computed the total SFR densities by integrating over a given S850 range in which the SFR contribution at a given S850 is the product of the excess number density of the submillimeter sources and their corresponding SFR based on the conversion. For each field, by considering a flux range of S850 = 1 − 20 mJy and assuming a sphere with an equivalent circular radius of the corresponding effective area, we obtain SFR densities of 1100 ± 500, 1100 ± 500, 2300 ± 1100, and 1400 ± 1100 M⊙ yr−1 Mpc−3 for Fabulous, Slug, Jackpot, and MAMMOTH-1 ELAN, and a weighted average SFR density of ΣSFR = 1200 ± 300 M⊙ yr−1 Mpc−3. We plot the results in Fig. 5, showing that they are consistent with those found in the Mpc-scale environments of other quasar samples or proto-clusters at z ∼ 2 − 3 (Clements et al. 2014; Dannerbauer et al. 2014; Kato et al. 2016). This result suggests that the star formation activities around ELANe are at a similar level of other dense systems in this redshift range, or, in other words, at a factor of about 300 greater than the cosmic mean.

Dudzevičiūtė et al. 2020
Dudzevičiūtė et al. (2020)


Most of our knowledge about reconnection comes from effectively 2D reconnection experiments, and only recently have efforts to understand 3D magnetic reconnection been pursued (Priest 2011; Pontin 2011; Shepherd & Cassak 2012; Janvier et al. 2014), revealing a much wider range of dynamics. Very little is known about the actual properties of the solar plasma during the reconnection process on the Sun. Many authors have studied the global and local reconnection rates and timescales of solar reconnection during solar flares based on analysis of the ribbon motions in the chromosphere (Fletcher & Hudson 2001; Qiu et al. 2002, 2010; Isobe et al. 2005; Jing et al. 2005; Saba et al. 2006; Miklenic et al. 2007; Xie et al. 2009). Generally, they use measurements of the magnetic flux at the photosphere, the velocity of the ribbons parallel to the PIL, and the 2D approximation of the standard flare model to determine the reconnected flux and the electric field and Poynting flux at the reconnection site. In a future paper, we plan to test the validity of this approximation. However, these studies are purely based on the ribbon dynamics and are not able to capture the dynamics of the 3D coronal magnetic field that is actually involved in the reconnection process. For example, to calculate the energy release rate from reconnection, one needs to combine observations with knowledge of the location and size (i.e., length—the width is generally below the resolution) of the reconnection current sheet, which can only be provided by data-constrained magnetic field models and extrapolations or by data-driven MHD simulations with the appropriate NLFFF initial conditions (and is still only an approximation). Aulanier et al. (2000, 2012) and Schrijver et al. (2011) utilize idealized MHD simulations to interpret the appearance of the flare ribbons. Although such studies show a qualitative similarity of the QSLs and flare ribbons and are valuable for determining the basic topology of the region, no actual estimates of the reconnection parameters can be obtained, which could be improved by the use of data-constrained and data-driven magnetic field modeling.


The recovery of the sky signal from these huge, noisy time streams, a process called map-making, represents one of the most important steps in CMB data analysis and, if the detector noise properties and scanning strategy are known, map-making becomes a linear inverse problem. The generalized least-squares (GLS) equation provides an unbiased solution to map-making for an arbitrary choice of weights given by a symmetric and positive definite matrix (Tegmark 1997a). Moreover, if we consider the inverse covariance of the time domain noise as the weights, the GLS estimate is also a minimum variance and a maximum likelihood solution to the problem. However, computation of the solution in such a case may require either an explicit factorisation of a huge, dense matrix (Tegmark 1997a; Borrill 1999; Stompor et al. 2002) or an application of some iterative procedure (Wright 1996; Oh et al. 1999; Doré et al. 2001; de Gasperis et al. 2005; Cantalupo et al. 2010). These latte typically involve several matrix-vector multiplications at each iteration step. What makes the map-making problem particularly challenging are the sizes of the current and forthcoming CMB data sets which are directly related to the number of floating point operations (flops) needed to achieve the solution and to the memory requirements due to the sizes of the arrays required for it. Both these factors set the requirements on computational resources and indeed many current CMB data analysis pipelines opt for massively parallel computing platforms. However, even in such circumstances, efficient algorithms are necessary to ensure that the analysis can indeed be performed. The computational complexity of the algorithms involving an explicit matrix inversion is

O
(

N

p

3

)

$ \textstyle\mathcal O(\mathbf N_\mathrm p^3) $

 flops, where Np is the number of pixels in the map, and therefore they are only suitable for cases where the estimated sky maps do not involve many sky pixels. Nonetheless, whenever feasible, the direct approaches can yield high-precision, unbiased estimates of the sky signal (e.g. Poletti et al. 2017, for a recent example). The next generations of the ground experiments, CMB-Stage III (Arnold et al. 2014; Henderson et al. 2016; Benson et al. 2014) and IV (Abazajian et al. 2016), however, are expected to observe significant fractions of the entire sky with high resolution, thus resulting in maps with Np ≃ 𝒪(106), rendering the direct approaches prohibitive even for the largest forthcoming supercomputers.


Diffuse interstellar bands (DIBs) are absorption features seen in the spectra of many astronomical objects in the visible and infrared wavelength regions. The total number of these features exceeds 400. These bands are observed in absorption in star light crossing translucent clouds and the carriers of only three such features have been proposed; none of them certain. The origin of the DIBs is as puzzling as since their first detection, more than 90 years ago. The central wavelengths of DIBs are not readily identified with any known atomic or molecular spectral lines. The profiles of DIBs are not just Gaussians as shown for the first time by Westerlund & Krełowski (1988) which may suggest their molecular carriers. Moreover, precisely determined DIB profiles (Galazutdinov, LoCurto & Krelowski 2008b), showing a specific substructure pattern each, should facilitate their carrier's identification. The better-substantiated hypothesis is that DIBs arise from absorption produced by polycyclic aromatic hydrocarbons (PAHs), although Cox (2011) and Salama & Ehrenfreund (2014) doubt this statement and no specific PAH has been identified until recently (Salama et al. 2011). The other possibility is that carbon chain molecules, similar to those observed in star-forming regions, may carry DIBs. but this idea also has no clear proof (Motylewski et al. 2000). Two DIBs, observed in the near-infrared, were tentatively ascribed to the bucky ball (C$_{60}^{+}$) molecule (e.g. Foing & Ehrenfreund 1994; Campbell et al. 2015). Nevertheless there is an indication that this identification was proposed but not finally proven. Recently it has been demonstrated that DIB profiles (at least some of them) change in unison with the rotational temperature of simple homonuclear molecules C2 and C3 (Kaźmierczak et al. 2009). The relation between temperatures of simple carbon chains and those of DIB carriers may suggest that there is a common chemical history and that the DIB carrier may be polyatomic centrosymmetric (non-polar) molecules as well. This is likely why the earlier attempts to match the electronic spectra of known polar molecules (identified in microwave region of wavelengths) and DIBs failed (Motylewski et al. 2000). In a certain sense, this phenomenon still remains an enigma for astrophysicists. For recent reviews see Cami & Cox (2014).


Several studies have discussed the radio luminosity of GLEAM-X J1627 during its radio outburst in comparison with the limits of its rotational energy (Erkut 2022; Hurley-Walker et al. 2022). In particular, assuming isotropic emission, the radio luminosity of the brightest single peaks (L
radio ∼ 1030–1031 erg s−1; Hurley-Walker et al. 2022) exceeds the limits on the rotational power of the source by a few orders of magnitude. Figure 6 shows those peak radio luminosities and the rotational power of GLEAM-X J1627 in comparison with other pulsars, rotating radio transients (RRATs) and radio-loud magnetars. For the radio-loud magnetars, given their large variability, we have chosen the brightest radio pulses reported in the literature (data collected from Camilo et al. 2006, 2007; Weltevrede et al. 2011; Deller et al. 2012; Lynch et al. 2015; Majid et al. 2017; Pearlman et al. 2018; Lower et al. 2020, and Esposito et al. 2021). It is well known that assuming isotropic radio emission is not realistic, and a beaming factor necessarily has to be present (see, e.g., Erkut 2022). However, the relation between the duty cycle and the spin period of canonical pulsars has a large spread (Manchester et al. 2005). Moreover, it is observed that this relationship does not apply to radio-loud magnetars, which in general show larger duty cycles than what one would expect from the extrapolation of this tentative relation for radio pulsars to magnetars (see, e.g., Camilo et al. 2006, 2007). To avoid the uncertainty of beaming models, which for magnetars are mostly unknown even theoretically, we plotted the isotropic radio luminosity for all the different pulsar classes in Figure 6. From this plot, at variance with canonical radio pulsars, we see how the brightest single peaks for radio-loud magnetars might exceed their rotational powers, in line with what is possibly observed for GLEAM-X J1627. While not resolving uncertainties related to the exact mechanism of radio emission or the beaming factor, Figure 6 shows that, under the assumption of isotropic emission, even for magnetars the brightest single peaks exceed their rotational energy budget. Considering all the uncertainties in the assumptions used to derive the radio luminosities plotted in Figure 6, GLEAM-X J1627’s radio luminosity excess over its rotational power cannot be used as an argument for or against its neutron star nature.


A third approach to assessing the central star formation is based on the presence of poly-aromatic hydrocarbons (PAHs), which are known to trace young stars, but over a wider range of ages (∼100 Myr) than the ionised line emission. However, there is a debate about whether the PAHs are excited by stars or by the AGN itself, or whether small PAHs are destroyed by the hard radiation from an AGN (Siebenmorgen et al. 2004; Smith et al. 2007; Sales et al. 2010). This may depend on which PAH feature one considers: Diamond-Stanic & Rieke (2010) found that in AGNs on kpc scales the 6.2, 7.7, and 8.6 μm features were suppressed, while the 11.3 μm feature was not. Partly for this reason, recent studies of PAHs close to AGNs have focussed on the feature at 11.3 μm. Esquej et al. (2014) detected PAHs on subarcsec scales in about half of their sample of 29 nearby Seyfert galaxies. They argued that the high column densities in the torus around the AGN would provide shielding that enables PAHs to survive, and the implied central star formation rate density was much higher than in the circum-nuclear region. A similar conclusion about PAH survival was reached by Esparza-Arredondo et al. (2018) for their sample of 19 AGNs, based on the lack of relation between the X-ray luminosity and a central PAH deficit – while PAHs were detected in most AGNs, the equivalent width was lower in the centre. They attributed this to low star formation rates in that region. On the other hand, while Jensen et al. (2017) also detected PAHs in a sample of 13 AGNs, they argued that the similarity and slope of the radial profiles from tens to hundreds of parsecs point towards an origin in a single compact source of excitation. In order to shed more light on the excitation of PAHs in this context, Alonso-Herrero et al. (2020) compared PAH line ratios in 22 AGNs to models of PAH excitation and analysed this in the context of the measured molecular gas content. They concluded that PAHs can be shielded from the hard AGN radiation.


Discovered in 1977 from its bright H α emission (Stephenson & Sanduleak 1977), SS433’s defining characteristics are undoubtedly the helical motion of highly collimated jets of plasma launched from its innermost regions, and mass-loaded, non-polar outflows (Fabian & Rees 1979; Margon et al. 1979) which together inflate the surrounding W50 supernova remnant. Knots in SS433’s jet can be resolved at radio frequencies using very long baseline interferometry (VLBI) and indicate the presence of highly relativistic electrons (Vermeulen et al. 1987), while the baryon content is revealed by emission lines ranging from H and He lines in the optical through to highly ionized Fe lines in the X-rays (Kotani et al. 1994; Marshall et al. 2013). The Doppler shifts of the lines indicate precession of the accreting system with a period of ≈ 162 d, also seen in optical (He ii) emission lines originating from the non-polar wind (Fabrika 1997). Both the jets and winds carry a large kinetic luminosity (>1038 erg s−1, e.g. Marshall et al. 2002), which requires extraction of energy via accretion on to a compact object. While the nature of the compact object in SS433 remains somewhat unknown (although dynamical arguments suggest the presence of a black hole – Blundell, Bowler & Schmidtobreick 2008), the rate of mass transfer from the companion star, as inferred from the IR excess (Shkovskii 1981; Fuchs et al. 2006), is thought to be ∼1 × 10−4 M⊙ yr−1, orders of magnitude in excess of the Eddington limit for any plausible stellar remnant (>300 times the Eddington mass accretion rate for a typical stellar mass black hole of around 10 M⊙). Classical theory and radiation magnetohydrodynamic (RMHD) simulations agree that such ‘super-critical’ rates of accretion will lead to a radiatively supported, large scale height (H/R ≈ 1, where H is the height of the disc at distance R from the compact object) accretion disc with powerful winds launched from the surface at mildly relativistic speeds (Shakura & Sunyaev 1973; Poutanen et al. 2007; Ohsuga & Mineshige. 2011; Takeuchi et al. 2013; Jiang et al. 2014; Sadowski et al. 2014).


Following the short gamma-ray burst (sGRB) associated with this event, GRB 170817A (Abbott et al. 2017a,b; Goldstein et al. 2017), radio emission was anticipated as the associated merger outflow interacted with the circum-merger medium. Monitoring the radio emission could therefore provide crucial information on the energetics and geometry of the outflow, as well as the ambient environment. At radio frequencies, telescopes were observing the Advanced LIGO–Virgo probability region for GW170817 within 29 min post-merger (Callister et al. 2017a), and subsequent monitoring of AT 2017gfo resulted in an initial radio detection 16 d after the event (Abbott et al. 2017a; Hallinan et al. 2017). Further monitoring, predominantly at frequencies between 0.6 and 15 GHz, has since taken place (e.g. Alexander et al. 2017, 2018; Corsi et al. 2018; Dobie et al. 2018; Margutti et al. 2018; Mooley et al. 2018a,b,c;Resmi et al. 2018; Troja et al. 2018, 2019). At these frequencies, a general picture emerged in which the radio light curve was first observed to steadily rise, before it turned over and began a more rapid decay. Using a compilation of 0.6–10 GHz radio data from 17 to 298 d post-merger, Mooley et al. (2018c) derived both a fitted time for the radio peak of 174$^{+9}_{-6}$ d and a fitted 3-GHz peak flux density of 98$^{+8}_{-9}\, \mu$Jy (also see similar analyses in Dobie et al. 2018 and Alexander et al. 2018). The fitted radio spectral index α1 from this study is −0.53 ± 0.04, consistent with broad-band spectral indices determined using radio, optical, and X-ray data at various epochs, where the typical value is approximately −0.58 (e.g. Alexander et al. 2018; Margutti et al. 2018; Troja et al. 2018, 2019; Hajela et al. 2019). Mooley et al. (2018c) also found power-law dependencies for the rise and decay phases of approximately t0.8 and t−2.4, respectively, where t is the time since the merger. Within the associated uncertainties, these results are consistent with the broad-band evolution of AT 2017gfo (e.g. Alexander et al. 2018; Hajela et al. 2019; Lamb et al. 2019; Troja et al. 2019).


Owing to their brightness at rest-frame FIR wavelengths, the ionized and neutral species of Carbon, Nitrogen, and Oxygen are powerful diagnostic lines for tracing the ISM of nearby and distant galaxies. When combined with photodissociation region (PDR) models (Tielens & Hollenbach 1985), measurement of the emission from different lines provide a means to constrain quantities such as the ionization rate and metallicity of the ISM of galaxies. Multilevel FIR transition lines have now been widely surveyed in local galaxies, originally by ISO (e.g. Luhman et al. 1998; Malhotra et al. 2001) and more recently using the PACS spectrometer (Poglitsch et al. 2010) on the ESA Herschel Space Observatory (Pilbratt et al. 2010). The [C ii]158 μm line is typically the brightest in star-forming galaxies, arising from ionized, and even neutral gas where it is the main coolant (Wolfire et al. 2003). Another commonly observed FIR line tracer of the ionized ISM is [N ii]122 μm. It has the advantage that it can be found associated with lower excitation gas, close to that observed in our own Galaxy (e.g. Goldsmith et al. 2015; Herrera-Camus et al. 2016). Another major coolant of the ISM is [O i]63 μm (Wolfire et al. 2003). Owing to its high excitation temperature and critical density, it can dominate the cooling in regions of starburst activity (Kaufman et al. 1999; Kaufman, Wolfire & Hollenbach 2006; Brauher, Dale & Helou 2008; Croxall et al. 2012; Narayanan & Krumholz 2017). When combined with measurements of the [C ii]158 μm line intensity and FIR luminosity, the [O i]63 μm line intensity can constrain the FUV field, G, and the gas density using PDR models. The luminosity in these FIR lines generally exhibits a deficit in the most FIR luminous galaxies compared to the trend expected from lower luminosity galaxies (e.g. Malhotra et al. 2001; Graciá-Carpio et al. 2011; Díaz-Santos et al. 2017). This has made the emission from lines like [O i]63 μm more challenging to detect at high-redshifts.


The albedo profile is then computed by cloudy after having specified the values of temperature T(r) and density ρ(r) for each radial patch (with r the radial distance). Results for the energy-dependent albedo profile A(Eloc) obtained for different radial patches in the cases of a = 0 (left), 0.9 (centre), and 0.998 (right) are shown in Fig. 8. As it can be clearly seen, in all the cases explored the simplifying assumption of 100 per cent albedo turns out to be a good approximation only at very high energies, i.e. Eloc ≈ 10–100 keV. Elsewhere, the albedo significantly deviates from unity (except for some values of r at lower energies), especially in the 0.1–10 keV band, which is indeed the working energy range of the forthcoming X-ray polarimeters like IXPE. Here different line features appear, more or less visible depending on the BH spin and radial distance, such as the clear iron absorption edge that occurs at around ∼6–7 keV (see e.g. Young, Ross & Fabian 1998). Plots in Fig. 9 give a more exhaustive view on how the albedo profile depends on the density of the slab in which calculations are performed. In this case the outputs are obtained for a = 0.998, three different values of the temperature, i.e. those corresponding to r = 2 (left), 5 (middle), and $10\, r_{\rm g}$ (right) according to the Novikov & Thorne (1973) temperature profile, and different values of the total hydrogen density n(H) between 1015 and 1023 cm−3. The plots show that the dependence of A(Eloc) on the density is stronger at low energies, where it exhibits an increasing behaviour by decreasing n(H). In particular, it attains values close to 0 at around 0.1 keV for particle densities in excess of 1022–1023 cm−3, especially for lower temperatures (i.e. for larger radial distances, see the right-hand panel). On the other hand, at higher energies ($\gtrsim 10$–20 keV), the albedo tends to reach the same value (≈1) in the entire range of densities explored.


Owing to their dusty circumstellar environments, a large mid-infrared (mid-IR) excess is a characteristic feature of post-AGB stars and a detection of cold circumstellar material using mid-IR photometry can be used to identify these objects. The first extensive search for these objects was initiated in the mid-80's using results from the Infrared Astronomical Satellite (Neugebauer et al. 1984) which enabled the identification of post-AGB stars in our Galaxy (Kwok 1993). The Toru$\acute{\rm n}$ catalogue (Szczerba et al. 2007) for Galactic post-AGB stars lists around 391 very likely post-AGB objects. The Galactic sample of post-AGB stars have been found to be a very diverse group of objects (Van Winckel 2003). Studies showed that the majority of the optically visible Galactic post-AGB stars could be classified based on their spectral energy distributions (SEDs) into two groups: shell-sources and disc-sources (Van Winckel 2003). The shell-sources show a double-peaked SED with the hot central star peaking at shorter wavelengths while the cold, detached, expanding dust shell peaks at longer wavelengths. This type of SED is considered to be characteristic of objects that follow the single-star evolution scenario mentioned above. The disc-sources do not show two distinct flux peaks in the mid-IR but they do display a clear near-infrared (near-IR) excess indicating that circumstellar dust must be close to the central star, near sublimation temperature. It is now well established that this feature in the SED indicates the presence of a stable compact circumbinary disc, and therefore these sources are referred to as disc-sources (de Ruyter et al. 2006; Deroo et al. 2007; Gielen et al. 2011a; Hillen et al. 2013). The rotation of the disc was resolved with the ALMA array (Bujarrabal et al. 2013a) in one object and using single dish observations Bujarrabal et al. (2013b) confirmed that disc rotation is indeed widespread. Moreover, these disc-sources are confirmed to be binaries and show orbital periods between 100 and 2000 d (Van Winckel et al. 2009; Gorlova et al. 2014). In contrast, for the Galactic shell-sources long-term radial velocity monitoring efforts have not yet resulted in any clear detected binary orbit (Hrivnak et al. 2011), which either confirms the single-star nature of these objects or introduces a possibility that these systems can have companions on very wide orbits.


For consistency, we adopt the translation of this to the absolute velocities of cluster galaxies normalized by their respective galaxy cluster velocity dispersions into the range $0.3 \lt |\Delta \mathrm{V}|/\sigma _{r_{200}} \lt 0.5$ as deduced by Pimbblet (2011). Thus, if the mode of the standardised velocities for a sub-population has its foci at around $0.3 \lt |\Delta \mathrm{V}|/\sigma _{r_{200}} \lt 0.5$ for values around the virial radius, which we assume to be Rvirial ∼ r200, said sub-population would be classified as infalling. In contrast, a sub-population of backsplash cluster galaxies would be expected to peak significantly at $|\Delta \mathrm{V}|/\sigma _{r_{200}}\sim 0$ for values at or beyond our definition of the virial radius, with their fraction reaching zero at some upper limit (e.g. Mamon et al. 2004; Pimbblet 2011; Bahé et al. 2013; Haggar et al. 2020). Therefore, with respect to Fig. 5, we see that the column of our non-merging sub-populations across both bins of radius do not show any significant difference in the distributions of velocities with the exception of those that lie ≤r200, which show the non-AGN sub-population to occupy a mode within the range that nominally represents infallers, most likely for cluster galaxies 0.5 ≤ r200  1.0 (Gill et al. 2005). Additionally, the AGN sub-population slightly deviates from the non-AGN velocity distribution with a mode centred at $|\Delta \mathrm{\it V}|/\sigma _{r_{200}}\sim 0.8$, which could indicate stronger infalling. In contrast, the column of our merging AGN sub-populations shows the strongest deviations from the distribution of non-AGN, especially with the >r200 bin showing a significant centrally dominated AGN sub-population, where such a central dominance in relative velocity corresponds to a sub-population that were predominantly backsplash cluster galaxies. However, the dependence of this being the true nature of the sub-population relies upon more precise definitions of the radii since there is a natural upper limit a bound cluster galaxy can extend outward to with respect to its galaxy cluster’s potential, known as the splashback radius (More et al. 2015, 2016). In addition, Haggar et al. (2020) show that the fraction of backsplash galaxies diminishes by 2r200 and 2.5r200 for massive (∼×1015M⊙) merging and non-merging cluster systems, respectively, thus demonstrating that merging cluster environments experience a greater decrease in the fraction of harbouring backsplash galaxies as one continues to extend beyond r200. Indeed, the sub-populations of the merging cluster galaxies present in the ≤r200 bin show more variations in their general distributions with the modes of both the AGN and non-AGN sub-populations lying around $0.3 \lt |\Delta \mathrm{V}|/\sigma _{r_{200}} \lt 0.5$, which eludes to mostly infalling sub-populations rather than those associated with backsplash. Finally, if one considers the equivalent peak of the AGN density histogram at $\Delta \mathrm{V}|/\sigma _{r_{200}}\sim 1.7$ it could be possible there is a mix of recently accreted cluster galaxies and those that are relaxing on to a common potential. Although it should be noted that not much information can be confidently derived from the AGN sub-populations within the bins that possess small samples size (N ≲ 100), especially with the merging AGN-hosting cluster galaxies at ≤r200 that only has N = 15.


In Figure 2, the reduced AKARI IRC spectra of all protostars are presented; the absorption features of the H2O, CO2, and CO ices are clearly detected. All of our targets show deep and broad absorption features of H2O ice in the wavelength range 2.7–3.4 μm. In the case of AFGL 7009S, strong extinction toward the source saturates the absorption features throughout the wavelengths from 2.7 to 3.6 μm, including H2O ice. Other ice features, such as CH4 (Lacy et al. 1991; Boogert et al. 2004) and CH3OH (Grim et al. 1991; Brooke et al. 1996), were observed at 3.3−3.5 μm, but it is difficult to extract their absorption profiles from the blended features due to the low spectral resolution of AKARI IRC. An absorption feature of the CO2 ice around 4.27 μm was clearly detected toward all targets. At the wavelength around 4.6 μm for Perseus 1 and 3, RNO 91, and AFGL 7009S, there is a hint for another ice component overlapping with the CO absorption feature at 4.67 μm. Many near-infrared observations have revealed the same feature on the blue wing part of the CO absorption feature (Tegler et al. 1995; Chiar et al. 1998; Whittet et al. 2001; van Broekhuizen et al. 2005; Aikawa et al. 2012), which was suggested as an absorption feature of XCN ice. Lacy et al. (1984) and Pendleton et al. (1999) reported that the 4.62 μm absorption feature of XCN ice consists of a nitrile group and an unknown component “X”. Many laboratory studies have suggested that UV photolysis or cosmic ray irradiation of ice mantle could make the solid state OCN− on grain surfaces (Lacy et al. 1984; Grim & Greenberg 1987; Bernstein et al. 2000; Palumbo et al. 2000; Hudson et al. 2001; van Broekhuizen et al. 2004). In addition to these ice components, there are some absorption features around 4.8 and 4.9 μm. For Perseus 3 and the background star, the absorption features with a peak position around 4.78 μm are likely associated with 13CO ice (Boogert et al. 2002; Pontoppidan et al. 2003). We also detected another absorption feature at 4.83 μm toward the low-luminosity targets. However, we could not find any corresponding ice features from previous studies. The 4.9 μm absorption feature detected toward all targets was identified as solid carbonyl sulfide (OCS) ice. OCS ice can be produced when the interstellar ices containing CO and CO2 are exposed to UV photons or cosmic rays (Palumbo et al. 1997).


In addition, if 26Al in the solar system was inherited from a molecular cloud, one would expect the solar system to have a (60Fe/26Al)0 ratio identical to that of the ISM. If the collapse timescales – depending on the amount of turbulence, the intensity of magnetic fields, and other complex parameters (McKee & Ostriker 2007) – exceed a few 26Al half lives, the solar system’s initial (60Fe/26Al)0 ratio is even expected to be higher than that of ISM because 26Al decays much faster than 60Fe. Both radionuclides have now been identified in the ISM via γ-ray astronomy (Diehl 2014). The measured ISM flux ratio 60Fe/26Al ratio is 0.15 (Wang et al. 2007), which translates into a mass ratio of 0.35. The ISM 60Fe/26Al mass ratio is therefore two orders of magnitude higher than the solar value of 3.9 × 10-3 (see Sect. 1), ruling out that both radionuclides were inherited from the ISM. Despite the observational evidence, and to keep alive the inherited model, Young (2014) proposed to decrease the theoretical 60Fe abundance in molecular clouds by assuming that stars more massive than 30 M⊙ do not explode as SNe. These stars would not contribute to the 60Fe inventory, bringing the theoretical ISM 60Fe/26Al ratio closer to that of the solar system. Because stars more massive than 30 M⊙ contribute to less than 50% of the 60Fe production2, this proposition cannot resolve the two orders of magnitude discrepancy between the model and observations. Furthermore, the recent discovery of a supernova whose progenitor mass was far above the threshold of 30 M⊙ is at odds with that solution (Gal-Yam et al. 2014). Finally, if 26Al was inherited from the natal molecular cloud, it would be homogeneously distributed in the SPD, which is contrary to observations (Krot et al. 2012). As discussed by Gounelle & Meynet (2012), some heterogeneity in the 26Al distribution is expected in the dense shell model because the shell collapse timescale (a few 105 yr) is comparable to the 26Al half life.


We constructed the gamma-ray folded light curve of 3FGL J2039.6–5618 using the orbital period from J. Strader et al. (2018, in preparation) and the two best periods in our searches using the full data and the data before MJD 57,040. The phase zero is defined to be the epoch of the optical maximum (T0 = 57,603.95787 in MJD). In order to maximize the signal-to-noise ratio, we use the method of photon weighting (Kerr 2011) instead of an aperture selection to produce the folded light curve. The probability that the photon is emitted by 3FGL J2039.6–5618 is assigned to each of the photons using gtsrcprob in the Science Tools. The orbital phase is calculated using the TEMPO2 package (Hobbs et al. 2006) with the Fermi pulg-in (Ray et al. 2011). In the timing model, we adopted the main-sequence/pulsar binary model (MSS; Wex 1998). Using the photon probabilities as the weights, the resulting weighted light curves are shown in Figure 4. From top to bottom, the orbital periods used in folding the light curves are PStrader = 0.22798177 days, Pfull = 0.2279757 days, and Pbefore = 0.2279808 days, respectively. Two orbital periods are shown for clarity. The light curve indicates that the modulation is a single peak. The FWHM of the peak spans from about ϕ = 0.25 to ϕ = 0.7, which occupies almost half of the orbital period. Although the best period found from the Rayleigh test has different values with different time spans, the folded light curves in Figure 4 generally show similar signal structures. As we speculate that the gamma-ray modulation disappears after MJD 57,040, it is not reliable to use the best period Pfull obtained from the full data set, which includes the no-signal duration. On the other hand, the best period Pbefore is obtained from the data only containing the portion before MJD 57,040; therefore, it may be biased to be applied to the study of the full data set. Therefore, with a negligible difference in the light curves and modulation significances (

 vs.

 for data before MJD 57,040), we adhere to the orbital period PB = PStrader = 0.2279817(7) days, which is reported from the independent optical observation by J. Strader et al. (2018, in preparation), for the rest of this study. Figure 5 shows the energy-dependent orbital light curves of 3FGL J2039.6–5618 in the energy ranges of 0.1–500 GeV (top), 0.1–3 GeV (middle), and 3–500 GeV (bottom). It is clear that the orbital modulation is mostly contributed by the lower part of the energy.


In this context, MWC 758 (HD 36112) offers a unique environment to probe the existence of planetary companions and to explore the connection between disk structures and planet formation. MWC 758 is a young stellar object (3.5 ± 2 Myr, Meeus et al. 2012) at a distance of 151
$^{+9}_{-8}$

151

−9

+8

4

 pc (Gaia Collaboration 2016) close to the edge of the Taurus star forming region (stellar properties are given in Table 1). Measurements of resolved CO emission around the star determined the stellar mass to be 2.0 ± 0.2 M⊙ and the disk to have an inclination of 21° ± 2° and a position angle of the semi-major axis of 65° ± 7° (Isella et al. 2010). The mass and age estimates were based on the previously adopted hipparcos distances of 200 pc (van den Ancker et al. 1998) and 279 pc (van Leeuwen 2007). Given the revised Gaia distance, the star could be older and lighter than previously thought. In this paper, we assume a stellar mass of 1.5 ±0.2 M⊙, reflecting the scaling of the dynamical mass estimate to the new Gaia distance. Based on its SED, MWC 758 has been classified as a pre-transition disk (Grady et al. 2013). Although a cavity of 55 astronomical units (au) in radius has been inferred from dust millimeter emission (Andrews et al. 2011), infrared polarized intensity observations have found no clear evidence for a cavity in scattered light (Grady et al. 2013; Benisty et al. 2015). Using Ks-band (2.15 μm) direct imaging andH-band (1.65 μm) polarimetric imaging with the High-Contrast Instrument with Adaptive Optics (HiCIAO) at the Subaru Telescope, Grady et al. (2013) detected two spiral arms and polarized light down to 0.′′ 1 (15 au) from the star. Recent VLT Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) observations in the Y band (1.04 μm) have confirmed the presence of scattered light at least down to 14 au (Benisty et al. 2015). The asymmetries observed by Isella et al. (2010) in the mm-dust distribution and in CO emission suggest that the disk may be gravitationally perturbed by a low-mass companion orbiting within a radius of 23 au (assuming a distance of 151 pc). The asymmetric cm-dust distribution was shown to follow the location of the mm-dust (Marino et al. 2015a), hinting towards the hypothesis of a dust trap, which could also be created by a companion in the gap through the Rossby wave instability (e.g., Pinilla et al. 2012b). Hydrodynamical simulations of the disk indicate that the observed spirals could instead be launched by a massive planet or brown dwarf at larger separations (~ 100 au based on the revised Gaia distance, Dong et al. 2015b). The presence of stellar companions down to a mass limit of 12 MJup at 0.′′ 25 and of planets outside 0.′′5 (5 MJup at 0.′′ 5, and 3 MJup at 1′′ , according to the BT-SETTL models; Allard et al. 2012) has been ruled out based on a combination of sparse aperture masking observations at L′ band and angular differential imaging at K′ and Ks bands (Grady et al. 2013).


The SFG sample was constructed using the Great Observatories All-Sky LIRG Survey (GOALS sample, Armus et al. 2009), from which we extracted 158 galaxies, with data from Inami et al. (2013), who report the fine-structure lines at high resolution in the 10 − 36 μm interval, and Stierwalt et al. (2014), who include the detections of the H2 molecular lines and the PAH features at low spectral resolution. For those galaxies in the GOALS sample that have a single IRAS counterpart, but more than one source detected in the emission lines, we have added together the line or feature fluxes of all components, to consistently associate the correct line or feature emission to the total IR luminosity computed from the IRAS fluxes. To also cover lower luminosity galaxies, as the GOALS sample only includes luminous IR galaxies (LIRGs) and ultra-luminous IR galaxies (ULIRGs), we included 38 galaxies from Bernard-Salas et al. (2009) and Goulding & Alexander (2009), to reach the total sample of 196 galaxies with IR line fluxes in the 5.5 − 35 μm interval in which an AGN component is not detected. For the Bernard-Salas et al. (2009), Goulding & Alexander (2009), and the GOALS samples, we excluded all the composite starburst-AGN objects identified as those with a detection of [NeV] either at 14.3 or 24.3 μm. It is worth noting that the original samples from Goulding & Alexander (2009) and Bernard-Salas et al. (2009) have spectra solely covering the central region of the galaxies. To estimate the global SFR, we corrected the published line fluxes of the Spitzer spectra by multiplying them by the ratio of the continuum reported in the IRAS point source catalogue to the continuum measured on the Spitzer spectra extracted from the CASSIS database (Lebouteiller et al. 2015). We assumed here that the line emission scales (at first order) with the IR brightness distribution. In particular, we considered the continuum at 12 μm for the [NeII]12.8 μm and [NeIII]15.6 μm lines, and the continuum at 25 μm for the [OIV]25.9 μm, [FeII]26 μm, [SIII]33.5 μm, and [SiII]34.8 μm lines. This correction was not needed for the AGN sample and the GOALS sample because of the greater average redshift of the galaxies in the 12MGS and GOALS samples. In particular, the 12MGS active galaxy sample has a mean redshift of 0.028 (Rush et al. 1993), while the GOALS sample has a mean redshift of 0.026. The galaxies presented by Bernard-Salas et al. (2009) have instead an average redshift of 0.0074, while the sample by Goulding & Alexander (2009) has an average redshift of 0.0044. For the other lines in the 10 − 36 μm interval, Goulding & Alexander (2009) did not report a detection, and we used the data presented in Bernard-Salas et al. (2009) for a total of 15 objects. Both Bernard-Salas et al. (2009) and Goulding & Alexander (2009) reported data from the high-resolution Spitzer-IRS spectra. Data in the 50 − 205 μm interval were taken from Díaz-Santos et al. (2017). For the GOALS sample, 20 starburst galaxies were taken from Fernández-Ontiveros et al. (2016), and 23 objects were taken from the ISO-LWS observations of Negishi et al. (2001). As a result, we obtained a total sample of 193 objects. Lastly, the PAH features’ fluxes were measured from the low-resolution Spitzer-IRS spectra by Brandl et al. (2006), including 12 objects from the sample of Bernard-Salas et al. (2009) and 179 objects from Stierwalt et al. (2014).


The formation and evolution of black holes (BHs) in the universe is one of the major issues to be addressed by the modern research in astrophysics and cosmology. In the mass range m
• ∼ 5–150 M
⊙, BHs are originated from the final, often dramatic stages in the evolution of massive stars (possibly hosted in binary systems). These compact remnants can produce luminous X-ray binaries (e.g., Mapelli et al. 2010; Farr et al. 2011; Inoue et al. 2016), can constitute powerful sources of gravitational waves for ground-based detectors like the current LIGO/Virgo facility (e.g., Belczynski et al. 2010; Dominik et al. 2015; Spera & Mapelli 2017; Boco et al. 2019; Spera et al. 2019; Abbott et al. 2021a, 2021b), can possibly energize short gamma-ray bursts and associated kilonovas (e.g., Abbott et al. 2020, 2021c; Ackley et al. 2020; Gompertz et al. 2020), can inject strong energy inputs in the primeval universe (e.g., Mirabel et al. 2011; Justham & Schawinski 2012; Artale et al. 2015; Madau & Fragos 2017; Lehmer et al. 2021), and can provide light seeds for the subsequent growth of more massive BHs (e.g., Madau et al. 2014; Volonteri et al. 2015; Lupi et al. 2016; Pacucci et al. 2017; Boco et al. 2020; Das et al. 2021). At the other end, in the range M
• ∼ 106–1010
M
⊙, supermassive BHs grow mainly by gaseous accretion that energizes the spectacular broadband emission of active galactic nuclei (AGNs). Such an activity can have a profound impact on galaxy evolution (e.g., Alexander & Hickox 2012; Lapi et al. 2014, 2018), as testified by the strict relationships between the relic BH masses and the physical properties of the hosts (e.g., Kormendy & Ho 2013; Shankar et al. 2016, 2020; Zhu et al. 2021). The intermediate-mass range m
• ∼ 103–106
M
⊙ is the most uncertain. So far, only tentative evidence of these systems has been identified (see Paynter et al. 2021). However, the chase is open in view of their astrophysical relevance. Most noticeably, they can provide heavy seeds for quick (super)massive BHs growth (e.g., Mayer & Bonoli 2019; Boco et al. 2020), as it seems required by the puzzling observations of an increasing numbers of giant monsters M
• ≳ 109
M
⊙ when the age of the universe was shorter than ≲0.8 Gyr (e.g., Mortlock et al. 2011; Venemans et al. 2017; Banados et al. 2018). Moreover, such intermediate-mass BHs will constitute important targets for space-based gravitational wave detectors like LISA and DECIGO (see eLisa Consortium 2013; Kawamura et al. 2021; also Barausse & Lapi 2021; Boco et al. 2021b).


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


There are also simplified problems, less complex than fully developed turbulence, in which one finds the formation of small scales in the direction perpendicular to an applied magnetic field

 It is well known that this effect appears in the context of MHD when imposed parallel-propagating waves interact with an inhomogeneous background consisting either of pressure-balanced structures or velocity shears (Ghosh et al. 1998). Phase mixing of torsional Alfvén waves in axisymmetric-equilibrium magnetic configurations have been studied in Ruderman et al. (1999), where possible applications to the solar corona and solar wind have been proposed. In two-dimensional (2D) equilibria, where the Alfvén velocity varies in directions perpendicular to the magnetic field, two mechanisms have been investigated in detail: (1) phase mixing (Heyvaerts & Priest 1983), in which differences in group velocity at different locations progressively bend wave fronts, and (2) resonant absorption, which concentrates the wave energy in a narrow layer where the wave frequency locally matches a characteristic frequency (Alfvén or cusp). These processes have been studied both by investigating normal modes of the inhomogeneous structure (Kappraff & Tataronis 1977; Mok & Einaudi 1985; Steinolfson 1985; Davila 1987; Hollweg 1987; Califano et al. 1990, 1992) and by considering the evolution of an initial disturbance (Lee & Roberts 1986; Malara et al. 1992, 1996). Effects of density stratification and magnetic line divergence (Ruderman et al. 1998), nonlinear coupling with compressive modes (Nakariakov et al. 1997, 1998), and evolution of localized pulses (Tsiklauri & Nakariakov 2002; Tsiklauri et al. 2003) have been considered. The propagation of MHD waves in inhomogeneous magnetic fields containing null points has also been studied in detail (Landi et al. 2005; see also McLaughlin et al. 2010 for a review). Phase mixing in 3D inhomogeneous equilibria has also been considered in the small-wavelength limit (Similon & Sudan 1989) using a WKB approximation (Petkaki et al. 1998; Malara et al. 2000), also within the problem of coronal heating (Malara et al. 2003, 2005, 2007). Particle acceleration in phase mixing of Alfvén waves in a dispersive regime has been studied by Tsiklauri et al. (2005) using particle-in-cell simulations, both in 2D (Tsiklauri 2011) and in 3D (Tsiklauri 2012) configurations. Finally, instabilities generating KAWs in a plasma with transverse density modulations have been considered by Wu & Chen (2013). Similar ideas involving dissipative mechanisms related to the interaction of Alfvén waves or KAWs and phase mixing have been examined in the context of the magnetospheric plasma sheet (Lysak & Song 2011) and in coronal loops (Ofman & Aschwanden 2002).


The origin of nitrogen in the Solar system is still an open question. More specifically, the main repository of nitrogen in the protosolar nebula (PSN) is still unclear, although there is some consensus that it may be atomic, N, or molecular, ${\rm N_2}$ (Schwarz & Bergin 2014). Furthermore, the large variations of the isotopic ratio of nitrogen (${\rm ^{14}N}/{\rm ^{15}N}$), as measured in various carriers within different types of Solar system objects, remain unexplained (Aléon 2010; Hily-Blant et al. 2013a, 2017; Füri & Marty 2015). One striking problem is the ${\rm ^{14}N}/{\rm ^{15}N}$ isotopic ratio of nitrogen in comets. Its average value, 144 ± 3 (Jehin et al. 2009; Bockelée-Morvan et al. 2015; Shinnaka et al. 2016; Hily-Blant et al. 2017), is three times lower than the bulk ratio of 441 ± 6 in the protosun as inferred from solar wind measurements (Marty et al. 2011). The reasons for these different ratios remain elusive, casting doubts on our understanding of the origin of the composition of comets and more generally of the origin of nitrogen in the Solar system. Several possibilities (not mutually exclusive) could explain the discrepancy: (i) the tracers of nitrogen observed so far in comets – HCN, CN, and ${\rm NH_2}$ – are minor reservoirs of cometary nitrogen and thus naturally do not reflect the bulk ratio in the PSN, (ii) efficient fractionation processes in the PSN at the time of comet formation, (iii) efficient fractionation processes in the parent interstellar cloud, and (iv) exchange processes within cometary ices since their formation. Recently, it was shown that protoplanetary discs – or equivalently PSN analogues – carry at least two isotopic reservoirs of nitrogen, traced, respectively, by CN and HCN, with HCN probing a secondary, fractionated, reservoir (Hily-Blant et al. 2017). Furthermore, the isotopic reservoirs traced by HCN and CN are found to be in a 1:3 ratio, respectively, reminiscent of the factor of 3 between the cometary and bulk isotopic ratios (144:441) in the PSN. It follows that exchange processes in parent bodies [possibily (iv) above] are not necessary. The PSN hypothesis is supported by models of selective photodissociation of ${\rm N_2}$ in protoplanetary discs (Heays et al. 2014) that predict a strong enrichment of HCN in ${\rm ^{15}N}$, but also of CN, in contrast with observations (Hily-Blant et al. 2017). At present, clear-cut observational evidences supporting the PSN or interstellar hypothesis are still lacking.


Solar wind velocity distribution moments are described in Behar et al. (2017). The ion density nsw is the moment of order 0, and the ion bulk velocity usw (a vector) appears in the moment of order 1, the flux density

$n_{\mathrm{sw}} \ \underline{\mathbf{u}_{\mathrm{sw}}}$

n

sw

u

sw

_

. The bulk speed can be defined as the norm of the bulk velocity, that is,

$u_{\mathrm{sw}} = |\underline{\vec{u}_{\mathrm{sw}}}$

u

sw

=|

u

sw

_

|. However, this bulk speed is representative of single-particle speeds as long as the velocity distribution function is compact (e.g., a Maxwellian distribution). Complex velocity distribution functions were observed by RPC-ICA within the atmosphere of 67P. For instance, partial ring distributions were frequently observed for solar wind protons at intermediate heliocentric distances, when the spacecraft approached the SWIC (Behar et al. 2017). To illustrate the effect of such distorted distributions, a perfect ring (or shell) distribution centered on the origin of the plasma reference frame can be imagined, in which all particles have the same speed of 400 km s−1. The norm of the bulk velocity in this case would be 0 km s−1, whereas the mean speed of the particles is 400 km s−1, which is the relevant speed for SWCX processes. This mean speed, noted Usw, of the particles is calculated by first summing the differential number flux over all angles, and then taking the statistical average (Behar 2018). Over the entire mission, the deceleration of the solar wind using the mean speed of the particles is much more limited than the deceleration shown by the norm of the bulk velocity (Behar et al. 2017): there is more kinetic energy in the solar wind than the bulk velocity vector would let us think. This is the main difference with the paradigm used at previously studied (and more active) comets (Behar et al. 2018b). These complex, nonthermal velocity distribution functions also prevent us from reducing the second-order moment (the stress tensor) to a single scalar value, which, for a Maxwellian distribution, could be identified with a plasma temperature. In the context of 67P and for an important part of the cometary orbit around the Sun, the temperature of the solar wind proton has no formal definition.


We first need to discuss that the environmental dependence of the metallicity of star-forming galaxies may depend on the scale at which the environment is defined. At small scales (a few tens of kpc), there is substantial evidence from observations and simulations for a decrement of metallicity and an enhancement of star-formation activity in galaxy close pairs, merging, and interacting systems compared to isolated, field galaxies, mostly attributed to the interaction-induced inflow of metal-poor gas from the periphery of interacting galaxies to the center, diluting their metal content, and increasing their gas fuel for star-formation (Mihos & Hernquist 1996; Kewley et al. 2006; Ellison et al. 2008, 2013; Michel-Dansac et al. 2008; Rupke et al. 2010; Sol Alonso et al. 2010; Perez et al. 2011; Scudder et al. 2012b; Ly et al. 2014). At intermediate group scales where galaxy interactions are more common compared to cluster and field environments (Perez et al. 2009; Tonnesen & Cen 2012)—owing to a combination of (1) a lower velocity dispersion of group galaxies relative to their cluster counterparts and (2) a higher number density of group galaxies compared to the field systems, which provide an ideal condition for interactions)—there is also evidence for a deficit of metals in group galaxies compared to control samples in the field (Lara-López et al. 2013b), possibly owing to a higher fraction of interacting galaxies. At larger filamentary and cluster scales, the slight metal enhancement of galaxies relative to the field might be due to (1) the inflow of already-enriched interafilamentary or interacluster gas into galaxies, as observations and simulations have shown a more metal-enriched intergalactic medium in cluster and filament environments compared to the field (Arnaud et al. 1994; Aracil et al. 2006; Stocke et al. 2006, 2007; Sato et al. 2007; Cen & Chisari 2011; Davé et al. 2011; Oppenheimer et al. 2012); (2) the environmental strangulation (Larson et al. 1980; Peng et al. 2015) of low-metallicity diluting gas falling from the surrounding LSS cosmic web into galaxies; (3) the environmental ram pressure stripping (Gunn & Gott 1972; Abadi et al. 1999) of the metal-poor diluting gas in the periphery of galaxies; and (4) trapping and recycling of metal-enriched outflows due to the hotter environment of filaments and clusters (Aracil et al. 2006; Cen & Ostriker 2006; Werner et al. 2008) compared to the field.


This paper focuses on the population of high-redshift radio galaxies (HzRGs; L500 MHz > 1026 W Hz−1Miley & De Breuck 2008), which are some of the most massive galaxies known at any redshift (with a narrow range in stellar masses of (1 − 6)×1011 M⊙ for 1  z  5.2; De Breuck et al. 2010). Their energetic radio jets are unique markers of concomitant powerful AGN activity, which place them amongst the most active sources at and near cosmic noon. High-redshift radio galaxies have furthermore been shown to be powerful beacons of dense (proto-)cluster environments in the early Universe (e.g., Le Fevre et al. 1996; Stern et al. 2003; Venemans et al. 2002, 2003, 2004, 2005, 2007; Wylezalek et al. 2013). The quasar-level AGN activity (Miley & De Breuck 2008) at the center is blocked by the thick dusty torus acting as the “coronograph” (Vernet et al. 2001); this makes HzRGs true obscured type-2 quasars, allowing us to probe their host galaxies and CGM without strong AGN contamination (e.g., for unobscured quasars, see Arrigoni Battaia et al. 2019, and for radio-quite type-2 sources, see Cai et al. 2017). Comprehensive studies using near-infrared integral field unit (IFU) instruments show that the ionized gas in HzRGs is highly perturbed (FWHM ∼ 1000 km s−1) at kiloparsec scales and is aligned with the radio jets (Nesvadba et al. 2006, 2007, 2008, 2017a,b; Collet et al. 2015, 2016). This implies that the energy and momentum transfer between the central quasar and their ISM is likely due to the jets. Radio-mode feedback may therefore play a fundamental role during the evolution of HzRGs. Recently, Falkendal et al. (2019) combined infrared and millimeter data and deduced a more robust result of a relatively low star formation rate (SFR) for a sample of HzRGs, suggesting evidence of rapid quenching compared to previous studies (e.g., Drouart et al. 2014). Using a small sample of HzRGs, Nesvadba et al. (2011) shows that they are going through a transition phase from active to passive. These observations indicate that HzRGs are on a different track of evolution compared to radio-quiet objects, assembling most of their stellar mass early (z ∼ 3; Seymour et al. 2007; De Breuck et al. 2010), and that radio jets may actively affect their quenching. However, there is also circumstantial evidence showing that the jet can induce star formation. Humphrey et al. (2006) found that HzRGs (z > 2 in the sample) with smaller radio sources and more perturbed gas (emission line) kinematics show lower UV continuum polarization, which could be due to the presence of more luminous young stellar populations and can possibly be explained by the interaction between radio jets and the ISM that enhances star formation. Besides, there is also an anticorrelation between the rest frame submillimeter flux density and radio size in HzRGs (Humphrey et al. 2011), although it is not clear if the physics behind this is feedback-induced star formation, a simultaneous triggering of star formation and the radio-loud AGN activity, or simply environmental effects. Some well-studied HzRGs show evidence of having high SFRs (e.g., 4C41.47 and PKS 0529−549; Nesvadba et al. 2020; Falkendal et al. 2019). In these sources, we may interestingly be witnessing both the jets compressing the gas, leading to enhanced SFRs (e.g., Fragile et al. 2017), and the feedback from the AGN and star formation quenching it (Man et al. 2019).

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