Here we give a simple estimate for the population of 2s-state hydrogen atoms by considering a three-level system (1s, 2s, and 3p). We set the rate equation for the 2s population as
(1)
\begin{eqnarray*}
n_{\rm H,1s}C_{\rm 1s,2s}+n_{\rm H,3p}A_{\rm 3p,2s}-n_{\rm H,2s}A_{\rm 2s,1s}=0,
\end{eqnarray*}
where nH, j is the number density of hydrogen atoms in the state j; Cj, k and Aj, k are the collisional excitation rate and spontaneous decay rate for the transition from j to k, respectively. For the bound states, we use the notation j = njlj, where nj is the principal quantum number of the state j. Similarly, lj = 0, 1, 2, 3, ..., nj − 1 (equivalently: s, p, d, f,...) is the orbital angular-momentum quantum number of the state j. Here we suppose that the depopulation term of 2s-state atoms is dominated by the spontaneous transition at the rate of A2s, 1s ≃ 8.2 s−1. In reality, the collisional transition from 2s to 2p can be a subdominant process for depopulation. For a collision at a velocity ∼108 cm s−1, which is a typical velocity scale for young SNR shocks, the cross-section is ∼10−13 cm2, giving a reaction rate ∼10−5 cm3 s−1 (e.g. Janev, Langer & Evans 1987; Sahal-Brechot et al. 1996). Thus, if the density is ∼106 cm−3, the collisional depopulation becomes important. Note that we assume no strong radiation field inducing the radiative transition from 2s to any other state.1 The occupation number of 3p, nH, 3p, depends on the absorption of Ly β. Here we assume an isotropic radiation field for Ly β. Then, we obtain the rate equation for 3p as
(2)
\begin{eqnarray*}
n_{\rm H,1s} \left(C_{\rm 1s,3p}{+}\int _0^{\infty } \frac{4\pi \sigma _\nu ^{\rm 1s,3p}}{h\nu }I_\nu {\rm d}\nu \right) {-}n_{\rm H,3p} \left(A_{\rm 3p,1s}+A_{\rm 3p,2s}\right){=}0, \nonumber \\
\end{eqnarray*}
where h, ν, $\sigma _\nu ^{\rm 1s,3p}$, and Iν are the Planck constant, frequency, absorption cross-section for the transition from 1s to 3p and the specific intensity, respectively. The intensity is set to be
(3)
\begin{eqnarray*}
I_\nu =S_\nu (1-{\rm e}^{-\tau _\nu }) =\frac{ \frac{h\nu }{4\pi } A_{\rm 3p,1s} n_{\rm H,3p} }{\sigma ^{\prime } n_{\rm H,1s}} (1-{\rm e}^{-\tau _\nu }),
\end{eqnarray*}
where Sν and τν are the source function and optical depth, respectively. σ′ is a combination of physical constants relevant to the radiative absorption cross-section. Thus, we derive the occupation number of 2s as
(4)
\begin{eqnarray*}
n_{\rm H,2s}=\frac{C_{\rm 1s,2s}}{A_{\rm 2s,1s}} \left[ 1+\frac{A_{\rm 3p,2s}}{ {\rm e}^{-\tau _0}A_{\rm 3p,1s}+A_{\rm 3p,2s} } \frac{ C_{\rm 1s,3p} }{ C_{\rm 1s,2s} } \right] n_{\rm H,1s},
\end{eqnarray*}
where τ0 is the optical depth at the line centre. Here we assume a narrow line profile function ϕν for which we can approximate as $\int _0^{\infty }(1-{\rm e}^{-\tau _\nu }){\rm d}\nu \approx 1-{\rm e}^{-\tau _0}$. The terms in the brackets [...] indicate the contribution of the combination of the absorption and cascades. Note that roughly say, the ratios are A3p, 2s/(A3p, 1s + A3p, 2s) ≃ 0.118, C1s, 3p/C1s, 2s ∼ 2–10, and C1s, 2s/A2s, 1s ∼ 10−9np, where np is the proton number density. Thus, if Ly β is in the optically thick limit, nH, 2s is enhanced roughly at most 10 times compared with the optically thin case. The absorption coefficient of H α at the line centre becomes
(5)
\begin{eqnarray*}
k_0({\rm H\alpha }) &=& \sigma _0({\rm H\alpha }) n_{\rm H,2s} \nonumber \\
&&{\sim} 10^{-23}\!-\!10^{-22}{\rm cm^{-1}} \!\left(\frac{T_0}{6000{\rm K}}\right)^{-\frac{1}{2}}\! \left(\frac{n_{\rm H,1s}}{ {\rm 1cm^{-3} } }\right)\! \left(\frac{n_{\rm p}}{ {\rm 1cm^{-3} } }\right)\!, \nonumber \\
\end{eqnarray*}
where σ0(Hα) is the radiative cross-section of H α at the line centre for given temperature T0. Thus, if the SNR shock interacts with somewhat dense clump with a density of ∼30 cm−3 and a size of ∼1 pc, the H α emission can be scattered. Note that the H β emission can also be scattered but its absorption coefficient is about quarter of the H α coefficient. The interaction between the shock and a dense clump is implied by the ripple of an SNR shock with a length-scale of ∼10 per cent of SNR radius (e.g. Ishihara et al. 2010; Williams et al. 2013, 2016; Miceli et al. 2014; Sano et al. 2017; Tsubone et al. 2017, and see the discussion of Shimoda et al. 2015). Note that according to magnetohydrodynamic simulations performed by Inoue, Yamazaki & Inutsuka (2009) and Inoue et al. (2012), even if the shock propagates into a simulated ISM having density contrast ranging in ∼1–30 cm−3 as a consequence of thermal instability, the scale length of rippling is ∼10 per cent of the length of sides of simulation box.


Among the species studied in this work, the detection of broad (Δv > 30 km s−1) line-wing H2O (312-221) emission implies the presence of shocked gas activity (e.g., van Dishoeck et al. 2011, 2013). Indeed, we only detect H2 O and CH3OH rotationally excited lines toward Orion S and BN/KL (Figs. 2 and B.1). Both species are abundant in the ice mantles that coat grains in cold dark clouds (e.g., Gibb et al. 2004). After the onset of protostellar outflows, high-velocity shocks sputter these grain mantles and heat the gas to high temperatures. Both effects enhance the abundance of gas-phase H2 O and CH3OH (e.g., Draine 1995; Jiménez-Serra et al. 2008). In OMC-1, the low- and high-velocity outflows from BN/KL plunge into the ambient molecular cloud (Genzel & Stutzki 1989) producing hot (from Tk ≃ 200–2000 K) and dense (up to n(H2) ≃ 106–107 cm−3) post-shocked gas in H2 Peaks 1 and 2 (e.g., González-Alfonso et al. 2002; Goicoechea et al. 2015b). In our HIFI maps, these extreme conditions can be inferred from the moderately extended emission of the HCN J = 13–12 line (Fig. B.2), a rotational transition with a critical density close to 1010 cm−3 (ncr = Aul∕γul(Tk), where γul is the collisional de-excitation rate coefficient in cm3 s−1), around BN/KL outflows. Interestingly, the observed HCN to HCO+ J = 6–5 line intensity ratio is ≥2 toward BN/KL, and 1 almost elsewhere (see Fig. B.4, right). This may reflect a change in the chemistry between the extended PDR cloud component and the shocked gas in BN/KL outflows. It may also reflect the much stronger mid-IR (MIR) radiation from the BN/KL region that favors the radiative pumping of HCN through its vibrational levels and enhances the high-J rotational emission (e.g, Carroll & Goldsmith 1981; Ziurys & Turner 1986). Finally, the maps show that both HCO+ and HCN J = 6–5 lines display widespread emission outside the main star-forming sites (see Fig. B.1). This suggests that the gas density of the extended cloud layers traced by HCO+ and HCN J = 6–5 lines is moderately high.


Supermassive black holes (SMBHs) are believed to exist in the centres of all massive galaxies (Kormendy & Richstone 1995). A small proportion of these are growing, with gas accretion rates ranging from ∼10−4 to 10 M⊙ yr−1 and a proportionately wide range of bolometric luminosities (∼1042–1047 erg s−1). These are active galactic nuclei (AGNs) and may accrete large fractions of their mass in bursts of rapid accretion (Croton et al. 2006), requiring rapid inflow of gas from galaxy length-scales. Stripping the gas of enough angular momentum to allow for such rapid accretion, thereby powering the most luminous AGN, proves extremely challenging. Theoretical work suggests major mergers can provide the torque to displace such an overwhelming fraction of the angular momentum of the gas, allowing for the highest accretion rates on to the central black hole whilst transforming the galaxy morphology (Toomre & Toomre 1972; Barnes 1988; BarnesBarnes & Hernquist 1991; Di Matteo, Springel & Hernquist 2005; Cox et al. 2008). Gas rich mergers may trigger nuclear and global starbursts (Mihos & Hernquist 1994, 1996; Hopkins et al. 2006) and major mergers disrupt the morphologies of the colliding galaxies, often exhibiting long tidal tails or shells of expelled gas and stars soon after the merger has begun. Detecting this can be challenging however, since the single new galaxy has a relaxation time-scale after which morphological features of mergers fade (Tinsley 1978; Kennicutt et al. 1987; Ellison et al. 2013). Observational evidence suggesting a link between major mergers and SMBH accretion has been mixed (e.g. Gabor et al. 2009; Cisternas et al. 2011; Schawinski et al. 2011; Kocevski et al. 2012; Treister et al. 2012; Ellison et al. 2013; Villforth et al. 2014; Kocevski et al. 2015; Villforth et al. 2017). Alternatively, AGNs may be triggered secularly through, for example, disc instabilities (Bournaud et al. 2011), bars (Knapen, Shlosman & Peletier 2000; Oh, Oh & Yi 2012) or otherwise by minor mergers (Kaviraj 2013). It remains unclear whether alternatives to major merger triggering can drive several M⊙ yr−1 of gas to the central SMBHs, as is necessary to power the most luminous AGN.


Kochanek (2009) examined the statistical properties expected for surviving binary companions to SNe assuming passively evolving systems (i.e. no binary interactions). As already noted, the companions are generally significantly fainter than the exploding star, although this is frequently not the case for stripped SN progenitors – for Type Ibc SNe, it should not be surprising to find that the binary companion is more visually luminous than the SN progenitor. This point is of considerable importance for the one candidate Type Ib progenitor iPTF13bvn (Cao et al. 2013, Groh, Georgy & Ekström 2013, Bersten et al. 2014, Fremling et al. 2014, Eldridge et al. 2015, Eldridge & Maund 2016, Folatelli et al. 2016). If the initial binary fraction is F, then the fraction of passively evolving binaries that are in stellar binaries at death is
(1)
\begin{eqnarray}
f_{\rm b} = { F \over 1 + F f_q } \quad {\rm where}\quad f_q = \int _{q_{{\rm min}}}^{q_{{\rm max}}} q^{x-1} P(q) {\rm d}q,
\end{eqnarray}
x ≃ 2.35 is the slope of the initial mass function (IMF), qmin ≤ q = M2/M1 ≤ qmax ≤ 1 is the mass ratio and P(q) with ∫dqP(q) ≡ 1 is the distribution of mass ratios. For a Salpeter IMF and a flat P(q) distribution extending over 0 ≤ q ≤ 1, fq = 0.426 and the fraction of SNe in stellar binaries at death is 23 per cent, 41 per cent, 57 per cent and 70 per cent for initial binary fractions of F = 25 per cent, 50 per cent, 75 per cent and 100 per cent, respectively. Such a flat f(q) distribution is commonly found for massive star binaries, although there is evidence that the widest binaries show a different distribution (e.g. Sana et al. 2012, Kobulnicky et al. 2014, Moe & Di Stefano 2016). Essentially, only the explosions of primaries occur in stellar binaries, so the fraction of SNe in stellar binaries is less than the initial fraction of binaries because some of the SNe are the explosions of secondaries. Binary evolution, particularly stellar mergers then adds further complications, but changes the rough statistics little (e.g. Sana et al. 2012).


We detect 1.33 mm continuum extended emission originating from HD 36546 (see Fig. 3). Peak and integrated flux, size, and inclination are reported in Table 2. Once deconvolved from the beam, the major axis of the disc spans 180 au, compatible with the size reported from scattered light observations (semimajor axis of 85 au, Currie et al. 2017). The inclination is directly provided by the casa tool, as obtained from the ratio of the major and minor axis deconvolved from the beam. The total mass can be estimated by assuming an optically thin dust disc as $M_d = \frac{F_{\nu } d^2}{B_{\nu }(T_{d,c}) \kappa _\nu }$, where Fν is the measured flux at 1.33 mm, d is the distance to the source, Bν is the Planck function at the corresponding dust temperature Td, c, and κν is the mass absorption coefficient that we take as κν = 2 cm2 g−1 following Nilsson et al. (2010). In order to estimate a temperature for the dust, we have fitted a modified blackbody to the available photometry at wavelengths longer than 10 µm (AKARI, WISE, IRAS, Herschel)3 and the new ALMA photometry using the emcee Affine Invariant Markov chain Monte Carlo Ensemble sampler implementation (Foreman-Mackey et al. 2013). This wavelength range was chosen to avoid the silicate emission observed in the mid-IR spectra reported by Lisse et al. (2017) around ∼10 µm. Additionally, there is some discrepancy between the photometric data of WISE, Herschel, and ALMA, and those of IRAS and AKARI. Given their larger point spread functions and lower sensitivites, we decided to exclude the latter two from the fitting. The modified blackbody model assumes all dust grains have the same composition and size, and accounts for changes in the dust emission efficiency (Qλ) via two additional free parameters: β and a reference wavelength λ0, such that the blackbody emission is modified by a factor Qλ = 1 − exp [(λ0/λ)β] (e.g. Williams et al. 2004) Therefore, our model has four free parameters: a scaling factor that controls the disc luminosity, the dust temperature, β, and λ0. Uniform priors were used for all parameters within reasonable ranges: scaling values that produce disc luminosities consistent with the observed photometry, dust temperatures between 20 and 250 K, β values between 0 and 1.5, and λ0 between 0.3 and 300 µm (the latter was explored in log scale). This analysis yields a dust temperature value of 153 ± 3 K, and a β value of 0.24 $^{+0.07}_{-0.05}$ as shown in Fig. 1. λ0 is unconstrained. Adopting this temperature value results in a dust mass of (9.0 ± 1.0) × 10−2 M⊕. Additionally, the resulting models yield Ldisc/L* = (4.43 ± 0.15) × 10−3, compatible with previous results (see Table 1).


We created 10 000 3D models of galaxies, each with an exponential disc plus a Sérsic bulge. We adopted the following functional form for the exponential disc (López-Corredoira et al. 2002): (1)\begin{equation} \label{eq:Corredoira}  \rho(R,z)=\rho_{\mathrm{0}}\cdot\exp{\Bigg(\frac{-R}{h_{R}}\Bigg)}\cdot \exp{\Bigg(\frac{-|z|}{h_{z}(R)}\Bigg)}\cdot \frac{h_{z}(R)}{h_{z}(0)} \cdot \end{equation}ρ(R,z)=ρ0·exp−RhR·exp−|z|hz(R)·hz(R)hz(0)·Following the observations, we explored the effect of a linear increase in the vertical scale height, as follows: (2)\begin{equation} \label{eq:Flares_linear} h_{z}(R) = \begin{cases} h_{z}(0) & \text{if } R \leq R_{\mathrm{flare}} \\ h_{z}(0) + \dhzdR \cdot R & \text{if } R > R_{\mathrm{flare}}. \end{cases} \end{equation}hz(R)=ifR≤RflareifR>Rflare.Graham (2001) analysed a sample of 86 face-on disc-dominated galaxies previously selected by de Jong & van der Kruit (1994). This author performed a bulge + disc decomposition for 69 galaxies in the I-band, correcting for the effects of the internal extinction, Galactic extinction, inclination, and cosmological dimming (Graham 2003), that we used as a reference for our models. We estimated stellar masses using the relationship between the V-band mass-to-light ratio of galaxies and their dust-corrected rest-frame colours derived by Wilkins et al. (2013). According to these authors, for z 0.1 the optimal observed colour is (B − V), so we have estimated this colour for the 69 galaxies of Graham (2003) from HyperLeda data1, and estimated the stellar mass of each galaxy using the relations in Wilkins et al. For those objects without (B − V) available in HyperLeda, we estimated them from their SDSS (g − r) colour following the transformations published in Jester et al. (2005). To simulate realistic images of the disc galaxies, we adopted the observational I-band distributions of Graham (2001, 2003) for the photometric parameters (re, Sérsic index n, hR, μ0, μe, B/T, the absolute magnitudes of the disc Mabs,disc and the bulge Mabs,bulge), and four morphological type bins (S0–Sa, Sb–Sbc, Sc–Scd and Sd–Sdm), in three mass bins (10  log 10M/M⊙ 10.7,10.7  log 10M/M⊙ 11 and log 10M/M⊙> 11) in order to explore realistic mass distributions for the morphological type bins. In Fig. 1 we represent the distributions of the structural and photometric parameters from which we created the models and compared them to the observations they are based on. For each morphological type bin we randomly chose the ratio of scale height to scale length (hz/hR) from the observational range of values corresponding to each type reported by Kregel et al. (2002) and Mosenkov et al. (2015) in the I-band, as shown in Fig. 1.


Other important result we reported in Section 3.3 is the reversing behaviour of red and blue galaxies with respect to velocity and groupcentric distances segregation, with redshift. Regarding velocity segregation, the preceding paragraph provides a qualitative scenario. Now, to explain the spatial segregation, we should notice that our analyses in Sections 3.2 and 3.3 take into account galaxies within 2R/R200. One can reasonably assume that such objects at lower redshifts correspond to a mixture of descendants of galaxies at higher redshifts in the same radii and of infalling objects from outer radii. Thus, both survival and replenishment of galaxies should be expected over the time, and two important factors come into play: (i) the accretion rate of galaxies; and (ii) the orbital dependence of galaxy properties (e.g. Biviano & Katgert 2004; Iannuzzi & Dolag 2012). Indeed, regarding velocity segregation, it has also been interpreted as red and blue galaxies having different kinds of orbits, with the orbits of blue galaxies being more anisotropic than the red ones (e.g. Biviano & Katgert 2004). Recently, Biviano et al. (2016) verified that the anisotropy profile of z ∼ 1 clusters is nearly isotropic near the cluster centre, and increasingly elongated with radius. This result is consistent with a halo evolution through an initial phase of fast collapse and a subsequent slow phase of inside-out growth by accrection of field material (e.g. Lapi & Cavaliere 2009). Since the accretion rate of galaxies from the field is higher at higher redshifts (e.g. McGee et al. 2009), our sample at z ∼ 0.8 is expected to be more affected by recent infalls, which had less time to go deeper into the group potential. This could explain the development of a more marked difference between the mean groupcentric distance of red and blue galaxies (see Fig. 12). After ∼3 Gyr, part of these infalling galaxies may reach the R  2R200 region, at z ∼ 0.4, mixing with virialized and backsplash objects, and thus presenting a less pronounced radial segregation between red and blue galaxies.


Massive stars are believed to exist in the accretion disks of active galactic nuclei (AGNs). Such AGN stars and compact objects can be either the result of in situ formation inside the accretion disk or be captured from the nuclear star clusters around the AGNs (e.g., Artymowicz et al. 1993; Collin & Zahn 1999; Goodman 2003; Goodman & Tan 2004; Wang et al. 2011, 2012; Fabj et al. 2020; Cantiello et al. 2021). These AGN stars will end up with supernovae (SNe), which can eject heavy elements into the disk; this offers a possible explanation for the observational features of high-metallicity environments in AGN disks (e.g., Artymowicz et al. 1993; Hamann & Ferland 1999; Warner et al. 2003). Some compact objects, including white dwarfs (WDs), neutron stars (NSs), and black holes (BHs), can be thus formed within AGN disks. These compact objects can also be captured from the surrounding nuclear star clusters. The disk of an AGN provides a natural environment for stars and compact objects to accrete materials and to migrate within it (e.g., McKernan et al. 2012; Yang et al. 2020; Dittmann et al. 2021; Jermyn et al. 2021; Wang et al. 2021; Tagawa et al. 2021; Kimura et al. 2021). Some of these stars can be very massive and have high spin caused by accretion (Dittmann et al. 2021; Jermyn et al. 2021), so that they can easily produce high-spin stellar remnants. Abundant compact objects, especially with the presence of the massive BHs (M > 10M⊙), would likely accrete, collide, and merge within the trapping orbits, and hence would grow into ∼100 M⊙ intermediate-mass BHs (McKernan et al. 2012; Secunda et al. 2019; Yang et al. 2019b). Some AGN stars can be tidally disrupted by these BHs that can power micro-tidal disruption events (Yang et al. 2021). The death of high-spin stars and neutron star mergers are expected to power gamma-ray burst (GRB) jets, which would be always choked by the dense atmosphere of the disks (Zhu et al. 2021a, 2021b; Perna et al. 2021a). Zhu et al. (2021a) suggested that these choked jets can produce high-energy neutrinos that may contribute a substantial fraction of the diffuse neutrino background. A candidate electromagnetic (EM) counterpart that emerged from an AGN, explained as ram pressure stripping of gas within the kicked BH hill sphere colliding with the AGN disk gas (McKernan et al. 2019), was reported by the Zwicky Transient Facility (Graham et al. 2020). This was thought to be associated with a (85 + 66)M⊙ binary BH merger (GW190521) detected by the LIGO/Virgo collaboration (Abbott et al. 2020). This connection provided plausible evidence of a potentially important AGN channel for compact star mergers.


Filippenko & Chornock (2001) first presented the dynamical estimate of mass of the source to be around 7.4 ± 1.1 M⊙. Recently, Radhika & Nandi (2014) claimed that the mass of XTE J1859+226 is perhaps in between 6.58 and 8.84 M⊙ which is similar to the prediction of Shaposhnikov & Titarchuk (2009), although the lower mass limit is estimated as 5.4 M⊙ by Corral-Santana et al. (2011). However, we consider the typical mass of the source as 7 M⊙. The distance of this source is around d ∼ 11 kpc (Filippenko & Chornock 2001). Steiner et al. (2013) measured the spin as ak ∼ 0.4; however, Motta et al. (2014b) recently reported that the spin of the source is ak ∼ 0.34. Since the spin predictions are quite close, we use ak ∼ 0.4 for this analysis. We estimate the fluxes Fx (see Table 1) of LHS and HIMS of the 1999 outburst of the source (Radhika & Nandi 2014). The corresponding disc luminosities are calculated as $L_{\rm disc}^{{\rm LHS}}=8.26 \times 10^{37}\ {\rm erg\ s^{-1}}$ and $L_{\rm disc}^{{\rm HIMS}}=1.85 \times 10^{38}\ {\rm erg\ s^{-1}}$, respectively. Now, it is reasonable to assume the accretion efficiency for rotating BH as η = 0.3 which corresponds to the accretion rate of the inflowing matter as ${\dot{M}}_{{\rm acc}}^{{\rm LHS}} = 0.304 {\dot{M}}_{{\rm Edd}}$ in LHS and ${\dot{M}}_{{\rm acc}}^{{\rm HIMS}} = 0.680 {\dot{M}}_{{\rm Edd}}$ in HIMS. For LHS, we use $R_{\dot{m}}=9.83$ per cent following our theoretical estimate where xs = 64.6rg for ak = 0.4, ${\mathcal {E}}=0.001\,98$ and λ = 3.18. Incorporating these inputs in equation (15), we obtain the jet kinetic power as $L^{{\rm LHS}}_{{\rm jet}} = 2.52\times 10^{37}\ {\rm erg\ s^{-1}}$. The maximum mass outflow rate for HIMS corresponding to ak = 0.4 is obtained from Fig. 9 as $R^{\rm max}_{\dot{m}}=17.5$ per cent for ${\mathcal {E}}=0.005\,47$ and λ = 3.1, where the shock transition occurs at 21.9rg. Using these values in equation (15), we obtain the maximum jet kinetic power as $L^{{\rm HIMS}}_{{\rm jet}} = 1.08\times 10^{38}\ {\rm erg\ s^{-1}}$ which we regard to be associated with the HIMS of this source.


An implication of the respective escape fractions of the two regimes is visible in Fig. 12. Here we show several values of NHI,cl for the static setup using τd,cl = 10-4 (empty symbols) and τd,cl = 1 (filled symbols), which correspond to metallicities of \hbox{$Z/Z_\odot = 0.63\left(\tau_{\rm d}/10^{-4}\right)\left(10^{17}\cm^{-2}/N_{\HI,\cl}\right)$}Z/Z⊙=0.63τd(/10-4)(1017 cm-2/NHI,cl) (Pei 1992; Laursen et al. 2009); this reaches clearly unrealistic values. However, as in this paper we are interested in the fundamental impact of the individual parameters, we also study these extreme values. Also shown in Fig. 12 (with a black [gray] solid line for the low [high] dust content) is the proposed analytic solution for fesc by Hansen & Oh (2006)(18)\begin{equation} f_{\rm esc}^{\rm HO06} = 1/{\rm cosh}(\!\sqrt{2 N_{\cl}\epsilon}), \label{eq:fescHO06} \end{equation}fescHO06=1/cosh(2Nclϵ),where for Ncl we used Eq. (8)(with (a1,b1) = (3/2, 2) as found in Sect. 4.1) and for the clump albedo (i.e., the fraction of incoming photons that are reflected) ϵ, we adopted a value of c1(1−e− τd,cl) with c1 = 1.6 [c1 = 0.06] to match the NHI,cl = 1022 cm-2 data points for τd,cl = 10-4 [τd,cl = 1]. The behavior for the low- and high-dust contents is quite different. On the one hand, the escape fractions versus NHI,cl scales for τd,cl = 1 (filled symbols in Fig. 12) as predicted by Hansen & Oh (2006) in their “surface scatter” approximation, that is, a larger clump hydrogen column density “shields” the dust better from the Lyα photons and thus prevents their destruction more efficiently. On the other hand, however, this is not the case for the low-dust scenario presented in Fig. 12 (with unfilled symbols) where a larger value of NHI,cl implies a lower fesc. This is because here the dust optical depth through all the clumps (shown in the black dotted line in Fig. 12) is lower than the accumulated dust optical depth through the subsequent random-walk clump encounters (black solid line), i.e., \hbox{$\exp(-4/3 \fc \tau_{\rm d, cl}) \lesssim f_{\rm esc}^{\rm HO06}$}exp(−4/3fcτd,cl)≲fescHO06. Consequently, configurations in the “free-streaming” regime can possess enhanced Lyα escape fractions compared to the “random walk” regime (see Sect. 5.2 for a more detailed discussion). Still, both cases possess (much) larger escape fractions than a homogeneous slab, which is shown in Fig. 12 with a black dashed line. Here, we use the derived escape fraction by Neufeld (1990) with NHI = 4/3 × fc1022 cm-2 and τd = 4/3fcτd,cl, i.e., with equal column densities as in the NHI,cl = 1022 cm-2 case.


From the early days of detection the weak lensing (Munshi et al. 2008) studies have matured to a point where weak lensing results from Euclid are expected to constrain the cosmological parameters to sub-per cent accuracy. However, weak lensing at smaller angular scales probes the non-linear regime of gravitational clustering, and is thus key to understanding the non-Gaussianity induced by the non-linearity and fullly exploiting in the weak lensing maps. The higher order statistics are also useful for the breaking of parameter degeneracies in studies involving the power spectrum analysis alone and they are also important in understanding the variance or error of estimation of lower order statistics. These higher order statistics including the cumulants (Bernardeau 1994b) and their correlators (Bernardeau 1996a; Calabrese et al. 2010; Munshi et al. 2011; Riquelme & Spergel 2012) are among the best-known diagnostics of the deviation from Gaussianity that characterizes the non-linear regime (Bartolo et al. 2004), with a long history analytical modelling (Bernardeau et al. 2002a). Most of these studies use extensions of perturbative results in the quasi-linear regime valid at large smoothing angular scales or variants of halo models (Cooray & Sheth 2002). Early studies concentrated on measurements of higher order correlation hierarchy in the angular space due to small survey size (Bernardeau, Mellier & van Waerbeke 2002b; Bernardeau, Waerbeke & Mellier 2003). However, the near all-sky coverage of future surveys such as Euclid will let us estimate higher order statistics in the harmonic domain with unprecedented accuracy (Amendola et al. 2013). While measurements of real space correlations are much simpler in the presence of complicated survey design, the measurements for different angular scales can be highly correlated (Munshi 2000; Munshi & Jain 2000). In comparison measurements in the harmonic domain are less correlated and each mode contains (nearly) independent information in the limit of all-sky coverage. The primary motivation of this study is to develop analytical predictions for one such statistic called the skew-spectrum, and test them against numerical simulations. We will borrow the concepts developed for constructing skew-spectra for the study of non-Gaussianity in the context of CMBR observations (Planck Collaboration XVII2016b). However, we also include gravity-induced secondary non-Gaussianity. The skew-spectrum is the lowest order member in the family of higher order spectra (Munshi et al. 2011a, 2020). In a series of papers, the one-point statistics such as the skewness and kurtosis were generalized to two-point cumulant correlator, e.g. the two-to-one correlator and its higher order generalizations. These can be represented in the harmonic domain by their associated spectra such as the skew-spectrum (Munshi & Heavens 2010) and its higher order generalizations (Munshi et al. 2011a, 2020). These spectra have already been used to analyse WMAP9 (Smidt et al. 2010) as well as Planck data (Planck Collaboration XVII2016b). They are useful tools to separate individual contributions and estimate systematics. In this paper, we will concentrate on the projected skew-spectrum and kurt-spectrum in the context of weak lensing surveys (Munshi et al. 2011c).


Analyses of 21-cm signals are mainly based on traditional N-point correlation statistics. Beyond the simplest two-point function (power spectrum), higher-order correlations are quite non-trivial to calculate and sometimes they suffer from conceptual challenges. On the other hand, the Minkowski functionals (MFs) are extremely useful tools in quantitatively describing the morphology because, in principle, they contain information on all the higher-order moments. The MFs were first introduced in cosmology by Mecke, Buchert & Wagner (1994). Since then they have been extensively employed to study the morphology of the large-scale structure of the universe and the cosmic web (Schmalzing & Buchert 1997; Sahni, Sathyaprakash & Shandarin 1998; Sathyaprakash, Sahni & Shandarin 1998; Bharadwaj et al. 2000; Hikage et al. 2003; Bharadwaj, Bhavsar & Sheth 2004; Pandey & Bharadwaj 2008; Einasto et al. 2011; Wiegand & Eisenstein 2017) as well as the CMB (Schmalzing & Gorski 1998; Novikov, Feldman & Shandarin 1999; Novikov, Schmalzing & Mukhanov 2000; Hikage, Komatsu & Matsubara 2006). Since the reionization landscape is similarly rich in geometrical properties because of growth and overlap of ionized ‘bubbles’, studying the morphology of reionization using MFs is highly compelling and feasible. The physics underlying the reionization process is expected to be manifested in the geometry and morphology of H i and H ii regions. The ratios of MFs are introduced in Sahni et al. (1998) as Shapefinders that precisely assess the shape of an object by directly estimating its physical dimensions. Therefore, using MFs and Shapefinders of the ionization field, it should be possible to probe the physics of the high-redshift universe. For instance, if reionization is driven in a non-standard manner through large energy output from multiple quasar jets, the very first ionized bubbles might be filamentary and not spherical (as they would be for point-like sources like stars in galaxies). Clearly the 3D structure of cosmological reionization in this scenario would be very different from the standard mechanism of point-like sources.


During the likelihood analysis, the normalizations and spectral parameters of all sources within 5° of 3FGL J1640.4-4634c, as well as the normalizations of the two diffuse backgrounds, are left free. First, we create a Test Statistic (TS) map by subtracting the emission from the sources and backgrounds in the best-fit model with gttsmap, which is shown in the top panel of Figure 1. Some residual emission are shown in this TS map. Then we add additional point sources with power-law spectra in the model. The accurate positions of these sources obtained using the gtfindsrc tool, together with their TS values, are listed in Table 1. Next, we adopt the position of 3FGL J1640.4-4634c provisionally provided by the 3FGL catalog (Acero et al. 2015) and investigate the spectrum of 3FGL J1640.4-4634c. We bin the data into 12 equal logarithmic energy bins from 1 to 500 GeV and repeat the same likelihood fitting for each energy bin. In the model, the normalization parameters of sources within 5° around 3FGL J1640.4-4634c and the two diffuse backgrounds are left free, while all spectral indices, except 3FGL J1640.4-4634c, are fixed. The 95% upper limits are calculated for energy bins with TS values smaller than 4. The resulting spectral energy distribution (SED) is shown in the bottom panel of Figure 1. An obvious spectral upturn is shown in the SED of 3FGL J1640.4-4634c at an energy of about 10 GeV. To test whether the upturn spectrum is intrinsic or is due to two overlapping sources, we do the same likelihood fitting using the events with energies of 1–10 GeV and 10–500 GeV, respectively. For each analysis, we create a TS map with all sources (except 3FGL J1640.4-4634c) included in the model, which are shown in the Figure 2. The TS maps show a clear difference between two energy bands, and the centroids of emission in both energy bands deviate from that of 3FGL J1640.4-4634c. We thus expect that 3FGL J1640.4-4634c should consist of two different sources (labeled as “Source A” for the 1–10 GeV source and “Source B” for the 10–500 GeV source), and the source in the 3FGL catalog is simply the sum of these two sources.


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


The exploration of the Universe out to times earlier than the point of complete reionization is rapidly advancing. One of the most informative probes of these epochs is the 21-cm line produced by hydrogen atoms in the neutral intergalactic medium (IGM) at redshifts z > 6. This line redshifts to frequencies below 200 MHz and can be detected by low-frequency radio telescopes. Global 21-cm experiments measure the spectrum of this line averaged over the sky. The first tentative detection of the Cosmic Dawn signal was recently made by the Low-Band implementation of the Experiment to Detect the Global EoR Signature (EDGES, Bowman et al. 2018). Other global 21-cm experiments, including the Large-Aperture Experiment to Detect the Dark Ages (Bernardi et al. 2016; Price et al. 2018), the EDGES High-Band (Bowman & Rogers 2010; Monsalve et al. 2017, 2018, 2019), and the Shaped Antenna measurement of the background RAdio Spectrum (Singh et al. 2017, 2018), provide upper limits on the signal from Cosmic Dawn and the Epoch of Reionization (EoR), ruling out some extreme astrophysical scenarios. A parallel effort is being made by interferometric radio arrays that are placing upper limits on the fluctuations of the 21-cm signal, including the Donald C. Backer Precision Array for Probing the Epoch of Reionization (Kolopanis et al. 2019), the Low Frequency Array (LOFAR, Patil et al. 2017; Gehlot et al. 2019; Mertens et al. 2020), the Giant Metrewave Radio Telescope (Paciga et al. 2013), the Murchison Widefield Array (Beardsley et al. 2016; Barry et al. 2019; Li et al. 2019; Trott et al. 2020), and the Owens Valley Radio Observatory Long Wavelength Array (Eastwood et al. 2019). The most recent upper limit reported by LOFAR (Mertens et al. 2020) made it possible to place (weak) upper limits on the temperature of the neutral gas and ionization state of the Universe at z = 9.1 (Ghara et al. 2020; Mondal et al. 2020). Upcoming arrays, including the Hydrogen Epoch of Reionization Array (DeBoer et al. 2017), the Square Kilometer Array (Koopmans et al. 2015), and the New Extension in Nancay Upgrading LOFAR (Zarka et al. 2012), will provide measurements of the power spectrum over a wide range of scales and redshifts.


It was soon realized that these frequencies are probably related to oscillations of the neutron star, and several groups tried to identify them as elastic oscillations of the crust (Duncan 1998; Messios et al. 2001; Strohmayer & Watts 2005; Piro 2005; Sotani et al. 2007; 2013, 2016; Samuelsson & Andersson 2007, 2009; Steiner & Watts 2009; Deibel et al. 2014), Alfvén oscillations (Cerdá-Durán et al. 2009; Sotani et al. 2008; Colaiuda et al. 2009), or coupled magneto-elastic oscillations (Levin 2006; 2007; Glampedakis et al. 2006; Gabler et al. 2011; 2012; Colaiuda & Kokkotas 2011; van Hoven & Levin 2011, 2012). The theoretical models based on the observed frequencies are very elaborate and may be able to constrain properties of high-density matter as found in the interior of neutron stars. Some of the models, for instance, require a superfluid component in the core of the star (van Hoven & Levin 2011, 2012; Glampedakis et al. 2011; Passamonti & Lander 2013, 2014; Gabler et al. 2013; 2016, and in prep.). Different models depend sensitively on the identification of the fundamental oscillation frequency, and may not explain all of the observed frequencies. Even when the fundamental frequency is identified, the interpretation and parameter estimation is not yet straightforward because of degeneracies in the parameter space. However, keeping other stellar parameters fixed, some general trends of the fundamental oscillation frequency can be summarized as follows (see Gabler et al. 2016, and in prep. for a detailed discussion): i) The frequency scales linearly with the magnetic field strength. ii) It decreases with increasing compactness (Sotani et al. 2008). The compactness is related to the hardness of the equation of state (EOS): Material with a stiff equation of state is harder to compress, leading to larger radii and hence lower compactnesses. iii) It can only reach the surface for significantly strong magnetic fields
$\bar B\gtrsim\bar
B_\text{outbreak}(\sqrt{c_s})$

B̄≳B̄outbreak(cs)

, whose thresholds depend on the square root of the shear velocity (Gabler et al., in prep.).


The polarimetric observations with ALMA at 0.87 mm toward B335 were conducted during 2016 to 2018, consisting of 13 successful executions (project code: 2015.1.01018.S). In the observations, 40–47 antennae were used in the configurations with baseline lengths ranging from 15 to 1400 m. The pointing center was α(J2000) = 19h37d00.s89, δ(J2000) = +7°34′096. The on-source integration time was 7.4 hr. The observations were conducted with the full polarization mode and at the frequency ranges of 335.5–339.5 GHz and 347.5–351.5 GHz with a total bandwidth of 8 GHz. In these observations, J1751−0939 was observed as the bandpass calibrator, J1938 + 0448 or J1935 + 2021 as the gain calibrators, and J1924−2914 or J2000−1748 for polarization calibration. The flux calibration was performed with the observations of quasars or the asteroid, Pallas. The data were manually calibrated by the EA ARC node using the Common Astronomy Software Applications (CASA) of the version 5.1.1 (McMullin et al. 2007). We additionally performed self-calibration of the phase using the Stokes I data. Then the calibrated visibility data were Fourier-transformed with the Briggs weighting with a robust parameter of +0.5 to generate Stokes IQU images, and the images were cleaned using the CASA task tclean. The achieved synthesized beam is 019 × 017. The noise level in the Stokes I image is 40 μJy beam−1, and it is 9 μJy beam−1 in the Stokes Q and U images. When we generated the polarized intensity (Ip) map, we debiased the polarized intensity (Ip) with

, where σQ, U is the noise level in Stokes Q and U (Wardle & Kronberg 1974; Simmons & Stewart 1985). To extract polarization detections, we first binned up the Stokes IQU and Ip maps to have a pixel size of 01, which is approximately half of the beam size, and computed polarization orientations and fractions. Thus, the minimal separation between two polarization detections is 01. The Stokes I and Ip maps with their original pixel size of 002 are presented below. The polarization detections are extracted when the signal-to-noise ratios (S/N) of both Stokes I and Ip are larger than three, and thus the expected uncertainties in the polarization orientations are ≲9°.


We fit the total foreground absorption column by applying two-component multiplicative absorption models, tbabs and tbnew.
8

8

https://pulsar.sternwarte.uni-erlangen.de/wilms/research/tbabs/
 The absorption component tbabs accounts for the Galactic absorption column N
H,Gal, and it is fixed at N
H,Gal = 6 × 1020 cm−2 (Dickey & Lockman 1990). The second absorption component, tbnew, accounts for the LMC absorption column, N
H,LMC and is varied in the fits. We use tbnew as the absorption column for LMC as it allows us to set individual elemental abundances associated with N
H,LMC at their respective LMC values. Recent measurements of the LMC abundances based on the X-ray spectral analysis of SNRs (Maggi et al. 2016; Schenck et al. 2016) suggest ∼50% lower LMC abundance values for O, Ne, Mg, and Fe than the previously estimated values (Hughes et al. 1998). Our derived shock parameters are consistent (within statistical uncertainties), assuming either set of these LMC abundances in tbnew. We tie N
H,LMC among all the fitted spectra, assuming no temporal variation in the LMC column for SNR 1987A. We obtain a best-fit total absorption column density,

NH=NH,Gal+NH,LMC=2.17−0.22+0.22×1021cm−2

. This value is comparable to estimates of N
H obtained by other X-ray analyses:

2.35−0.08+0.09×1021cm−2

 (Park et al. 2006),

1.44−0.12+0.16×1021cm−2

(Zhekov et al. 2009), and

2.60−0.05+0.05×1021cm−2

 (Alp et al. 2021). We note that more recent H i surveys have suggested much higher N
H,Gal values toward the LMC, i.e., ∼(2.5–4) × 1021 cm−2 (Kalberla et al. 2005; Willingale et al. 2013; HI4PI Collaboration et al. 2016). By adopting these high Galactic columns, the overall fits are equally good, but this results in a negligible LMC column. The implied negligible LMC column does not appear to be reasonable because optical extinction estimates show that the LMC contribution is greater than the Milky-Way contribution (Fitzpatrick & Walborn 1990; France et al. 2011). A detailed analysis of the contribution of the Galactic N
H toward total absorption column density is beyond the scope of our work. While this issue was similarly outlined by Alp et al. (2021) in relation to their analysis of the XMM-Newton data of SNR 1987A, we note that the total columns (Galactic + LMC) are generally consistent between either values of the Galactic column, and thus that the best-fit parameters in our spectral model fits (i.e., electron temperatures, ionization age, abundances, and volume-emission measures) are not significantly affected (within statistical uncertainties).


The B/T ratio of a galaxy is the fraction of total luminosity contributed by the bulge component of the galaxy. Bulges are the central component of disc galaxies which appear as central bright cores in galaxy images or as excess-light over the disc light in the inner region of galaxy light profiles. The B/T ratio is an important indicator of galaxy structure and is well correlated with several other physical quantities of interest in studies of galaxy evolution, such as galaxy morphology (Graham & Worley 2008), kinematics (Cappellari et al. 2013), stellar mass, and star formation rate (Bluck et al. 2014). The B/T ratio also directly determines the bulge luminosity which in turn correlates with the mass of the central supermassive black hole of the galaxy (Kormendy & Richstone 1995; Marconi & Hunt 2003; Kormendy & Ho 2013). Galaxies having different B/T ratios are thought to have undergone evolution along different evolutionary paths. A high value of B/T of a galaxy generally indicates its evolutionary history dominated by galaxy mergers (Hopkins et al. 2010). On the other hand, majority of low B/T systems are often pseudobulge hosting galaxies (Fisher & Drory 2008; Gadotti 2009) which are thought to undergo slow evolution through internal, secular evolution processes (Kormendy & Kennicutt 2004). It must be noted that unlike visual morphology which is a qualitative measure, the B/T ratio is a quantitative measure of the galaxy morphology. It is the only reliable way to separate ellipticals and disc galaxies when morphological features such as spiral arms cannot be resolved by the telescope (due to resolution or sensitivity limitations, particularly at high redshifts). The quantitative nature of the B/T ratio also allows direct comparison of galaxies with their counterparts in cosmological simulations. One can study these simulated galaxies to understand the origin of various properties of real galaxies. All these factors make the B/T ratio an important parameter to measure in studies of galaxy formation and evolution.


Supermassive black holes (SMBH) with masses M• ∼ 109–1010

 are recognized to be present at redshifts as high as z ≃ 6–7.5, when the universe was 650–800 Myr young (Fan et al. 2003; Willott et al. 2010; Mortlock et al. 2011; Bañados et al. 2014, 2018; Wu et al. 2015; Decarli et al. 2018; Izumi et al. 2019)—in total more than 150 such SMBHs are already known (see, e.g., Fan et al. 2019). Their origin remains elusive—it is unclear how massive their seeds were, how efficient their growth rate was, and what was the mass reservoir for their growth. To fit the existence of the quasars J0100 + 2802 (z = 6.33), J1120 + 0641 (z = 7.09), and J1342 + 0928 (z = 7.54) with SMBH masses M• = 1.2 × 1010,  2 × 109, and 7.8 × 108

 respectively, one has to assume that their masses grow as M• = M•,0 exp [t/(47 Myr)], corresponding to the standard Eddington limit with a 10% radiative efficiency , the Salpeter growth time tS = cσT/(4πGmp) = 47 Myr, and the seed mass M•,0 ≥ 103

 at z ≥ 40 (Bañados et al. 2018). In this scenario SMBHs have to begin growing even earlier than the very first stars are assumed to have appeared (see discussion in Barkana & Loeb 2001). Moreover, it suggests that the accretion is tightly tuned to the Eddington rate, which seems physically unlikely (see discussion in Haiman & Loeb 2001; Volonteri & Rees 2005; Haiman 2013; Alexander & Natarajan 2014; Madau et al. 2014). Lower-mass black holes with M• ∼ 100

, originated from Population III stars, are apparently unlikely to serve as seeds for growing SMBHs, because photoionization and photoheating from their massive progenitors strongly suppress further supply of cold mass onto the BH (Johnson & Bromm 2007), and would require even more time for the black hole to grow. Note, however, that this channel for SMBH seeds is currently widely discussed (see references in Natarajan et al. 2019). Also note that this problem of the presence of such enormously massive BHs in a younger than 1 Gyr universe can be to a certain extent eased when possible magnification of z > 6 SMBHs due to gravitational lensing is considered (Fan et al. 2019; Pacucci & Loeb 2019a, 2019b). Recent millimeter observations of the quasar J0100 + 2802 (z = 6.33) with the most massive BH, M• ∼ 1.2 × 1010

, known at z > 6, indicate strong lensing with a magnification factor of ∼450 (Fujimoto et al. 2019). As a result, the estimate of the SMBH mass may be reduced by more than an order of magnitude, though this still remains exceedingly large for a 1 Gyr universe ∼109

 (Fujimoto et al. 2019). The fraction of so strongly magnified quasars is fairly low considering the very small typical angular size of such lenses, as a rule ≪1″ (see, e.g., Pei 1995; Bolton et al. 2008; Pacucci & Loeb 2019b).


Galaxy interactions represent a fundamental component of our current view of hierarchical galaxy evolution. Studies based on both observations and simulations have shown that galaxy collisions and mergers can dramatically affect the galaxies undergoing the interaction, by, e.g. triggering nuclear activity (e.g. Kennicutt 1984; Kennicutt et al. 1987; Ellison et al. 2011, 2013a; Silvermann et al. 2011; Satyapal et al. 2014), producing colour changes (e.g. Larson & Tinsley 1978; Darg et al. 2010; Patton et al. 2011), disrupting morphologies (e.g. Kaviraj et al. 2011; Patton et al. 2016; Lofthouse et al. 2017), and altering the metallicities (e.g. Rupke et al. 2010; Perez, Michel-Dansac & Tissera 2011; Scudder et al. 2012; Torrey et al. 2012). The most evident effect driven by galaxy encounters is probably the triggering of new episodes of star formation, which can occur both in the pre-merger regime between first pericentre and coalescence (e.g. Nikolic, Cullen & Alexander 2004; Ellison et al. 2008, 2013b; Patton et al. 2011; Scudder et al. 2012), and in the post-merger phase, where the two nuclei of the interacting galaxies have merged together (e.g. Kaviraj et al. 2012; Kaviraj 2014; Ellison et al. 2013a). The idea that galaxy mergers have a strong impact on the star formation activity is supported by studies of Ultra-Luminous InfraRed Galaxies (ULIRGs), i.e. galaxies with IR luminosities exceeding 1012 L⊙ and characterized by star formation rates (SFRs) up to ∼1000 M⊙ yr−1 (e.g. Barnes & Hernquist 1991; Mihos & Hernquist 1994; Daddi et al. 2010; Scoville et al. 2015). Observations have revealed that the majority of ULIRGs reside in interacting systems (e.g. Sanders & Mirabel 1996; Veilleux, Kim & Sanders 2002; Kartaltepe et al. 2010, 2012; Haan et al. 2011). Nevertheless, ULIRGs are rare and extreme examples of highly star-forming galaxies. Most galaxy–galaxy interactions result in SFR increases of at most a factor of a few, as shown in both numerical simulations (e.g. Di Matteo et al. 2008) and observations of galaxy pairs and post-mergers (Ellison et al. 2008; Martig & Bournaud 2008; Jogee et al. 2009; Robaina et al. 2009; Scudder et al. 2012).


Detections of ionic, atomic, and molecular species in exoplanetary atmospheres serve as a unique and strong diagnostic of those chemical and dynamical processes driving their formation and evolution. Their detection and abundance measurements could act as indicators of planetary formation scenarios and reveal connections to the primordial protoplanetary disc and the host star (Williams & Cieza 2011; Mordasini et al. 2016; Madhusudhan et al. 2017). Furthermore, discoveries of atmospheric chemical species allow us to better understand various thermodynamical processes and chemistry, winds in the upper atmosphere (Goodman 2009; Snellen et al. 2010; Brogi et al. 2016; Madhusudhan et al. 2016; Wyttenbach et al. 2020), and to probe planetary interiors and various bulk properties through their abundances (Kite et al. 2016; Thorngren & Fortney 2019; Madhusudhan et al. 2020). A whole host of ions, atoms, and molecules have been detected through a variety of, often complementary, techniques, such as differential spectrophotometry using low-to-mid resolution spectroscopy (e.g. Gibson et al. 2012, 2017; Deming et al. 2013; Kreidberg et al. 2014; Kirk et al. 2016; Nortmann et al. 2016), and high resolution spectroscopic techniques (e.g. Redfield et al. 2008; Snellen et al. 2008; Rodler, Lopez-Morales & Ribas 2012; Birkby et al. 2013; Hoeijmakers et al. 2015, 2018, 2020; Brogi et al. 2016; Birkby et al. 2017; Žák et al. 2019; Ehrenreich et al. 2020). To date, ionic species such as Fe ii and Ti ii (Hoeijmakers et al. 2019), atomic absorption from Na, K, H α, and He (e.g. Redfield et al. 2008; Sedaghati et al. 2016; Casasayas-Barris et al. 2017; Spake et al. 2018; Chen et al. 2020; Seidel et al. 2020), and molecules such as H2O, CH4, and CO (e.g. Konopacky et al. 2013; Brogi et al. 2014; Fraine et al. 2014; Barman et al. 2015; Sing et al. 2016) have been detected through the aforementioned techniques. Needless to say that this list of detected constituents is by no means exhaustive, nor that of methods employed to detect exoplanetary atmospheres. For instance, high-resolution imaging instruments such as SPHERE (Beuzit et al. 2019) and GRAVITY (Gravity Collaboration et al. 2017), both at the VLT (ESO’s Very Large Telescope), through combination with low-dispersion spectroscopy, have facilitated direct measurements of exoplanetary atmospheres (Samland et al. 2017; Gravity Collaboration et al. 2020).


Galactic BHXBs offer excellent laboratories in which to study jet interaction zones, as their jets evolve on day to month time-scales, they are located at nearby distances, and they are thought to be good analogues for AGNs. Given their incredible diagnostic potential, over the last couple of decades there have been many observational campaigns searching for these highly sought after interaction sites near BHXBs. To date, several candidate jet–ISM interaction sites have been identified; SS 433 (Dubner et al. 1998), Cygnus X–1 (Gallo et al. 2005; Russell et al. 2007), 1E 1740–2942 (Mirabel et al. 1992), GRS 1758−258 (Martí et al. 2002), GRS 1915+105 (Rodríguez & Mirabel 1998; Chaty et al. 2001; Kaiser et al. 2004), H1743–322 (Corbel et al. 2005), XTE J1550–564 (Corbel et al. 2002; Kaaret et al. 2003; Migliori et al. 2017), XTE J1748–288 (Brocksopp et al. 2007), GRO J1655–40 (Hjellming & Rupen 1995; Hannikainen et al. 2000), GX 339-4 (Gallo et al. 2004), 4U 1755–33 (Kaaret et al. 2006), XTE J1752–223 (Yang et al. 2010; Miller-Jones et al. 2011; Yang et al. 2011; Ratti et al. 2012), XTE J1650–500 (Corbel et al. 2004), XTE J1908+094 (Rushton et al. 2017), 4U 1630–47 (Neilsen et al. 2014; Kalemci, Maccarone & Tomsick 2018), LMC X–1 (Russell et al. 2006; Cooke et al. 2007; Hyde et al. 2017), and GRS 1009–45 (Russell et al. 2006). From these past works, it is clear that finding and confirming interaction sites can be incredibly difficult and often observationally expensive (e.g. requiring deep, wide-field radio continuum observations). This difficulty mainly results from the fact that interaction sites can manifest with a wide variety of morphologies and emission properties, likely dependent on the properties of the BHXB (e.g. space velocity; Miller-Jones et al. 2008; Heinz et al. 2008; Wiersema et al. 2009) and/or local ISM properties (e.g. density; Heinz 2002; Kaiser et al. 2004). Once identified, detailed calorimetric calculations of interaction sites are highly sensitive to the properties of the ISM (i.e. density, kinetic temperature, shock velocity; Russell et al. 2007; Sell et al. 2015), and thus require accurate constraints on the physical conditions in the interacting gas, which cannot be derived with continuum observations alone. Therefore, developing and implementing new methods that allow us to identify and place improved observational constraints on these parameters at multiple interaction sites, is crucial for taking full advantage of the diagnostic potential of these regions.


In 2018, a deep spectral feature centred at 78 MHz was reported by the EDGES collaboration (Bowman et al. 2018). The feature was presented as the long sought-after 21-cm absorption feature seen against the CMB during the CD at z ∼ 17. The location of this putative absorption trough is consistent with redshift predictions from theoretical models and simulations of the CD (Furlanetto et al. 2006; Pritchard & Loeb 2010; Mesinger, Ferrara & Spiegel 2013; Cohen et al. 2017). However, the depth of the feature is ΔT21 ∼ 0.5 K ($99{{\ \rm per\ cent}}$ confidence level), which is two to three times stronger and considerably wider (Δν ∼ 19 MHz) than that predicted by the most optimistic astrophysical models (e.g. Pritchard & Loeb 2010; Fialkov, Barkana & Visbal 2014; Fialkov & Loeb 2016; Cohen et al. 2017). Moreover, the observed feature is flat-bottomed instead of a smooth Gaussian-like shape. Several ‘exotic’ theoretical models have already been proposed which might explain the depth of the feature, such as a considerably colder IGM due to interaction between baryons and dark matter particles causing a lower spin-temperature and therefore a deeper absorption feature (e.g. Barkana 2018; Fialkov, Barkana & Cohen 2018), or a stronger radiation background against which the absorption is taking place (e.g. Dowell & Taylor 2018; Ewall-Wice et al. 2018; Feng & Holder 2018; Fialkov & Barkana 2019). Although the 21-cm signal is expected to be stronger at these redshifts, the foreground emission is several times brighter at these frequencies compared to EoR 21-cm signal observations at 150 MHz (Bernardi et al. 2009, 2010). Moreover, ionospheric effects are amplified at lower frequencies (de Gasperin et al. 2018; Gehlot et al. 2018), rendering the measurement of the signal equally (or even more) challenging than in EoR experiments. As of now, Ewall-Wice et al. (2016) reported a systematics-limited power spectrum upper limit of $\Delta _{21}^2 \lt (10^4~\text{mK})^2$ on co-moving scales $k\lesssim 0.5~h\, \text{cMpc}^{-1}$ (in 3 h of integration) on the 21-cm signal brightness temperature in the redshift range 12 ≲ z ≲ 18 using MWA. This overlaps with the low-redshift edge of the 21-cm absorption feature (Bowman et al. 2018). Gehlot et al. (2019) provided a 2σ upper limit of $\Delta _{21}^2 \lt (1.4\times 10^4~\text{mK})^2$ on the 21-cm signal power spectrum at $k = 0.038~h\, \text{cMpc}^{-1}$ (in 14 h of integration) using the LOFAR-Low Band Antenna (LBA) system in the redshift range 19.8 ≲ z ≲ 25.2, which corresponds to the high-redshift edge of the absorption feature. More recently, Eastwood et al. (2019) used OVRO-LWA observations to report a 2σ upper limit of $\Delta _{21}^2 \lt (10^4~\text{mK})^2$ at $k \approx 0.1~h\, \text{cMpc}^{-1}$ (in 28 h of integration) at redshift z ≈ 18.4.


The lifetime of molecular clouds (MCs) remains an active research topic in the study of the interstellar medium and star formation, and most recent studies, both observational and theoretical, place this lifetime at a few times 107 yr for clouds in the 105–106M⊙ mass range (e.g. Blitz & Shu 1980; Kawamura et al. 2009; Zamora-Avilés, Vázquez-Semadeni & Colín 2012; Zamora-Avilés & Vázquez-Semadeni 2014; Lee, Miville-Deschênes & Murray 2016). In addition, several observational studies have suggested that the star formation rate (SFR) of the clouds appears to increase over their lifetimes. For example, studies of young clusters embedded in moderate-mass MCs (∼104M⊙) (e.g. Palla & Stahler 1999, 2000; Da Rio et al. 2010) have shown that their age histograms contain a large majority of young (1–2 Myr) objects, but also a tail of older (up to several Myr) ones suggesting an accelerating star formation activity, sometimes followed by a subsequent decline (see also Povich et al. 2016; Schneider et al. 2018). In addition, Kawamura et al. (2009) reported a clear evolutionary process over the lifetime of giant molecular clouds (GMCs; of masses ∼105–106M⊙) in the Large Magellanic Cloud, evidenced by the increasing number of massive stars across the sequence of GMC ‘classes’ proposed by those authors. Finally, on the basis of the large scatter in the observed star formation efficiency (SFE) in Milky Way GMCs, Lee et al. (2016) have concluded that the SFR in those clouds must also be time variable. Numerical simulations of MC formation and evolution also exhibit time varying, increasing SFRs during their early stages (e.g. Vázquez-Semadeni et al. 2007; Hartmann, Ballesteros-Paredes & Heitsch 2012). Also, in the presence of stellar feedback, at late times the SFRs reach a maximum and begin to decrease again (e.g. Vázquez-Semadeni et al. 2010; Colín, Vázquez-Semadeni & Gómez 2013). Vázquez-Semadeni, González-Samaniego & Colín (2017) have recently shown that the simulations of Colín et al. (2013) in fact produce stellar age histograms highly resemblant of the observed ones (Palla & Stahler 1999, 2000; Da Rio et al. 2010), and reproduce observed radial age gradients in clusters (Getman et al. 2014) as well as bottom-heavy stellar initial mass functions (IMFs) in scattered regions of massive star formation (Povich et al. 2016).


Still unconstrained are the mechanisms that are able to modify both SF and morphology and their corresponding time-scales. Several hypotheses have been proposed to explain the quenching of the SF in blue galaxies, such as gas stripping (e.g. Gunn & Gott 1972), morphological or gravitational quenching (Martig et al. 2009; Genzel et al. 2014), shock heating of infalling cold gas by the hot halo (Dekel & Birnboim 2006) or an exhaustion of the gas supply (e.g. Larson, Tinsley & Caldwell 1980). Moreover, in massive galaxies, the role of AGNs in influencing galaxy evolution and quenching SF is supported by several observations (Hopkins et al. 2005; Kaviraj et al. 2007; Diamond-Stanic et al. 2012; Fabian 2012, and references therein, Cimatti et al. 2013; Cicone et al. 2014; Förster Schreiber et al. 2014) and corroborated by the theoretical results obtained combining N-body simulations of dark matter haloes evolution (Springel et al. 2005; Boylan-Kolchin et al. 2009) with semi-analytic models for galaxy formation (White & Frenk 1991; Springel et al. 2005; Lu et al. 2011; Benson 2012). However, other models are capable of forming rapidly quiescent galaxies without invoking the AGN feedback (e.g. Khochfar & Silk 2006; Naab, Khochfar & Burkert 2006, 2009; Johansson, Thomas & Maraston 2012). Stellar or supernova (SN) feedback is most likely channel for the SF quenching in low-mass galaxies (e.g. 1010 M⊙; Kaviraj et al. 2007). Several mechanisms have also been invoked to explain the morphological transformation. Numerical simulations have shown that major merging can give rise to elliptical and S0 galaxies (Bekki 1998) and that also minor merging can play an important role in spheroid and bulge growth (Bournaud, Jog & Combes 2007; Naab et al. 2007). From an observational point of view, evidence that the morphological transformation can also be induced by environmental mechanisms (Larson et al. 1980; Farouki & Shapiro 1981; Moore et al. 1999; Quilis, Moore & Bower 2000; ; Bekki, Couch & Shioya 2002) or by the secular growth of pseudo-bulges (Courteau, de Jong & Broeils 1996; Norman, Sellwood & Hasan 1996; MacArthur, Courteau & Holtzman 2003; Kormendy & Kennicutt 2004; Debattista et al. 2006) has been found.


Several consortia have been actively approaching the question based on large photometric and spectroscopic surveys such as 2dF and SDSS, covering large sky areas and redshift ranges (Lewis et al. 2002; Balogh et al. 2004; Kauffmann et al. 2004; Poggianti et al. 2017). All these efforts have found indisputable evidence for the impact of environment in galaxy evolution (and references therein; Boselli & Gavazzi 2006, 2014; Cortese et al. 2021). However, understanding the role played by different physical mechanisms exerted under diverse environment conditions constitutes the matter of a very active debate. The involved physical mechanisms are classified in two types: hydrodynamic and gravitational. Hydrodynamic effects concern the stripping of cold/warm interstellar gas (H i and H2) by the hot intracluster medium (ICM). The ram-pressure stripping (RPS, Gunn & Gott 1972) and the viscous stripping (Nulsen 1982) are the most studied cases. On the other side, we have the tidal (gravitational) mechanisms occurring between a galaxy and the cluster potential (Byrd & Valtonen 1990) or among neighbour galaxies (Merritt 1983; Barnes & Hernquist 1996; Walker, Mihos & Hernquist 1996). These include major mergers, accretion of low-mass satellites, and the accumulation of fast speed encounters between galaxies (the galaxy harassment, Moore, Katz & Lake 1996). The removal of the galaxy halo gas, known as galaxy starvation (e.g. Larson, Tinsley & Caldwell 1980), is predicted to occur either by hydrodynamic or gravitational interactions. Most of these mechanisms are predicted to transform a spiral galaxy into an S0, and it is known that more than one process might act simultaneously on a single galaxy. The pre-processing of galaxies occuring within groups infalling towards clusters and seems to be particularly important (Donnari et al. 2021). Groups of galaxies are known to have lower velocity dispersions than clusters, allowing slower and deeper tidal interactions among their members. Several authors (Fadda et al. 2008; Poggianti et al. 2009b) provided substantial evidence that strong galaxy evolution is occurring in low-mass systems at a large distance from the cluster core. However, the debate pre-processingversuscluster effects remains open because many variables are involved, such as the infalling orbits, initial gas/stellar masses, the group/cluster properties, and even the surrounding large-scale structure (Rhee et al. 2020; Salerno et al. 2020).


But if, as our studies in this Letter indicate, microstreams might be the result of accumulated and persistent velocity enhancements resulting from a series of switchbacks, then it could be that individual switchbacks result from coronal jets, and the microstreams are a consequence of a series of such jet-driven switchbacks occurring in close succession. Thus, this would be a modification of the idea put forth by Neugebauer (2012) whereby a series of minifilament eruptions capable of producing coronal jets could accumulate and generate a microstream. In fact, homologous jets, continuing for hours at a time, have been commonly observed (e.g., Chifor et al. 2008; Cheung et al. 2015; Panesar et al. 2016a, 2016b; Sterling et al. 2017; Joshi et al. 2017; Paraschiv & Donea 2019; Moore et al. 2021). Under the minifilament-eruption scenario, the multiple minifilament/flux ropes would be ejected as long as the cancellation continues (Panesar et al. 2016a; Sterling et al. 2017). A swarm of such homologous jets, produced over a several-hour time period, conceivably could account for a microstream peak. Additionally, there is some recent evidence (Bale et al. 2021; Fargette et al. 2021) that switchbacks have an extent similar to the scale size of supergranules (∼30,000 km). Measurements of the lengths of the erupting minifilaments that produce jets range from ∼8000 km (Sterling et al. 2015) to ∼18,000 (Panesar et al. 2016a), and thus of similar order to (albeit somewhat smaller than) a typical supergranule diameter. Fargette et al. (2021) also found switchbacks to occur on another size scale, one that approximately corresponds to the size of photospheric granules, ∼1000 km. Chromospheric spicules have widths of some fraction of this size, and thus their observation could be consistent with some spicules resulting from the minifilament-eruption-jet mechanism as suggested in Sterling & Moore (2016), and then those spicules making smaller-scale switchbacks as suggested in Sterling & Moore (2020).


Mid-infrared and millimeter polarimetric observation has so far been considered as the best method to probe the magnetic field. This is because if aspherical grains in disks become aligned with the magnetic field as is the case in the interstellar medium (ISM), the polarization vector arising from thermal emission of the aligned grains becomes perpendicular to the local magnetic field line (Cho & Lazarian 2007, henceforth CL07, Matsakos et al. 2016; Yang et al. 2016b; Bertrang et al. 2017). At mid-infrared wavelengths, Li et al. (2016) performed a polarimetric imaging observation of AB Aur using CanariCam. As a result, they detected a centrosymmetric polarization pattern, and the degree of polarization was as high as 1.5% at large radii. At millimeter wavelengths, polarimetric observations of disks have been performed (e.g., Hughes et al. 2009, 2013; Rao et al. 2014; Stephens et al. 2014; Cox et al. 2015; Kataoka et al. 2016b). Polarized emission from a circumstellar disk has been detected in the Class 0 phase (Rao et al. 2014; Cox et al. 2015). More evolved disks do not show a degree of linear polarization larger than 0.5% (Hughes et al. 2009, 2013). It should be mentioned that Stephens et al. (2014) detected polarized flux from HL Tau, which is classified as a Class I-II, with an average degree of linear polarization of 0.9%. More recently, Kataoka et al. (2016b) reported the first submillimeter polarization observation of a disk obtained with ALMA, and they clearly detected polarized flux from HD 142527. The polarization fraction at a peak position of polarized intensity was 3.26%, and the maximum polarization fraction was as high as 13.9%. The disk reveals radial polarization vectors; however, they flip by 90° in its northeast and northwest regions. In addition, the detected polarization fraction is much larger than the stringent limit set by Hughes et al. (2009, 2013), and further polarimetric observations by ALMA will reconcile this discrepancy.


We attempted to find a correlation between the mean magnetic field and the outflow and minor axis of the cloud CB 17. Relative orientations between various quantities of CB 17 are presented in the first row of Table 6, along with a comparative study of the same for some dark clouds. The first column gives the cloud ID and columns 2–6 give the position angles of the mean magnetic field at the envelope ($\lt \theta ^{\rm env}_B\gt $), mean magnetic field at the core ($\lt \theta ^{\rm core}_B\gt $), outflow axis (θout), minor axis (θmin) of the core of the cloud and Galactic plane (θGP), respectively. $\lt \theta ^{\rm env}_B\gt $ of CB 17 is found to be almost aligned along the Galactic plane over that region of the sky (column 7), which indicates the dominance of the Galactic magnetic field over the envelope magnetic field of the cloud and thus we cannot infer much about the magnetic field structure from the optical study. A similar feature has also been observed in the cases of CB 34 (Das et al. 2016), L328, L673-7 (Soam et al. 2015), CB 26 (Halder et al. 2019), CB 3 and CB 246 (Ward-Thompson et al. 2009). However, $\lt \theta ^{\rm core}_B\gt $ of CB 17 (obtained by submm polarimetry) turned out to be perpendicular to $\lt \theta ^{\rm env}_B\gt $ (column 8); a similar phenomenon has been observed in the case of CB 34-C1 (Das et al. 2016), IRAM 04191 (Soam et al. 2015) and CB 54 (Wolf et al. 2003). Since, in the case of CB 17, $\lt \theta ^{\rm env}_B\gt $ is along the Galactic plane orientation, this implies that only $\lt \theta ^{\rm core}_B\gt $ (denser region) is linked with the ongoing physical phenomena in the cloud. $\lt \theta ^{\rm core}_B\gt $ is oriented perpendicular to θGP as well (column 9) and a similar orientation has been observed in the case of CB 34-C1 (Das et al. 2016), IRAM 04191 (Soam et al. 2015), CB 230 and CB 244 (Wolf et al. 2003) as well. Moreover, $\lt \theta ^{\rm core}_B\gt $ is found to be almost aligned along the minor axis of the core of the cloud; the angular offset is nearly 5.9° (column 10). The alignment of $\lt \theta ^{\rm core}_B\gt $ with the minor axis of the cloud fits the magnetically regulated star formation model, in which the magnetic field should lie along the minor axis of the cloud (Mouschovias & Morton 1991; Li 1998), and the same feature has also been observed for the clouds CB 34-C1 (Das et al. 2016) and IRAM 04191 (Soam et al. 2015). The angular offset between $\lt \theta ^{\rm core}_B\gt $ and the outflow axis is found to be 80.9° (column 11), that is, the core-scale magnetic field is oriented almost perpendicular to the outflow direction and a similar phenomenon has also been observed in the case of CB 34 (Das et al. 2016), CB 68 (Bertrang et al. 2014), B335, CB 230, CB 244 (Wolf et al. 2003) and CB 3 (Ward-Thompson et al. 2009). The angular offset between θout and θmin is found to be 75° and the same feature has been observed for CB 34-C1 (Das et al. 2016).


On larger scales, the clusters in which BCGs reside can generally be divided into two categories: cool core clusters, which exhibit very peaked surface brightness distributions at X-ray wavelengths, and non cool core clusters, with similar overall X-ray luminosities but with smoother, less peaked X-ray surface brightness distributions. Some authors (e.g. Hudson et al. 2010; Santos et al. 2010) define an intermediate category called moderate or weak cool core clusters. Since cool core clusters have short radiative cooling time-scales on the order of 108 yr in their centres (e.g. Voigt & Fabian 2004; McNamara & Nulsen 2007, 2012; Hlavacek-Larrondo et al. 2012), starbursts are expected to be common at the centre of such clusters. Indeed, the central cool gas in these clusters should condense onto the BCG, forming stars at rates of hundreds of solar masses per year (e.g. Fabian 1994). However, most BCGs are relatively quiescent and those that do show evidence of star formation generally tend to have star formation rates 1 order of magnitude smaller, on the order of $1-150 \, \mathrm{M_{\odot }\, {yr}^{-1}}$ (e.g. Donahue et al. 2007; Bildfell et al. 2008; O’Dea et al. 2008, 2010; Rawle et al. 2012). This mismatch between expected and observed star-forming rates, known as the cooling flow problem, is thought to be caused by active galactic nuclei (AGNs) feedback processes from the BCG. AGNs can release copious amounts of energy into the intracluster medium (ICM) through many ways, including: jetted outflows that inflate cavities, weak shocks, sound waves, or turbulence in the ICM (e.g. Markevitch & Vikhlinin 2007; McNamara & Nulsen 2007, 2012; Zhuravleva et al. 2014; Fabian et al. 2017). Alone, the energy released by jetted outflows appears to be on the same order as the energy needed to offset cooling (e.g. Rafferty et al. 2006; McNamara & Nulsen 2007; Hlavacek-Larrondo et al. 2012), therefore suggesting that AGN feedback is a good candidate for solving the cooling flow problem.


Comparison of 1D marginal posterior distributions over the parameters S8 ≡ σ8(Ωm/0.3)0.5, σ8 and Ωm, from DES Y3 data as well as other experiments, and consistency tests for this work (in blue). (a) Constraints obtained from the harmonic (this work) and real (Amon et al. 2022; Secco et al. 2022) space analyses of DES Y3 data are shown in blue and green (see also Fig. 14), both with and without shear ratio information (SR; Sánchez et al. 2021). (b) Constraints from other weak lensing surveys, namely HSC Y1 (Hikage et al. 2019; Hamana et al. 2020, 2022b), KiDS-1000 (Asgari et al. 2021), and KiDS-450 (Hildebrandt et al. 2017; Köhlinger et al. 2017) are shown in grey, and constraints from cosmic microwave background observations from Planck 2018 are shown in yellow (Planck Collaboration VI 2020). (c) Constraints from four weak lensing analyses of DES Y3 data are compared, including the analysis of mass map moments (Gatti et al. 2021b) and peaks (Zürcher et al. 2022), and illustrating a high level of consistency (see also Fig. 15). (d) Consistency tests where redshift bins are removed one at a time (first four) and where the data vector is split into its large- and small-scale data points (last two) (see also Appendix C). (e) Various other consistency tests: removing autopower spectra, swapping the covariance matrix, and marginalizing over redshift distribution uncertainties with HyperRank and MultiRank(see also Appendix C). (f) Modelling robustness test for intrinsic alignment (IA), including B-mode power spectra, or replacing TATT by NLA, or removing IA contributions altogether (see also Section 6.2, Fig. 12). (g) Other robustness test, freeing the dark energy equation-of-state w or fixing the neutrino mass to 0.06 eV. (h) Baryonic feedback tests where the matter power spectrum is computed with HMCode instead of HaloFit, and fiducial scale cuts are replaced with kmax = 1, 3, and 5 $h\, {\rm Mpc}^{-1}$ scale cuts (see also Section 6.3 and Fig. 13).


The studies of emission lines, however, which for wide-field cameras require specific and expensive narrow-band (NB) filters of large physical size, have thus far been limited to pointed observations. Very deep Hα observations of a few galaxies in nearby clusters, including our recent observations with MegaCam, have led to several intriguing discoveries. They have shown that the ionised phase appears to be an ideal tracer of stripped gas in dense regions: approximately 50% of late-type galaxies show extended (~50 kpc) tails of ionised gas with surface brightness Σ(Hα) of approximately a few 10−18 erg s−1 cm−2 arcsec−2 (Boselli & Gavazzi 2014), while only a handful of galaxies have extended cold or hot gaseous tails (Chung et al. 2007; Sun et al. 2006, 2007, 2010; Scott et al. 2012; Sivanandam et al. 2014; Jáchym et al. 2014). In some objects, the cometary shape of the tails indicates that the gas has been stripped by the interaction with the hot ICM (Gavazzi et al. 2001; Yoshida et al. 2002; Yagi et al. 2010; Fossati et al. 2012, 2016, 2018 – paper II; Zhang et al. 2013; Boselli et al. 2016a); in other systems, bridges of ionised gas linking different nearby galaxies are associated with tidal tails in the stellar component, suggesting gravitational perturbations with nearby companions or within infalling groups (i.e. pre-processing; Kenney et al. 2008; Sakai et al. 2002; Gavazzi et al. 2003a; Cortese et al. 2006). They have also shown that within the tails of stripped gas, star formation in compact HII regions occurs in some but not in all objects (Gavazzi et al. 2001; Yoshida et al. 2008; Hester et al. 2010; Fumagalli et al. 2011a; Fossati et al. 2012; Boissier et al. 2012; Yagi et al. 2013; Kenney et al. 2014; Boselli et al. 2016a, 2018 – paper III). The removal of the gas affects the activity of star formation of galaxies on different timescales that depend on the perturbing mechanism (Larson et al. 1980; Boselli et al. 2006, 2016b; Bekki 2009, 2014; McGee et al. 2009; Cen 2014; Fillingham et al. 2015; Rafieferantsoa et al. 2015). The distribution and the morphology of the star-forming regions within galaxies is also tightly connected to the perturbing mechanisms (increases in the nuclear star formation activity and asymmetric distributions of star-forming regions are typical in gravitational interactions, radially truncated star-forming discs in interactions with the ICM, and fainter star formingdiscs in starvation, Kennicutt & Keel 1984; Barton et al. 2000; Boselli et al. 2006; Ellison et al. 2008; Woods et al. 2010; Scudder et al. 2012; Patton et al. 2011, 2013). All these pieces of evidence underline the power of NB Hα imaging data in identifying the dominant perturbing mechanism in dense environments.


The relxillDCp model combines the ionized disc reflection code xillverDCp (García et al. 2013, 2016) with the convolution model relconv (Dauser et al. 2013). The relconv model determines the relativistic effects in the reflection spectrum and assumes a broken power-law emissivity profile for the illumination of the disc by an X-ray corona. The emissivity profile has the following form: $\epsilon (r)\propto r^{-q_{{\rm in}}}$ for rin ≤ r ≤ rbr, and $\epsilon (r)\propto r^{-q_{{\rm out}}}$ for $r_{\rm br}\le r\le r_{{\rm {\rm out}}}$, where qin and qout represent inner and outer emissivity indices, respectively, rbr is the break radius, rin and rout are the inner and outer disc radii, respectively. The other parameters that characterize the disc reflection model are: black hole spin (a), the inclination angle (θ○) of the disc to the observer, reflection fraction (refl_frac), iron abundance (AFe), ionization state (log ξ), and number density (ne) of electrons in the disc atmosphere. The disc irradiation profile is considered Newtonian over the outer regions of the disc, and hence we fixed the outer emissivity index at 3. We fixed the break radius at 6rg, which is a typical AGN coronal radius (e.g. Wilkins & Fabian 2011; Mallick et al. 2021). We assume the solar abundance of iron and fixed the inner and outer radii of the accretion disc at the innermost stable circular orbit (risco) and 1000rg (rg = GMBH/c2), respectively. We set refl_frac=−1 in the relxillDCp model to solely describe the disc reflection. Since relxillDCp considers the thermal Comptonization model nthComp (Zdziarski, Johnson & Magdziarz 1996; Źycki, Done & Smith 1999) as the irradiating (primary) continuum, we replaced the zpowerlw continuum with nthComp. The slope of the nthComp and relxillDCp components are tied. The seed photon temperature in the nthComp model was set at the maximum possible disc temperature (see column 8 of Table 2) for each source. We fixed the electron temperature of the hot coronal plasma at a typical value of 100 keV. The relative strength of reflection was measured as a ratio of the disc reflected flux to the irradiating primary source flux in the 0.3–10 keV band. We find that the broad-band best-fitting spectral model is Tbabs×(relxillDCp+nthComp) for all the sources in the sample, except for J1559 and POX 52. The source, J1559, showed an absorption feature at ∼0.7 keV, which was modeled by a Gaussian absorption line gabs. The gabs component improves the fit statistic by Δχ2 = 92.9 for 3 free parameters. The expression for the broad-band best-fit model of J1559 is Tbabs×gabs×(zgauss+relxillDCp+nthComp). To model the absorption curvature present in the 1–2 keV band of POX 52, we included an ionized partial covering absorption component (zxipcf; Reeves et al. 2008). The zxipcf model has three free parameters: column density (NH,wa), ionization state (log ξwa) of the absorbing medium and covering fraction (Cf). The inclusion of the ionized absorption component provided an improvement of Δχ2 = 237.5 for three additional free parameters. The maximum-likelihood ratio (MLR) test suggests that the zxipcf model component is ≥99.99 per cent significant. The best-fitting model for POX 52 has the following expression: Tbabs×zxipcf×(relxillDCp+nthComp). We find that the relativistic reflection from an ionized, higher density accretion disc can self-consistently explain the soft X-ray excess emission for the low-mass AGN sample. The best-fitting unfolded spectral models, model components, and data-to-model ratio plots are shown in Fig. 1. We show the broad-band photon count spectra, best-fitting models, and residuals plots in Fig. A2.


To estimate the total integrated intensity of a shock-excited molecular line coming from a GMC, the shock models are scaled up so that the total energy dissipated in shocks is equal to the expected turbulent energy dissipation rate of the molecular cloud, as done in Basu & Murali (2001) and Pon et al. (2012). The dissipation rate of the turbulent energy of a molecular cloud, Lturb, is
2

where ρ is the gas density, σ is the one-dimensional velocity dispersion, R is the radius of the (spherical) cloud, and κ is the ratio of the dissipation timescale to the flow crossing timescale of the cloud. For this paper, κ is taken to be equal to 1, in agreement with numerical simulations of decaying turbulence (Gammie & Ostriker 1996; Mac Low et al. 1998; Stone et al. 1998; Mac Low 1999; Padoan & Nordlund 1999; Ostriker et al. 2001). This value of κ, however, is relatively uncertain, such that the predicted integrated intensities should only be considered to be accurate to a factor of a few. The integrated intensity of any shock-powered line, assuming a mean mass per hydrogen nuclei of 2.77 amu, is thus
3

where  is the fraction of the shock energy being emitted in the line. While the total turbulent energy of the cloud depends on the cube of the radius, the conversion of a luminosity to an intensity introduces an r−2 dependence, and setting the dissipation timescale to be equal to the turbulent crossing time introduces a further r−1 dependence, such that this predicted integrated intensity is independent of the size of the cloud. Pon et al. (2012) show that if the velocity distribution of gas particles in a molecular cloud is Gaussian and isotropic, then the shock velocity at which the peak energy dissipation occurs is approximately 3.2 times larger than the one-dimensional velocity dispersion of the gas, since the energy dissipation rate of a shock scales with the third power of the shock speed, but the probability of gas particles having a particular velocity difference decreases with increasing velocity. We assume that all of the turbulent energy in a cloud is dissipated at a shock speed of 3 km s−1, which would be the peak energy dissipation velocity for a velocity dispersion of roughly 1 km s−1 that would lead to observed FWHMs of 2.3 km s−1. While this velocity dispersion is on the lower end for what is usually associated with IRDCs (e.g., Paper II), slightly larger velocity dispersions should create larger peak temperatures and larger energy dissipation rates, such that our shock models can be considered to be conservative estimates for the shock emission. See Pon et al. (2012) for a more detailed discussion about this method of scaling the shock models.


In the coupled ADAF-jet model, the accretion flow ADAF and the jet are connected by a defined parameter, $\eta \equiv \dot{M}_{\rm jet}/\dot{M}$, and $\dot{M}_{\rm jet}$ is input by assuming a value of, η, which is free parameter in the present model. The half-opening angle ϕ of the jet in the low/hard state of NS-LMXBs is uncertain. In this paper, we fix ϕ = 0.1 as assumed by several other authors for modelling the SED of the BH-LMXBs (e.g. Yuan et al. 2005; Zhang et al. 2010). Observationally, the bulk Lorentz factor of the jet in the low/hard state of X-ray binaries can be restricted in a relatively narrow range and the velocity of the jet is mildly relativistic, i.e. Γjet ≲ 2. More strictly, the bulk Lorentz factor is restricted to be as Γjet ≲ 1.67 (Gallo et al. 2003), and Γjet ≲ 1.2 (Fender 2006). In the internal shock model, the energy density of the internal shock increases with increasing Γjet, which finally will result in an increase of both the radio emission and X-ray emission (Yuan et al. 2005). However, since Γjet is restricted in a very narrow range by observations, we expect that a slight change of Γjet will result in a slight change of the jet emission. In this paper, we fix Γjet = 1.2 corresponding the bulk velocity of the jet 0.55c (Fender 2006). The value of ϵe and ϵB describing the fraction of the internal energy of the internal shock stored in the accelerated electrons and the magnetic field, and the index, pjet, describing the power-law distribution of the electrons in the jet after the acceleration by the shock are uncertain. Qiao & Liu (2015) tested the effect of ϵe and ϵB on the emergent spectrum of the jet in an observationally inferred range of 0.01  ϵe  0.1 and 0.01  ϵB  0.1. It was found that a change of ϵB in the range of 0.01–0.1, the emergent spectrum of the jet nearly does not change (see the right-hand panel of fig. 3 of Qiao & Liu 2015). A change of ϵe in the range of 0.01–0.1, the radio spectrum nearly does not change. However, the X-ray luminosity changes obviously by changing the value of ϵe from 0.01 to 0.1 (see the left-hand panel of fig. 3 of Qiao & Liu 2015). As shown in the left-hand panel of fig. 2 of Qiao & Liu (2015), the X-ray emission is completely dominated by the accretion flow (corona) in the luminous X-ray state, which is also true in this paper, i.e. the X-ray emission from the ADAF completely dominates the X-ray emission from the jet. In this paper, we fix ϵe = 0.04 and ϵB = 0.02, respectively, throughout the paper as (Qiao & Liu 2015). The value of the power-law index pjet of the electron distribution in the jet predicted by the shock acceleration is 2  pjet  3. By modelling the SEDs of three BH-LMXBs, the value of the power-law index pjet of the electron distribution is constrained to be 2.1 (Zhang et al. 2010). Meanwhile, a change of pjet in the range of 2  pjet  3 has very minor effect on the X-ray spectrum. In this paper, we fix the power-law index pjet = 2.1 throughout the paper.


Running penumbral waves in velocity and intensity observations were first reported by Giovanelli (1972) and Zirin & Stein (1972). Later, they were found in the photosphere as well (Musman et al. 1976), but there they appear to be more intermittent and to have higher radial phase velocity (40–90 km s−1) than the waves in Hα. Whereas the velocity amplitudes are less in the photosphere than in the chromosphere, the density is very low there and most of the wave energy lies in the photosphere and subphotosphere. Larger amplitudes on the disk-side penumbra demonstrate an alignment of the oscillations along the magnetic field. Running waves are also detected in the umbra, but the waves were believed to be unrelated to those in the penumbra (Kobanov & Makarchik 2004). In the chromosphere, the frequency of travelling waves decreases as they propagate from the umbra into the outer penumbra (e.g., Lites 1988). A similar effect is also found in measurements of the propagation velocity of travelling waves (Brisken & Zirin 1997; Sigwarth & Mattig 1997; Alissandrakis et al. 1998; Kobanov & Makarchik 2004; Tziotziou et al. 2006, 2007). Generally, the waves decelerate from 40 km s−1 near the inner part of the penumbra to 10 km s−1 or less near the outer edge of the penumbra. More recently, from a multi-wavelength study including the coronal channels of the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO), Jess et al. (2015) revealed the presence of a wide range of frequencies, with longer periodicities preferentially occurring at increasing distance from the umbra. The phase speeds also tend to decrease with increasing periodicity as the waves propagate away from the umbral barycenter. These observations also suggest that these slow waves are driven by a regular coherent source. The physical nature of running penumbral waves has been controversial. Some researchers have regarded them as trans-sunspot waves originating from umbral oscillations since they detected waves starting from the umbra and propagating through the penumbra (e.g., Alissandrakis et al. 1992; Tsiropoula et al. 1996, 2000). However, others suggest that the trans-sunspot (i.e., outward) motion is apparent to a given line of sight, and that these oscillations actually represent the upward propagation of field-guided magnetoacoustic waves from the photosphere (e.g., Christopoulou et al. 2000, 2001; Georgakilas et al. 2000; Rouppe van der Voort et al. 2003; Bogdan & Judge 2006; Kobanov et al. 2006; Bloomfield et al. 2007; Jess et al. 2013, 2015). The gradual change in the inclination of the penumbral field lines is responsible for changes in the oscillation periods and phase speeds.


Even though the physical processes giving rise to the flaring emission of blazars remain debatable, considerable progress has been made in characterizing the statistical properties of blazar variability at different wavelengths, and in different time domains. In particular, it has been demonstrated repeatedly that the power spectral density (PSD) of blazar light curves is, in general, of a power-law form (Simonetti et al. 1985; Kataoka et al. 2001; Brinkmann et al. 2003; Papadakis et al. 2003; Aharonian et al. 2007; Ciprini et al. 2007; Chatterjee et al. 2008, 2012; Abdo et al. 2010a; Carini et al. 2011; Kastendieck et al. 2011; Edelson et al. 2013; Nakagawa & Mori 2013; Max-Moerbeck et al. 2014; Park & Trippe 2014; Revalski et al. 2014; Sobolewska et al. 2014; Aleksić et al. 2015; Isobe et al. 2015; Kasliwal et al. 2015). A physical process with such a variability power spectrum, denoted hereafter as

, where νk is the temporal frequency (corresponding to the timescale 1/νk), A is the normalization constant, and β is the spectral slope, is called white noise when β = 0, flicker (pink) noise when β = 1, and Brownian (red) noise when β = 2 (Press 1978). The PSD integrated over some variability frequency range is then a measure of the variance of the underlying signal in the time series within the corresponding range of variability timescales. Breaks in the slope or in the normalization of a PSD may appear, signaling characteristic/critical variability timescales in the system. In the case of blazars, various segments of radio, optical, X-ray, and γ-ray power spectra within the variability time domains from years to days (and in some instances, even sub-hour timescales), are characterized by spectral slopes 1 ≤ β  3, meaning that the variability amplitude increases with increasing variability timescale. Rarely, however, have blazar PSDs been analyzed in a systematic way at different wavelengths across the electromagnetic spectrum and over a truly broad range of temporal frequencies. It is important to note that colored-noise-type power spectra are expected to flatten on longer variability timescales (to preserve the total finite variance), and to cut-off at frequencies corresponding to the shortest variability timescale in a system. The detection of such cutoffs in blazar periodograms would be of primary importance for constraining the physics of blazar jets; however, such detections may be hampered by the finite duration of available monitoring blazar data on the one hand, and statistical fluctuations resulting from the measurement errors on the other hand.


Under the Applegate model, the change in orbital period is directly related to the change in the companion star’s gravitational quadrupole moment Q (Applegate & Patterson 1987),
(8)$$\begin{eqnarray*}
\frac{\Delta P_{\rm orb}}{P_{\rm orb}} = -9\frac{\Delta Q}{M_{\rm c} A^2},
\end{eqnarray*}$$where A = x(1 + q)/sin i is the orbital separation. For comparison, the total quadrupole moment induced by the spin of the companion star and the tidal distortion in the pulsar’s gravitational field is (Voisin, Breton & Summers 2020a)
(9)$$\begin{eqnarray*}
\frac{Q}{M_{\rm c} A^2} = -\frac{2}{9} k_2 \left(\frac{R_{\rm c}}{A}\right)^5 \left(4 q + 1\right),
\end{eqnarray*}$$where Rc is the radius of the companion star and k2 is the apsidal motion constant, a parameter describing the deformability of the companion star (Sterne 1939). For solar-type stars k2 ∼ 0.035 (Ogilvie 2014), while if we assume that redback companions are akin to the companions in CV systems whose outer envelopes have also been stripped through accretion, then we may expect a smaller value k2 ∼ 10−3 (Cisneros-Parra 1970). For J2039, the hyperparameter $h = 3.9^{+2.2}_{-1.2}$ s corresponds to the typical fractional amplitude for the variations in orbital phase. Taking the simpler squared exponential covariance function of equation (4) corresponding to n → ∞, then the deviations in orbital period have covariance function,
(10)$$\begin{eqnarray*}
K_{\Delta P_{\rm orb}/P_{\rm orb}}(t_1,t_2) &=& \frac{\partial ^2 K}{\partial t_1 \partial t_2} \nonumber\\
&=& \frac{h^2}{l^2} \exp \left(\!-\frac{(t_1 - t_2)^2}{2\ell ^2}\!\right) \left(\!1 - \frac{(t_1 - t_2)^2}{\ell ^4}\!\right).
\end{eqnarray*}$$The typical (fractional) amplitude of the orbital period variations is therefore ΔPorb/Porb ∼ h/ℓ = (3 ± 1) × 10−7, corresponding to $\Delta Q / Q \sim 3\times 10^{-5} k_2^{-1}$. The time-varying component to the gravitational quadrupole moment is therefore required to be of order a few per cent of the total expected quadrupole moment at most to explain the observed orbital period variations. From this, it seems plausible that the observed period variations can be powered by quadrupole moment changes, without requiring that a large fraction of the star be involved in the process. The required fractional quadrupole moment changes are very similar to those recently calculated for the companion to the black widow PSR J2051–0827 by Voisin et al. (2020b), despite the large difference in their masses.


We have seen that some of our runs show clear activity cycles. Therefore we expect to see a corresponding modulation of the flow. In Fig. 13, we show for Run A the temporal variation of the mean large-scale magnetic field (\hbox{$\mean B$}B) normalized by Beq, the latitudinal component of the meridional circulation uθ(r, ± 32°) at r ≈ 0.95 R⊙ and r ≈ 0.73 R⊙, the mean rotation rate \hbox{$\mean\Omega(0.95~R_\odot,\pm32^\circ)$}Ω(0.95R⊙,±32◦), \hbox{$\overline\Omega(r,0^\circ)$}Ω(r,0◦) at r = 0.73 R⊙ and r = 0.95 R⊙, as well as the latitudinal and radial differential rotation \hbox{$\Delta_\Omega^{(r)}$}ΔΩ(r) and \hbox{$\Delta_\Omega^{(\theta)}$}ΔΩ(θ), defined in Eq. (13). We see that the meridional circulation varies with the magnetic field, becoming weaker during maximum and stronger during minimum, the overall temporal variation being about 50% in this case. (The linear correlation coefficient between \hbox{$\mean B$}B and uθ(0.95 R⊙, ± 32°) ≈  −0.36, − 0.38.) This kind of weak anti-correlation between the activity cycle and the meridional flow has been found in solar observations (Chou & Dai 2001; Hathaway & Rightmire 2010) and is believed to arise at least in part from the Lorentz force of the dynamo-generated magnetic fields (see, e.g., Rempel 2006, Karak & Choudhuri 2012, Passos et al. 2012).The meridional circulation at the bottom is also weakly correlated with the activity cycle (correlation coefficients between \hbox{$\mean B$}B and uθ(0.73 R⊙, ± 32°) ≈  −0.22, − 0.47). We see that \hbox{$\mean\Omega(0.95~R_\odot,\pm32^\circ)$}Ω(0.95R⊙,±32◦) (Fig. 13c) also shows a weak anti-correlation with the magnetic variations (having correlation coefficient ≈ − 0.25). The strong magnetic fields during maxima change \hbox{$\mean\Omega$}Ω by a few per cent (≈ 6%). However \hbox{$\mean\Omega(0.95~R_\odot,0^\circ)$}Ω(0.95R⊙,0◦) (Fig. 13d) shows positive correlation (correlation coefficient ≈ 0.36) and the overall variation is larger (≈ 12%). Because of this variation of \hbox{$\mean\Omega$}Ω at the equator, the values of \hbox{$\Delta_\Omega^{(r)}$}ΔΩ(r) and \hbox{$\Delta_\Omega^{(\theta)}$}ΔΩ(θ) (Figs. 13e, f) show a positive correlation with the magnetic field (correlation coefficients 0.36, 0.21) with the overall variation being ~ 75% and 166%, respectively.