The study of cometary plasma composition has been subjected to a great interest after the ion mass spectrometer onboard Giotto spacecraft detected many peaks in the mass range 12 and 120 amu (Balsiger et al. 1986; Krankowsky et al. 1986; Mitchell et al. 1987; Altwegg et al. 1993). By developing photochemical models, numerous studies focused on comet 1P/Halley explained the observed ion distribution in a water-dominated coma (Allen et al. 1987; Wegmann et al. 1987; Schmidt et al. 1988; Cravens 1989; Bhardwaj, Haider & Singhal 1990, 1996; Gan & Cravens 1990; Ip et al. 1990; Haider, Bhardwaj & Singhal 1993; Häberli et al. 1995; Haider & Bhardwaj 1997, 2005; Bhardwaj 1999; Rubin et al. 2009; Cordiner & Charnley 2014). By making 2 yr of observations, the recent Rosetta space mission on comet 67P/Churyumov–Gerasimenko has revolutionized our understanding of the activity of the cometary coma. During the Rosetta observation period, continuous measurements around the nucleus were helpful to study the evolution of ion and neutral distribution and also the driving photochemical processes in the coma. Several modelling works on this comet have shown that ion composition in the coma varies based on the sublimation rate of the nucleus (Vigren & Galand 2013; Fuselier et al. 2015, 2016; Galand et al. 2016; Heritier et al. 2017, 2018; Vigren et al. 2017; Beth, Galand & Heritier 2019). All these studies show that solar photons are the primary energy source that determines the ion composition in the inner coma. Solar extreme ultraviolet photons having an energy more than 12 eV ionize H2O and produce H2O+, and the collisions among these species quickly lead to the formation of H3O+. The sublimated parent species such as CH3OH, NH3, HCN, HCOOH, and CH3CHO, have high proton affinities compared to that of H2O, causing the loss of H3O+ in the inner coma. Haider & Bhardwaj (2005) developed a comprehensive chemical network to study the ion distribution in comet 1P/Halley. Their calculations show that NH$_4^+$ is the most dominant ion in the inner coma followed by H3O+ and CH3OH$_2^+$ ions. Similarly, the model calculations of Heritier et al. (2017) on comet 67P/Churyumov–Gerasimenko showed that NH$_4^+$, CH3OH$_2^+$, H3O+, H3S+, and HCNH+ are the important ions in the inner coma. They also showed that the densities of these ions vary with the relative mixing ratios of corresponding proton affinity species coming from the nucleus. Even if the mixing ratios of parent species, which have high proton affinity, are very low (2 per cent), they can play a significant role in modifying the ionospheric composition of the inner coma. Hence, the ion distribution in the cometary coma essentially depends on the neutral composition and photochemical reactions.


As for the ETGs, which are spheroid-dominated, most of these that are more massive than ∼2 × 1010 M⊙ are old, implying that the SF has strongly declined long time ago and no recent bursts of SF have occurred. Early formation and rapid quenching mechanisms are expected for those galaxies, where the quenching mechanisms are likely to be associated with their morphological transformation through wet major mergers and disc instabilities. These processes lead to compaction and strong bursts of SF that consume the gas (e.g. Hopkins et al. 2008; Barro et al. 2013; Dekel & Burkert 2014), as well as strong AGN/QSO and Supernova feedback that will heat and expel the gas (e.g. Granato et al. 2004; Sijacki et al. 2007; Somerville et al. 2008; Vogelsberger et al. 2014). At intermediate and low masses, the environment-driven quenching mechanisms (e.g. ram-pressure and tidal striping, strangulation, etc.) can also be relevant (e.g. Kauffmann et al. 2004; Peng et al. 2010; Schawinski et al. 2014). Note that these mechanisms are expected to lead also to morphological transformation (e.g. Gunn & Gott 1972; Moore et al. 1996; Abadi, Moore & Bower 1999; Bekki, Couch & Shioya 2002; Aragón-Salamanca, Bedregal & Merrifield 2006). However, as M* is lower there is an increasing fraction of ETGs with intermediate values of Agelw, or even low values (Table 3), though not as low as in the case of low-mass LTGs (see Fig. 16). This population of ETGs is partially associated to the Blue Star-forming and Recently Quenched Early-type galaxies, for which rejuvenation processes (Thomas et al. 2010) by gas infall or late gas-rich mergers were proposed in Lacerna et al. (2016, 2020). In fact, the $Age_{\rm mw}/{Age_{\rm lw}}$ ratio of these galaxies is large, which implies that they did not form so late but they contain some (small) fractions of very young stellar populations. Finally, for the ITGs, the Agelw distribution in the ∼0.5–5 × 1010 M⊙ mass range is roughly bimodal (Fig. 16), with a large fraction of them in the intermediate age region (or green valley in the colour–M* diagram), showing that the quenching time-scales for these galaxies with a significant bulge are slow (quenching mechanisms like those driven by morphology, halo mass, and environment; see above). For the most massive S0–Sa galaxies, ${Age_{\rm lw}}\gt 4$ Gyr, that is, they are mostly quenched, while for the lest massive, ${Age_{\rm lw}}\lesssim 2$ Gyr, which imply some rejuvenation processes.


On the other hand, the Australia Telescope Compact Array (ATCA) 21 cm line survey of GRB host galaxies revealed high levels of atomic hydrogen (H i), suggesting that the connection between atomic gas and star formation is stronger than previously thought (Michałowski et al. 2015). Star formation may be directly fuelled by atomic gas, as has been theoretically shown to be possible (Glover & Clark 2012; Krumholz 2012; Hu et al. 2016), and this is supported by the existence of H i-dominated, star-forming regions in other galaxies (Bigiel et al. 2008, 2010; Fumagalli & Gavazzi 2008; Elmegreen et al. 2016). This can happen in a low metallicity gas that is recently acquired, even if the metallicity in other parts of a galaxy is higher, near the onset of star formation because cooling of gas (necessary for star formation) is faster than the H i-to-H2 conversion (Krumholz 2012). Indeed, large atomic gas reservoirs, together with low molecular gas masses (Hatsukade et al. 2014; Stanway et al. 2015b) and stellar masses (Perley et al. 2013, 2015; Vergani et al. 2015), indicate that GRB hosts are preferentially galaxies that have very recently started a star formation episode. This provides a natural route for forming GRBs in low-metallicity environments, as found for most GRB hosts (Fruchter et al. 2006; Modjaz et al. 2008; Levesque et al. 2010a; Han et al. 2010; Boissier et al. 2013; Schulze et al. 2015; Vergani et al. 2015; Japelj et al. 2016; Perley et al. 2016), except of a few examples of hosts with solar or super-solar metallicities (Prochaska et al. 2009; Levesque et al. 2010b; Krühler et al. 2012; Savaglio et al. 2012; Elliott et al. 2013; Schulze et al. 2014; Hashimoto et al. 2015; Schady et al. 2015; Stanway et al. 2015a). Indeed, the GRB collapsar model requires that most of the GRB progenitors have low metallicity (below solar) in order to reduce the loss of mass and angular momentum that is required for launching the jet (Yoon & Langer 2005; Yoon et al. 2006; Woosley & Heger 2006). We note however that other models, while still predicting the metallicity preference (e.g. Izzard et al. 2004; Podsiadlowski et al. 2004; Detmers et al. 2008), allow higher metallicities owing to differential rotation (Georgy et al. 2012), binary evolution (Podsiadlowski et al. 2010; van den Heuvel & Portegies Zwart 2013), or weaker magnetic fields (Petrovic et al. 2005).


Dust distribution:We employed the standard flared disk model with well-mixed gas and dust, which has been successfully used to explain the observed SEDs of a large sample of young stellar objects and BDs (e.g., Wolf et al. 2003; Sauter et al. 2009; Harvey et al. 2012a; Joergens et al. 2013; Liu et al. 2015). The structure of the dust density is assumed with a Gaussian vertical profile (1)\begin{equation} \rho_{\rm{dust}}=\rho_{0}\left(\frac{R_{*}}{\varpi}\right)^{\alpha}\exp\left[-\frac{1}{2}\left(\frac{z}{h(\varpi)}\right)^2\right], \label{dust_density} \end{equation}ρdust=ρ0R∗ϖαexp−12zh(ϖ)2,and the surface density is described as a power-law function (2)\begin{equation} \Sigma(\varpi)=\Sigma_{0}\left(\frac{R_{*}}{\varpi}\right)^p, \end{equation}Σ(ϖ)=Σ0R∗ϖp,where ϖ is the radial distance from the central star measured in the disk midplane, and h(ϖ) is the scale height of the disk. The disk extends from an inner radius Rin to an outer radius Rout. To the best of our knowledge, among our sample, there are five objects that have been identified as binary systems so far. They are 2M1207 (a~55 AU, Chauvin et al. 2004), J04221332+1934392 (a~7 AU, Todorov et al. 2014), J04414489+2301513 (a~15 AU, Todorov et al. 2014), USD161833 (a~134 AU, Bouy et al. 2006), and USD161939 (a ~ 26 AU, Bouy et al. 2006), where a refers to the separation within the system. The disks around individual components in binary systems are expected to have truncation radii of the order of (0.3 − 0.5)a (Papaloizou & Pringle 1977). We adopted 0.5 a as the disk outer radii for 2M1207, USD161833, and USD161939. For the close pairs (a ≲ 15 AU, J04221332+1934392 and J04414489+2301513), dynamical simulations of star-disk interactions suggest that individual disks are unlikely to survive (e.g., Artymowicz & Lubow 1994). Disk modeling is complicated in those close multiple systems. For simplicity, we assume that the emission is associated with circumbinary disks of 100 AU in size. For other objects, we fix Rout = 100 AU in the modeling because the choice of this parameter value makes essentially no difference to the synthetic SEDs in the simulated wavelength range (Harvey et al. 2012a). The scale height follows the power-law distribution(3)\begin{equation} h(\varpi) = H_{100}\left(\frac{\varpi}{100\,\rm{AU}}\right)^\beta,\\ \end{equation}h(ϖ)=H100ϖ100 AUβ,with the exponent β characterizing the degree of flaring and H100 representing the scale height at a distance of 100 AU from the central star. The indices α, p, and β are codependent through p = α − β. We fix p = 1, which is the typical value found for T Tauri disks in the sub-millimeter (e.g., Isella et al. 2009; Guilloteau et al. 2011), since only spatially resolved data can place constraints on this parameter (e.g., Ricci et al. 2013, 2014).               Dust properties:We assume the dust grains to be a homogeneous mixture of 75% amorphous silicate and 25% carbon with a mean density of ρgrain = 2.5 g cm-3 and the complex refractive indices given by Jäger et al. (1994, 1998), and Dorschner et al. (1995). Porous grains are not considered because the fluxes at wavelengths beyond ~ 2 μm are almost independent of the degree of grain porosity in low-mass disks, as shown by Kirchschlager & Wolf (2014). The grain size distribution is given by the standard power law dn(a) ∝ a-3.5da with minimum and maximum grain sizes amin = 0.1 μm and amax = 100 μm, respectively. The choice of the minimum value for the grain size, amin, ensures that its exact value has a negligible impact on the synthetic SEDs. Since there is no information about the maximum grain sizes of our target disks, as provided, e.g., by the (sub)millimeter spectral index, we adopt amax = 100 μm. The Herschel/PACS far-IR observations are sensitive to dust grains with this assumed sizes. Strong grain growth up to millimeter sizes as detected in some BD disks (e.g., Ricci et al. 2012, 2013, 2014; Broekhoven-Fiene et al. 2014) would remain undetected in our data and could affect the disk mass. Our prescription for the dust properties is identical to those used in Liu et al. (2015).


The FOCAS and NIRSPEC spectra of PSO J006+39 were obtained at two different epochs separated by 1 yr and 9 months (by slightly less than 3 months in the quasar rest frame). Previously, we found that the PS1 y-band light curve of PSO J006+39 shows brightness variations with a peak-to-peak amplitude of ∼0.7 mag over ∼4 yr (Koptelova et al. 2017), which might be due to the flux variations of both continuum and Lyα line of PSO J006+39. To infer the brightness state of PSO J006+39 at the epochs of its FOCAS and NIRSPEC observations, we first calculated the spectral slope of the quasar continuum from the NIRSPEC spectrum with a wider wavelength coverage than that of the FOCAS spectrum. Using wavelength intervals of 11100–11300, 11400–11600, 13085–13400, and 14700–15200 Å we measured a spectral slope of αλ = −1.35 ± 0.26, where the quoted uncertainty is the statistical error of the fit. The fitted power law is shown in Figure 2 with a solid line. The estimated continuum slope is consistent but somewhat flatter than the typical slope of luminous quasars (Zheng & Malkan 1993; Vanden Berk et al. 2001; Selsing et al. 2016). We then fitted the FOCAS data using the power law with a fixed spectral slope of αλ = −1.35 and spectral windows of 9700–9850 and 10050–10100 Å. The spectral windows adopted for the analysis of the FOCAS and NIRSPEC spectra were taken to be similar to the rest-frame wavelength intervals commonly used to fit the continua of quasars (Vanden Berk et al. 2001; Decarli et al. 2010; Lusso et al. 2015) and less affected by the contribution from emission lines on the red side of the Big Blue Bump (BBB; e.g., Malkan 1983). The estimated continuum flux of PSO J006+39 at the epoch of its FOCAS observations is shown in Figure 2 with a dashed line. By comparing the continuum flux at the epochs of the FOCAS and NIRSPEC observations, we find that the brightness state of PSO J006+39 was different at these two epochs. PSO J006+39 was brighter by about 0.8 mag during the FOCAS observations than during the NIRSPEC observations. Thus, the continuum flux of PSO J006+39 might be different at different epochs depending on the brightness state of the quasar. Figure 2 also shows the fluxes of PSO J006+39 in the FOCAS Y, and NIRSPEC N2, N4, and N6 bands at the epochs of the FOCAS and NIRSPEC observations (see also Table 1).


The present analysis builds upon the macroscopic-kinetic model of the solar wind, originally formulated by Yoon & Seough (2014) for the proton temperatures. The same model was recently generalized to include collisional dissipation (Yoon 2016a, 2016b). The basic methodology is similar to that of Marsch & Tu (2001) and Jasperse et al. (2006), especially in regards to treating the particle aspect, but unlike earlier works (Marsch & Tu 2001; Jasperse et al. 2006), which do not treat the waves self-consistently, Yoon & Seough (2014) and Yoon (2016a, 2016b) discuss the wave generation in a self-consistent manner by solving the adiabatic dispersion relation and wave kinetic equation for each spatial location. We now extend the original formalism (Yoon & Seough 2014) in another direction. We include dynamic electrons, but unlike the two later works (Yoon 2016a, 2016b), we ignore collisional dissipation. For an inhomogeneous plasma immersed in a diverging or converging magnetic field, the kinetic equation for the particles subject to perturbations propagating in parallel direction, s, is given by
1

where, for cylindrical velocity coordinate system, the velocity diffusion coefficient tensor is given by
2

and where

 is the complex angular frequency, which must be determined by the local dispersion relation,
3

In the above relation, ea and ma are unit electric charge and mass for particles species a (a = p for protons and a = e for electrons,

 for protons and

 for electrons);

 stands for cyclotron frequency for species a, B0 and c being the ambient magnetic field intensity and the speed of light in vacuo;

 is the square of the plasma frequency defined for species a, n0 being the ambient plasma density, and

 being the perturbed electric field associated with the unstable transverse mode propagating parallel (and anti-parallel) to the ambient magnetic field, ± denoting the right/left-hand circular polarization. The spectral electric field wave energy density

 must be determined by solving the wave kinetic equation, the simplest form of which is given by the quasilinear theory,
4


In the first scenario, we assume that neither the characteristic velocity dispersion (σ*) nor the number density (n*) of galaxies evolves with redshifts (νn = νv = 0). Given the redshift coverage of the lensing galaxies in the lens sample (0.06  zl  1.0), if we constrain a non-evolving VDF using the lens data, then, assuming the VDF evolution with redshift is smooth, the fits on the VDF parameters may represent the properties of ETGs at an effective epoch of z ∼ 0.5. Such non-evolving VDF has been extensively applied in the previous studies on lensing statistics (Chae & Mao 2003; Ofek et al. 2003; Capelo & Natarajan 2007; Cao et al. 2012a). By applying the above-mentioned χ2 – minimization procedure to Sample A – we obtain the best-fitting values and corresponding 1σ uncertainties (68.3 per cent confidence level): $\alpha =0.66^{+2.13}_{-0.66}$, $\beta =2.28^{+0.24}_{-0.18}$. It is obvious that the full sample analysis has yielded improved constraints on the high-velocity exponential cut-off index β, compared with the previous analysis of using the distribution of image separations observed in CLASS and PANELS to constrain a model VDF of ETGs (Chae 2005). Suffering from the limited size of lens sample, such analysis (Chae 2005) found that neither of the two VDF parameters (α, β) can be tightly constrained, due to the broad regions in the α − β plane. Consequently, the image separation distribution is consistent with the SDSS measured stellar VDF (Sheth et al. 2003) and the Second Southern Sky Redshift Survey (SSRS2) inferred stellar VDF (Chae & Mao 2003), although the two stellar VDFs are significantly different from each other concerning their corresponding parameter values. We also consider constraints obtained for the Sample B (defined in previous section), with the likelihood is maximized at $\alpha =1.00^{+2.38}_{-1.00}$ and $\beta =2.34^{+0.26}_{-0.24}$, from which one could clearly see the marginal consistency between our fits and recent measurements of three stellar VDFs (especially the SDSS DR5 VDF of ETGs).


Micro-porosity is the porosity arising from the organisation of the condensate monomers (e.g. Mg2 SiO4 in Mg2 SiO4[s]) within a cloud particle during growth. This is different from the porosity that can be used to characterise aggregates that originate from particle-particle collision processes (coagulation, e.g. Dominik & Tielens 1997; Blum & Wurm 2000), which we do not considerhere. On Earth, the material density of water ice is dependent on the ambient temperature at formation. Snowflakes are known to form many types of crystal structures that can be up to 84% porous for millimetre-sized cloud particles when compared toice material density (Hales 2005), leading to the possibility of altitude-dependent porosity in terrestrial snow clouds. Earth-like exoplanets, mini-Neptunes, and T-type brown dwarfs may form water clouds, composed of liquid or solid particles, but warmer planets and brown dwarfs of L-type and later have been shown to form cloud particles made of a mix of materials that is dominated by Mg, Si, Fe, and O and to a lesser extent by Ti, Al, K and other elements (e.g. Witte et al. 2009; Lee et al. 2015; Helling et al. 2019a). There are many ways in which this micro-porosity might be incorporated into mineral cloud particles, for example lattice faults at the interfaces between two different condensation species owing to the different lattice structures. Even for homogeneous growth, single species often have multiple crystal structures (Sood & Gouma 2013), which can also generate lattice faults at their interfaces. For example, the TiO2 [s] rutile and anatase forms are both stable at atmospheric pressures for temperatures greater than 1100 K (Jung & Imaishi 2001; Hanaor & Sorrell 2010). Additionally, within crystal structures, there are many known types of defect that might further decrease material density (e.g. Schottky defects in TiO2 [s] and MgO[s] crystals Ménétrey et al. 2004). Furthermore, these cloud particles not only change their material composition when falling through the atmosphere, but their particle sizes will also change such that the largest cloud particles are forming the innermost part of the cloud, which often sits deep inside the optically thick part of the atmosphere. Because cloud particles made of a mix of many thermally stable materials fall into warmer atmospheric regions, the low-temperature materials (such as SiO[s], MgSiO3[s]) become thermally unstable, they evaporate and leave behind a skeleton made of high-temperature materials (such as Fe[s], TiO2[s], Al2O3[s]). Whilst this may be a source of micro-porosity of cloud particles, Juncher et al. (2017) noted that this may also lead to a reduction in micro-porosity because the structural integrity of the particle is weakened and dangling structures break off. These micro-porous mineral cloud particles we call “mineral snowflakes”.


Similarly to former works (e.g., Zhang et al. 2010, 2012; Kang et al. 2014, 2016; Yan et al. 2016), we neglect the low-frequency radio data and consider the data with

 (or

) in our SED fitting with the one-zone model due to the fact that radio emission should come from the large-scale jet and cannot be accounted for with a one-zone model. The variability correlation between millimeter, optical, X-ray, and γ-ray emission support the fact that they come from more or less the similar region (e.g., Sikora et al. 2008; León-Tavares et al. 2012; Wehrle et al. 2012; D’Ammando et al. 2013; Orienti et al. 2013). In four LSP blazars (0333 + 321, 0430 + 052, 2145 + 067, 2230 + 114), the putative UV excesses are not included in our SED fitting, as they should come from the cold accretion disk (Shakura & Sunyaev 1973; Ghisellini et al. 2013; Ajello et al. 2016). On average, there are 17 data points in our fitting. As an example, we show the multi-wavelength SED and its fitting for 2200 + 420 (BL Lac) in Figure 1 (left panel), where only the SSC process is considered due to the EC not being important in this source. In the right panel of Figure 1, we show the probability distributions of the model parameters, where

 G,

,

,

,

,

, and

 (upper and lower limits represent 1σ errors, see also Table 1). The source of 1219+285 is also a BL Lac object, for which the EC component is negligible. For the remaining 23 LSP sources, both the SSC and EC component are considered, where the SEDs and the fitting are shown in Figures 2–6. For each source, the SED fitting with seed photons from the torus and BLR are presented in left and right panels, respectively. In our SED fitting, we find that most LSP blazars have

 (20 of 23 sources,

 for the two other sources and only one has the ratio ∼0.6, see Table 1), where the distribution of the ratio

 is shown in Figure 7. Our results suggest that the SED fitting with the seed photons from torus are better than with those from the BLR, which supports the notion that the location of the γ-ray emitting region should stay outside of the BLR. In the following work, therefore, we consider the model parameters from the SED fittings with the torus seed photons.


Using our stellar parameters, we derived an estimate of the spectroscopic distances of XO-2N and XO-2S by means of the following procedure. We generated Monte Carlo (MC) normal distributions for each spectroscopic parameter Teff, [Fe/H], and log  g, composed of 10 000 random values and centred on the best estimates (Table 2). By keeping the stellar radii fixed to the values listed in Table 2 (for XO-2N we used the most accurate estimate), for each MC simulation we first determined the stellar bolometric luminosity L∗ (in solar units) from the Stefan-Boltzmann law, and then we derived the absolute bolometric magnitude Mbol from the relation Mbol = 4.75 − 2.5·log (L∗). By estimating the appropriate bolometric correction (BC), a value for the absolute magnitude in V-band MV was then obtained. The BC term was evaluated using the code provided by Casagrande & VandenBerg (2014). An additional input is the colour excess E(B − V) of the star, which we derived through the relation E(B − V) = AV(s)/3.1, where AV(s) is the interstellar dust extinction in V-band integrated at the distance s of the star (in pc) and measured along the line of sight. We derived AV(s) by adopting a simplified model of the local distribution of the interstellar dust density (Drimmel & Spergel 2001), expressed by the relation ρ = ρ0·sech2(z/hs), where z is the height of the star above the Galactic plane and hs is the scale-height of the dust, for which we adopted the value of 190 pc. The term z is related to the distance s and the Galactic latitude of the star b by the formula z = s·sinb. From this model we obtained the relation AV(s) = AV(tot)·sinh(s·sin b/hs)/cosh (s·sin b/hs), where AV(tot) is the interstellar extinction in V band along the line of sight integrated through the Galaxy, and can be estimated from 2D Galactic maps. For this purpose we used the value AV (tot) = 0.16 mag derived from the maps of Schlafly & Finkbeiner (2011)6. By assuming s = 150 pc as a prior distance of the stars (Burke et al. 2007), we obtained AV (150 pc) ~ 0.06 mag, corresponding to E(B − V) = 0.019 mag. This is the value used as input to the code of Casagrande & VandenBerg (2014) to obtain a first guess of the BC in V-band. This in turn was used in the distance modulus formula V − (Mbol − BCV) = 5·log (s) −5 − AV(s), to obtain a new value for the stellar distance s. The new distance was used to repeat the procedure iteratively, by determining at each step a new value of AV(s) and BCV(s), and finally another estimate of s. When the absolute difference between the last and previous calculated values of s was below 0.1 pc, the iterative process was interrupted and the last derived value for s was assumed as the distance of the star for the Nth Monte Carlo simulation. The adopted estimates for the distance of the XO-2 components are the median of the distributions of the 10 000 MC values, and the asymmetric error bars defined as the 15.85th and 68.3th percentile (see Table 1). Because they are model-dependent, we do not argue here whether the difference of ~2.5 pc between the XO-2S and XO-2S distances is real. We only note that the two values are compatible within the uncertainties and that our best estimate for the distance of XO-2N locates the star a few parsec closer than reported by Burke et al. (2007).


When energy flows from the interior of the Sun outward into the solar atmosphere, why is the Sun’s outer atmosphere, the corona, much hotter than the inner atmosphere, the underlying chromosphere and photosphere? This is the long-standing problem of the coronal heating, which is one of the eight key mysteries in modern astronomy (Kerr 2012). For about 80 yr since the discovery of the extremely hot corona around the late 1930s (Grotian 1939; Edlen 1945), people have worked hard on addressing this issue, and great advances have been made in observation and theoretical studies (Parnell & De Moortel 2012; Amari et al. 2015; Arregui 2015; Cargill et al. 2015; De Moortel & Browning 2015; Jess et al. 2015; Klimchuk 2015; Longcope & Tarr 2015; Peter 2015; Schmelz & Winebarger 2015; Velli et al. 2015; Wilmot-Smith 2015). Especially during recent decades, high-resolution observations of solar super-fine structures indicate that small spicules, minor hot jets along small-scale magnetic channels from the low atmosphere upwards to the corona, petty tornados and cyclones, and small explosive phenomena such as mini-filament eruptions and micro- and nano-flares—all of these small-scale magnetic activities contribute greatly to coronal heating (De Pontieu et al. 2011; 2018; Zhang & Liu 2011; Parnell & De Moortel 2012; Klimchuk 2015; Peter 2015; Schmelz & Winebarger 2015; Henriques et al. 2016; Li et al. 2018a). Additionally, contributions of MHD waves to heating the corona have been observationally illustrated (van Ballegooijen et al. 2011; Jess et al. 2015; Kubo et al. 2016; Morton et al. 2016; Soler et al. 2017; Morgan & Hutton 2018). Meanwhile, with the progress of observational studies, two groups of theoretical models, magnetic reconnection models and magnetohydrodynamic wave models, have traditionally attempted to explain coronal heating, but so far no models can address the key mystery perfectly (van Ballegooijen et al. 2011; Arregui 2015; Cargill et al. 2015; Peter 2015; Velli et al. 2015; Wilmot-Smith 2015). Maybe we do not need to intentionally take to heart such the classical dichotomy, because waves and reconnections may interact with each other (De Moortel & Browning 2015; Velli et al. 2015). Additionally, statistical studies may look at coronal heating from a comprehensive perspective. Li et al. (2018b) found that the long-term variation of the heated corona, which is represented by coronal spectral irradiances, and that of small-scale magnetic activity are in lockstep, indicating that the corona should statistically be effectively heated by small-scale magnetic activity. Observational and theoretical model studies through heating channels and modes, and statistical studies by means of heating effect (performance of the heated corona), both suggest that coronal heating originates from small-scale magnetic activity.


The rotational spectrum of NaCl has been obtained using two different FTMW spectrometers constructed at the University of Valladolid. A solid rod was prepared by pressing the NaCl fine powder mixed with a small amount of commercial binder and was placed in the ablation nozzle (Alonso et al. 2009; Mata et al. 2012). A picosecond Nd:YAG laser (12 mJ per pulse, 20 ps pulse width) was used as a vaporization tool. Then, NaCl neutral molecules were supersonically expanded using the flow of a carrier gas (Ne at backing pressure of 15 bars) into the spectrometer chamber. NaCl was first investigated using a chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer with a laser ablation source (Mata et al. 2012; Bermúdez et al. 2013) operating between 6.0 and 12.0 GHz to sample swiftly the rotational spectra of the different species present in the supersonic expansion. Chirped pulses of 4 μs directly generated by the 24 Gs s−1 AWG were amplified to about 300 W peak power using a traveling wave tube amplifier. The amplified pulse is broadcasted into the vacuum chamber through two microwave horns, interacting with the vaporized molecules in the pulsed jet. Finally, a total of 40,000 free induction decays (4 FID emissions per gas pulse), of 10 μs length duration, were averaged and digitized using a 50 Gs s−1 digital oscilloscope. Line widths of the order of 100 kHz FWHM were achieved. The sub-Doppler resolution LA-MB-FTMW spectrometer, described elsewhere (Alonso et al. 2009), operating from 4 to 26 GHz, was used to record the NaCl spectra with the resolution necessary to analyze the hyperfine structure due to the presence of two nuclei with I = 3/2 in the molecule. Microwave pulses of 0.3 μs duration with powers of 140 mW were applied to polarize the molecules in the jet. The free induction decay (FID) was recorded for 100 μs in the time domain at 40–100 ns sample intervals and then converted to the frequency domain by Fourier transformation. All the transitions appeared as Doppler doublets due to the parallel configuration of the molecular beam and the microwave radiation. The resonance frequency was determined as the arithmetic mean of the two Doppler components. The estimated accuracy of the frequency measurements is greater than 3 kHz. From 10 (in the case of the ground state and the lower vibrational states) to 2500 (for the higher vibrational states) averages were phase-coherently co-added to achieve reasonable signal-to-noise ratios.


The size of ENLRs have been defined in different ways in the literature. Bennert et al. (2002) and Schmitt et al. (2003b) used the Hubble Space Telescope (HST) to obtain narrow band images of $\rm [O\, III]$, and adopted the maximum 3σ detected radius as the radius of the ENLR. This method is subject to the instrumental sensitivity limit that could be very different in different observations. Studies with long-slit spectroscopic observations define the radius based on isophote (Greene et al. 2011; Hainline et al. 2013, 2014), or the distance at which the ionization state changes from AGN to star-forming activities (Bennert et al. 2006a,b). The long-slit based observations also have drawbacks: the morphology of ENLR is sometimes irregular so that the derived size depends on the orientation of slits (Greene et al. 2011; Husemann et al. 2013). We have compared the measured size based on the IFU and the mock long-slit observation in Fig. 4 following the method discussed below. In most cases, long-slit observations tend to underestimate the true size of ENLR. IFU spectroscopic data allow us to use 2D maps to define the sizes of ENLRs. Common definitions include the radius of a specified $\rm [O\, III]$ surface brightness isophote (Liu et al. 2013, 2014), or the $\rm [O\, III]$ flux weighted radius (Husemann et al. 2013, 2014; Bae et al. 2017). We followed the same method as Liu et al. (2013) but chose a different threshold. The isophote threshold of 10−15$\rm erg\, s^{-1}cm^{-2}arcsec^{-2}$ was used for quasars related studies. This is suitable for such bright objects but are not as useful for fainter Syferts in our sample as it will leave a large number of AGN undetected. The typical 3σ depth of the MaNGA observation in $\rm [O\, III]$ surface brightness can reach 10−17$\rm erg\, s^{-1}cm^{-2}arcsec^{-2}$. For our AGN sample, the majority of AGN spaxels have surface brightnesses above 10−16$\rm erg\, s^{-1}cm^{-2}arcsec^{-2}$ which is thus adopted in this work as the threshold to define the sizes of the ENLRs (hereafter R16). If all spaxels are above this threshold, we extrapolated the fitted $\rm [O\, III]$ surface brightness profile to determine R16 (see Section 3.4 for more detail). It should be noted that the surface brightness can be affected by cosmological dimming, which has a scale factor of (1 + z)4 (Liu et al. 2013; Hainline et al. 2014). That is important for works trying to compare sample with different redshift, especially for high redshift quasars.


Understanding how angular momentum and chemicals are transported in the interiors of stars (and planets) along their evolution is one of the key challenges of modern stellar (and planetary) astrophysics. Indeed, rotation modifies their structure, their chemical stratification, their internal flows and magnetism, and their mass losses and winds (e.g. Maeder 2009; Mathis et al. 2013; Aerts et al. 2019, and references therein). In this quest, asteroseismology has bought a fundamental breakthrough by demonstrating that all stars are the seat of a strong extraction of angular momentum during their evolution in comparison with the predictions by stellar models taking the rotation into account following the standard rotational transport and mixing theory (Eggenberger et al. 2012; Marques et al. 2013; Ceillier et al. 2013; Cantiello et al. 2014; Ouazzani et al. 2019). This was first obtained thanks to mixed pulsation modes splitted by rotation propagating in evolved low- and intermediate-mass stars (Beck et al. 2012, 2014, 2018; Mosser et al. 2012; Deheuvels et al. 2012, 2014, 2015; Deheuvels et al. 2020; Di Mauro et al. 2016; Triana et al. 2017; Gehan et al. 2018; Tayar et al. 2019). Then, observations of oscillation modes in F- and A-type stars (Kurtz et al. 2014; Saio et al. 2015; Bedding et al. 2015; Keen et al. 2015; Van Reeth et al. 2015, 2016, 2018; Schmid & Aerts 2016; Murphy et al. 2016; Sowicka et al. 2017; Guo et al. 2017; Saio et al. 2018, 2021; Mombarg et al. 2019; Li et al. 2019, 2020; Ouazzani et al. 2020) and in B-type stars (Pápics et al. 2015, 2017; Triana et al. 2015; Moravveji et al. 2016; Kallinger et al. 2017; Buysschaert et al. 2018; Szewczuk & Daszyńska-Daszkiewicz 2018; Pedersen et al. 2021; Szewczuk et al. 2021) provided us new Rosetta stones to constrain the transport of angular momentum in the whole Hertzsprung-Russell diagram. More particularly, this pushes gravity- and gravito-inertial mode pulsators such as γ-Doradus and SPB stars at the forefront of this research. For instance, recent theoretical developments have demonstrated how it is possible to probe stellar internal rotation in γ-Doradus stars from their surface to their convective core (Ouazzani et al. 2020; Saio et al. 2021). These stars are rapid rotators for a large proportion of them. Therefore, it is necessary to study gravito-inertial modes. These modes are gravity modes, which propagate only in stably stratified stellar radiation zones under the action of the restoring buoyancy force in the absence of rotation, which are modified by rotation. If their frequency is super-inertial (i.e. above the inertial frequency 2Ω, Ω being the stellar angular velocity), they are propagating in stellar radiation zones and evanescent in convective regions. If their frequency is sub-inertial (below 2Ω) they propagate in an equatorial belt in radiation zones and they become propagative inertial waves in convective regions (e.g. Dintrans & Rieutord 2000; Mathis et al. 2014). The challenge of studying these waves is that the equation describing their dynamics are intrinsically bi-dimensional and non-separable (Dintrans et al. 1999; Prat et al. 2016, 2018; Mirouh et al. 2016). This makes the development of seismic diagnosis difficult analytically (Prat et al. 2017) or expansive in computation time when using 2D oscillation and stellar structure codes (e.g. Ouazzani et al. 2017; Reese et al. 2021) in the general case.


In this study, we have outlined and successfully tested a refined technique to measure in contemporary lensing surveys the scale-dependent galaxy bias down to non-linear scales of k ~ 10 h−1 Mpc for lens galaxies at z ≲ 0.6. To test our reconstruction technique, we employ a fiducial survey with a sky coverage of ~ 1000 deg2, and a photometry and a survey depth as in CFHTLenS. To construct realistic samples of lenses and sources, we have prepared mock catalogues that are consistent with those used in SES13 and Saghiha et al. (2017). Despite some variations in survey depth and area, these survey parameters are similar to the ongoing Kilo-Degree Survey (KiDS), Dark Energy Survey (DES), or the survey with the Hyper Suprime-Cam (Kuijken et al. 2015; Becker et al. 2016; Aihara et al. 2018). If the galaxy-bias normalisation is perfect, our technique applied to these data can achieve a statistical precision within the range of 5–10% (68% CL), if similar lens and source samples are targeted, and a slightly better accuracy of 3−7% (68% CL; see Table 3). For the high-z samples, the accuracy will be somewhat higher with 3−5%. On the other hand, it is clear from our overview Table 4 that the accuracy of the galaxy-bias normalisation is in fact limited, mainly by our knowledge of the intrinsic alignment of sources, cosmological parameters, and the galaxy redshift distributions. With a broad knowledge of |Aia|≲ 2 and the specifications for the normalisation errors in Table 4, we conclude that systematic errors would potentially degrade the overall accuracy to approximately 15% for b(k) and 10% for r(k). For fully controlled intrinsic alignment of sources, these errors could be reduced by 5%. An additional reduction by 3% may be possible by controlling the redshift distributions (their mean and variance) in the normalisation to 1% accuracy. For the fiducial cosmology, the knowledge of Ωm is of most importance while the normalisation of the ratio statistics is less affected by σ8.


Recently, one of the hot topics in solar physics is the understanding of solar filaments in the corona, including their distribution, formation, eruption, and stability (Yang et al. 2008; Kong et al. 2015; Su et al. 2015; Yan et al. 2015). Martin (1998) and Gaizauskas (2002) have shown that convergence and cancellation of flux play an important role in the formation of filament channels and filaments. Flux ropes and magnetic dips represent the magnetic structures of filaments, which were reported by many authors (van Ballegooijen & Martens 1989; Mackay et al. 1999; Litvinenko & Wheatland 2005; Aulanier et al. 2006; Canou & Amari 2010). Many reports on the eruption of filaments are concerned with torus instability or/and kink instability (Török & Kliem 2003; Kliem & Török 2006; Török et al. 2010; Yan et al. 2014a, 2014b), and magnetic flux emergence and cancellation are also known to play a key role in these eruptions (Magara & Longcope 2003; Archontis & Török 2008; Yan et al. 2011). The transverse component of photospheric magnetic fields near the PIL increase after a filament’s eruption or flares (Liu et al. 2012; Sun et al. 2012; Wang et al. 2013). Sun et al. (2012) indicated that the substantial electric current increases with the emergence of flux during the formation of the filament. A downward collapse of coronal current after the eruption of the filament was also reported by Liu et al. (2012). Nonlinear force-free field (NLFFF) model extrapolation is the most powerful tool to reconstruct the magnetic field above the photosphere from photospheric vector magnetograms (VMs) thus far (Sakurai 1981; Wheatland et al. 2000; Amari et al. 2006; Canou & Amari 2010; Jiang et al. 2014), since the chromospheric and coronal magnetic fields are hard to measure exactly. Even so, it is still a long way to completely understand filaments. Regardless of its formative or eruptive process, and the variation of parameters including the electric current, magnetic field and plasma motion in the evolution of filament are not yet really clear. Investigating the electric current associated with the filament is helpful for understanding the characteristic of solar filaments.


Momentum and kinetic energy can be directly transferred to the gas, suppressing inflows. The fast-moving jets can also shock heat the surrounding gas. Many models have invoked kinetic jets to suppress cooling flows and SFRs in massive haloes (e.g. Dubois et al. 2010; Gaspari et al. 2012a; Li & Bryan 2014a; Prasad et al. 2015; Yang & Reynolds 2016a). Many models in the literature also invoke the idea that AGN can effectively drive strong pressure-driven outflows and offset cooling if a large fraction of the accretion energy is thermalized (Begelman 2004; Springel, Di Matteo & Hernquist 2005; Di Matteo, Springel & Hernquist 2005; Hopkins et al. 2006a, b, 2007, 2008; Johansson, Naab & Burkert 2009; Hopkins & Elvis 2010; Ostriker et al. 2010; Faucher-Giguère & Quataert 2012; Dubois et al. 2013; Barai et al. 2014; Weinberger et al. 2017a; Pillepich et al. 2018; Richings & Faucher-Giguère 2018a, b; Torrey et al. 2020). Physically, as the jet propagates, part of the kinetic energy can thermalize through shocks. Some studies have argued that the heat from those weak shocks can suppress cooling flows and SFRs in massive haloes (Yang & Reynolds 2016b; Li, Ruszkowski & Bryan 2017; Martizzi et al. 2019). The magnetic fields carried by the jet at its launch might also help suppress cooling flows by providing additional pressure support (Soker & Sarazin 1990; Beck et al. 1996, 2012), although our studies find that they have limited effects on global star formation properties of sub-L* galaxies (Su et al. 2017).1 Finally, CRs arise generically from processes that occur in fast shocks, so they could come from shocked winds or outflows. But they are particularly associated with relativistic jets from AGN (where they can make up the bulk of the jet energy; Berezinsky, Gazizov & Grigorieva 2006; Ruszkowski, Yang & Reynolds 2017b) and hot, relativistic plasma-filled ‘bubbles’ or ‘cavities’ (perhaps inflated by jets in the first place) around AGN. Different authors have argued that they could help suppress cooling flows by providing additional pressure support to the gas, driving pressurized outflows in the galaxy or CGM, or via heating the CGM/ICM directly via collisional (hadronic & Coulomb) and streaming-instability losses (Guo & Oh 2008; Sharma, Parrish & Quataert 2010; Enßlin et al. 2011; Fujita & Ohira 2011; Fujita, Kimura & Ohira 2013; Pfrommer 2013; Wiener, Oh & Guo 2013; Jacob & Pfrommer 2017a, b; Pfrommer et al. 2017; Ruszkowski et al. 2017a, b; Jacob et al. 2018).


Out of these sites (a) might provide the conditions for a very weak r-process and νp-process, whether only up to Sr, Y, Zr or up to (but not beyond) the A = 130 peak is still debated (Wanajo et al. 2018; Curtis et al. 2019; Fischer et al. 2020a; Ghosh et al. 2022). (b) is a class of supernovae whose existence is put into question after recent re-determinations of the electron capture rate of 20Ne (Kirsebom et al. 2019a,b), but is not firmly excluded, however, leading to a too strong decline in abundances as a function of A for realistic Ye-conditions (Wanajo et al. 2011). (c) could plausibly lead to magnetars, neutron stars with surface magnetic fields of the order 1014 G, which form in ∼1 out of 10 of core collapse supernovae (e.g., Beniamini et al. 2019). Dependent on the initial fields, varying weak (probably dominating) to strong r-process conditions can be obtained, the latter, however, only for precollapse fields beyond 1012 G (Winteler et al. 2012; Mösta et al. 2014, 2015, 2018; Halevi & Mösta 2018; Nishimura et al. 2015, 2017; Bugli et al. 2020; Reichert et al. 2021). Case (d) has been proposed for a while. Dependent on the nuclear equation of state for massive core-collapse events, the collapse of the proto-neutron star to a black hole can be avoided (in a narrow stellar mass range) due to a quark-hadron phase transition with the right properties. The ejecta would experience a weak r-process, but populating even the actinides, however, with negligible abundances (Fischer et al. 2020b). Case (e) has been extensively discussed in the context of long-duration gamma-ray bursts (Woosley 1993; MacFadyen & Woosley 1999; MacFadyen et al. 2001). They involve the collapse of massive stars that rotate rapidly enough so that an accretion torus can form outside of the last stable orbit of a forming black hole, and they go along with relativistic polar and nonrelativistic torus outflows. This scenario has been proposed by Cameron (2003) as an r-process site and recently been examined in more detail by Siegel et al. (2019) and Siegel (2019). The remaining site, (f), is related to compact binary mergers (see Thielemann et al. 2017; Rosswog et al. 2017; Cowan et al. 2021, for overviews).


The most unique and characteristic observational feature of blazars’ highly variable broadband emission is the broad bimodal SED extending from the lowest accessible EM band, i.e., the radio, to the highest accessible, i.e., GeV-TeV γ-rays. The broadband SED of all blazars can be categorized into three different spectral subclasses: low-energy-peaked (LBL/LSP), intermediate-energy-peaked (IBL/ISP), and high-energy-peaked (HBL/HSP; Fossati et al. 1998; Abdo et al. 2010), based on the location of the low-energy hump. A remarkable property of each spectral subclass is the stability of the location of the two peaks despite huge variations in flux and often spectral shape. Only in a few rare instances has an appreciable shift in the location of the peaks been observed, e.g., the 1997 outburst of Mrk 501 (Pian et al. 1998; Ahnen et al. 2018) and the activity of OJ 287 from the end of 2015 to the middle of 2017 (Kushwaha et al. 2018a, 2018b). Even these two cases are remarkably different. In the case of Mrk 501, the locations of both the peaks shifted to higher energies. On the contrary, in OJ 287, a shift in the location of only the high-energy peak was observed during the 2015–2016 activity (Kushwaha et al. 2018a, 2019), while in 2016–2017 a new broadband emission component overwhelmed the overall emission, appearing as an overall shift in both the peaks as revealed in the detailed study by Kushwaha et al. (2018b). With the SED being the prime observable for exploration of the yet-debated high-energy emission mechanisms, such changes offer invaluable insights about the emission processes. For example, in Mrk 501 the shift in both peaks strongly implies the same particle distribution for the overall emission, while for OJ 287 the shift of only the high-energy peak can be reproduced by either inverse Compton scattering of the broad-line region photon field (Kushwaha et al. 2018a) or emission of hadronic origin (Oikonomou et al. 2019; Rodríguez-Ramírez et al. 2020).


Fig. 7 also shows that there is little evidence for a relation between the Ly α luminosity and M1500 for Ly α-selected sources at z = 5.7 in our UV and Ly α luminosity range. As both M1500 and LLy α are, to first order, related to the SFR, we would have expected a correlation. To illustrate this, we show lines at constant Ly α escape fractions (based on the assumption that SFRUV = SFRH α, case B recombination with T = 10 000 K and ne = 100 cm−3 and no attenuation due to dust). This result resembles the well-known Ando et al. (2006) diagram, which reveals a deficiency of luminous LAEs with bright UV magnitudes between z ≈ 5 and 6. More recently, other surveys also revealed that the fraction of high-EW Ly α emitters increases towards fainter UV magnitudes (e.g. Schaerer, de Barros & Stark 2011; Stark, Ellis & Ouchi 2011; Cassata et al. 2015). The lack of a strong correlation between M1500 and LLy α might indicate that the SFRs are bursty (because emission-line luminosities trace SFR over a shorter time-scale than UV luminosity), or that the Ly α escape fraction is anti-correlated with M1500 (such that Ly α photons can more easily escape from galaxies that are fainter in the UV). A possible explanation for the latter scenario is that slightly more evolved galaxies (which are brighter in the UV) have a slightly higher dust content (e.g. Bouwens et al. 2012), affecting their Ly α luminosity more than the UV luminosity. It is interesting to note that several galaxies lie above the 100  per cent Ly α escape fraction line. This implies bursty or stochastic star formation (which is more likely in lower mass galaxies with faint UV luminosities, e.g. Mas-Ribas, Dijkstra & Forero-Romero 2016), alternative Ly α production mechanisms to star formation (such as cooling), a higher ionizing production efficiency (for example due to a top-heavy IMF or binary stars, e.g. Gotberg, de Mink & Groh 2017), or dust attenuating Ly α in a different way than the UV continuum (e.g. Neufeld 1991; Finkelstein et al. 2008; Gronke et al. 2016).


We considered a homogeneous, collisionless two species plasma consisting of electrons and ions (H+ ions) in the simulation model. The ambient plasma parameters for ions and electrons are given in Table 2. The ions and electrons are considered to be fluid and their dynamic is incorporated into the simulation model using the following model equations viz., the continuity, momentum, and pressure equations of each species, and the Poisson equation (Kakad et al. 2014) given by
1

∂nj∂t+∂(njvj)∂x=0,

2

∂vj∂t+vj∂vj∂x+1mjnj∂Pj∂x−qjmjE=0,

3

∂Pj∂t+vj∂Pj∂x+γjPj∂vj∂x=0,

4

∂E∂x=∑jqjnj/ϵ0.

Here, the electric field E = −∂ϕ/∂x and the variables n

j
, P

j
, and v

j
 are the plasma density, thermal pressure, and velocity of species j, respectively. The subscripts j = e and j = i are, respectively, used for electrons and ions. m

j
 and q

j
 represent the mass and the charge of species j, respectively. For electrons q

e
 = −e and ions q

i
 = e., ϵ
0 is the electric permittivity. In Equation (3), electrons and ions are treated as adiabatic with the same adiabatic index γ

e
 = γ

i
 = 3. The above set of equations is solved numerically. The spatial derivatives in these equations are solved using the fourth order central finite difference method and time derivatives are integrated using the leap-frog method to achieve second order accuracy. The details of the development of the simulation model are given in Kakad et al. (2013). We used a compensated filter to eliminate the small wavelength modes linked with such numerical noise (Lotekar et al. 2016; Kakad et al. 2016b). These numerical schemes are highly stable, and in the past, several electrostatic solitary wave structures have been modeled using such fluid simulations in multispecies plasmas (Kakad et al. 2014, 2016a). Δx and Δt are respectively considered as the grid size in spatial and time domain, and their values are taken in such a way that it fulfills the Courant–Friedrichs–Lewy condition, i.e.,

cΔtΔx≤1

, which is necessary for the convergence of the explicit finite difference method. Here, c is the speed of light. We performed two simulation runs in a one-dimensional system with the periodic boundary conditions by considering the observed ambient parameters as (i) T

e
 = 60 eV, T

i
 = 300 eV, n

i0 = 15/cc, n

e0 = 15/cc, V
di = V
de = −50 km s−1 (2) T

e
 = 30 eV, T

i
 = 300 eV, n

i0 = 15/cc, n

e0 = 15/cc, V
di = V
de = −50 km s−1 (see Table 2 for more details). In the simulations, we considered the real mass ratio, i.e., m

i
/m

e
 = 1836. The background electron and ion densities satisfy the quasi-neutrality, i.e., n

e0 = n

i0 = n
0. For electron temperature, two values are considered based on the observations, i.e., 60 and 30  eV (see Figure 6(d)). The values of ω
pi, ω
pe, λ

i
, and λ

e
 for the considered parameters are 5.1 × 103 rad s−1, 2.18 × 105 rad s−1, 33.3 m, and 14.9 m, respectively. To initiate the simulations, we used a localized Gaussian-type initial density perturbation in the equilibrium electron and ion densities given by
5

δn=Δnexp−x−xcl02.

Here, Δn and l
0 are the amplitude and width of the initial density perturbations, respectively. Thus, the perturbed density at t = 0 is n

j
(x) = n

j0 + δn. We consider the simulation system length as L

x
, and x

c
 = L

x
/2 is the center of the simulation system. We performed two simulation runs for the parameters given in Table 2. For these simulation runs, we consider the time interval dt = 1 × 10−3, the grid spacing dx = 0.2, system length L

x
 = 7000, l
0 = 1, and Δn = 0.1. Here, time is expressed in units of ω
pi
−1, space is in λ
di, and density is in units of n

i0.


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.

Differences Similarities Similarities Differences


From the result of the χ2 minimization, we found that the minimized χ2 values agree with the expected values, i.e. the computed χ2 are typically in the range of ($\mathrm{d.o.f.}-\sqrt{2 \mathrm{d.o.f.}}$, $\mathrm{d.o.f.}+\sqrt{2 \mathrm{d.o.f.}}$), where d.o.f. is the number of degrees of freedom. This means that the fits describe the observed data rather well. The only exception is with χ2 ≈ 20, which occurs for nearby AGN, z  0.2, and for the highest energy band, E > 10 GeV. Note that there is a strong contribution of the source, Mrk 421, in the first redshift interval at high energies, E > 10 GeV for quiescent states. Mrk 421 is a very hard spectrum γ-ray source with a photon index of ≈1.77 and its semiminor and semimajor axes at 68 per cent confidence are of 0$_{.}^{\circ}$0067 as derived in Nolan et al. (2012). Semiminor and semimajor axes of many 2FGL sources are derived with one order of magnitude higher uncertainties than those for Mrk 421 in the 2FGL catalogue (Nolan et al. 2012). We noted that the discrepancy between the observation and model is particularly strong in the annular bin, r  0$_{.}^{\circ}$05, for the redshift interval z  0.2 and for the highest energy band, E > 10 GeV. If we exclude photons from Mrk 421, then the minimized χ2 value is 7.5 and is consistent with the expected one. In the limit of a large number of counts in each bin, the likelihood is given by $\mathcal {L}=\text{exp}(-\chi ^{2}/2)$, so that minimizing χ2 is equivalent to maximizing the likelihood, $\mathcal {L}$. We found that the inclusion of a pair halo component in the model does not improve the likelihood value sufficiently to establish the presence of this pair halo component in the data. Therefore, we derived the one-sided 95 per cent upper limit on the fraction of photons attributable to a pair halo component by fitting the normalization of this component, for which we increase its normalization until the maximum likelihood decreases by 2.71/2 in logarithm. The computed upper limits are between 2 and 6 per cent depending on energy band and redshift interval. These upper limits are stronger than those obtained before. Note that the model for a point-like source used in the likelihood analysis is considered to be precisely established, however, the number of photons recorded during flaring states is close to those numbers of photons recorded during quiescent states for each of these redshift intervals. The expression, such as equation (1), leads to more conservative upper limits on the fraction of photons attributable to a pair halo component, since it takes the error bars assigned to the model into account. If the point-like source model is considered well established, then the error bars shown in Table 3 would decrease by a factor of ≈1.5.


The knowledge of physical properties, the structure, and the kinematics of the matter in the vicinity of supermassive black holes (SMBH) is essential to build detailed models of the clumpy outflow and to test the disc-wind scenario. While X-ray variability studies can provide accurate information on the atomic and ionized matter on scales of the BLR, the radio emission from luminous H2O masers (the so-called “megamasers”) constitutes a fundamental instrument to study the geometry and kinematics of the molecular gas at sub-parsec distance from SMBH. H2O masers may trace distinct regions in the AGN environment, from nearly edge-on accretion discs to nuclear outflows in the form of jets or winds (for recent reviews see Henkel et al. 2005; Lo 2005; Greenhill 2007; Tarchi 2012). Very Long Baseline Interferometry (VLBI) and single-dish monitoring studies of disc-masers allow us to map accretion discs and to determine the enclosed dynamical masses (e.g. Kuo et al. 2011). Jet-masers observations, instead, can provide estimates of the velocity and density of jet material (Peck et al. 2003). H2O maser emission have been also found to be associated with nuclear winds at 1 pc from the nuclear engine. In particular, water maser observations in Circinus (Greenhill et al. 2003) and NGC 3079 (Kondratko et al. 2005) seem to have resolved individual outflowing torus clouds. In fact, Greenhill et al. (2003) discovered that the H2O masers in Circinus trace both a Keplerian disc and a wide-angle outflow which appears to be collimated by the warps of the disc. In NGC 3079, VLBI observations of the maser emission revealed a clumpy thick disc. In addition to that, four maser features were found to be located at high latitude above the disc (at ~0.5 pc from the disc plane) and interpreted as part of a nuclear wind by Kondratko et al. (2005). Proper motion measurements and comparison of these outflow-masers with their disc counterpart provide the most promising method for probing the structure and kinematics of the torus molecular clouds (Nenkova et al. 2008).


GX 301-2 is an HMXB consisting of a highly magnetized (B ∼ 4 × 1012 G, or even larger Doroshenko et al. 2010) pulsar and a B-type hyper-giant star Wray 977 (Vidal 1973; Kaper et al. 1995; Staubert et al. 2019). According to modelling of high-resolution optical spectra, Wray 977 has a mass of 43 ± 10 $\, \mathrm{M}_{\odot }$, a radius of 62 R⊙, and looses mass through powerful stellar winds at a rate of $\sim \! 10^{-5}\, \mathrm{M}_\odot \, {\rm yr}^{-1}$ with terminal velocity of 300 $\rm km\, s^{-1}$ (Kaper, van der Meer & Najarro 2006). The system is highly eccentric (e ∼ 0.46), with an orbital period of ∼41.5 d, and exhibits strong variation of the X-ray flux with orbital phase (Koh et al. 1997; Doroshenko et al. 2010). In particular, periodic outbursts at the orbital phase ∼1.4 d before the periastron passage (Sato et al. 1986), and a fainter one near the apastron passage are observed (Pravdo et al. 1995). The broad-band X-ray spectrum is orbital phase-dependent and can be approximately described as a power law with a high-energy cutoff and a cyclotron resonant scattering feature around 40 keV (Kreykenbohm et al. 2004; Mukherjee & Paul 2004; La Barbera et al. 2005; Doroshenko et al. 2010; Suchy et al. 2012; Islam & Paul 2014; Fürst et al. 2018; Nabizadeh et al. 2019). During the periastron flares, the source exhibits strong variability with an amplitude of up to a factor of 25, reaching a few hundreds mCrab in the energy band of 2–10 keV (e.g. Rothschild & Soong 1987; Pravdo et al. 1995). The flares are accompanied by the variability of the equivalent hydrogen column density ($\rm \mathit{ N}_{\rm H}$) and of the fluorescent iron lines, which is believed to be associated with clumpiness of the stellar wind, launched from the donor star (Mukherjee & Paul 2004). We note the clumpiness in this paper refers to any inhomogeneities in the stellar wind/stream, which are higher density regions, regardless of its specific formation mechanisms. On the other hand, Fürst et al. (2011) reported a long XMM–Newton observation in GX 301-2 around its periastron, which also exhibits systematic variations of the flux and $\rm \mathit{ N}_{H}$ at a time-scale of a few kiloseconds. Several wind accretion models, consisting of stellar winds and a gas stream, were proposed to explain the observed flares (e.g. Haberl 1991; Leahy 1991; Leahy & Kostka 2008; Mönkkönen et al. 2020).


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


NGC 2110. NGC 2110 is another nearby (z = 0.00779, Gallimore et al. 1999), X-ray bright Seyfert galaxy. Diniz et al. (2015) report a black hole mass of

2
.

7

−
2.1

+
3.5

×

10
8

M
⊙

$ 2.7^{+ 3.5}_{- 2.1} \times 10^{8}\,{{M}_{\odot}} $

, from the relation with the stellar velocity dispersion. From BeppoSAX data, Malaguti et al. (1999) found the X-ray spectrum to be affected by complex absorption. This has been later confirmed by Evans et al. (2007), who find the Chandra+XMM–Newton data to be well fitted with a neutral, three-zone, partial-covering absorber. Rivers et al. (2014) find the Suzaku data to be well fitted with a stable full-covering absorber plus a variable partial-covering absorber. A soft excess below 1.5 keV is also present (Evans et al. 2007), and possibly due to extended circumnuclear emission seen with Chandra (Evans et al. 2006). No Compton reflection hump has been detected with Suzaku (Rivers et al. 2014) or NuSTAR (Marinucci et al. 2015), despite the presence of a complex Fe Kα line. According to the multi-epoch analysis of Marinucci et al. (2015), the Fe Kα line is likely the sum of a constant component (from distant, Compton-thick material) and a variable one (from Compton-thin material). Concerning the high-energy cut-off, ambiguous results have been reported in literature (see Table 1). Ricci et al. (2017) report a value of

448

−
55

+
63

$ 448^{+63}_{-55} $

 keV, while Lubiński et al. (2016) report a coronal temperature of

230

−
57

+
51

$ 230^{+51}_{-57} $

 keV and an optical depth of

0
.

52

−
0.13

+
0.14

$ 0.52^{+ 0.14}_{- 0.13} $

. From 2008–2009 INTEGRAL data, Beckmann & Do Cao (2010) report a cut-off of ∼80 keV with a hard photon index, but these results are not confirmed by NuSTAR (Marinucci et al. 2015). Indeed, only lower limits to the high-energy cut-off have been found with NuSTAR (210 keV: Marinucci et al. 2015), Suzaku (250 keV: Rivers et al. 2014) and BeppoSAX (143 keV: Risaliti 2002). No hard X-ray spectral variability has been detected by Caballero-Garcia et al. (2012) and Soldi et al. (2014) from BAT data, despite the significant flux variability.


Inspection of Equation (25) reveals that for pitch angles satisfying

,

 so that curvature drift energization is more efficient than generalized betatron energy loss during incompressible contraction/merging of small-scale flux ropes. When μ2  1/3, betatron energy loss dominates curvature drift energization. That is why the net acceleration obtained from the two competing acceleration mechanisms depends sensitively on the anisotropy characteristics of the energetic particle pitch-angle distribution as discussed above. Consider the following three possibilities: (1) If energetic particles maintain a highly beamed pitch-angle distribution (which requires negligible pitch-angle scattering), curvature drift energy gain strongly dominates generalized betatron energy loss, and for all practical purposes we have a first-order Fermi acceleration mechanism as a consequence of incompressible contraction or merging of curved flux-rope magnetic fields (de Gouveia dal Pino & Lazarian 2005; Drake et al. 2006, 2010). (2) If the energetic particle distribution stays purely isotropic (extremely strong pitch-angle particle scattering), we can average the last terms in Equation (25) over all μ values to find

, indicating that the probability for curvature drift energy gain equals the probability for betatron energy loss (Drake et al. 2010). This supports the conclusion made above that net acceleration requires and depends only on the anisotropic part of the distribution. (3) The energetic particle distribution maintains a particle distribution with a small pitch-angle anisotropy (efficient pitch-angle scattering consistent with the diffusion approximation). In this case particle energization by incompressible contraction or merging of curved flux-rope magnetic fields becomes a second-order Fermi acceleration process (Drake et al. 2013; Zank et al. 2014; le Roux et al. 2015a). The small anisotropy option is supported by self-consistent particle simulations of turbulent magnetic reconnection and island formation at stacked primary current sheets in the absence of a guide field (Schoeffler et al. 2011; Drake et al. 2013), because energetic particles are scattered by fluctuations generated by plasma instabilities such as the firehose and magnetic mirror instabilities, resulting in energetic charged particle distributions with small anisotropies. However, in the presence of a strong guide field, particle simulations suggest larger anisotropies owing to weaker instabilities (Dahlin et al. 2017; Li et al. 2018).


Traditionally, GCs have been considered as relatively simple spherical, non-rotating, and almost completely relaxed systems. However, observational results obtained in the past few years are demonstrating that they are much more complex than previously thought. In particular, the classical simplified approach of neglecting rotation in GCs has become untenable from the observational point of view. In fact, there is an increasing wealth of observational results suggesting that, when properly surveyed, the majority of GCs rotate at some level. As of today, more than $50{{\ \rm per\ cent}}$ of the sampled GCs show clear signatures of internal rotation (e.g. Anderson & King 2003; Bellazzini et al. 2012; Fabricius et al. 2014; Bianchini et al. 2018; Ferraro et al. 2018; Kamann et al. 2018a; Lanzoni et al. 2018a,b; Sollima, Baumgardt & Hilker 2019). Moreover, evidence of rotation has also been reported for intermediate-age clusters (Mackey et al. 2013; Kamann et al. 2018b), young massive clusters (Hénault-Brunet et al. 2012; Dalessandro et al. 2021), and nuclear star clusters (Nguyen et al. 2018; Neumayer, Seth & Böker 2020) indicating that internal rotation is a common ingredient across dense stellar systems of different sizes and ages. On the theoretical side, the presence of internal rotation has strong implications on our understanding of the formation and dynamics of GCs and affects, for example, their long-term evolution (Einsel & Spurzem 1999; Ernst et al. 2007; Breen, Varri & Heggie 2017) and their present-day morphology (e.g. Hong et al. 2013; van den Bergh 2008). Moreover, signatures of internal rotation could be crucial in revealing the formation mechanisms of the so-called multiple stellar populations (MPs) in GCs (Bekki 2010; Mastrobuono-Battisti & Perets 2013; Hénault-Brunet et al. 2015) differing in terms of their light-element (such as He, Na, O, C, N) abundances (see Bastian & Lardo 2018; Gratton et al. 2019 for recent reviews on the subject), and which are observed in almost all GCs now. Differences in the rotation amplitudes of MPs have been observed in two cases so far, namely M 13 and M 80 (Cordero et al. 2017; Kamann et al. 2020)1 and in both clusters the Na-rich population (also known as second population or generation – SP) is found to rotate with a larger amplitude than the first population FP (Na-poor).


Molecular CO gas is observed in the sub-mm with both single-dish telescopes (JCMT, APEX) and interferometers such as ALMA, the SMA or NOEMA. For the brightest targets, ALMA's high-resolution and unprecedented sensitivity allow us to obtain CO maps for different lines and isotopes showing the location of CO belts and giving an estimate of their mass (see the CO gas disc around β Pic, Dent et al. 2014; Matrà et al. 2017). Atomic species are also detected around a few debris disc stars. In particular, Herschel was able to detect the O i and C ii fine structure lines in two and four systems, respectively (e.g. Riviere-Marichalar et al. 2012, 2014; Roberge et al. 2013; Cataldi et al. 2014; Brandeker et al. 2016). Also, metals have been detected, using UV/optical absorption lines, around β Pictoris (Na, Mg, Al, Si and others, Roberge et al. 2006), 49 Ceti (Ca ii, Montgomery & Welsh 2012) and HD 32297 (Na i, Redfield 2007). Some of these metals are on Keplerian orbits but should be blown out by the ambient radiation pressure (Olofsson, Liseau & Brandeker 2001). It is proposed that the overabundant ionized carbon observed around β Pic, which is not pushed by radiation pressure could brake other ionized species due to Coulomb collisions with them (Fernández, Brandeker & Wu 2006). A stable disc of hydrogen has not yet been observed in these systems (Freudling et al. 1995; Lecavelier des Etangs et al. 2001) but some high velocity H i component (presumably falling on to the star) was detected recently with the HST/COS around β Pic (Wilson et al. 2017). All these observations need to be understood within the framework of a self-consistent model. Models of the emission of the gas around main sequence stars have been developed, but gas radial profiles were not derived self-consistently and often assumed to be Gaussian (e.g. Zagorovsky, Brandeker & Wu 2010) or not to be depleted in hydrogen compared to solar (as expected in debris discs, e.g. Gorti & Hollenbach 2004) or both (e.g. Kamp & Bertoldi 2000).


Observational evidence suggests that SNe IIn are aspherical and may have high polarization signals. An ∼ 20 per cent level of SN asphericity may result in a detectable 1 per cent linear polarization signal (Höflich 1991; Leonard & Filippenko 2005). While a number of efforts have been made to explain core-collapse SNe in terms of axisymmetric jets (Khokhlov et al. 1999; Wheeler, Meier & Wilson 2002; Wang et al. 2002), observational evidence in the form of loops in the Q/U plane suggests that even these axisymmetric models may not be sufficient for all types of core-collapse SNe (Hoffman et al. 2008; Wang & Wheeler 2008; Maund et al. 2009). In contrast to SNe IIn, SNe II-P generally have shown very low levels of polarization at early times (Leonard & Filippenko 2001; Leonard et al. 2002a; however, see Leonard et al. 2016; Mauerhan et al. 2017). The initially low polarization levels often rise during the plateau phase (e.g. Leonard et al. 2016), with a polarization angle that typically remains nearly fixed throughout (e.g. Leonard et al. 2001; Mauerhan et al. 2017). Occasionally, a sharp rise in the polarization signal is seen during the transition to the nebular phase (Leonard et al. 2006; Chornock et al. 2010), perhaps suggesting that the core of the SN is more aspherical than the early-time photosphere (Chugai et al. 2005; Chugai 2006). However, as demonstrated by the modelling of Dessart & Hillier (2011), it is also possible that even large asymmetries during the plateau phase will produce very little polarization, owing to the high optical depth to electron scattering and the fact that geometric information is lost due to multiple scatters. The ‘spike’ that is sometimes seen during the drop off of the plateau may, therefore, be more of an optical-depth effect (i.e. the ‘spike’ occurs when $\tau _{e^-}$ has decreased to unity) than a demonstration of increasing asphericity with depth in the atmosphere (Leonard et al. 2012). The picture for SNe IIn, on the other hand, is not as well understood. The primary reason for this is that an effective model for a SN IIn must not only account for the geometry of the SN ejecta, but also the geometry of the CSM interaction region (Chugai 2001). In such cases, the temporal evolution that multi-epoch spectropolarimetry provides becomes particularly important in establishing a physical model.


Different methods have been proposed to detect the hot, highly ionized WHIM gas: detection in galaxy groups with Sunyaev–Zeldovich effect (Hill et al. 2016; de Graaff et al. 2019; Lim et al. 2020; Tanimura et al. 2020) using autocorrelation function measurements (Galeazzi et al. 2010), with absorption lines in quasar sightline (Kovács et al. 2019) and using CMB as a backlight (Ho, Dedeo & Spergel 2009). Given the challenges of X-ray data, observations at longer wavelengths (UV and optical) benefit from higher instrumental throughout, enhanced spectral resolution. By reverting to ground-based facilities, longer exposure times and larger number of targets become possible. Nevertheless, the UV lines have so far mostly been used to detect absorbing gas with temperature range $10^5\, \mathrm{K} \lt T \lt 10^6\, \mathrm{K}$ from either O vi (Tripp, Savage & Jenkins 2000; Danforth & Shull 2005; Danforth & Shull 2008; Tripp et al. 2008; Savage et al. 2014; Werk et al. 2014; Danforth et al. 2016; Sanchez, Morisset & Delgado-Inglada et al. 2016) or BLAs (Lehner et al. 2007; Danforth, Stocke & Shull 2010). Recently, Zastrocky et al. (2018) have constrained the Milky Way’s hot (T = 2 × 106 K) coronal gas using the forbidden 5302 Å transition of Fe xiv. Only recently, some highly ionized iron UV lines detected in emission have been used as diagnostics of gas at temperatures of T = 107 K. Out of several forbidden lines in the UV that could trace this gas temperature range, and from various species of highly ionized iron, the emission of [Fe xxi] is the brightest (Anderson & Sunyaev 2016). Anderson & Sunyaev (2018) report the discovery of [Fe xxi] in emission in a filament projected 1.9 kpc from the nucleus of M87. Theoretically, the highly ionized iron UV lines can be observed in absorption as well. The forbidden line of [Fe xxi], in particular, has the largest effective cross-section for absorption and a rest wavelength λ1354 Å, conveniently close to Ly α λ1215 Å.


The MOJAVE survey provides access to excellent Very Long Baseline Array (VLBA) data taken at 15 GHz. This is of great value for investigating AGN properties on a statistical basis (e.g., Lister et al. 2016; Homan et al. 2015). Whereas the MOJAVE team is providing a statistical analysis of the complete sample, our approach is to select and focus on specific sources which appear to be special due to unique or rare properties. Although a statistical analysis of large numbers of sources is certainly of utmost importance and great value, a detailed analysis concentrating on peculiar properties – that are not necessarily common to the AGN population – can produce complementary results. We re-modeled fifty VLBA observations of 1308+326 obtained at 15 GHz (taken from the online MOJAVE archive webpage) between 1995.05 and 2014.07 with Gaussian components within the difmap-modelfit program (Shepherd 1997). The modelfit program fits image-plane model components to the visibilities in the uv plane. We did not apply self-calibration but used the calibration as provided by the MOJAVE team. Only circular components were used. The use of exclusively circular Gaussian components proved to be the most efficient way to parameterize the component properties. It reduces the number of free parameters, compared to the use of elliptical Gaussians, and allows a more secure identification of components across the epochs. Although it might have advantages to model the data of some of the epochs with elliptical components, our experience is that circular component modeling allows a more homogeneous analysis of all the epochs and more trustworthy identification of individual components in their long-term motion and evolution. Every epoch was modeled independently starting from a point source model. The errors were estimated from deviations in all parameters derived by calculating fits to models with ±1 component. All the images with model-fits superimposed are displayed in Figs. A.1–A.13. The parameters and corresponding uncertainties of the model-fits are listed in Table A.1. Components labeled with an “x” denote the presence of features that could not be reliably traced across the epochs. In addition we analyzed single-dish total intensity and polarization radio monitoring data at three radio frequencies, which was observed by the UMRAO monitoring program.


In this study, we use a model atom of Li i which was originally developed and tested by Cayrel et al. (2007) and Sbordone et al. (2010). For the purposes of the current work, the model atom was updated and now consists of 26 levels and 123 (96 of which are radiative) bound-bound transitions of Li i and the ground level of Li ii, with each level of Li i coupled to the continuum via bound-free transitions. (The ground state of Li ii in the current model atom is always in LTE, since lithium is mostly fully ionized throughout the model atmospheres studied in this work.) This renders the model atom complete up to the principal quantum number n = 6 and spectroscopic term \hbox{$^2{\rm F}^{\rm o}$}Fo2, with additional energy levels up to n = 9 and term 2D (Fig. 1). Data concerning atomic energy levels and transitions (level energies and statistical weights; wavelengths and Einstein coefficients of the bound-bound transitions) were taken from the NIST database. We used electron collisional excitation and ionization rates from the quantum mechanical computations of Osorio et al. (2011) for the energy levels of up to 5s (2S). Elsewhere, collisional excitation by electrons for radiatively permitted transitions was accounted for by using the classical formula of van Regemorter (1962), while the formula of Seaton (1962) was used to compute collisional electron ionization rates. To account for the collisional excitation by hydrogen, we used collisional excitation rates computed by Barklem et al. (2003), while the classical formula of Drawin (in the formulation of Lambert 1993) was used for radiatively permitted transitions when no quantum mechanical data were available. Hydrogen H–Li charge transfer rates were taken from Barklem et al. (2003) for the atomic levels up to 4p inclusive. Bound-free transitions resulting from collisions with hydrogen were expected to be inefficient and thus were ignored. Photoionization cross sections were taken from TOPBASE (Cunto et al. 1993). No scaling of collisional rates was applied in the calculations of bound-free and bound-bound transitions. Information about the energy levels and bound-bound radiative transitions, included in the present version of the Li i model atom, are provided in Tables A.1 and A.2, respectively. Twenty-seven transitions in the model atom are purely collisional. Collisional radiatively-forbidden transitions involving Li i levels beyond 5s were not accounted for since reliable quantum-mechanical data for these transitions are not available. We note that the role of the omitted transitions between the higher levels is minor: when they are taken into account using the formula of Allen (1973), collision strength Ω = 1, the change in the estimated abundance (which directly applies to abundance corrections, too) is always less than 0.05 dex, with typical values being significantly smaller.


Currently, the concept of the existence of genetic relations between comets and meteoroid streams as well as near-Earth asteroids (NEAs) is generally accepted. As a consequence, a new definition, the ‘comet–asteroid–meteoroid complex’, was introduced for the indication of the families of objects with a common origin. The certainty of the existence of such associations has been proved by numerous studies of the dynamical properties of some small bodies. For instance, the association of comet 2P/Encke with the Taurid meteoroid stream was confirmed by a number of investigations and does not raise any doubts. Furthermore, it was shown that more than 40 asteroids belong to the Taurid complex, i.e. they move on orbits close to those of the comet Encke and the Taurid stream. A cometary nature of these NEAs was suggested and a conclusion was made that they are either extinct fragments of comet Encke or represent (together with comet Encke) the remnants of a larger comet-progenitor of the stream (Asher, Clube & Steel 1993a; Babadzhanov 2001; Porubcan, Kornos & Williams 2004, 2006; Babadzhanov, Williams & Kokhirova 2008a; Rudawska, Vaubaillon & Jenniskens 2012a,b; Madiedo et al. 2013). This family of near-Earth objects with a common origin is named the Taurid comet–asteroid–meteoroid complex. The Quadrantid comet–asteroid–meteoroid complex is another well-known set of related NEOs that very probably includes comet 96P/Machholz 1 and certainly NEA 2003EH1 and the Quadrantid meteoroid stream, producing eight meteor showers observable on the Earth. It was shown that asteroid 2003EH1 is in fact the extinct fragment of a parent comet of the Quadrantid stream (Jenniskens 2004; Williams et al. 2004; Babadzhanov, Williams & Kokhirova 2008b; Neslusan, Hajdukova & Jakubik 2013). It turned out that the Piscid meteoroid stream contains three related NEAs moving within the stream and representing the extinct debris of a larger comet-progenitor of this complex (Babadzhanov & Williams 2007; Babadzhanov, Williams & Kokhirova 2008c). Based on investigation of the dynamical properties, it was found that three NEAs with similar comet-like orbits are associated with the ι Aquariid meteoroid stream and this asteroid–meteoroid complex is the result of the break-up of a parent comet (Babadzhanov, Williams & Kokhirova 2009).


We used the FLASH code (Fryxell et al. 2000) to perform the calculations. In particular we solved the equations for compressible gas dynamics with the FLASH implementation of the piecewise-parabolic method (Colella & Woodward 1984). The radiative losses Λ in Equation (2) are calculated through a table lookup/interpolation method. Also we extended the code by additional computational modules to calculate the deviations from electron-proton temperature-equilibration and the deviations from equilibrium of ionization of the most abundant ions. For the former, we calculated the ion and electron temperatures in each cell of the post-shock medium, taking into account the effects of Coulomb collisions (see Orlando et al. 2015 for the details of the implementation). According to Ghavamian et al. (2007), first the electrons are assumed to be heated at the shock front almost istantaneously up to kT ∼ 0.3 keV by lower hybrid waves. This istantaneous heating does not depend on the shock Mach number and is expected for fast shocks (i.e., >103 km s−1) as those simulated here. Then we considered the effects of the Coulomb collisions to calculate the evolution of ion and electron temperatures in each cell of the post-shock medium in the time Δtj = t − tshj, where tshj is the time when the plasma in the jth domain cell was shocked and t is the current time. The time tshj is stored in an additional passive tracer added to the model equations. To estimate the deviations from equilibrium of ionization of the most abundant ions, we adopted the approach suggested by Dwarkadas et al. (2010). In fact, this approach ensures high efficiency in the calculation (expecially in the case of 3D simulations as in our case) as well as a reasonable accuracy in the evaluation of the non-equilibrium of ionization effects. The approach consists of the computation of the maximum ionization age in each cell of the spatial domain τj = nejΔtj, where nej is the electron density in the jth cell and Δtj is the time since when the plasma in the cell was shocked (see above).


The first study, to our knowledge, to notice the net increase in the abundance of slow (s) neutron capture elements in young stellar populations is D’Orazi et al. (2009), in which the abundance of barium in young star clusters was seen to be higher than in the older ones. Maiorca et al. (2011, 2012) added a few more elements with important s-process contributions (yttrium, zirconium, lanthanum, and cerium), confirming the increasing trend towards younger ages. Subsequently, a number of works have attempted to both clarify the origin of this increase (see, e.g., Bisterzo et al. 2014; Mishenina et al. 2015; Trippella et al. 2016; Magrini et al. 2018; Spina et al. 2018; Busso et al. 2021) and to use their abundances to estimate the ages of stars, often using neutron capture s-process elements in combination with other elements with opposite behaviours, such as α elements – that we indicate as chemical clocks – and thus maximising the dependence of the relationship with age (see, e.g., Tucci Maia et al. 2016; Nissen 2016; Feltzing et al. 2017; Fuhrmann et al. 2017; Slumstrup et al. 2017; Titarenko et al. 2019). Once the existence of a relationship between age and chemical clocks was established (see, e.g., Spina et al. 2016; Delgado Mena et al. 2019; Jofré et al. 2020), the next steps were the following: (i) to clarify the applicability of these relationships with luminosity class (dwarf or giant) (see, e.g., Tucci Maia et al. 2016; Slumstrup et al. 2017; Casamiquela et al. 2021), metallicity (see, e.g., Feltzing et al. 2017; Delgado Mena et al. 2019; Casali et al. 2020), and population type (thin disc, thick disc, halo) (see, e.g., Titarenko et al. 2019; Nissen et al. 2020; Tautvaišienė et al. 2021), or even in dwarf galaxies (Skúladóttir et al. 2019; ii) to calibrate them with a sample of stars with reliable age determination, which are usually open star clusters (OCs), solar twins, or targets with asteroseismic observations. Finally, it is essential to understand whether these relationships are valid throughout the Galactic disc, or whether they are necessarily position-dependent. For the first time, Casali et al. (2020) applied the relations derived from a large sample of solar-like stars located in the solar neighbourhood and noted that they fail to reproduce the ages of star clusters in the inner disc. They concluded that the relationship between age and chemical clocks is not universal and that it varies with galactocentric position. Later, Magrini et al. (2021b) suggested that the differences in the relationships between age and chemical clocks in different parts of the Galactic disc are due to the strong dependence on the metallicity of the yields of low-mass stars, which produce s-process elements during the final stages of their evolution. Casamiquela et al. (2021) used red clump stars in open clusters to investigate the age dependence of several abundance ratios, including those that contain s-process and α elements. They found that the relationship between [Y/Mg] and ages outlined by open clusters is similar to the one found using solar twins in the solar neighbourhood. They also found that the abundance ratios involving Ba are those with the highest correlation with age. However, they also note that as one moves away from the solar neighbourhood, the dispersion increases and is in agreement with the findings of Casali et al. (2020), which attributed this to the spatial variation of the star formation history along the galactocentric radius.


Besides the Patchy and the LN mocks, we also model the multipoles of the BOSS CMASS two-point correlation function using an analytic approach, which is required to run the Monte Carlo analysis (see Section 5). The 2PCF can be obtained from the Fourier transform of the matter power spectrum, P(k), for which we assume the template from Padmanabhan & White (2008):
(10)$$\begin{eqnarray*}
P(k)=\left[P_{\rm {lin}}(k)-P_{\rm {dw}}(k)\right]e^{-k^2\Sigma _{\rm {nl}}^2/2}+P_{\rm {dw}}(k) .
\end{eqnarray*}$$In the equation above, Plin(k) is the linear matter power spectrum computed using the Boltzmann code CLASS (Lesgourgues 2011), assuming the Planck 2015 (Ade et al. 2016) fiducial cosmology. The Pdw(k) term is the de-wiggled power spectrum (Eisenstein & Hu 1998), while the Σnl parameter encodes the smoothing of the BAO peak due to non-linear effects (Crocce & Scoccimarro 2006). The multipoles of the analytic 2PCF are defined as
(11)$$\begin{eqnarray*}
\xi _l(s) = \frac{i^l}{2\pi ^2}\int _0^{\infty } P_l(k)j_l(ks)k^2{\rm d}k ,
\end{eqnarray*}$$from which we recover the monopole (l = 0) and the quadrupole (l = 2). In equation (11), jl(x) represents the spherical Bessel function of first kind and order l, while Pl(k) are the multipoles of the power spectrum defined as
(12)$$\begin{eqnarray*}
P_l(k)=\frac{2l+1}{2}\int ^1_{-1}\left(1+f\mu ^2\right)^2P(k)L_l(\mu){\rm d}\mu ,
\end{eqnarray*}$$where Ll(x) is the Legendre polynomial of order l and P(k) is the template given in equation (10). By replacing equation (12) in equation (11), the analytic expressions for monopole (l = 0) and quadrupole (l = 2) are respectively (Xu et al. 2012):
(13)$$\begin{eqnarray*}
\xi _{\rm {model}}^{(0)}(s) = B_0\xi _0(\alpha s)+a_0^{(0)}+\frac{a_1^{(0)}}{s}+\frac{a_2^{(0)}}{s^2} ,
\end{eqnarray*}$$(14)$$\begin{eqnarray*}
\xi _{\rm {model}}^{(2)}(s) = B_2\xi _2(\alpha s)+a_0^{(2)}+\frac{a_1^{(2)}}{s}+\frac{a_2^{(2)}}{s^2} ,
\end{eqnarray*}$$where α is the shift parameter, while $(a_1^{(i)},a_2^{(i)},a_3^{(i)})$ are linear nuisance parameters.


The technique of weak lensing offers direct measurement of the total matter distribution of a galaxy cluster (baryonic and dark matter), and can thus provide an unbiased mass calibration. Weak lensing manifests itself as small but coherent distortions of distant galaxies that result from the gravitational deflection of light due to foreground structures (e.g., Kaiser 1992). Cluster weak lensing appears as a tangential shear of background galaxy shapes around a cluster. Numerous attempts to calibrate SZ masses have been made in the literature using ACT clusters (Miyatake et al. 2013; Jee et al. 2014; Battaglia et al. 2016), SPT clusters (McInnes et al. 2009; High et al. 2012; Schrabback et al. 2018; Stern et al. 2019; Dietrich et al. 2019), Planck clusters (von der Linden et al. 2014b; Hoekstra et al. 2015; Penna-Lima et al. 2017; Sereno et al. 2017; Medezinski et al. 2018a), Planck and SPT clusters (Gruen et al. 2014), and other massive cluster samples (Marrone et al. 2009, 2012; Hoekstra et al. 2012; Smith et al. 2016). The mass calibration is often parameterized as
1

where MSZ is the SZ mass and Mtrue is the true cluster mass, which for this paper we take to be the weak-lensing mass MWL. This ratio can be taken for individual clusters or for an ensemble average and these values will be consistent as long as the appropriate weights are used (Medezinski et al. 2018a). Recently, Planck Collaboration et al. (2016d) reported a disagreement between 1−b obtained by weak-lensing calibrations of Planck SZ cluster masses (e.g., von der Linden et al. 2014b; Hoekstra et al. 2015) and that inferred from reconciling the Planck primary CMB parameters with the Planck SZ cluster counts. This disagreement is not statistically significant (∼2σ) and will decrease after accounting for additional bias corrections, like Eddington bias (Battaglia et al. 2016) and new optical depth measurements (Planck Collaboration et al. 2016e). However, if such a disagreement persists as the precision of cluster measurements improves, then it could reveal the need for extensions to the standard cosmological model (Planck Collaboration et al. 2016c), like a non-minimal sum of neutrino masses (e.g., Wang et al. 2005; Shimon et al. 2011; Carbone et al. 2012; Mak & Pierpaoli 2013; Louis & Alonso 2017; Madhavacheril et al. 2017), or illuminate additional systematic effects in cluster abundance measurements.


With a stellar mass of 5 × 1010 M⊙ (Viaene et al. 2014), Andromeda belongs to the transition regime between the active blue-sequence galaxies and passive red-sequence galaxies (e.g. Bower et al. 2017; Baldry et al. 2006), which happens around the stellar mass of 3 × 1010 M⊙ (e.g. Kauffmann et al. 2003). This galaxy is a prototype galaxy from the Local Group where the star formation has been quenched in the central part. Andromeda hosts both very little gas and very little star formation, while the black hole is basically quiet and has some murmurs (Li et al. 2011). In a previous study about M 31 nucleus, Melchior & Combes (2017) have shown that there is no gas within the sphere of influence of the black hole. Indeed, the gas has been exhausted. Most scenarios of the past of evolution of Andromeda reproduce the large scale distribution and show evidence of a past activity rich in collisions (Ibata et al. 2001, 2014; Thilker et al. 2004; Gordon et al. 2006; McConnachie et al. 2009; Miki et al. 2016; Hammer et al. 2018). However, the exact mechanism quenching the activity in the central kiloparsec is still unknown (Tenjes et al. 2017). Block et al. (2006) proposed a frontal collision with M 32, which could account for the two ring structures observed in the dust distribution. Melchior & Combes (2011, 2016) showed the presence of gas along the minor axis and support the scenario of the superimposition of an inner 1 kpc ring with an inner disc. Melchior & Combes (2013) estimated a minimum total mass of 4.2 × 104 M⊙ of molecular gas within a (projected) distance to the black hole of 100 pc. This is several orders of magnitude smaller than the molecular gas present in the central molecular zone of the Milky Way (Pierce-Price et al. 2000; Molinari et al. 2011). In the Galaxy, while large amounts of dense gas are present in the central region, Kruijssen et al. (2014) discussed the different processes that combine to inhibit star formation, which was observed to be a factor ten times weaker than expected (e.g. Leroy et al. 2008).