The diffuse hot gas X-ray luminosities in the 0.3–8 keV band are taken from the work of KF15. They have carefully removed the contribution from discrete sources such as low-mass X-ray binaries (Fabbiano 2006) to the total X-ray luminosity, leaving the diffuse gas contribution LX, Gas. A correction to bolometric would increase the X-ray luminosities by 0.08 dex on average. Most of the X-ray data come from Chandra observations. However, for some high-mass galaxies, the X-ray emission is particularly extended (e.g. NGC 4374, 4486, 4649, 5846) and in those cases ROSAT data from O‘Sullivan et al. (2001), corrected to the Chandra energy band, are used. Although the contribution from discrete sources in the ROSAT data cannot be subtracted as accurately as it can for Chandra data, their contribution is only about 1 per cent of the diffuse gas luminosity for these high-mass galaxies (see O'Sullivan et al. 2001). For further details, see KF15. Here we make a very small correction to the KF15 LX,Gas luminosities for the distances used in the SLUGGS survey (Brodie et al. 2014). The KF15 compilation did not include several galaxies that appear in the Alabi et al. (in preparation) study. Here we also include the X-ray luminosities for NGC 720, NGC 1316 and NGC 3115 from Boroson et al. (2011), and for NGC 5128 from KF13. Su et al. (2014) conducted a detailed XMM and Chandra study of NGC 1400. As well as the X-ray emission centred on NGC 1400, they detected an enhanced region of X-rays to the NE of the galaxy that they associated with stripped gas. Here we use the X-ray luminosity centred on NGC 1400 with a small adjustment to our X-ray band and distance, and assume an uncertainty of 20 per cent. We note that the X-ray luminosity would double if the enhanced region were also included. Two galaxies in Alabi et al. (in preparation) but not included here are NGC 2974 (not observed by Chandra) and NGC 4474 (the Chandra observation was only 5 ks).


Supernovae (SNe) play a dual role in the evolution of interstellar dust. On one hand, they are the most important source of dust production in galaxies, but on the other had had also the most important source of grain destruction. Theoretical models show that most of the heavy elements produced can precipitate out of the gas and form refractory grains (Sarangi & Cherchneff 2013, 2015; Sluder, Milosavljević & Montgomery 2018; Sarangi, Matsuura & Micelotta 2019). Infrared and submilimetre observations of Cassiopeia A (Barlow et al. 2010; Arendt et al. 2014; De Looze et al. 2017), SN 1987A (Matsuura et al. 2011; Indebetouw et al. 2014; Matsuura et al. 2015), Crab Nebula (Gomez et al. 2012), and young Galactic (up to ∼2000 yr old) SN remnants (Chawner et al. 2019) confirm the presence of ∼0.1–1.0 M⊙ of dust, indicating that a substantial fraction of refractory elements in their ejecta went to dust grains. If the majority of dust in SNe can survive the shock interactions, SNe could be an important source of dust production in the ISM (Dwek & Cherchneff 2011). The fate of this newly-formed dust is still a subject of active studies. The reverse shock traveling through the ejecta can destroy newly-formed dust (Dwek, Foster & Vancura 1996; Schneider, Ferrara & Salvaterra 2004; Nozawa et al. 2007; Biscaro & Cherchneff 2014, 2016; Silvia, Smith & Shull 2010; Micelotta, Dwek & Slavin 2016; Kirchschlager et al. 2019). Any grains surviving the reverse shock may also be destroyed during the injection phase into the interstellar medium (ISM; Slavin et al. 2020) Thereafter, ISM dust will be subject to destruction as it encounters the SN remnant shocks. The grain destruction efficiency and ISM dust lifetimes are highly uncertain since they depend on a long list of parameters. Macroscopic parameters include the energy of the SN explosion, the morphology of the medium surrounding the SN (Slavin et al. 2020), and that of the general ISM. Microscopic parameters include the composition and size distribution of the SN condensates, and the detailed interaction of the dust with the shocked gas and other grains (Dwek & Arendt 1992; Jones, Tielens & Hollenbach 1996; Slavin, Dwek & Jones 2015; Kirchschlager, Mattsson & Gent 2021; Priestley, Chawner & of 2021). Because the evolution of dust in the ISM is a fine balance between dust production and destruction, intense investigations are currently underway into dust production and destruction by SNe. In this paper, we examine the latter point of view, and investigate how dust grains are impacted by SN shocks over time.


The only non-standard term involves the factor $\frac{\mathrm{d} q}{\mathrm{d} \eta }$. As usual, the perturbation Ψ of the unperturbed phase-space distribution f0 = 1/(exp (ε/T0) − 1) is introduced as
(36)
\begin{eqnarray*}
f = f_0(\epsilon) \left(1 + \Psi \right)\, ,
\end{eqnarray*}
where the co-moving energy ε reads
(37)
\begin{eqnarray*}
\epsilon \equiv \left(q^2 + a^2 \frac{m_{V_\pm }^2}{{\cal S}^2\, T_0^2}\right)^{1/2}\, .
\end{eqnarray*}
The scaling function $\mathcal {S}$ is defined in equation (5). Since the term $\frac{\mathrm{d} q}{\mathrm{d} \eta }$ is determined by the geodesic equation for a massive point particle, we may write
(38)
\begin{eqnarray*}
\frac{\mathrm{d} q}{\mathrm{d} \eta } \frac{\partial f}{\partial q} &=& \left(q \dot{\phi } - \epsilon n_i \partial _i \psi - \frac{a^2 m_{V_\pm } \dot{m}_{V_\pm }}{q} \right)\nonumber\\
&& \times \,\left(\frac{\partial f_0}{\partial q} (1 + \Psi) + f_0 \frac{\partial \Psi }{\partial q}\right).
\end{eqnarray*}
The use of the geodesic equation for a quasi-particle must be questioned, if this particle associates with pure quantum fluctuations (Hofmann 2017). If at all, temperature fluctuations in the V± sector can thus only be coherently propagated via the low-frequency regime of γ fluctuations in terms of classical electromagnetic waves (Hofmann 2016b). To do this, a residual interaction between V± and γ is required. Albeit when such an interaction occurs (Hofmann 2016a), its efficiency in conveying the coherent propagation of V± temperature fluctuations must be questioned, especially at high temperatures (Falquez et al. (2010). To ignore the V± Boltzmann equations and associated source terms in linearized Einstein equations thus is a physically motivated option. On the other hand, considering the evolution of V± temperature fluctuations via the coherently propagating low-frequency sector in γ implies that ε = q in the V± geodesic equation. At the same time, $m_{V_\pm }\gt 0$ is required in f0. Since the structure of temperature fluctuations is mainly imprinted before and during recombination, setting $m_{V_\pm }=0$ in the geodesic equation does not influence the prediction for the power spectra in practice. Note that due to equation (37) an explicit dependence of f0 on η needs to be considered via a = a(η). Transforming equation (35) into k space and otherwise following the standard procedure of linear perturbation theory (Ma & Bertschinger 1995), one arrives at the following hierarchy:
(39)
\begin{eqnarray*}
\dot{\Psi }_0 = - k\Psi _1 - \frac{\mathrm{d} \ln f_0}{\mathrm{d} \ln q}\dot{\phi } - \frac{1+\Psi _0}{f_0} \frac{\partial f_0}{\partial \eta }\, ,
\end{eqnarray*}
(40)
\begin{eqnarray*}
\dot{\Psi }_1 = \frac{k}{3 }(\Psi _0 - 2 \Psi _2) - \frac{1}{3} \frac{\mathrm{d} \ln f_0}{\mathrm{d} \ln q} k \psi - \frac{\Psi _1}{f_0} \frac{\partial f_0}{\partial \eta },
\end{eqnarray*}
(41)
\begin{eqnarray*}
\dot{\Psi _l} = \frac{k}{(2l+1)}\left[l \Psi _{l-1}-(l+1)\Psi _{l+1} \right] -\frac{\Psi _l}{f_0} \frac{\partial f_0}{\partial \eta },
\end{eqnarray*}
where the $\Psi _l(\vec{k},q,\eta)$ are the expansion coefficients for $\Psi (\vec{k},\hat{n},q,\eta)$ into Legendre polynomials.


In the absence of dust, the spectral emission of a normal star-forming galaxy is dominated by stellar populations of different ages with superimposed nebular emission, mainly in the form of recombination lines as well as continuum. The interaction with dust has a dramatic effect, both dimming and reddening the emission from stars and ionized gas. This negatively impacts our ability to measure star formation as energetic photons produced by massive young stars are far more easily attenuated than longer wavelength photons, and even a small quantity of dust can lead to a significant attenuation in the ultraviolet (UV). In the case of particularly dust-rich galaxies, it can render their detection in the rest-frame UV especially difficult. However, as the FUV emission vanishes due to dust attenuation, this dust re-emits the absorbed energy in the mid-infrared (MIR) and far-infrared (FIR), which can in turn be exploited to trace star formation. Except for the most extreme cases (e.g., when the dust content is negligible or, conversely, when almost all of the UV photons are absorbed by dust), an attenuation correction must be carried out to retrieve the star formation rate (SFR). One of the most direct ways is to simply apply a hybrid SFR estimator combining the rest-frame UV with the IR (e.g., Hao et al. 2011; Boquien et al. 2016). The obvious downside is that this requires observations of the dust emission that are costly and difficult to obtain, and even more so at increasing redshifts, where they tend to be limited to vanishingly small samples. With the rest-frame UV emission being relatively easy to obtain from the ground from z ∼ 2 and beyond, techniques have been developed to relate the UV slope (β) to the UV attenuation (the IRX-β relation). While this approach initially appeared to work remarkably well in the case of starburst galaxies (Meurer et al. 1999), there is now ample evidence that there is no tight universal relation between the UV slope and the attenuation (e.g., Buat et al. 2005; Seibert et al. 2005; Howell et al. 2010; Casey et al. 2014). In fact, this relation relies on two strong underlying assumptions: the intrinsic UV slope of the stellar populations in the absence of dust and the exact shape of the attenuation curve. Numerous studies have analyzed their respective impact in an attempt to understand why and when such relations fail and build more reliable ones (e.g., Kong et al. 2004; Boquien et al. 2009, 2012; Popping et al. 2017, and many others). In particular, the recent study of Salim & Boquien (2019) found that the diversity of attenuation curves is a strong driver of the scatter around the IRX-β relation. This finding, which is consistent with simulations (Narayanan et al. 2018b; Liang et al. 2021), is especially important in that we can observe a broad variety of attenuation curves at all redshifts (e.g., Salmon et al. 2016; Buat et al. 2018; Salim et al. 2018). With the shape of the attenuation curve being strongly dependent on the relative geometry of stars, ionized gas, and dust (Salim & Narayanan 2020), from the disturbed morphologies observed at higher redshifts, we can only expect important variations there as well (e.g., Faisst et al. 2017). However, due to the great difficulty in measuring them and given the sparsity of the data available, our knowledge of attenuation curves beyond z = 4 remains limited. In effect, most observational studies on the attenuation properties of distant galaxies tend to concentrate on redshifts between 2 and 4 (e.g., Noll et al. 2009b; Buat et al. 2012, 2019; Reddy et al. 2012, 2015; Shivaei et al. 2015; Álvarez-Márquez et al. 2016; Salmon et al. 2016; Fudamoto et al. 2017, 2020b; Lo Faro et al. 2017; Álvarez-Márquez et al. 2019; Reddy et al. 2018; Koprowski et al. 2020). There is only a handful of examples at higher redshift (Capak et al. 2015; Scoville et al. 2015; Bouwens et al. 2016; Barisic et al. 2017; Koprowski et al. 2018). Because of the inherent limits of the observations, studies based on numerical simulations of galaxies at very high redshift (e.g., Mancini et al. 2016; Cullen et al. 2017; Di Mascia et al. 2021) are an important source of information. However, they lead to contrasted results, finding both flat (Cullen et al. 2017) and steep (Mancini et al. 2016) attenuation curves.


On the other hand, PT has experienced many developments in recent years (Matsubara 2008a; Baumann et al. 2012; Carlson et al. 2013), in part because it can be useful to analytically understand different effects in the power spectrum and correlation function for the dark matter clustering. These effects can be confirmed or refuted, and further explored with simulations to ultimately understand the outcomes of present and future galaxy surveys, such as eBOSS (Zhao 2016), DESI (Aghamousa et al. 2016), EUCLID (Amendola et al. 2013), and LSST (LSST Dark Energy Science Collaboration 2012). Two approaches have been used to study PT: the Eulerian standard PT (SPT) and Lagrangian PT (LPT), which both have advantages and drawbacks, but they are complementary in the end (Tassev 2014). The nonlinear PT for MG was developed initially in (Koyama et al. 2009), and has been further studied in several other works (Taruya et al. 2014a,b; Brax & Valageas 2013; Bellini & Zumalacarregui 2015; Taruya 2016; Bose & Koyama 2016, 2017; Barrow & Mota 2003; Akrami et al. 2013; Fasiello & Vlah 2017; Aviles & Cervantes-Cota 2017; Hirano et al. 2018; Bose et al. 2018; Bose & Taruya 2018; Aviles et al. 2018). The LPT for dark matter fluctuations in MG was developed in Aviles & Cervantes-Cota (2017), and further studies for biased tracers in Aviles et al. (2018). The PT for MG has the advantage that it allows us to understand the role that these physical parameters play in the screening features of dark matter statistics. We here study some of these effects through screening mechanisms by examining them at second- and third-order perturbation levels using PT for some MG models. To this end, we build on the LPT formalism developed in Aviles & Cervantes-Cota (2017), which was initially posited for MG theories in the Jordan frame, in order to apply it to theories in the Einstein frame. Because of the direct coupling of the scalar field and the dark matter in the Klein–Gordon equation, the equations that govern the screening can differ substantially from those in Jordan-frame MG theories. In general, screening effects depend on the type of nonlinearities that are introduced in the Lagrangian density. We present a detailed analysis of screening features and identify the theoretical roots of their origin. Our results show that screenings possess peculiar features that depend on the scalar field effective mass and couplings, and that may in particular cases cause anti-screening effects in the power spectrum, such as in the symmetron model. We perform this analysis by separating the growth functions into screening and non-screened parts. We note, however, that we do not compare the perturbative approach with a fully nonlinear simulation. We refer to (Koyama et al. 2009), for instance, for investigations like this at the level of the power spectrum.


The past two decades have seen rapid progress in the field of solar magnetoseismology (SMS; for recent reviews, see e.g., Nakariakov & Verwichte 2005; Banerjee et al. 2007; De Moortel & Nakariakov 2012; Nakariakov et al. 2016; Wang 2016). Among the rich variety of low-frequency waves observed in the Sun’s atmosphere, flare-related quasi-periodic fast propagating wave trains have received much attention (see Liu & Ofman 2014, for a recent review). Their quasi-periods usually range from 25 to 400 s. These wave trains were discovered (Liu et al. 2011) and extensively observed in images acquired with the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO/AIA; Liu et al. 2012; Shen et al. 2013; Yuan et al. 2013; Nisticò et al. 2014; also see Lemen et al. 2012 for a description of the instrument). On the other hand, quasi-periodic signals in coronal emissions presumably from density-enhanced loops have been known since the 1960s (e.g., Frost 1969; Parks & Winckler 1969; Rosenberg 1970; McLean & Sheridan 1973; see Table 1 of Aschwanden et al. 1999 for a comprehensive compilation of measurements prior to 2000). The quasi-periods P of a considerable fraction of these signals were of the order of seconds. While these measurements were largely spatially unresolved, more recent high-cadence instruments imaging the corona at total eclipses indicated the presence in coronal loops of quasi-periodic signals both with

 s (Williams et al. 2001, 2002; Katsiyannis et al. 2003) and with

 s (Samanta et al. 2016). In addition, quasi-periodic pulsations in the lightcurves of solar flares with similar periods have also been measured using imaging instruments such as the Nobeyama Radioheliograph (e.g., Asai et al. 2001; Nakariakov et al. 2003; Melnikov et al. 2005; Kupriyanova et al. 2013), SDO/AIA (e.g., Su et al. 2012), and more recently with the Interface Region Imaging Spectrograph (IRIS; Tian et al. 2016; see also De Pontieu et al. 2014 for a description of IRIS).


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


The late-time matter density PDF at a given smoothing scale is mostly sensitive to the skewness of the primordial density field at that scale and to the running of that skewness around the smoothing scale. As such – unless the PDF is measured on a wide range of smoothing scales – it can only poorly distinguish between different primordial bispectrum shapes. Any model that produces mainly one of the possible bispectrum template can however be successfully tested with PDF measurements. In this paper, we consider an analysis of the PDF at redshift z = 1 in a survey volume of V = 100(Gpc h−1)3, which is smaller than the effective volume of upcoming surveys such as Spherex with Veff ≈ 150(Gpc h−1)3 and somewhat larger than existing surveys such as BOSS with Veff ≈ 55(Gpc h−1)3 (Doré et al. 2014; Alam et al. 2017). At a smoothing scale of 30 Mpc h−1 we find our PDF model to agree with the high-resolution run of the Quijote N-body simulations (Villaescusa-Navarro et al. 2019) to $\lesssim 0.2{{\ \rm per\ cent}}$ accuracy over a range of δ[30 Mpc h−1] ∈ [−0.3, 0.4]. This is within cosmic variance of the considered volume of 100(Gpc h−1)3 (which is also the combined volume of the Quijote high-resolution boxes). Restricting to this smoothing scale and to these mildly non-linear densities we find that a PDF based analysis can measure the amplitude of different primordial bispectrum shapes to an accuracy of $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 7.4\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 22.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 46.0$ – even when marginalizing over the non-linear variance of the density field as a free parameter. When pushing to smaller scales and assuming a joint analysis of the PDF with smoothing radii of 30  and 15 Mpc h−1 (δ[15 Mpc h−1] ∈ [−0.4, 0.5]) this improves to $\Delta f_{\mathrm{NL}}^{\mathrm{loc}} = \pm 3.3\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{equi}} = \pm 11.0\ ,\ \Delta f_{\mathrm{NL}}^{\mathrm{ortho}} = \pm 17.0$ – even when marginalizing over the non-linear variances at both scales as two free parameters. Especially, such an analysis can simultaneously measure fNL and the amplitude and slope of the non-linear power spectrum. Note that any dependence of these forecasts on σ8 is completely mitigated by this marginalization. We do not consider the impact of Ωm on our signals (see Uhlemann et al. 2019, for an investigation of the general cosmology dependence of the PDF) though Friedrich et al. (2018) and Gruen et al. (2018) have demonstrated that parameters of the ΛCDM model and higher order moments of the density field can be measured simultaneously from what they call lensing-around-cells. Ultimately, we are working towards a combination of a late-time PDF analysis with the early-universe results of Planck Collaboration IX (2019). These two analyses have the potential to complement each other: the CMB providing information about the background ΛCDM space–time, the late-time density PDF providing information about non-linear structure growth and both of them containing independent information about the imprint of primordial non-Gaussianities on the large-scale structure.


The progenitors of SNe Ib/c have been thought to be Wolf-Rayet (W-R) stars with high initial masses (MZAMS ≳ 25 M⊙; Crowther 2007). Before core collapse, these stars usually have experienced severe mass loss through strong stellar winds or due to interaction with companion stars (van der Hucht 2006; Paxton et al. 2015). As the evolution of massive stars is usually dominated by binary evolution (Heger et al. 2003) and also depends largely on metallicity, rotation, and so on (Heger et al. 2003; Georgy et al. 2013, 2012), this makes the direct identification of their progenitors complicated (Smartt 2015). However, there are increasing studies suggesting that a lower-mass binary scenario is more favorable for most SNe Ib/c, considering the measured low ejecta masses (Eldridge et al. 2013; Lyman et al. 2016). In addition, the H/He envelopes of the progenitor stars are stripped by binary interaction. There are many detections of progenitor stars for SNe II. For example, most SNe IIP are found to originate from red supergiants (Smartt et al. 2009), while SNe IIL are typically from progenitors with somewhat warmer colors (see Smartt 2015, for a review), and SNe IIb are from those with higher effective temperatures such as yellow supergiants that have had their H/He envelopes partially stripped through binary interaction (e.g., SN 1993J; Podsiadlowski et al. 1993; Maund et al. 2004; Fox et al. 2014). Until recently, there has been only one report of the possible identification of a progenitor star for SNe Ib, namely, iPTF 13bvn, which was proposed to spatially coincide with a single W-R-like star identified on the pre-explosion Hubble Space Telescope (HST) images (Cao et al. 2013; Groh et al. 2013). But such an identification is still controversial (e.g., Bersten et al. 2014; Fremling et al. 2014; Eldridge et al. 2015; Eldridge & Maund 2016). Direct detection of progenitor stars is still elusive for SNe Ic, which prevents us from further testing the theoretical evolution of massive stars (Eldridge et al. 2013).


There are a plethora of data available in the form of spectra, astrometric, and photometric information, as well as multiwavelength maps with the advent of large-scale spectroscopic (Apache Point Observatory Galactic Evolution Experiment/APOGEE: Eisenstein et al. 2011, RAdial Velocity Experiment/RAVE: Steinmetz et al. 2006, Gaia-ESO: Gilmore et al. 2012, Large Sky Area Multi-Object Fiber Spectroscopic Telescope/LAMOST: Cui et al. 2012, Galactic Archaeology with HERMES/GALAH: De Silva et al. 2015, Abundances and Radial velocity Galactic Origins Survey/ARGOS: Ness et al. 2012), astrometric (Hipparcos: Perryman et al. 1997, Gaia: Gaia Collaboration 2016), and photometric surveys (Two-Micron All Sky Survey/2MASS: Skrutskie et al. 2006, Sloan Digital Sky Survey/SDSS: Stoughton et al. 2002, Vista Variables in the Vía Láctea/VVV: Minniti et al. 2010, the SkyMapper Southern Survey : Wolf et al. 2018). These surveys have enabled the chemo-dynamic characterization of stellar populations in the Milky way that constitute different Milky Way components like thin disc, thick disc, halo, bulge, etc. For example, star count observations in the solar neighbourhood (Yoshii 1982; Gilmore & Reid 1983) led to the discovery of the thick disc, followed by its characterization as the old α-enhanced population in the double sequence exhibited by the solar neighbourhood stars in the [α/Fe] versus [Fe/H] plane (Fuhrmann 1998; Bensby, Feltzing & Lundström 2003; Reddy, Lambert & Allende Prieto 2006; Adibekyan et al. 2012; Haywood et al. 2013). At present, data from large-scale spectroscopic surveys (Anders et al. 2014; Hayden et al. 2015; Weinberg et al. 2019) have led to the discovery of this trend at different galactocentric radius, R, and average height, |Z|, across the Galaxy shedding light on the disc formation and evolution scenarios. In addition, many age determination methods have been developed that uses these survey data to provide valuable information about the star formation histories and age metallicity relation of disc stellar populations (Casagrande et al. 2011; Bedell et al. 2018; Lin et al. 2020; Nissen et al. 2020). Secular processes such as radial migration (Sellwood & Binney 2002; Schönrich & Binney 2009; Minchev & Famaey 2010), which leads to the mixing of stars across the Galaxy, are also being explored using a combination of accurate phase space information from Gaia (Gaia Collaboration 2018) and chemistry and age information of stars from large-scale spectroscopic surveys (Buder et al. 2019). The discovery of streams and dynamically different stellar populations in the Milky Way halo, considered to be the result of past accretion/merger events (Belokurov et al. 2018; Helmi et al. 2018; Ibata, Malhan & Martin 2019; Myeong et al. 2019) using the Gaia data and their further exploration with chemistry from large-scale spectroscopic surveys (Buder et al. in preparation) is another example. Multiple components in the Bulge metallicity distribution function discovered by multiple individual and large-scale spectroscopic observations, are being studied in detail to understand the origin of the Bulge and its connection with the Milky Way bar and Galaxy evolution (Ness et al. 2013; Rojas-Arriagada et al. 2017, 2020). There are many upcoming surveys [4-metre Multi-Object Spectroscopic Telescope/4MOST: de Jong et al. (2019), Sloan Digital Sky Survey/SDSS-V: Kollmeier et al. (2017), WEAVE: Dalton et al. (2018)] that will further improve our understanding of the formation and evolution of the Milky Way and its components.


Irrespective of its origin, the [C II] emission is linked to the presence of stellar far-ultraviolet (FUV) photons (E 13.6 eV). As FUV photons are tied to the presence of massive O and B stars that have short lifetimes, the [C II] 158 μm line is also astar formation rate (SFR) indicator. Indeed, ISO, Herschel and SOFIA observations have demonstrated the good correlation between the [C II] luminosity and the SFR in the Milky Way and in regions of massive star formation in other galaxies (e.g., Kramer et al. 2013, 2020; Pineda et al. 2014, 2018; Herrera-Camus et al. 2015, 2018; De Looze et al. 2011). With ALMA and NOEMA, ground-based observations of the [C II] 158 μm line in high redshift galaxies have come into reach and such data are routinely used to infer SFRs (e.g., Walter et al. 2012; Venemans et al. 2012; Knudsen et al. 2016; Bischetti et al. 2018; Khusanova et al. 2021) based upon validations of this relationship in the nearby Universe (Herrera-Camus et al. 2018; De Looze et al. 2011). However, it is well-understood that the intensity of the [C II] line depends on the local physical conditions (Hollenbach & Tielens 1999). Observationally, the presence of the so-called [C II]-deficit – a decreased ratio of [C II] 158 μm luminosity to FIR dust continuum with an increasing dust color temperature and also with FIR luminosity – is well established (Malhotra et al. 2001; Díaz-Santos et al. 2013; Magdis et al. 2014; Smith et al. 2017). This deficit is particularly pronounced in (local) ultraluminous infrared galaxies (ULIRGs), very dusty galaxies characterized by vigorous embedded star formation (e.g., Luhman et al. 2003; Abel et al. 2009; Graciá-Carpio et al. 2011). This deficit, however, does not necessarily hold in the early Universe at high redshift (e.g., Stacey et al. 2010; Brisbin et al. 2015; Capak et al. 2015). Some studies have indicated that not only [C II] emission is deficient in some sources, but other FIR cooling lines ([O I], [O III], [N II]), as well (e.g., Graciá-Carpio et al. 2011; Herrera-Camus et al. 2018). These deficits must be linked to the global ISM properties and star-formation characteristics in these galaxies.


Magnetic reconnection (MR) may occur in various space and astrophysical plasma environments, among which the planetary magnetopause boundaries separating the solar wind and magnetospheric origins of plasmas and magnetic field are some of the most likely sites for the occurrence of MR. Due to the easy access to the in situ spacecraft observations the Earth’s magnetopause is the most widely studied space plasma environment for MR (Paschmann et al. 1979; Vaivads et al. 2004; Graham et al. 2014). In particular, the Magnetospheric Multiscale (MMS) mission has contributed greatly to the kinetic physics of magnetopause reconnection (Burch et al. 2016; Hasegawa et al. 2017; Zhong et al. 2020). Many studies have shown that an initial Harris type equilibrium profile with constant total pressures

 and antiparallel magnetic field with or without a guide field (Harris 1962) may tend to develop MR geometry. In particular, two major categories of MR have been proposed: the steady state model with a single X line and the outflow approaching the Alfvén speed (Petschek 1964), and the tearing mode instability with a series of X and O lines and mild plasma velocity (Furth et al. 1963). Numerous fluid and kinetic simulations have been carried out to examine the various aspects of MR processes for the past 50 yr (Hau & Chiou 2001; Guo et al. 2015; Landi et al. 2015). In particular, the effects of pressure or temperature anisotropy on MR have been examined by a number of authors (Chen & Palmadesso 1984; Shi et al. 1987; Birn & Hesse 2001; Chiou & Hau 2002, 2003; Hung et al. 2011). In the MHD models the double-polytropic (DP) laws are widely adopted as the energy closures to study the effects of temperature anisotropy and energy closures on MR and tearing mode instability (Chiou & Hau 2002, 2003; Hung et al. 2011). It is shown that the mirror type temperature anisotropy of

 may greatly enhance the growth rate of tearing mode instability and the merging rate of single X-line reconnection. In particular, the coupling of tearing and mirror instabilities may lead to relatively larger magnetic islands as compared to the cases with isotropic pressure and the mirror waves with anticorrelated density and magnetic field may be present in the vicinity of X lines.


The room-temperature millimeter wave rotational spectrum of ethyl isocyanate in Fig. 1 presents an exceptionally high line density. Its analysis was started using predictions from the spectroscopic constants obtained in the previous microwave works (Heineking et al. 1994; Kasten et al. 1983; Sakaizumi et al. 1976) for the stable cis configuration. It is characterized by a relatively large dipole moment along the a inertial axis (|µa| = 2.81 D and |µb| = 0.03 D (Sakaizumi et al. 1976), Cs symmetry, and dihedral angle τ(C–C–N = C) = 0◦ (see Fig. 1). The identification of Ka = 0 and lower-frequency Ka = 1 transitions, originating from J0 J and J1 J energy levels, was relatively straightforward and their assignment and analysis could be easily expanded up to 340 GHz (J˝ = 64) with the help of the Loomis-Wood-type plot technique from the AABS package (Kisiel et al. 2005) and SP-FIT/SPCAT program suite (Pickett 1991). The upper-frequency Ka = 1 transitions (J1 J−1 levels), which became degenerate with Ka = 2 transitions (J2 J−1 levels) for J˝ > 45, were subsequently localized, however, their analysis quickly ran into problems. As shown in Fig. 2, significant departures from the predicted positions were observed at high J˝ even though it was clear from the Loomis-Wood-type plots that the assignments were correct. Similar situations also occurred for higher Ka transitions and with increasing value of Ka, the limit of J up to which the rotational transitions were amenable to the simple semirigid-rotor Hamiltonian analysis, was decreasing (see Fig. 2). Only those transitions that supported the semirigid-rotor treatment were retained in the analysis. These transitions were finally combined with hyperfine-free transitions (5–24 GHz, J˝ = 0−7, K˝a = 0−3) from Heineking et al. (1994) and globally fitted using Watson’s S -reduced Hamiltonian in Ir representation. The adjusted rotational and centrifugal distortion constants are given in Table 1. The list of experimental frequencies is provided in the Table 4. Finally, the deviation trends observed in the Loomis–Wood type plots, such as those in Fig. 2, were advantageously followed to measure the frequencies of more than 200 transitions that could not be encompassed in the semirigid rotor fit. These transitions are collected in the Table 5.


RR Lyrae are old low-mass stars that, during the central helium-burning phase, show mainly radial pulsation while crossing the classical instability strip in the colour–magnitude diagram. From the observational point of view, they represent the most numerous class of pulsating stars in the Milky Way and, being associated with old stellar populations, are typically found in globular cluster and abundant in the Galactic halo and bulge. The investigation of RR Lyrae properties is motivated by their important role both as distance indicators and tracers of old stellar populations. In particular, evolving through the central helium-burning phase, they represent the low-mass, Population II counterparts of Classical Cepheids, as powerful standard candles and calibrators of secondary distance indicators. In particular, they can be safely adopted to infer distances to Galactic globular clusters (see e.g. Coppola et al. 2011; Braga et al. 2016, 2018, and references therein), the Galactic centre (see e.g. Contreras Ramos et al. 2018; Marconi & Minniti 2018; Griv, Gedalin & Jiang 2019), and Milky Way satellite galaxies (see e.g. Coppola et al. 2015; Martínez-Vázquez et al. 2019; Vivas et al. 2019, and references therein). Being associated with old stellar populations, they represent the basis of an alternative Population II distance scale (see e.g. Beaton et al. 2016, to the traditionally adopted Classical Cepheids), more suitable to calibrate secondary distance indicators that are not specifically associated with spiral galaxies (e.g. the globular cluster luminosity function, see Di Criscienzo et al. 2006, and references therein). The properties that make RR Lyrae standard candles are (i) the well-known relation connecting the absolute visual magnitude MV to the metal abundance [Fe/H] (see e.g. Sandage 1993; Caputo et al. 2000; Cacciari & Clementini 2003; Catelan, Pritzl & Smith 2004; Di Criscienzo, Marconi & Caputo 2004; Federici et al. 2012; Marconi 2012; Marconi et al. 2015, 2018; Muraveva et al. 2018, and references therein); (ii) the period–luminosity relation in the near-infrared (NIR) filters and in particular in the K 2.2 μm band (see e.g. Longmore et al. 1990; Bono et al. 2003; Dall’Ora et al. 2006; Coppola et al. 2011; Ripepi et al. 2012; Coppola et al. 2015; Marconi et al. 2015; Muraveva et al. 2015; Braga et al. 2018; Marconi et al. 2018, and references therein). In spite of the well-known advantage of using NIR filters (see e.g. Marconi 2012; Coppola et al. 2015, and references therein), in the last decades there has been a debate on the coefficient of the metallicity term of the KB and PL relation (see e.g. Bono et al. 2003; Sollima, Cacciari & Valenti 2006; Marconi et al. 2015, and references therein). On the other hand, it is interesting to note that many recent determinations (see e.g. Sesar et al. 2017; Muraveva et al. 2018) seem to converge towards the predicted coefficient by Marconi et al. (2015), with values in the range 0.16-0.18 mag dex−1. As for the optical bands, our recently developed theoretical scenario (Marconi et al. 2015) showed that, apart from the MV−[Fe/H] relation that is affected by a number of uncertainties (e.g. a possible non-linearity, the metallicity scale with the associated α elements enhancement and helium abundance variations, as well as evolutionary effects, see Caputo et al. 2000; Marconi et al. 2018, for a discussion), the metal-dependent Period–Wesenheit (PW) relations are predicted to be sound tools to infer individual distances. In particular, for the B-, V- band combination, Marconi et al. (2015) demonstrated that the inferred PW relation is independent of metallicity. In order to test this theoretical tool, we need to compare the predicted individual distances with independent reliable distance estimates, for example, the astrometric ones recently obtained by the Gaia satellite (Gaia Collaboration 2016). To this purpose, in this paper we transform the predicted light curves derived for RR Lyrae models with a wide range of chemical compositions (Marconi et al. 2015, 2018) into the Gaia bands, derive the first theoretical PW relations in these filters and apply them to Gaia Data Release 2 Data base (hereinafter Gaia DR2; Gaia Collaboration 2018; Clementini et al. 2019; Ripepi et al. 2019). The organization of the paper is detailed in the following. In Section 2, we summarize the adopted theoretical scenario, while in Section 3 we present the first theoretical light curves in the Gaia filters. From the inferred mean magnitudes and colours, the new theoretical PW relations are derived in Section 4 that also includes a discussion of the effects of variations in the input chemical abundances. In Section 5, the obtained relations are applied to Gaia Galactic RR Lyrae with available periods, parallaxes, and mean magnitudes to infer independent predictions on their individual parallaxes, to be compared with Gaia DR2 results. The conclusions close the paper.


AGN feedback can exist in several forms such as radiation, thermal, or non-thermal (cosmic rays) pressure-driven winds, jet-mode feedback, and via magnetic forces on accretion disc scales. AGN feedback can explain several observed properties such as the presence of high velocity (>1000 km s−1) multiphase gas outflows in low and high redshift galaxies and observations of bubbles or cavities in X-ray observations of galaxy clusters (e.g. Blanton et al. 2011; Fabian 2012; Sanders et al. 2014; Feruglio et al. 2015; Laha et al. 2021). High velocity outflows from AGN host galaxies have been reported in numerous studies in the literature (see Veilleux et al. 2020 for a review and the references therein) using optical spectroscopy (e.g. Greene et al. 2011; McElroy et al. 2015; Sun, Greene & Zakamska 2017; Durré & Mould 2018; Manzano-King, Canalizo & Sales 2019; Perna et al. 2020; Santoro et al. 2020; Trindade Falcão et al. 2021), near-infrared spectroscopy (e.g. Kakkad et al. 2016; Zakamska et al. 2016; Bischetti et al. 2017; Diniz et al. 2019; Riffel, Zakamska & Riffel 2020a; Riffel et al. 2020b) and sub-mm spectroscopy (e.g. Michiyama et al. 2018; Zschaechner et al. 2018a; Audibert et al. 2019; Impellizzeri et al. 2019; García-Bernete et al. 2021). One of the key quantities that is not well understood through these observations is how efficiently does the outflow couple with the ISM (e.g. Harrison et al. 2018). The coupling efficiency i.e. the ratio between the kinetic power of the outflow ($\dot{E}_{\rm kin}$) and the bolometric luminosity of the AGN (Lbol) or the star formation rate (SFR) of the host galaxy is critical to quantify the true impact of AGN feedback on host galaxies – the higher the efficiency, the easier it is for these outflows to heat the gas or propagate the outflows to the galaxy outskirts. An accurate measurement of mass outflow rate and kinetic energy is therefore necessary to estimate the true coupling efficiency, which can also be used as constraints in cosmological simulations.


The field of extrasolar planetary transits is one of the most productive and innovative subject in astrophysics in the last decade. Transit observations can be used to measure the size of planets, their orbital parameters (Seager and Mallén-Ornelas 2003), and stellar properties (Mandel & Agol 2002; Howarth 2011), to study the atmospheres of planets (Brown 2001; Charbonneau et al. 2002; Tinetti et al. 2007), and to detect small planets (Miralda-Escudé 2002; Agol et al. 2005) and exomoons (Kipping 2009a, 2009b). In particular, the study of planetary atmospheres requires a high level of photometric precision, i.e., one part in ∼104 in stellar flux (Brown 2001), which is comparable to the effects of current instrumental systematics and stellar activity (Berta et al. 2011; Ballerini et al. 2012), hence the necessity of testable methods for data detrending. In some cases, different assumptions, e.g., using different instrumental information or functional forms to describe them, leed to controversial results even from the same data sets; examples in the literature are Tinetti et al. (2007), Ehrenreich et al. (2007), Beaulieu et al. (2008) and Désert et al. (2009, 2011) for the hot-Jupiter HD 189733b, and Stevenson et al. (2010), Beaulieu et al. (2011) and Knutson et al. (2011, 2014) for the warm-Neptune GJ436b. Some of these controversies are based on Spitzer/IRAC data sets at 3.6 and 4.5 μm. The main systematic effect for these two channels is an almost regular undulation with period ∼3000 s, so called pixel-phase effect, as it is correlated with the relative position of the source centroid with respect to a pixel center (Fazio et al. 2004; Morales-Caldéron et al. 2006). Conventional parametric techniques correct for this effect by dividing the measured flux by a polynomial function of the coordinates of the photometric centroid; some variants may include time-dependence (e.g., Stevenson et al. 2010; Beaulieu et al. 2011). Newer techniques attempt to map the intra-pixel variability at a fine-scale level, e.g., adopting spatial weighting functions (Ballard et al. 2010; Cowan et al. 2012; Lewis et al. 2013) or interpolating grids (Stevenson et al. 2012a, 2012b). The results obtained with these methods appear to be strongly dependent on a few assumptions, e.g., the degree of the polynomial adopted, the photometric technique, the centroid determination, calibrating instrument systematics over the out-of-transit only or the whole observation (e.g., Beaulieu et al. 2011; Diamond-Lowe et al. 2014; Zellem et al. 2014). Also, the very same method, applied to different observations of the same system, often leads to significantly different results. Non-parametric methods have been proposed to guarantee a higher degree of objectivity (Carter & Winn 2009; Thatte et al. 2010; Gibson et al. 2012; Waldmann 2012, 2014; Waldmann et al. 2013). Morello et al. (2014, 2015) reanalyzed the 3.6 and 4.5 μm Spitzer/IRAC primary transits of HD 189733b and GJ436b obtained during the cryogenic regime, so called “cold Spitzer” era, adopting a blind source separation technique, based on an Independent Component Analysis (ICA) of individual pixel timeseries, in this paper called “pixel-ICA”. The results obtained with this method are repeatable over different epochs, and a photometric precision of one part in ∼104 in stellar flux is achieved, with no signs of significant stellar variability as suggested in the previous literature (Désert et al. 2011; Knutson et al. 2011). The use of ICA to decorrelate the transit signals from astrophysical and instrumental noise, in spectrophotometric observations, has been proposed by Waldmann (2012, 2014) and Waldmann et al. (2013). The reason to prefer such blind detrending methods is twofold: they require very little, if any, prior knowledge of the instrument systematics and astrophysical signals, therefore they also ensure a higher degree of objectivity compared to methods based on approximate instrument systematics models. As an added value, they give stable results over several data sets, also in those cases where more conventional methods have been unsuccessful. Recently, Deming et al. (2015) proposed a different pixel-level decorrelation method (PLD) that uses pixel timeseries to correct for the pixel-phase effect, while simultaneously modeling the astrophysical signals and possible detector sensitivity variability in a parametric way. PLD has been applied to some Spitzer/IRAC eclipses and synthetic Spitzer data, showing better performances compared to previously published detrending methods.


The large Jovian irregular satellites have been observed and analyzed using their light curves, colours, and reflectance spectra but the reported measurements are sometimes contradictory. The multicolour observation of some retrograde and prograde Jovian irregular satellites by Tholen & Zellner (1984) suggested C-class surface composition for prograde and more diverse colours for the retrograde families with a mixture of C- and D-type spectra. They noted that Carme had a flat visible wavelength reflectance spectrum, but with a strong upturn in the ultraviolet. Tholen & Zellner (1984) suggested that Carme might be showing low-level cometary activity with CN emission at 0.388 μm. Luu (1991) identified C- and D-type asteroid spectral features for both prograde and retrograde families based on spectroscopic observations of JV-JXIII and suggested them to be similar to Jupiter’s Trojan asteroids. Based on 1.3–2.4 μm near-IR (NIR) observations, Brown (2000) reported their compositions as being similar to P- and D-class asteroids from the outer asteroid belt, while their visible spectra resemble C-class asteroids. Cruikshank (1977) and Degewij et al. (1980) observed Himalia in the NIR and confirmed that its surface composition is similar to that of C-type asteroids. Brown (2000) concluded that NIR spectra of Himalia and Elara are featureless between 1.4 and 2.5 μm and do not contain any water-ice absorption features. Subsequently, Brown & Rhoden (2014) supported these findings and suggested that these objects lacked aqueously altered phyllosilicates based on the absence of a 3 μm absorption band. Brown et al. (2003) and Chamberlain & Brown (2004) studied Himalia using data acquired by the Visual and Infrared Mapping Spectrometer (VIMS) on-board Cassini spacecraft during Jupiter’s fly-by and found that its spectrum (0.3–5.1 μm) has low reflectance, a slight red slope, and an apparent absorption near 3-μm suggesting the presence of water in some form. In addition, Jarvis et al. (2000) reported a weak absorption at 0.7 μm in Himalia’s spectrum and attributed it to oxidized iron. Contrary to this result, Brown & Rhoden (2014) found no evidence for aqueously altered phyllosilicates in the 2.2–3.8 μm region.


It is also possible that these clusters have a smaller extent and can just be missed by our extent selection as our detection algorithm sets the extent to zero if it is smaller than 6 (Brunner et al. 2022). Following the method presented in Ghirardini et al. (2021a), we estimated several dynamical properties of the clusters in the point source sample and compared them with the extent-selected sample presented in Ghirardini et al. (2021a). In Fig. 5 we compare the distributions of the core radii (Rcore) constrained by the V06 model and the concentration parameter (cSB) between these two samples. The concentration parameter is defined as the ratio of the surface brightness within 0.1 R500 to the surface brightness within R500 (Ghirardini et al. 2021a; Santos et al. 2008; Maughan et al. 2012). Intuitively, the expectation is that the smaller the core radius, the more compact the cluster. The left panel of Fig. 5 clearly shows that the clusters in the point source sample have relatively smaller core radii, hence the emission is more concentrated in a smaller area. Consistently, the concentration of the point source sample shows a clear excess in higher values than the extent-selected sample, indicating that a significantly larger fraction of cool-core clusters and clusters host a central AGN. We performed the same experiment by applying cuts in flux 1.5 × 10−14 ergs s−1 cm−2 and in detection likelihood to test whether the clusters are missed by the extent selection because they are fainter and/or more compact than the extent-selected clusters. The distribution of number density, core radius, and concentration parameter remains the same, indicating that the population of clusters in the point source catalog is more compact than the extent-selected sample. The extent-selected sample does not show a clear bias toward cool-core clusters or clusters with a central AGN, but contains the fraction of cool-cores is similar to that of SZ surveys (Ghirardini et al. 2021a). In this sample, we observe the opposite trend.


The observational and theoretical studies of nitrogen isotope fractionation in star-forming regions can help to constrain nitrogen chemistry. Nitrogen has two stable isotopes, 14N and 15N. The elemental abundance ratio [14N/15N]elem in the local interstellar medium (ISM) has been estimated to be ~200–300 from the absorption line observations of N-bearing molecules toward diffuse clouds (Lucas & Liszt 1998; Ritchey et al. 2015). L1544 is a prototypical prestellar core located in the Taurus molecular cloud complex. In L1544, the 14N/15N ratio of several different molecules has been measured:

14

N

2

H

+

=

920

−
200

+
300

,

14

N

2

H

+

/

NNH

+

=

1000

−
220

+
260

$ {}^{14}{\mathrm N}_2\mathrm H^+=920_{-200}^{+300},^{14}{\mathrm N}_2\mathrm H^+/\mathrm{NNH}^+=1000_{-220}^{+260} $

 (Bizzocchi et al. 2013; Redaelli et al. 2018), NH2D/15NH2D > 700 (Gérin et al. 2009), CN/C15N = 500 ± 75 (Hily-Blant et al. 2013b), and HCN/HC15N = 257 (Hily-Blant et al. 2013a). Among the measurements, the significant depletion of 15N in N2H+ is the most challenging for the theory of 15N fractionation. In general, molecules formed at low temperatures are enriched in 15N through gas-phase chemistry triggered by isotope exchange reactions (e.g., Terzieva & Herbst 2000). A 15N-bearing molecule has a slightly lower zero-point energy than the corresponding 14N isotopolog. This results in endothermicity for the exchange of 15N for 14N, which inhibits this exchange at low temperature enabling the concentration of 15N in molecules. Astrochemical models for prestellar cores, which consider a set of nitrogen isotope exchange reactions, have indeed predicted that atomic N is depleted in 15N, while N2 (and thus N2H+) is enriched in 15N (e.g., Charnley & Rodgers 2002). The model prediction clearly contradicts the observation of the N2H+ isotopologs in L1544. The 15N depletion in N2H+ was recently found in other prestellar cores as well, such as L183, L429, and L694-2 (Redaelli et al. 2018). Furthermore, Roueff et al. (2015) recently pointed out the presence of activation barriers for some key nitrogen isotope exchange reactions, based on their quantum chemical calculations. Then 15N fractionation triggered by isotope exchange reactions may be much less efficient than previously thought (Roueff et al. 2015, but see also Wirström & Charnley 2018).


Currently, this 53Mn–53Cr age of 4566.6 ± 0.6 Ma for crystallization for EC 002 represents the oldest record of volcanism in the Solar system. For example, the oldest crust formation of Earth and Moon only dates back to ∼4.3–4.4 Ga (O’Neil & Carlson 2017; Borg et al. 2019), and Mars, Vesta, and the angrite and main-group aubrite parent bodies show ages of mantle–crust differentiation at ∼4547 Ma (Bouvier et al. 2018), 4564.8 ± 0.6 Ma (Trinquier et al. 2008), 4563.2 ± 0.2 Ma (Zhu et al. 2019b), and 4562.5 ± 1.1 Ma (Zhu et al. 2020b), respectively. The crystallization age of EC 002 also predates all those of the other dated achondrites, such as angrites (Amelin 2008a, b; Connelly et al. 2008), ureilites (Goodrich et al. 2010; Bischoff et al. 2014), NWA 8704/6693, NWA 11119 (Srinivasan et al. 2018), and NWA 7325 (Koefoed et al. 2016). The result strongly supports the notion that advanced silicate differentiation occurred and evolved planetary crust formation very early in the Solar system, i.e. within the first 1 Ma after CAI formation (4567.3 ± 0.1 Ma; Amelin et al. 2010; Connelly et al. 2012). The crystallization of andesitic crust must post-date both accretion and core formation on the EC 002 parent body, which is also consistent with evidence for early core formation for some asteroids derived from some iron meteorites (Kruijer et al. 2014; Anand et al. 2021). The age for EC 002 is older than some of the chondrule formation ages (Connelly et al. 2012; Bollard et al. 2017; Zhu et al. 2020b). This observation supports previous suggestions that many chondrites and their components reflect younger nebular processes, post-dating the oldest differentiated planetesimals, such as the EC 002 parent body. Thus, chondrules may not necessarily reflect an important ingredient in the accretion history of terrestrial planets (Johansen et al. 2015), although this cannot be excluded for earlier chondrule precursors with older generations (Zhu et al. 2019a). Considering its very old age and the short half-life of 0.7 Ma of 26Al, the heat source for melting of the EC 002 parent body must have been the decay of 26Al. The reason why EC 002 cooled and crystallized so early might have been that its parent body was of a much smaller size than the terrestrial planets, since small bodies cannot retain their heat well. The size of the EC 002 parent body may have been smaller than the size of asteroids like Vesta (with mean radius of 262.7 km; Russell et al. 2012) and the angrite and aubrite (main-group) parent bodies, which differentiated later, at 2.5–5 Ma after CAIs (Amelin 2008a; Trinquier et al. 2008; Zhu et al. 2019b, 2021b).


Comparison of apparent effective diameters of these sources to direct size measurements supports a similar conclusion. Simpson et al. (2015) present ALMA observations of 23 SCUBA-2-selected SMGs with a median physical half-light diameter of 2.4 ± 0.2 kpc, while Ikarashi et al. (2015) show ALMA observations of 13 AzTEC-selected SMGs with a median physical half-light diameter of $1.34^{+0.26}_{-0.28}$ kpc. ALMA observations of four SPT-selected lensed SMGs give a mean physical half-light diameter of 2.14 kpc (Hezaveh et al. 2013b). This measurement is consistent with a recent lensing analysis of a significantly expanded SPT-selected DSFG sample (Spilker et al. 2016). These high-resolution ALMA observations constrain the FIR sizes of the sources to be 1.0–2.5 kpc. Earlier observations of the physical sizes of SMGs by CO detection and 1.4 GHz imaging suggest larger sizes (e.g. Tacconi et al. 2006; Biggs & Ivison 2008; Younger et al. 2008). However, Simpson et al. (2015) point out that the submillimetre sizes are consistent with resolved 12CO detections, while the sizes derived from 1.4 GHz imaging are about two times larger because of the cosmic ray diffusion, which can explain the results before higher frequency observations at ALMA were possible (Chapman et al. 2004; Tacconi et al. 2006; Biggs & Ivison 2008; Younger et al. 2008). Similarly, Ikarashi et al. (2015) reveal that the 12CO detected sizes and the 1.4 GHz imaging sizes of similar sources are greater than their submillimetre sizes as well. Furthermore, observations of local galaxies also show the submillimetre sizes are smaller than the CO detected sizes (e.g. Sakamoto et al. 2006, 2008; Wilson et al. 2008) and the 1.4 GHz continuum sizes (e.g. Elbaz et al. 2011). Our photometrically derived $\sqrt{\mu }d$ is best compared to the submillimetre continuum sizes. With a median apparent effective diameter of $4.2^{+1.7}_{-1.0}$ kpc, the $\sqrt{\mu }d$ of our sample is one to six times the observed intrinsic diameters (1.0–2.5 kpc). Lensing (or multiplicity) increases the apparent effective size of a source, so this comparison favours a lensing (or multiplicity) interpretation for the ACT-selected sources.


While these S/Ns may not look promising, there is an interesting question that one can ask: How much LUVOIR-15 m time is needed to detect the present Earth-level concentration of NO2 around a Sun-like star at 10 pc? Figure 6(a) shows the spectrum of the difference in geometric albedo with and without NO2. Also shown as dashed lines are the noise levels for 10 (blue), 300 (red), and 1200 (black) hr of LUVOIR-A observation times. The present Earth level of NO2 seems to be well above the noise level after 300 hr of observation time (compare the solid green curve with dashed red line), indicating that it might be detectable. To find out with what S/N it would be detectable, Figure 6(b) shows the “net S/N” to detect present Earth-level NO2 as a function of observation time. To achieve a net S/N of 5 (dashed red line), it would take LUVOIR-15 m about 400 hr. For comparison, to obtain the Hubble Ultra Deep Field (UDF) image, ∼400 hr of actual observation time (∼1 yr in real time) was needed (Beckwith et al. 2006). In fact, Hubble has run even larger programs, such as the CANDLES galaxy evolution survey (Grogin et al. 2011) with 902 orbits (∼900 hr of observation time assuming ∼1 hr per orbit). This took about 3 yr in real time. However, these large programs also obtained data on a huge sample size with thousands of galaxies. LUVOIR is envisaged to be 100% community-competed time, and the final report of the LUVOIR team laid out a Design Reference Mission (DRM) in which comparable allocations of time were spent on general astrophysics observations and exoplanet detection and characterization observations during the first 5 yr of the mission. So, over the course of the nominal LUVOIR mission lifetime of about 5 yr, it may be possible to take data with ∼400 hr observation time on a prime HZ planet candidate(s) within 10 pc, to potentially obtain an S/N ∼ 5 for an NO2 feature at the present Earth level on an Earth–Sun system at 10 pc. An even more interesting aspect is that we can place upper limits on the amount of NO2 available on that planet as we spend more observation time on a prime HZ candidate. This could potentially indicate the presence or absence or the level of technological civilization on that planet.


If we recall the tight, monotonic dependence of the position of galaxies along the SF sequence in the diagram with metallicity (as outlined in Section 3.1), we can interpret our global results of Figs 4 and 5 as a manifestation of the existence of an O/H versus N/O relation for SDSS star-forming galaxies, whose intrinsic scatter is reflected and, to some extent, translated into the observed distribution of emission line ratios within the [N ii]-BPT. A tight relationship between O/H and N/O abundances is indeed observed in both H ii regions and local galaxies, especially at M⋆ ≳ 109.5M⊙ (Vila Costas & Edmunds 1993; van Zee et al. 1998; Pérez-Montero & Contini 2009; Pilyugin et al. 2012; Andrews & Martini 2013; Hayden-Pawson et al. 2021), and it is set by the predominant nucleosynthetic origin of nitrogen from CNO burning of pre-existing stellar carbon and oxygen in low- and intermediate-mass stars experiencing the AGB phase (i.e. the ‘secondary’ nitrogen production mechanism, Kobayashi, Karakas & Umeda 2011; Ventura et al. 2013; Vincenzo et al. 2016); alternatively, Vincenzo & Kobayashi (2018) reproduced the observed N/O-O/H relation introducing failed supernovae (SNe) in massive stars within their cosmological simulations. Recently, such relationship between O/H and N/O has been suggested as even tighter than the one between M⋆ and N/O (Hayden-Pawson et al. 2021), in contrast to what claimed by previous studies (e.g. Andrews & Martini 2013; Masters et al. 2016). In light of our results, this would confirm that deviations in N/O at fixed O/H are more likely to be related to the offset from the SF sequence in the [N ii]-BPT than relative variations in M⋆, although the two are clearly physically correlated. The connection between the two diagrams is also readily evident if we look at the distribution of our galaxy sample in the N/O versus O/H diagram, as shown in Fig. 8 (where [N ii] λ6584/[O ii] λ3727, 29 is converted to N/O following the Te-based calibrations presented in Hayden-Pawson et al. 2021); here, each hexagonal bin is colour-coded by the average distance D of galaxies from the best-fitting line of the [N ii]-BPT, almost perfectly tracing the scatter around the median N/O versus O/H relation.


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


By radio continuum surveys of interstellar space and direct in situ measurements in the solar system, it is well established that for many scenarios the background magnetic fields are spatially varying. However, the above research about parallel and perpendicular diffusion only explored the uniform mean magnetic field. One can show that the spatially varying background magnetic fields lead to the adiabatic focusing effect of charged energetic particle transport and introduces correction to the particle diffusion coefficients (see, e.g., Roelof 1969; Earl 1976; Kunstmann 1979; Beeck & Wibberenz 1986; Bieber & Burger 1990; Kóta 2000; Schlickeiser & Shalchi 2008; Shalchi 2009b, 2011; Litvinenko 2012a, 2012b; Shalchi & Danos 2013; Wang & Qin 2016; Wang et al. 2017b). To explore the influence of adiabatic focusing on particle transport, the perturbation method is frequently used (see, e.g., Beeck & Wibberenz 1986; Bieber & Burger 1990; Schlickeiser & Shalchi 2008; Schlickeiser & Jenko 2010; Litvinenko & Schlickeiser 2013; He & Schlickeiser 2014). To use the perturbation method, since the anisotropic distribution function is an implicit function, by using the iteration method, one can find that the anisotropic distribution function becomes an infinite series of the spatial and temporal derivatives of the isotropic distribution function. Therefore, the governing equation of the isotropic distribution function derived from the Fokker–Planck equation contains infinite terms because of the infinite series of the anisotropic distribution function. By using the truncating method to neglect the higher-order derivative terms, the approximate correction formulas of parallel or perpendicular diffusion coefficients were obtained (see, e.g., Schlickeiser & Shalchi 2008; Schlickeiser & Jenko 2010; He & Schlickeiser 2014). However, the higher-order derivative terms probably also make the correction to the parallel and perpendicular diffusion much like the lower-order derivative ones do. The magnitude of the correction from higher-order derivative term might not necessarily be a higher-order small quantity than the magnitude of the lower-order derivative terms. Therefore, the correction obtained by the previous authors is likely to contain significant errors. In this paper, by considering the higher-order derivative terms, we derive the parallel and perpendicular diffusion coefficients and obtain the correction formulas coming from all order derivative terms by using the improved perturbation method (He & Schlickeiser 2014) and the iteration operation. And for the weak adiabatic focusing limit we evaluate the correction to the parallel diffusion coefficient and compare it with the correction obtained in the previous papers.


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


It is still unclear whether this incompatibility is evidence against the spatially flat ΛCDM model or is caused by unidentified systematic errors in one of the established cosmological probes or by evolution of the parameters themselves with the redshift (Dainotti et al. 2021b, 2022). Newer, alternate cosmological probes could help alleviate this issue. Recent examples of such probes include reverberation-mapped quasar (QSO) measurements that reach to redshift z ∼ 1.9 (Czerny et al. 2021; Khadka et al. 2021a,b; Yu et al. 2021; Zajaček et al. 2021), H ii starburst galaxy measurements that reach to z ∼ 2.4 (Mania & Ratra 2012; Chávez et al. 2014; González-Morán et al. 2019, 2021; Cao, Ryan & Ratra 2020, 2022a; Cao et al. 2021a; Johnson, Sangwan & Shankaranarayanan 2022; Mehrabi et al. 2022), QSO angular size measurements that reach to z ∼ 2.7 (Cao et al. 2017, 2020, 2021a; Ryan, Chen & Ratra 2019; Lian et al. 2021; Zheng et al. 2021), QSO flux measurements that reach to z ∼ 7.5 (Risaliti & Lusso 2015, 2019; Khadka & Ratra 2020a,b, 2021, 2022; Lusso et al. 2020; Yang, Banerjee & Ó Colgáin 2020; Li et al. 2021; Lian et al. 2021; Luongo et al. 2021; Rezaei, Solà Peracaula & Malekjani 2021; Zhao & Xia 2021),1 and the main subject of this paper, gamma-ray burst (GRB) measurements that reach to z ∼ 8.2 (Amati et al. 2008, 2019; Cardone, Capozziello & Dainotti 2009; Cardone et al. 2010; Samushia & Ratra 2010; Dainotti et al. 2011, 2013a,b; Postnikov et al. 2014; Wang, Dai & Liang 2015; Wang et al. 2016, 2022; Fana Dirirsa et al. 2019; Khadka & Ratra 2020c; Hu, Wang & Dai 2021; Dai et al. 2021; Demianski et al. 2021; Khadka et al. 2021c; Luongo et al. 2021; Luongo & Muccino 2021; Cao et al. 2021a). Some of these probes might eventually allow for a reliable extension of the Hubble diagram to z ∼ 3–4, well beyond the reach of Type Ia supernovae. GRBs have been detected to z ∼ 9.4 (Cucchiara et al. 2011), and might be detectable to z = 20 (Lamb & Reichart 2000), so in principle GRBs could act as a cosmological probe to higher redshifts than 8.2.


In addition to thermal excitation through collisions with H2 and He, absorption of infrared photons and pumping to excited vibrational states, followed by radiative decay to rotational levels in the ground-vibrational state, is an important excitation mechanism of molecules in IRC +10216 (Deguchi & Uyemura 1984; Agúndez & Cernicharo 2006; González-Alfonso et al. 2007; Agúndez et al. 2008, 2015; Cordiner & Millar 2009; Daniel et al. 2012; De Beck et al. 2012). Here, we have included excitation through infrared pumping for all studied species, mostly through bands lying in the mid-infrared, where the flux in IRC +10216 is large (Cernicharo et al. 1999). To facilitate the excitation and radiative transfer calculations, we have collapsed the fine rotational structure of the radicals and simply treated these species as linear molecules with a 1Σ electronic state. For C2H, we have included the first four vibrationally excited states of the bending mode (ν2 = 1, 2, 3, 4), and the first vibrationally excited states of the stretching modes (ν1 = 1 and ν3 = 1). The vibrationally excited state that plays the most important role, through infrared pumping, in the excitation of C2H in IRC +10216 is ν2 = 1, which lies 371 cm-1 above the ground-vibrational state. The wavelengths and strengths of the vibrational bands have been taken from Tarroni & Carter (2004). For the radical CN, we have included the v = 0 → 1 band, lying at 2042 cm-1 (Hübner et al. 2005; Brooke et al. 2014), which plays a minor role on the excitation of the λ 3 mm lines in IRC +10216, however. For HC3N, we have included the first excited states of the vibrational bending modes ν5 and ν6, which have strong fundamental bands at 663 and 498 cm-1. The wavelengths and strengths of the vibrational bands are from the compilation by J. Crovisier1, which are based on extensive laboratory work (e.g., Uyemura et al. 1982; Jolly et al. 2007). For cyanodiacetylene, we have included the first excited states of the vibrational bending modes ν7 and ν8, whose calculated fundamental bands, lying at 566 and 685 cm-1, have been found to be important for the rotational excitation of HC5N in IRC +10216 (Deguchi & Uyemura 1984). For the radicals C4H, C6H, and C3N there is little information on the wavelengths and strengths of vibrational bands. For these species we have instead included a generic vibrationally excited state lying at 15 μm above the ground-vibrational state, with an Einstein coefficient of spontaneous emission of 5 s-1 for the P(1) transition of the vibrational band. A similar treatment, with slightly different parameters, was adopted for C4H and C6H by Cordiner & Millar (2009).


Another possibly important cooling delay may arise from the phase separation of 22Ne during crystallization (Isern et al. 1991; Althaus et al. 2010). Our current best understanding is that at the small 22Ne concentrations typical of C/O white dwarfs (∼1% by number), the presence of 22Ne should not affect the phase diagram, except near the azeotropic point of the C/O/Ne phase diagram. Thus, the crystallization of the C/O core initially proceeds as in the case without 22Ne with no redistribution of neon ions between the solid and liquid phases. After a significant fraction of the core has crystallized, the temperature approaches the azeotropic point and the existing calculations indicate that the liquid phase is enriched in 22Ne relative to the solid (Segretain 1996; García-Berro et al. 2008). The 22Ne-poor solid is lighter than the surrounding liquid and floats upward where it eventually melts. This gradually displaces the 22Ne-rich liquid downward toward the solid–liquid interface until the azeotropic composition is reached, thereby releasing a considerable amount of gravitational energy. Given our very limited knowledge of the ternary C/O/Ne phase diagram (Segretain 1996; Hughto et al. 2012), this effect cannot be quantitatively implemented in our evolution models. However, we note that our current understanding of 22Ne phase separation is remarkably consistent with the missing cooling delay. In Fig. 2 we show the luminosity function obtained by adding an artificial 0.6 Gyr delay when 60% of the core is crystallized. These parameters are entirely consistent with those found in preliminary studies (Segretain 1996; García-Berro et al. 2008) and yield an excellent fit to the crystallization pile-up3. Based on the current (albeit limited) knowledge of the C/O/Ne phase diagram, we propose that the phase separation of 22Ne in the advanced stage of crystallization significantly contributes to the pile-up in the luminosity function of 0.9−1.1 M⊙ white dwarfs (Fig. 2).


The high-resolution imaging observations of TR from IRIS reveal the ubiquitous presence of network jets. We have used three different IRIS observations of the quiet sun, which are located near the disk center. On the basis of careful inspection, 51 network jets are identified from three QS observations and used for further analysis. These 51 network jets are very well resolved and are not affected by the dynamics of other jets. The study is focused on the rotating motion of network jets along with the estimation of their other properties (speed, height, and lifetime). The mean speed, as predicted by statistical distributions of the speed, is 140.16 km s−1 with a standard deviation of 39.41 km s−1. The mean speed of network jets is very similar, as reported in previous works (e.g., Tian et al. 2014; Narang et al. 2016). However, in case of their lifetimes, we found a value that is almost double (105.49 s) that of the previously reported mean lifetime of the network jets (49.6 s; Tian et al. 2014). As mentioned above, we took only those network jets that are very well resolved in space and in the time; these criteria exclude short lifetime network jets. Therefore, our statistical distribution of the lifetime predicts a higher mean lifetime. The mean length of the network jets is 3.16 Mm with a standard deviation of 1.18 Mm. In the case of CH network jets, Tian et al. (2014) have reported that most of the network jets have lengths from 4.0 to 10.0 Mm. However, the mean length for QS network jets is smaller (3.53 Mm; Narang et al. 2016). So, the mean length for QS network jets from the present work is in good agreement with Narang et al. (2016). In addition, the apparent speed and length of these network jets are positively correlated, which is very similar to what has already been reported in previous works (Narang et al. 2016). Finally, we can say that these networks jets are very dynamic features of the solar TR, as revealed by their estimated properties.


Single-burst stellar population (SSP) models mimic uniform stellar populations of fixed age and metallicity, and are an important tool to study unresolved stellar clusters and galaxies. They are created by populating theoretical stellar evolutionary tracks with stars of a stellar library, according to a prescription given by a chosen initial mass function (IMF). Thus, the quality of the resulting SSP models depends significantly on the completeness of the used input stellar library in terms of evolutionary phases represented by the atmospheric parameters temperature, Teff, surface gravity, log (g), and metallicity. A sufficiently large spectral coverage is equally crucial when constructing reasonable SSP models. Theoretical stellar libraries like, e.g. BaSeL (Kurucz 1992; Lejeune et al. 1997, 1998; Westera et al. 2002), or PHOENIX (Allard et al. 2012; Husser et al. 2013) are generally available for both a large range in wavelength and in stellar parameters, whereas empirical libraries are found to be more incomplete in both respects. However, the advantage of the latter ones is that they are not hampered by the still large uncertainties in the calculation of model atmospheres. Examples of empirical stellar libraries in the optical wavelenth range encompass the Pickles library (Pickles 1998), ELODIE (Prugniel & Soubiran 2001), STELIB (Le Borgne et al. 2003), Indo-US (Valdes et al. 2004), MILES (Sánchez-Blázquez et al. 2006), and CaT (Cenarro et al. 2001, 2007). In the near-infrared (NIR) and mid-infrared (MIR)1, only very few empirical libraries have been observed so far (e.g. Lançon & Wood 2000; Cushing et al. 2005; Rayner et al. 2009). The NASA Infrared Telescope Facility (IRTF) spectral library, described in the latter two papers, is to date the only empirical stellar library in the NIR and MIR which offers a sufficiently complete coverage of the stellar atmospheric parameter space to construct SSP models. In the future, the X-Shooter stellar library, which contains around 700 stars, and which covers the whole optical (see Chen et al. 2014) and NIR wavelength range until 2.5 μm, will clearly improve the current situation in the NIR.


The age of a neutron star is difficult to measure, as for many other astronomical sources. The most robust way to do it is by identifying the birth supernova of the neutron star. However, this can be done precisely only for a very small number of objects, as 5–10 supernovae have historically been observed in our galaxy (Stephenson & Green 2005), and neutron stars are faint sources–practically undetectable at distances beyond the Magellanic Clouds. The explosions, however, leave imprints in the interstellar medium that can remain visible at radio wavelengths for 10 − 100 kyr (Sarbadhicary et al. 2017), thereby allowing the association of pulsars with supernova remnants (SNRs). However, pulsars are rarely found at the centre of SNRs (Frail et al. 1994), as most are expelled like bullets during the explosions possibly due to asymmetries in the process (e.g. Socrates et al. 2005). The transverse velocities of pulsars (based on proper motion and distance estimates) are particularly large, with a mean close to 310 km s−1 (Hobbs et al. 2005), which is at least ten times larger than the average velocities for stars in the solar neighbourhood (e.g. Gaia Collaboration 2018). Moreover, some measured velocities range as high as 1000 km s−1 (Chatterjee et al. 2005; Deller et al. 2019). Thus, associations between SNRs and pulsars are not always straightforward to make (e.g. see the chapter on young pulsars in Lyne & Graham-Smith 2012). The farther the pulsar is from the explosion site, the higher the possibility that the pulsar and SNR are unrelated. In order to confirm an association, it could be necessary to account for up to 100 kyr of evolution of the SNR (that we assume as the maximum possible age of a SNR), and movement across the Galaxy of the pulsar (e.g. Suzuki et al. 2021). In some situations, proper motion measurements for the pulsars can shed light on the matter. For an association to be secure, the pulsar must be moving away from where the explosion took place (usually adopted as the centre of the SNR), and the time necessary to move the pulsar to its current position must match the age of the system. If such time coincided with an independent age measurement of the SNR or the pulsar, or both, then the association would be concretely confirmed. However, this is rarely possible as SNR and pulsar ages are hard to obtain.


Set II: we now focus on the observational constraints on the model parameters after the inclusion of the local measurement of H0 by Riess et al. (2018) with the previous data sets (CMB, Pantheon, and CC) in order to see how the parameters could be improved with the inclusion of this data point. Since for this present UM, the estimation of H0 from CMB alone is compatible with the local estimation of H0 by Riess et al. (2018), thus, we can safely add both the data sets to see whether we could have something interesting. Following this, we perform another couple of tests after the inclusion of R18. The observational results on the model parameters are summarized in Table 4. However, comparing the observational constraints reported in Table 3 (without R18 data) and Table 4 (with R18), one can see that the inclusion of R18 data (Riess et al. 2018) does not seem to improve the constraints on the model parameters. In fact, the estimation of the Hubble constant H0 remains almost similar to what we found in Table 3. In order to be more elaborate in this issue, we have compared the observational constraints on the model parameters before and after the inclusion of R18 to other data sets. In Figs 7 (CMB versus CMB+R18), 8 (CMB+CC versus CMB+CC+R18), 9 (CMB+Pantheon versus CMB+Pantheon+R18), and 10 (CMB+Pantheon+CC versus CMB+Pantheon+CC+R18), we have shown the comparisons which prove our claim. One can further point out that the strong correlation between the parameters μ and H0 as observed in Fig. 5 still remains after the inclusion of R18 [see specifically the (μ, H0) planes in Figs 7–10]. The physical nature of μ does not alter at all. That means the correlation between H0 and μ is still existing after the inclusion of R18 to the previous data sets, such as CMB, Pantheon, and CC. In addition to that since μ ≲ 0.9 according to all the observational data sets, thus, the transition from past decelerating era to current accelerating era occurs to be around z ≲ 0.6, similar to what we have found with previous data sets (Table 3).


In a similar fashion to what done by the CARLA survey, the COBRA (Clusters Occupied by Bent Radio AGN) program (Paterno-Mahler et al. 2017) searches for overdense regions around radio-AGN with double-lobed structures which are not aligned with each other, but bent by forming angles 180∘\documentclass[12pt]{minimal}
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				\begin{document}$$180^\circ$$\end{document}. The rationale behind this search is that the radio lobes of these AGNs are most likely bent because of the ram pressure that occurs due to the relative motion of the AGN host galaxy and the ICM (e.g., Feretti et al. 1992; Blanton et al. 2001; Giacintutti and Venturi 2009; Wing and Blanton 2011), which makes these sources good tracers for finding galaxy clusters. Indeed, out of 646 bent radio-AGN, 530 (corresponding to ∼\documentclass[12pt]{minimal}
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				\begin{document}$$\sim$$\end{document} 82% of the original sample) are associated with over-densities—mostly at high, z=1-3\documentclass[12pt]{minimal}
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				\begin{document}$$z=1-3$$\end{document}, redshifts—in the Spitzer/IRAC maps, and 190 are associated with galaxy cluster candidates. By following up on the previous work, Golden-Marx et al. (2021) also show for a subsample of 36 high-z (0.35z2.2\documentclass[12pt]{minimal}
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				\begin{document}$$0.35z2.2$$\end{document}) cluster candidates that radio-AGN with narrower (≲80∘\documentclass[12pt]{minimal}
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				\begin{document}$$\lesssim 80^\circ$$\end{document}) opening angles reside in richer clusters (cf. Fig. 26), clearly indicating that the cluster environment impacts radio morphology.


At high redshift, the mapping of the extended Lyα haloes around galaxies (non-AGN) is however a lot more difficult because of sensitivity and resolution limitations. Detections of extended Lyman alpha emission at high redshift have been obtained in the past. While some large Lyα blobs have been observed (e.g. Steidel et al. 2000; Matsuda et al. 2004, 2011), most of these studies were forced to employ stacking analyses because of sensitivity limitations. The first tentative detections of Lyα haloes around normal star-forming galaxies emitting Lyα emission using narrowband (NB) imaging methods were reported by Møller & Warren (1998) and Fynbo et al. (2001). Later, Hayashino et al. (2004) observed 22 Lyman break galaxies (LBG) and detected extended Lyα emission by stacking the NB images. These authors were followed six years later by Ono et al. (2010) who detected Lyα haloes in their composite NB images of 401 Lyα emitters (LAEs) at z = 5.7 and 207 at z = 6.6. Matsuda et al. (2012) and Momose et al. (2014) significantly increased the size of LAEs samples used by stacking ≈2000 and ≈4500 LAEs at redshift z ≃ 3 and 2.2 ≤ z ≤ 6.6, respectively. Momose et al. (2014) found typical Lyα halo exponential scale lengths of 5–10 physical kpc. Matsuda et al. (2012) found that Lyα halo sizes are dependent on environmental density; these halo sizes extend from 9 to up to 30 physical kpc towards overdense regions. More recently, Xue et al. (2017) studied ≈1500 galaxies in two overdense regions at z ≈ 3 and 4. Using stacking methods these authors reported Lyα halo exponential scale lengths of 5–6 physical kpc and found that Lyα halo sizes correlate with the UV continuum and Lyα luminosities, but not with overdensity. Steidel et al. (2011) stacked 92 brighter (RAB ≃ 24.5) and more massive LBGs at z = 2.3−3, finding large Lyα extents of ≈80 physical kpc beyond the mean UV continuum size at a surface brightness level of ~10-19 erg s-1 cm-2 arcsec-2. Put together, all these studies showed that Lyman alpha emission is on average more spatially extended than the UV stellar continuum emission from galaxy counterparts.

Momose et al. (2014)
Momose et al. (2014)


In equations (2) and (3), $\boldsymbol{f}_{\rm rad}=(f_{{\rm rad},\, r},\, f_{{\rm rad},\theta })$ is the radiation force described as
(6)$$\begin{eqnarray*}
\boldsymbol{f}_{\rm rad}=\frac{\sigma _{\rm e} \boldsymbol{F}_{\rm D}}{c}+\frac{\sigma _{\rm e} \boldsymbol{F}_{\rm line}}{c}M,
\end{eqnarray*}$$where σe is the mass-scattering coefficient for free electrons, $\boldsymbol{F}_{\rm D}$ is the radiation flux emitted from the accretion disc integrated by the wavelength throughout the entire range, and $\boldsymbol{F}_{\rm line}$ is the line-driving flux, which is the same as $\boldsymbol{F}_{\rm D}$ but integrated across the UV band of 200–3200 Å. The second term of equation (6) is the line force. As mentioned in Section 1, the line transitions depend on the wavelength of the radiation. The line force is exerted mainly by the radiation flux in the UV band (200–3200  Å), because the metal lines are densely distributed (e.g. Castor, Abbott & Klein 1975; Stevens & Kallman 1990). Thus, in this paper, we evaluate the line force using the UV (200–3200  Å) radiation flux and the corresponding force multiplier M same as Proga & Kallman (2004). Here M is the numerical factor indicating how much the spectral lines enhance the radiation force compared to the Thomson scattering. The radial components of the fluxes are estimated as $F^r_{\rm D}= F^r_{\rm D,\, thin}e^{-\tau _{\rm e}}$ and $F^r_{\rm line}= F^r_{\rm line,\, thin}e^{-\tau _{\rm e}}$, respectively, where τe is the electron-scattering optical depth estimated as $\tau _{\rm e} =\int ^r_{r_{\rm in}} \sigma _{\rm e} \rho (r^{\prime },\, \theta) \mathrm{ d}r^{\prime }$, where rin is the inner boundary of the computational box. We ignore the attenuation in the θ-direction as $F^\theta _{\rm D}= F^\theta _{\rm D,\, thin}$ and $F^\theta _{\rm line}= F^\theta _{\rm line,\, thin}$. We calculate $\boldsymbol{F}_{\rm D,\, thin}$ and $\boldsymbol{F}_{\rm line,\, thin}$ by integrating intensity transferred in the optically thin media from the grids on the disc to the point of interest. Here we employ the standard disc model (Shakura & Sunyaev 1973). We divide the hot region of the disc where the effective temperature is larger than $3\times 10^3\, {\rm K}$ into the grids. In contrast to the previous method where we prepared 4096 uniform grids both in the r- and φ-directions, we here prepare 12 800 grids whose sizes are determined by Δri/Δri − 1 = 1.0005 in the r-direction. In the φ-direction, we set 1600 uniform grids in the range of 0 ≤ φ  2π. In order to resolve the hot region of the disc ($T_{\rm eff}\gt 3\times 10^3 \, {\rm K}$) for the IMBHs (MBH = 103–$10^6 \, M_\odot$), a large number of grids is required in the r-direction. This is because the size of the hot region normalized by Schwarzschild radius RS increases with the decrease of the BH mass. For example, the outer radius of the hot region is ∼1000RS for $M_{\rm BH}=10^8\, M_\odot$ while it reaches as far as 3 × 104RS for $M_{\rm BH}=10^3\, M_\odot$.


In order to calculate oxygen fugacities, we follow the methods described by Doyle et al. (2019). From the element abundance ratios, we assign oxygen to Mg, Si, Ca, and Al in the necessary proportions to obtain the relative abundances of the charge-balanced rock-forming oxide components MgO, SiO2, CaO, and Al2O3. The remaining excess oxygen (

), is assigned to Fe to make FeO until either O or Fe is exhausted. The excess oxygen available to make FeO is obtained using
4

where

 is the amount of oxygen needed to form the metal oxide, i, and OTotal is the total abundance of oxygen in the system. Other studies have used similar methods for budgeting oxygen (Klein et al. 2010, 2011; Farihi et al. 2011, 2013, 2016; Raddi et al. 2015). Once the relative abundances of the oxides are obtained, they are normalized to 1, yielding mole fractions and permitting application of Equation (3). In principle, if insufficient oxygen exists to pair with Fe to make FeO, then the Fe that remains should have been present as a metal in the accreted parent body. We emphasize that oxygen fugacity is recorded by the mole fraction of FeO, which depends on all of the oxides (FeO, SiO2, MgO,

, CaO) and not simply the FeO/Fe ratio for the body. It is possible for metal and water to have coexisted in the parent body if it was undifferentiated, meaning that oxygen which is attributed to FeO in this calculation may have existed as H2O in the parent body. However, during the differentiation of a rocky body, the oxygen from ices will oxidize metallic Fe to form FeO. We are assuming here that the bodies we are observing in the WDs were either differentiated themselves, or they are the building blocks of differentiated bodies (chondrite meteorites would be the appropriate analog). Where a parent body was composed in part of Fe metal and H2O, our calculation is a measure of the prospects for FeO, and thus the ΔIW expected for the body taken as a whole, including accreted rock and ices.


In the first stages of star formation, protostars are still embedded in their parental cloud, where an active gas-grain chemistry is at work. Using either (i) background stars for dense clouds or (ii) a nascent protostellar object once it is able to emit sufficient light flux in the vibrational infrared wavelength range, or in a few protoplanetary disks well inclined towards the observer, the infrared pencil beam allows the probing of the composition of the cloud or circumstellar dust. The low-temperature ice mantles formed on top of or mixed with refractory dust (silicates and/or organics) can be retrieved. A harvest of astronomical observations from ground-based telescopes (e.g. UKIRT, IRTF, CFHT, and VLT) or satellites (e.g. IRAS, ISO, Akari, and Spitzer) of such lines of sight has led, since the late seventies, to the deciphering of the chemical compositions, column densities, and variations associated with these ice mantles (e.g. Boogert et al. 2008, 2015; Öberg et al. 2011; Dartois 2005; van Dishoeck 2004; Gibb et al. 2004; Keane et al. 2001; Dartois et al. 1999b; Brooke et al. 1999, and references therein). The interpretation of these observed spectra is mainly based on their comparison with the infrared spectra of laboratory-produced ice films of well-controlled composition and cryogenic temperatures (e.g. Hudson et al. 2014, 2021; Palumbo et al. 2020; Rachid et al. 2020; Terwisscha van Scheltinga et al. 2018; Öberg et al. 2007; Dartois et al. 2003, 1999a,b; Moore & Hudson 1998; Ehrenfreund et al. 1997; Gerakines et al. 1995; Hudgins et al. 1993). The routes investigated are the influence of the ice mixture on the line width and position, temperature modifications, segregation (phase separation), and/or intermolecular interactions (polar or apolar ices and molecular complexes). The impact of a distribution of grain shapes, mainly in the Rayleigh regime, is also explored in some cases. The literature is dominated by analyses based on the decomposition of the observed astronomical profiles into principal components from different ice mixtures. When dust grains evolve from the diffuse interstellar medium (ISM) to the dense phase and the protoplanetary phases, grains grow. This will affect the observed profiles and is expected to be, at least partly, responsible for enhanced scattering effects in dense cloud evolution, often referred to as cloudshine or coreshine effects (Ysard et al. 2016, 2018; Saajasto et al. 2018; Jones et al. 2016; Steinacker et al. 2015; Lefèvre et al. 2014). The growth can also be inferred from the evolution of the silicate-to-K band ratio (τ9,7/AK; e.g. Madden et al. 2022; van Breemen et al. 2011; Chiar et al. 2007).