RX J1347.5–1145 is one of the most luminous X-ray galaxy clusters and is located at a redshift of z = 0.451. It was thought to be a relaxed cluster when it was discovered in the ROSAT all sky survey (Schindler et al. 1997). Komatsu et al. (1999) made the first measurements of the Sunyaev–Zel’dovich effect (SZE: Sunyaev & Zeldovich 1972) toward this cluster with the James Clerk Maxwell Telescope at 350 GHz as well as with the 45 m Nobeyama Radio Telescope at 21 and 43 GHz. A higher angular resolution observation of the SZE was performed by Komatsu et al. (2001) using the Nobeyama Bolometer Array and they found a prominent substructure which has no counterpart in the soft X-ray image from ROSAT. The presence of the substructure has been confirmed by Chandra and XMM-Newton (e.g., Allen et al. 2002; Gitti & Schindler 2004) as well as by more recent SZE measurements (Mason et al. 2010; Korngut et al. 2011; Plagge et al. 2013; Adam et al. 2014; Kitayama et al. 2016). Allen et al. (2002) measured the mean temperature of the ICM to be over 10 keV, which is relatively high compared to other typical clusters. Kitayama et al. (2004) and Ota et al. (2008) found a very hot (>20 keV) component of the ICM in this cluster. In addition, the radial profile and spatial distribution of the ICM temperature indicate that the temperature drops to ∼6 keV toward the cluster center so that the cool core is formed (e.g., Allen et al. 2002; Ota et al. 2008; Kreisch et al. 2016). A disturbed morphology is further supported by radio synchrotron observations (e.g., Ferrari et al. 2011) and gravitational lensing maps (e.g., Köhlinger & Schmidt 2014). The total mass of RX J1347.5–1145 within r200 is estimated to be ∼1.5 × 1015 h−1

  using weak-lensing analysis, where r200, the radius within which the mean mass density is 200 times the critical density of the universe, is 1.85 h−1 Mpc (Lu et al. 2010) for this galaxy cluster.18

18
They adopted the Hubble constant of 70 km s−1 Mpc−1.


Our analysis on the LAMOST-RC stars by dissecting the MAPs shows that the chemical bimodality is observed throughout the Galactic disk, and the high- and low-[α/Fe] sequences are corresponding to the thick and thin disks of the Milky Way, respectively. How to explain the formation mechanism of the stellar thin and thick disks is beyond the scope of this paper, but our results provide some observational constraints to the model of the chemodynamical evolution of the Milky Way disk. Our flared vertical profiles for the thin and thick disks are in good agreement with the prediction of the thin+thick flaring disk model (López-Corredoira & Molgó 2014), and are consistent with the number simulations of the chemodynamical evolution in Galactic disks formed in the cosmological context (Minchev et al. 2013, 2014, 2015, 2017), as well as the cosmological zoom simulation of VINTERGATAN (Agertz et al. 2021). These model simulations suggest that the vertical flaring trends are a natural consequence of inside-out, upside down growth coupled with disk flaring (see also Bird et al. 2013; García de la Cruz et al. 2021), which allows for the low-[α/Fe] stars to exist several kpc above the disk’s midplane. As analyzed by B16, the exponential flaring profiles for the low-[α/Fe] MAPs suggests that radial migration played an important role in the formation and evolution of the thin disk. Radial migration of stars via cold torquing, also known as “churning,” by a bar and spiral waves (Minchev et al. 2013) then allows for the populations to spatially overlap in the solar neighborhood. Similar to the flared thin disk, the flaring profile for the high-[α/Fe] MAP indicates the radial migration has occurred in the formation of the thick disk as suggested by model simulations (e.g., Schönrich & Binney 2009; Minchev et al. 2015; Li et al. 2018). Of course, we cannot rule out the other formation scenarios of the thick disk, such as the accreted gas from satellites (Brook et al. 2004), accreted stars from galaxy mergers (Abadi et al. 2003), or from disk-crossing satellites heating up the thin disk (Read et al. 2008). On the other hand, the broken exponential radial profiles for the thin and thick disks cannot be explained by any model of the galactic disks. In fact, nearly all the models we mentioned above present a single-exponential profile decreasing with the increasing of R (e.g., Minchev et al. 2015; Li et al. 2018; Agertz et al. 2021). And the smooth downtrend of radial profile in the outer disk R > Rpeak, as shown in Figure 10, means that there is no cut-off of the stellar component at R = 14–15 kpc as stated by Ruphy et al. (1996), which is also discovered by B16.


The planetary physical properties that can be derived from measurements with the two most successful exoplanet detection techniques, that is, with the radial velocity method and the transit method, are the planet radius (if the planet transits its star), mass (a lower limit if the planet does not transit its star), and the orbital period and distance, eccentricity, and inclination (if the planet transits its star) (see Perryman 2018, and references therein). The upper atmospheres (above optically thick clouds) of giant exoplanets and those of smaller planets around M stars can be probed using spectroscopy during primary and/or secondary transits (Bean et al. 2010; Swain et al. 2009, 2008; Tinetti et al. 2007; Nakajima 1983). It appears to be virtually impossible to characterize the (lower) atmospheresand surfaces of small, Earth-like planets in the habitable zones of solar-type stars (Bétrémieux & Kaltenegger 2014; Misra et al. 2014; Kaltenegger & Traub 2009), in particular because the light of the parent star is refracted while traveling through the lower atmosphere of its planet and emerges forever out of reach of terrestrial telescopes (García Muñoz et al. 2012). The (lower) atmosphere and surface of a planet are crucial for determining the habitability of a planet, as they hold information about cloud composition, trace gases in disequilibrium and probably most importantly, liquid surface water (see, e.g., Schwieterman et al. 2018; Kiang et al. 2007a,b, and references therein). For such a characterization of terrestrial-type planets, direct observations of the thermal radiation that they emit or of the light of their parent star that they reflect are required. The numerical results that we present in this paper concern the reflected starlight. Because of the huge distances involved, any measured reflected starlight pertains to the (illuminated and visible part of the) planetary disk. It therefore is a disk-integrated signal.


Information about the composition and structure of astrophysical ices, and in particular the presence of solid methanol, is obtained by comparing astrophysical observations in the infrared to laboratory data (Dartois et al. 1999; Pontoppidan et al. 2003; Boogert et al. 2008; Bottinelli et al. 2010). The main infrared absorption features used for solid CH3OH identification in interstellar ices are the 3.53 μm (2833 cm−1) and 9.74 μm (1027 cm−1) bands. They correspond to the CH3 symmetric stretching mode and the CO
stretching mode, respectively. The laboratory data most widely used for comparison to observations are those provided by d’Hendecourt & Allamandola (1986), Hudgins et al. (1993), and Kerkhof et al. (1999). The first reference gives IR spectra and band strengths of methanol ice at 10 K in the 2.5–20 μm range. The second reference presents a thorough infrared study providing a compendium of band strengths and optical constants in the 2.5–200 μm interval for ices of astrophysical relevance. For pure methanol, optical constants are given for an ice grown at 10 K and subsequently warmed to 50 K, 75 K, 100 K, and 120 K. Band strengths at 10 K are also given. As far as we know, these are the only optical constants available in the literature for solid methanol. The third reference reports band strength variations of methanol absorptions in the mid-IR region with dilution in H2O ice, or in H2O and CO2 ice mixtures. Additional laboratory works provide infrared band strengths of this species at 10 K. Specifically, the data in Palumbo et al. (1999) correspond to the mid-IR (MIR), and the data in Sandford & Allamandola (1993) and Gerakines et al. (2005) to the near-IR (NIR). Finally, a recent paper by Bouilloud et al. (2015) presents a compilation and new measurements of MIR band strengths of methanol ice at low temperatures. Since methanol ice densities were unknown, the uncertainty on band-strength determination is very large. In particular, a discrepancy among the literature results up to 40% for the strength of the 9.74 μm band has been pointed out.


The standard single-frequency detection methods for point sources in the CMB and far IR are based on wavelet techniques (Vielva et al. 2003; Barnard et al. 2004; González-Nuevo et al. 2006) or on the matched filter (or MF hereafter, Tegmark & de Oliveira-Costa 1998; Herranz et al. 2002; Barreiro et al. 2003; López-Caniego et al. 2006, see also Herranz & Vielva 2010 for a review.). Wavelets are well suited for the detection of compact sources due to their good position-scale determination properties, whereas the MF is the optimal linear detector-estimator because it provides the maximum signal-to-noise (S/N) amplification for a source with a known shape (usually the point-spread function, or PSF hereafter, of the telescope) embedded in statistically homogeneous and spatially correlated noise. By default, these techniques are applicable only to single-frequency sky images: even for multiwavelength observatories such as the Herschel Space Observatory (Pilbratt et al. 2010) or Planck (Tauber et al. 2010), the standard detection pipelines have produced individual source catalogs for each frequency band (see e.g., Planck Collaboration VII 2011; Planck Collaboration XXVIII 2014; Planck Collaboration XXVI 2016; Maddox et al. 2018). The next logical step is to boost the signal of faint sources by combining the different bands into a single detection, that is, “multifrequency detection”. Most of the blind component separation algorithms that are used for diffuse components in microwave and far IR astronomy can not deal with the high diversity of spectral behaviors associated to the different populations of extragalactic compact sources (see for example Leach et al. 2008). However, over the last few years a number of multifrequency compact source detection techniques have been proposed in the literature (Herranz & Sanz 2008; Herranz et al. 2009; Lanz et al. 2010, 2013; Planck Collaboration Int. LIV 2018). A review on the topic can be found in Herranz et al. (2012). In particular, if the spatial profile and the spectral energy distribution (SED) of the sources are known, and if the cross-power spectrum is known, or can be estimated from the data, the optimal linear detection method is the matched multifilter (or MMF hereafter, Herranz et al. 2002). Lanz et al. (2010) also showed that the MMF can be generalized for the case where the SED of the sources is not known. This generalization outperforms the single-frequency MF in terms of S/N and can be used to infer the spectral index of synchrotron-dominated radio sources, as shown in Lanz et al. (2013). However, in this paper we will incorporate a specific SED to the MMF in order to derive a photometric redshift estimation of dusty galaxies and high-redshift star forming galaxies detected in the IR part of the spectrum1. We will do so by applying the multifrequency MMF filter to the first and second data releases of the Herschel Astrophysical Terahertz Large Area Survey (the Herschel-ATLAS or H-ATLAS, Eales et al. 2010), the largest single key project carried out in open time with the Herschel Space Observatory. We restrict our multifrequency analysis to the three wavelength bands covered by the SPIRE instrument aboard Herschel (Griffin et al. 2010), centered around 250, 350 and 500 μm. As discussed in Hopwood et al. (2010), Lapi et al. (2011), González-Nuevo et al. (2012), Pearson et al. (2013) and Donevski et al. (2018), the SPIRE bands are ideal for capturing the peak in the SED corresponding to dust emission of star-forming galaxies at z ∼ 2, that is redshifted from its rest-frame wavelength around 70–100 μm to the SPIRE wavelengths: This is the redshift range where galaxies have formed most of their stars. At higher redshifts, dusty star-forming galaxies (DSFGs) occupy the most massive halos and are among the most luminous objects found at z ≳ 4 (Michałowski et al. 2014; Oteo et al. 2016; Ikarashi et al. 2017). These high-redshift DSFGs have markedly red colors as seen by SPIRE, with rising flux densities from 250 to 500 μm (the so-called “500 μm-risers”), and have received a great deal of attention in the recent years (see for example Ivison et al. 2016; Negrello et al. 2017; Strandet et al. 2017). The DSFGs, and particularly the 500 μm risers uncovered by Herschel, are providing much insight into the early star forming history of the universe. However, sensitivity and limited angular resolution severely constrain the power of this type of objects as astrophysical probes. The sensitivity of SPIRE allows for the direct detection of only the brightest, and thus rarest objects, at the bright end of the luminosity function. By means of our multifrequency MMF technique, we intend to enhance the detectability and statistical significance of very faint red objects in the H-ATLAS source catalog and so expand the list of reliable 500 μm-riser candidates.


In general, the most important effect of the ICME passage in generating major FDs is ascribable to the energetic interplanetary shock/sheath region, although it has been proposed that the MC effect could even be dominant (e.g., Sanderson et al. 1990). Intense shocks are associated with the fast ICME propagation and may overcome the MC effect in modulating the GCR intensity, as turbulent magnetic fluctuations within the sheath can influence the GCR propagation significantly (e.g., Wibberenz et al. 1998). However, the minimum intensity occurs after the arrival of the MC (Badruddin 1986; Zhang & Burlaga 1988). For slower ICMEs, the effect of shock and turbulent sheath on the GCR intensity could be similar to that associated with the MC and sometimes it could be negligible. Therefore, if no interplanetary shock is found leading an ICME and a weak magnetic field turbulence is observed in the sheath region, the FD evolution mostly depends on the magnetic configuration of the ICME. A statistical study was performed by Richardson & Cane (2011) on more than 300 ICMEs, showing that 80% of them is associated with an FD, detected by the anticoincidence guard data on the International Monitoring Platform (IMP-8; Cane 2000), and that the minimum GCR intensities occur within the MC. They also concluded that ICMEs containing MCs cause deeper FDs on average with respect to ICMEs that do not have any MC structure. Despite numerous attempts to relate the properties of FDs with those of ICMEs at 1 au (Richardson et al. 1996; Belov et al. 2001, 2014; Belov 2008; Dumbović et al. 2012) there are significant gaps in our understanding of their underlying physical mechanisms. A renewed interest in studying GCR FDs has been fostered by the most recent S/C observations in the near-Earth space at the lower rigidities with respect to NMs, for which FDs appear larger allowing for the study of the fine structure of the decrease formation. For instance, different data sets have been used to study GCRs and the associated FDs recorded by a radiation monitor on board LISA Pathfinder (LPF; Armano et al. 2018), the Electron Proton Helium INstrument detector on board the Solar and Heliospheric Observatory (SoHO) and the Chandra X-ray observatory (Heber et al. 2015; Dumbović et al. 2018), and the anticoincidence shield of the International Gamma-Ray Astrophysics Laboratory’s spectrometer (Jordan et al. 2011). FDs have also been observed at several solar distances by the Radiation Assessment Dosimetry dose rates on the Mars Science Laboratory (Guo et al. 2018; von Forstner et al. 2018, 2020; Papaioannou et al. 2019), the Cassini’s Magnetosphere Imaging Instrument and Low Energy Magnetospheric Measurement System measurements (Roussos et al. 2018) and beyond (Witasse et al. 2017; Winslow et al. 2018).


In addition to confirming the origin of some short GRBs, combining data from observations of GW170817 and GRB 170817A allowed for the inference of basic properties of short GRB jets. These include the isotropic equivalent luminosity of the jet, determined through a redshift measurement made possible by the optical follow-up of the GW localization (Abbott et al. 2017a; Goldstein et al. 2017), and the geometry of the GRB jets (Williams et al. 2018; Farah et al. 2020; Mogushi et al. 2019). The precise mechanism by which the jet is launched is still unknown, although it is typically believed to be either neutrino-driven or magnetically driven (Nakar 2007, but see also Liu et al. 2015 and references therein). Indeed, the scientific debate about the emission profile of the jet and the subsequent gamma-ray production mechanism of GRB 170817A is still ongoing (Hallinan et al. 2017; Kasliwal et al. 2017; Lamb & Kobayashi 2017; Troja et al. 2017; Gottlieb et al. 2018b; Lazzati et al. 2018; Gill & Granot 2018; Mooley et al. 2018; Zhang et al. 2018; Ghirlanda et al. 2019). It is generally believed that there are symmetric polar outflows of highly relativistic material that travel parallel to the total angular momentum of the binary system (Aloy et al. 2005; Kumar & Zhang 2014; Murguia-Berthier et al. 2017). These jets are thought to be collimated and roughly axisymmetric, emitting preferentially in a narrow opening angle due to a combination of outflow geometry and relativistic beaming. The data from extensive multi-wavelength observation campaigns that ran for nearly 20 months following the merger (Fong et al. 2019; Makhathini et al. 2020; Troja et al. 2020) are in agreement with a structured jet model, in which the energy and bulk Lorentz factor gradually decrease with angular distance from the jet symmetry axis (e.g., Dai & Gou 2001; Lipunov et al. 2001; Rossi et al. 2002; Zhang & Mészáros 2002; Ghirlanda et al. 2019; Beniamini et al. 2020). Further, according to one of the models proposed, as the jet drills through the surrounding merger ejecta it inflates a mildly relativistic cocoon due to interactions between the material at the edge of the jet and the ejecta (Lazzati et al. 2017; Gottlieb et al. 2018a). In this case, it is possible that the cocoon alone could produce the gamma-rays observed from GRB 170817A (Gottlieb et al. 2018b). Additional joint detections of GRBs and GWs will significantly aid our understanding of the underlying energetics (Lamb & Kobayashi 2017; Wu & MacFadyen 2018; Burns et al. 2019), jet geometry (Farah et al. 2020; Mogushi et al. 2019; Biscoveanu et al. 2020; Hayes et al. 2020), and jet ignition mechanisms (Veres et al. 2018; Ciolfi et al. 2019; Zhang 2019) of binary neutron star (BNS) coalescences.


Braukmuller et al. (2018) proposed that all elements fall into one of four categories based on their condensation temperature: refractory elements (50% condensation temperature, Tc,50 > 1400 K), which exhibit approximately uniform enrichments in their Si-normalized concentrations in CC chondrites compared to CI chondrites by a factor of ∼1–1.4; main component elements (1300 K  Tc,50  1400 K), which have approximately the same Si-normalized elemental abundances in CC chondrites as CI chondrites (differ by a factor of ∼0.8–1.1); slope-volatile elements (800 K  Tc,50  1300 K), which exhibit monotonically decreasing Si-normalized concentrations with decreasing Tc,50 compared to CI chondrites; and plateau volatile elements (Tc,50  800 K), which display uniform depletions in Si-normalized concentrations compared to CI chondrites by a factor of ∼0.1–0.7 that are characteristic of each CC chondrite group. Given their uniform nature with Tc,50 and comparatively well-constrained isotopic and elemental compositions, we chose to focus on the concentrations of refractory, main component, and plateau volatile elements in this study. For the refractory and main component elements in CC chondrites, we examine the elemental and isotopic compositions of Ti and Cr, respectively, because these are lithophile elements whose isotopic compositions have been measured precisely for a large number of chondrites and their components (Trinquier et al. 2007, 2009; Qin et al. 2010; Olsen et al. 2016; Van Kooten et al. 2016; Gerber et al. 2017; Davis et al. 2018; Zhu et al. 2019; Schneider et al. 2020; Williams et al. 2020). For CC iron meteorites, we examine the isotopic compositions of Mo and Ni, respectively, because these are siderophile elements (so are therefore present in appreciable concentrations in iron meteorites, unlike Ti and Cr) whose compositions have also been relatively well studied in a number of iron meteorites as well as chondrites and their components (Burkhardt et al. 2011; Budde et al. 2016; Kruijer et al. 2017; Bermingham et al. 2018; Nanne et al. 2019; Budde et al. 2019; Worsham et al. 2019; Brennecka et al. 2020; Spitzer et al. 2020). For the plateau volatile elements, we examine the elemental compositions of six elements (Bi, Ag, Pb, Zn, Te, and Sn) that exhibit a number of desirable properties: their concentrations have been relatively well constrained in CC chondrites; they show a range of lithophile, siderophile, and chalcophile behaviors; their concentrations do not appear to be strongly dependent on redox state; they show minimal variability among NC chondrite groups. Our reasoning for not considering the isotopic compositions of these elements is discussed in Section 2.3. The adopted isotopic and chemical composition of each element used in this study in CC chondrites, CC iron meteorites, CAIs, CI chondrites, and NC chondrites are included in Table 1. Uncertainties on elemental concentrations have not been routinely reported throughout the literature, although these values are typically ±5 wt% (e.g., Lodders 2003; Palme et al. 2014). CAIs can be categorized into six groups based on their compositions (Stracke et al. 2012). For the purposes of this study, we adopt the composition of type I CAIs as the representative value of refractory objects because they are seemingly the most abundant type and lack the characteristic elemental depletions of other CAI groups (e.g., Stracke et al. 2012; Brennecka et al. 2020). We also focus largely on ordinary chondrites (OC) as representative NC meteorites rather than enstatite chondrites (EC) or Rumuruti chondrites (RC). This is because EC chondrites formed under more reducing conditions than OC and RC chondrites, which introduced a compositional signature for some elements to EC chondrites that is not present in OC, RC, or CC chondrites (presumably due to their formation in more oxidizing environments) so is not representative of large-scale mixing in the disk (Alexander 2019b). Additionally, the isotopic compositions of RC chondrites are sparsely measured compared to OC and EC chondrites. NC meteorites could have experienced a number of processes (e.g., mixing, chondrule formation, volatile loss, the addition of refractory materials, etc.) that gave these meteorites their specific chemical and isotopic signatures (Alexander 2019b). We do not explore these processes in this study and simply adopt the measured elemental and isotopic compositions of NC chondrites as potential end-members for the compositions of CC meteorites.


Unlike BH–BH mergers, binary neutron star (BNS) merger mechanisms are expected to yield an optical counterparts powered by the radioactive decay of rapid neutron capture process (r-process) elements synthesized in the merger ejecta (Li & Paczyński 1998; Metzger et al. 2010) or by the cooling of shock-heated material around the neutron star (NS; Piro & Kollmeier 2018). On 2017 August 17, the LVC detected the first and best example of a BNS merger: GW170817 (Abbott et al. 2017a). Only two seconds after its detection, a short gamma-ray burst (GRB 170817A) was detected (Connaughton et al. 2017; Goldstein et al. 2017). GRB 170817A was followed by the discovery of the optical counterpart Swope Supernova Survey 17a [SSS17a (AT 2017gfo)] ∼11 h later in the galaxy NGC 4993 (Coulter et al. 2017) and later confirmed by others teams (Abbott et al. 2017c; Arcavi et al. 2017; Covino et al. 2017; Díaz et al. 2017; Drout et al. 2017; Kilpatrick et al. 2017; Lipunov et al. 2017; McCully et al. 2017; Pian et al. 2017; Shappee et al. 2017; Smartt et al. 2017; Soares-Santos et al. 2017; Troja et al. 2017; Utsumi et al. 2017; Valenti et al. 2017). The combination of EM and GW information on the BNS can be used to constrain the mass and the radii of NS (Margalit & Metzger 2017) or their equation of state (Bauswein & Janka 2012; Annala et al. 2018). Also, observations of the optical–infrared (IR) ‘kilonova’ counterpart (Chornock et al. 2017; Cowperthwaite et al. 2017; Drout et al. 2017; Kilpatrick et al. 2017; Nicholl et al. 2017; Shappee et al. 2017; Valenti et al. 2017; Villar et al. 2017) provided the first observational confirmation that NS mergers produce the majority of the r-process elements heavier than iron (Burbidge et al. 1957; Cameron 1957; Kasen et al. 2017; Pian et al. 2017; Metzger 2019). They also permit tests of theoretical kilonova models. For example, Drout et al. (2017) showed that the temperatures cooled from 10 000 to 5100 K in between 12 and 36 h after the event, confirming model predictions. Also, Shappee et al. (2017) used spectra taken 11.76 and 12.72 h after the merger to show that the photosphere was expanding at ∼0.3c.


We used the theoretical models by Eggleton et al. (2008), Charbonnel & Lagarde (2010), and Lagarde et al. (2012) for the comparison. They provide quantitative values representing the first dredge-up, thermohaline (TH), and thermohaline and rotation (TH+V) induced mixing. Eggleton et al. (2008) estimated the mixing speed with their formula for the diffusion coefficient and found that a range of three orders of magnitude in their free parameter can lead to the observed levels of 12C /13C. Their predicted value of the 12C /13C ratio for a solar-metallicity 2 M⊙ star at the RGB tip is 17. A more recent model of the thermohaline-induced mixing by Charbonnel & Lagarde (2010) lists for the same stars a higher value of about 20. The model of Charbonnel & Lagarde (2010) of thermohaline instability induced mixing and the model by Eggleton et al. (2008) are both based on the ideas of Eggleton et al. (2006) and Ulrich (1972). It includes developments by Charbonnel & Zahn (2007). Eggleton et al. (2006) found a mean molecular weight (μ) inversion in their 1 M⊙ stellar evolution model, which occurred after the so-called luminosity bump on the RGB, when the hydrogen-burning shell reaches the chemically homogeneous part of the envelope. The μ-inversion is produced by the reaction \hbox{$^3{\rm He(}^3{\rm He}, 2p)^4{\rm He}$}He(33He,2p)4He, as predicted in Ulrich (1972). It does not occur earlier because the magnitude of the μ-inversion is low and negligible compared to a stabilising μ-stratification. Charbonnel & Zahn (2007) computed stellar evolution models including the ideas of Kippenhahn et al. (1980), who extended Ulrich’s equations to the case of a non-perfect gas. Charbonnel & Zahn (2007) also introduced a double diffusive instability (i.e. thermohaline convection) and showed its importance in the chemical evolution of red giants. This mixing connects the convective envelope with the external wing of the hydrogen-burning shell and induces surface abundance modifications in evolved stars (Charbonnel & Lagarde 2010).


Cluster cosmology requires jointly modelling the physical parameters describing the evolution of the intra-cluster medium (ICM) alongwith the impact of selection procedure. While the first self-consistent methods have followed a backward modelling of the recovered cosmology-dependent, mass function (e.g. Vikhlinin et al. 2009), more recent studies moved to a forward approach whose likelihood includes physical quantities such as luminosity, temperature, or gas fraction (e.g. Mantz et al. 2014, 2015). Cluster number counts from Sunyaev-Z’eldovich surveys are routinely modelled in terms of the signal-to-noise ratio (S/N) or the Compton parameter of the detections, which can be related to the cluster mass via scaling relations from X-ray, lensing, or velocities (e.g. Vanderlinde et al. 2010; Hasselfield et al. 2013; Benson et al. 2013; Bocquet et al. 2015; Planck Collaboration XXIV 2016). In this context, we are developing a cosmological analysis method (ASpiX) based on X-ray cluster number counts that does not explicitly rely either on cluster mass determinations or physical quantities. This method consists in the modelling of the multidimensional distribution of a set of directly measurable X-ray clusters quantities, namely: count rates (CRs), hardness ratios (HRs), and apparent size (rc), which are all cosmology independent. This method is particularly suited to rather shallow survey-type data, when the number of collected X-ray photons is too low to enable detailed spectral and morphological analyses. Thanks to its modularity, the ASpiX method considerably eases the process by simultaneously fitting in the observed parameter space, the effect of cosmology, selection, and cluster physics. Depending on the volume surveyed, that is, the number of clusters involved in the analysis, the number of parameters that may be fitted can increase from a few to 15 or more, including in particular scatter and evolution in the scaling relations. This method cannot rival approaches including deep pointed X-ray observations along with ancillary data from other wavebands and, fundamentally, faces the same uncertainties as to the observable-mass transformation. However, the method allows the inclusion of the vast majority of the detected clusters even when only a few tens of photons are available. Furthermore, when cosmological simulations are produced at a significantly high rate, the method will allow us to totally bypass any mass estimate or scaling-relation related formalism; instead, it will solely rely on the simulations by comparing the observed and simulated parameter distributions (Pierre et al. 2017). In the end, neitherassumptions based on the hydrostatic equilibrium nor any modelling of the mass function will be necessary.


While using the Padé(2,1) approximation, we checked the influence of the quasar relation on the cosmological constraints. We first provide the constraints considering a free quasar relation. Then combining that with the following two special cases, the effect of the slope parameter γ is studied. One case is the fitting parameters q0 and j0 in the case of fixed parameters δ, γ, and β. The other is to refit q0 and j0 by changing the setting of the fixed parameter γ within a 1σ error (0.005). The fixed parameters δ, γ, and β are given in terms of the best fitting results from 1598 quasars in a flat ΛCDM model. By substituting Eqs. (25) into (26), and replacing dL with Eq. (6), we obtained the best fits, that is

Ω
m

=
0
.

65

−
0.19

+
0.16

$ \Omega_{m} = 0.65^{+0.16}_{-0.19} $

, δ = 0.23  ±  0.01, γ = 0.62  ±  0.01, and β = 7.60  ±  0.28. This result is consistent with previous research within a 1σ error (Lusso & Risaliti 2016; Melia 2019; Salvestrini et al. 2019; Khadka & Ratra 2020a, 2022; Liu et al. 2020; Wei & Melia 2020). Here, it is worth noting that the 1σ errors of the γ best fit from previous research are both larger than 0.01. Figure 4 shows the fitting results with a free quasar relation. The best fits are δ = 0.23  ±  0.01, γ = 0.64  ±  0.01,

β
=
7
.

17

−
0.27

+
0.28

$ \beta = 7.17^{+0.28}_{-0.27} $

, q0 = −0.67  ±  0.04, and

j
0

=
2
.

43

−
0.46

+
0.51

$ j_{0} = 2.43^{+0.51}_{-0.46} $

. This result is in line with the previous results obtained by the logarithmic polynomials. The corresponding q0 − j0 projection is also plotted in Fig. 5 as a gray contour. In addition, we also show the confidence contours of the other two special cases. (1) When we chose δ = 0.23, γ = 0.62, and β = 7.60 (best fits from 1598 quasars in a flat ΛCDM model), the results are q0 = −0.82  ±  0.05 and

j
0

=
4
.

99

−
0.63

+
0.69

$ j_{0} = 4.99^{+0.69}_{-0.63} $

, which is represented by the red contours in Fig. 5. There exists more than a 4σ tension with the flat ΛCDM. (2) In only changing γ = 0.625, the new result is q0 = −0.58  ±  0.03 and

j
0

=
1
.

19

−
0.31

+
0.34

$ j_{0} = 1.19^{+0.34}_{-0.31} $

 which is described by the blue contours of Fig. 5. We find that the γ value changes from 0.62 to 0.625 (within a 1σ error of 0.01), and the 4σ tension disappears. This result is consistent with the ΛCDM model within a 1σ level. We find that the quasar relation can obviously affect the cosmographic constraint, especially the slope parameter γ.


In order to make a linear analysis, first we have to prepare the PNS models as a background. The PNS properties depend on not only the density and pressure profiles but also the distributions of temperature (or entropy per baryon) and electron fraction inside the PNS, while such profiles can be determined only via the numerical simulation of the core-collapse supernova explosion. In this study, as in Sotani & Sumiyoshi (2019), we particularly adopt the profiles obtained via the numerical simulations performed by solving the general relativistic neutrino-radiation hydrodynamics under the spherical symmetry. In the simulations, hydrodynamics and neutrino transfer in general relativity are solved simultaneously (Yamada 1997; Yamada, Janka & Suzuki 1999; Sumiyoshi et al. 2005). To describe the neutrino transfer, the Boltzmann equation is directly solved with the multi-angle and multi-energy neutrino distributions for four species, νe, $\bar{\nu }_\mathrm{ e}$, νμ/τ, and $\bar{\nu }_{\mu /\tau }$, i.e. we implement six species of neutrinos by assuming μ-type and τ-type (anti-)neutrinos have identical distributions. For the collision term associated with neutrino emission, absorption, and scattering with leptons, nucleons, and nuclei handles, the basic neutrino reactions are adopted (Bruenn 1985; Sumiyoshi et al. 2005). The metric adopted in the numerical code is given by
(1)$$\begin{eqnarray*}
\mathrm{ d}s^2 = -\mathrm{ e}^{2\Phi (t,m_\mathrm{ b})}\mathrm{ d}t^2 + \mathrm{ e}^{2\Lambda (t,m_\mathrm{ b})}\mathrm{ d}m_\mathrm{ b}^2 + r^2(t,m_\mathrm{ b})(\mathrm{ d}\theta ^2 + \sin ^2\theta \mathrm{ d}\mathrm{ }\phi ^2), \nonumber\\
\end{eqnarray*}$$where t and mb denote the coordinate time and the baryon mass coordinate, respectively (Misner & Sharp 1964). In addition, mb is related to the circumference radius (r) via the baryon mass conservation, while the metric functions, Φ(t, mb) and Λ(t, mb), are evolved together with hydrodynamical variables in the numerical simulations (Yamada 1997). The numerical simulations for core-collapse supernovae have been done with 255 grid points in the radial mass coordinate, 6 grid points in the neutrino angle, and 14 grid points in the neutrino energy. The rezoning of radial mesh is made during the simulations to resolve the accreting matter. We remark that the radial grids of mass coordinate are non-uniformly arranged to cover not only the dense region inside the central object but also the region for accreting matter.


Many low-luminosity active galactic nuclei (LLAGN) display prominent jets and compact cores that are sources of highly nonthermal continuum radio emission (see, e.g., Heeschen 1970; Wrobel & Heeschen 1991). The observational signatures of the compact cores have been reproduced using models that produce self-absorbed synchrotron emission in the jet (Falcke & Biermann 1995; Falcke et al. 2004) or in a magnetized accretion flow (Narayan et al. 1998; Yuan et al. 2003; Broderick & Loeb 2006; Moscibrodzka et al. 2009; Dexter et al. 2009; see also Falcke et al. 2001). This radiation is emitted by relativistic electrons gyrating around magnetic field lines. In the optically thin limit, the emission is significantly polarized (Jones & Hardee 1979), an effect that has been observed in higher-luminosity AGN sources (Gabuzda et al. 1996; Gabuzda & Cawthorne 2000; Lyutikov et al. 2005). The polarized emission from an accreting AGN can therefore yield information about the magnetic-field morphology of the source, which may be crucial to the evolution of the accretion flow of the AGN. The Event Horizon Telescope (EHT) is a worldwide millimeter-wavelength array capable of resolving the black-hole shadow (Goddi et al. 2017; Event Horizon Telescope Collaboration 2019); this is a characteristic feature of the radio-frequency emission from optically thin AGN at the scale of the event horizon (Falcke et al. 2000; Broderick & Narayan 2006), although the black-hole shadow may be obscured or exaggerated in certain accretion scenarios (see Gralla et al. 2019 and Narayan et al. 2019). The EHT can also determine the polarization state of such emission: Johnson et al. (2015) report 1.3 mm observations (230 GHz) that indicate partially ordered magnetic fields within a region of about six Schwarzschild radii around the event horizon of Sagittarius A* (Sgr A*), the supermassive black hole in the center of the Milky Way. Bower et al. (2003) reported stable long-term behavior and short-term variability in Sgr A* rotation measure, implying a complex inner region (within 10 Schwarzschild radii) in which both emission and propagation effects are important to the observed polarization. Hada et al. (2016) studied the central black hole in the galaxy M 87, and observed a bright feature with (linear) polarization degree of 0.2 at 86 GHz at the jet base. Observations in infrared by Gravity Collaboration (2018) were consistent with a model in which a relativistic “hot spot” of material, orbiting near the innermost stable circular orbit (ISCO) of Sgr A* in a poloidal magnetic field, emits polarized synchrotron radiation.


Galactic winds: Galactic winds driven by CRs have often been simulated in two limits: a diffusion-dominated regime, due possibly to ‘extrinsic confinement’, where CRs are scattered by extrinsic turbulence, and/or due to various wave damping mechanisms (e.g. ion neutral damping) and streaming-dominated ‘self confinement’, where CRs are confined by Alfven waves they produce via the gyroresonant streaming instability. In the diffusive ‘extrinsic confinement’ case, CRs do not heat the gas.19 In the streaming dominated ‘self confinement’ case, CR transport heats gas at a rate vA · ∇Pc. The diffusive case fits γ ray observations better, because CRs can propagate out of the galaxy faster (Chan et al. 2019). It is also much better at driving winds, because the CRs do not suffer strong energy losses via Alfven wave heating (Wiener et al. 2017b; Hopkins et al. 2020). However, we expect self-confinement to be very strong at the ∼GeV energies where CR energy peaks (Kulsrud & Pearce 1969; Farmer & Goldreich 2004; Wiener et al. 2013), while extrinsic compressible turbulence is strongly damped at small scales, and unlikely to efficiently scatter ∼GeV CRs (Yan & Lazarian 2002). Thus, CR winds should be streaming dominated and relatively inefficient. The CR staircase changes these dichotomies by changing the structure of the wind. We have seen how CR pressure can build up in streaming dominated simulations, due to trapping at bottlenecks. This increases mass outflow rates, similar to the effect of increased opacity in radiative outflows. In CR streaming simulations of isothermal winds where the CR acoustic instability arose, Quataert et al. (2022a) found an increase in wind mass loss rates by an order of magnitude, compared to analytic models without a CR staircase, illustrating the potential impact of CR staircases. High-resolution cosmological zoom simulations of CR staircases are actually well within reach. As seen in Appendix Section B, all that is required is that the diffusion length $l_{\rm diff} \sim \kappa /c_{\rm s} \sim 2 \, {\rm kpc} \, \left(\frac{\kappa }{10^{29} {\rm cm^2 s^{-1}}} \right)\left(\frac{c_{\rm s}}{150 \, {\rm km \, s^{-1}}} \right)^{-1}$ is resolved. However, to date only the FIRE collaboration has implemented the two moment method (capable of dealing with CR streaming) in such simulations, and – in contrast to, for instance, van de Voort et al. (2021) – the plasma β in their winds is too high for the acoustic instability to develop (Hopkins et al. 2020). But alternate setups where CR staircases appear are certainly numerically feasible.


We repeated the plasma pressure calculation presented by Schwadron et al. (2011) and Fuselier et al. (2012) for the new ENA energy spectrum. The results for the downwind hemisphere and for the Voyager 1 region are summarized in Table 3. The measured intensity

j

ENA

 of neutralized hydrogen at a given energy translates into a pressure of the parent ion population in the heliosheath times the integration length along the line of sight, ΔP × l, in the following way:
3

Δ
P
×
l
=

4
π

3

n

H

m

H

v

j

ENA

(
E
)

σ
(
E
)

Δ
E

c

f

4

c

f

=

(
v
+

u

R

)

2

v

4

(

v

2

+
4

u

R

2

+
2

u

R

v
)
.

In Equation (3), ΔE denotes the width of the respective energy bin; for the typical radial velocity of solar wind in the flanks and the downwind hemisphere of the inner heliosheath, we assumed uR = 140 km s−1 as measured by Voyager 2, whereas uR = 40 km s−1 for the heliosheath in the Voyager 1 direction (Schwadron et al. 2011; Gloeckler & Fisk 2015). For the density of neutral hydrogen in the inner heliosheath a constant nH = 0.1 cm−3 is assumed (Schwadron et al. 2011; Gloeckler & Fisk 2015). The charge-exchange cross section between protons and neutral hydrogen decreases from (4 to 2) × 10−15 cm−2 for 0.015 to 1.821 keV (Lindsay & Stebbings 2005). The integration length l for ENA production in the plasma is approximately the thickness of the inner heliosheath. The part of Equation (3) without the velocity factor cf can be interpreted as stationary pressure. The total pressure or dynamic pressure is the stationary pressure times this factor. Integrating over all energy bins in Table 3, we obtain the total plasma pressure times heliosheath thickness as P × l = 304 pdyn cm−2 au for the downwind hemisphere and 66 pdyn cm−2 au for the Voyager 1 region (1 pdyn cm−2 au = 0.015 N m−1). If we want to put these numbers into the context of other studies, we face two problems. First, the uncertainty of the total pressure is large given the upper limits in the two lowest energy bins. Second, heliosheath plasma more energetic than 2 keV will produce ENAs that cannot be detected with IBEX-Lo. We therefore used the observed median j = 0 cm−2 sr−1 s−1 keV−1 for heliospheric ENAs in the two lowest energy bins of IBEX-Lo and relied on the study by Livadiotis et al. (2013). They compared the expected plasma pressure from a kappa distribution of protons with the plasma pressure derived from IBEX-Hi energy spectra: the energy range between 0.03 and 2 keV, roughly corresponding to the IBEX-Lo range, covered more than half of the total plasma pressure predicted from a kappa distribution. The authors found a total plasma pressure of P = 2.1 pdyn cm−2 for all sky directions except for the ENA Ribbon. Gloeckler & Fisk (2015) presented a multi-component plasma model for the heliosheath to explain Voyager and IBEX observations. At low energies they assumed the ENA energy spectra provided by Fuselier et al. (2012). They derived a total pressure of 2.5 pdyn cm−2 in all three plasma regions in the nose of the heliotail (Gloeckler & Fisk 2015). Pressure contributions from the slowed solar wind, magnetic pressure, and the pressure exerted from pickup ions and anomalous cosmic rays all had to be taken into account to obtain this total pressure.


We futher examine the distributions of the radial number fraction of satellites with different colors in different LSE in Figure 5 to study the role central galaxies play in SCA. It can be seen, in general, that the intersections of these lines for each subsample are located between

 to

, and with a mean value of

. Satellites (especially red satellites) prefer to reside in the inner part of groups and the number fraction decreases with the increasing radius. Such evolutionary behavior is consistent with “strangulation” wherein cold gas that could be used for star formation is depleted as satellites are accreted (e.g., Kauffmann et al. 2004; Kang et al. 2005; Luo et al. 2016). The shapes of each curve (the maximum value, the decrease gradient) not only depend on the color of central and satellite galaxies but also depend on the LSE. In the inner part of halos, the fraction of satellites is lower in the more dense LSEs. In the outer parts, it is the opposite, namely, in knots there is a higher fraction of satellites. It must be pointed out is that, in a given environment and for a given central color, the fraction of blue satellites is always higher than red satellites in outer regions. For wall environments, about 25% ∼ 30% satellites reside at the low values of

, and the fraction decreases very quickly. Additionally, in the inner parts, the fraction of satellites of red centrals (red dashed line in the top left panel of Figure 5) is ∼5% higher than those in blue centrals (blue dashed line in the top left panel of Figure 5). The radial distributions of satellites in filaments are almost absent with the different colors of both central and satellite galaxies. However, in a knot environment, blue centrals have ∼3% more satellites than red centrals at low values of projected radius. These radial satellite distributions with different colors in different LSE indicate that, red central galaxies have merged more satellites than blue central galaxies in the knot LSE, which means satellites with a red central galaxy may be more affected by the interaction with central galaxies and represent a better SCA, especially in the inner region.


In the currently accepted model of star formation, most stars form in families of star clusters within giant molecular clouds (GMCs). However, clusters and their families can be quite diverse, and there is no consensus yet on a general model for cluster formation. An additional complication is that once stars are born, they destroy most of the evidence relating to the initial stages of their formation. In this sense, determining the early stages of cluster formation in GMCs may be key to understanding many distinct and complex processes involved in such a phenomenon. The Pipe Nebula, a nearby (d = 130 pc) GMC with a total mass of 7.9 × 103 M⊙ (Lada, Lombardi & Alves 2010) and very little star formation activity (Brooke et al. 2007; Forbrich et al. 2009, 2010) has played a workhorse role in a number of previous studies (e.g. Alves, Lombardi & Lada 2007; Muench et al. 2007; Alves, Franco & Girart 2008; Lada et al. 2008; Rathborne et al. 2009; Román-Zúñiga, Lada & Alves 2009; Román-Zúñiga et al. 2010; Peretto et al. 2012; Frau et al. 2015; Hasenberger et al. 2018). Many of these works have the common goal of determining how GMCs are organized in the stages that precede their collapse and the consequent conversion of gas into stars. Interestingly, despite the fact that it is almost starless, the column density peaks1 in the Pipe appear to show a clear imprint of clustering, as well as segregation by density and mass (e.g. Román-Zúñiga et al. 2010; Alfaro & Román-Zúñiga 2018, hereafter RAL10 and AR18, respectively). The Pipe was also the first cloud where a ‘core mass function’ (see Alves et al. 2007; Rathborne et al. 2009) was constructed, leading to many subsequent studies that have discussed what appears to be a clear homology to its stellar counterpart (e.g. Alves et al. 2007; Goodwin et al. 2008; Swift & Williams 2008; Kainulainen et al. 2009). These findings are suggestive of a primordial organization of clouds towards the formation of groups and clusters, evident in the properties of density peaks.


For the uncertainty from the Fermat potential, which is determined by lens modeling, source host galaxies without dazzling AGNs are conducive to the reconstruction of the mass distribution of the lens galaxies in lensed FRB systems. Simulations show that the Fermat potential component contributes approximately ∼0.8% uncertainty on DΔt (Li et al. 2018b). Actually, in lens modeling, except for the contamination from the light of the dazzling AGN in the source, mass-sheet degeneracy (MSD; a family of mass density profiles that could reproduce the same lensing observables, e.g., image positions and relative fluxes, but yields different measured values of H0) also plays an important role in leading to the loss of precision and accuracy. In recent years, this issue has been intensively investigated. Generally, there are two ways, which include applying theoretical priors (make radial-mass density profile assumptions) and appealing nonlensing data (e.g., stellar kinematics) to break the MSD. For instance, the TDCOSMO collaboration (Millon et al. 2020) has achieved ∼2% in the inference of H0 from time-delay cosmography under the assumption that the radial-mass distribution of the lens can be described by a power-law mass profile or a composite of a dark-matter halo (Navarro et al. 1997) and baryon matter. Meanwhile, Gomer & Williams (2020) tested the effects of the power-law assumption and found that the power-law assumption would introduce significant bias in the recovery of H0. In practice, as suggested in Li et al. (2018b), a high-quality optical/IR image of the source–lens system could be very helpful to avoid choosing the wrong models. That is, the model we choose to characterize the mass distribution of the lens according to the high-resolution image might be more complex than the simple power-law one, and thus could significantly reduce the bias. However, it is difficult to choose an exactly right model for the lens, thus the uncertainty of the Fermat potential might be larger than 0.8% in real observations. For example, using eight time-delay galaxy lenses and more flexible modeling methods, a precision of 4.97% on H0 was achieved (Denzel et al. 2021). With spatially resolved kinematics and external observations to break MSD, a 5% precision of H0 was inferred by assuming that the deflector of TDCOSMO and the Sloan Lens ACS (SLACS) lenses are drawn from the same population (Birrer et al. 2020). It is promising that by increasing the size of samples and applying the hierarchical framework introduced by Birrer et al. (2020), a precision of 1.5% or 1.2% on H0 will be achieved without assumptions on the radial-mass profile of lens galaxies (Birrer & Treu 2021). More recently, Ding et al. (2021) implemented realistic simulations in lens modeling based on HST WFC3 observations from transient sources (e.g., supernovae, gamma-ray bursts, FRBs, and GWs) to compare the precision of H0 inferred from the transient case and the lensed AGN case. They found that, compared with traditional lensed quasars, the precision for inferring the Shapiro delay and the geometric delay could be improved by a factor of 3.8 and 4.7 for lensed transient systems, respectively. It means that the precision of the Fermat potential reconstruction could be improved by a factor of about 6. Furthermore, the lensed transient system also facilitates the determination of higher signal-to-noise stellar kinematics of the main deflector, and thus its mass density profile, which in turn plays a key role in breaking the mass-sheet degeneracy. With the abovementioned investigations taken into consideration, we first take 0.8% relative uncertainty on the Fermat potential on the basis of simulations presented in Ding et al. (2021) and Li et al. (2018b). In addition, we also consider a more conservative 1.5% relative uncertainty on Fermat potential for comparison.


Along with the flare related changes, we also examine possible orbital variations by dividing the overall quiescent spectra in periods dubbed as “Quiet 1” and “Quiet 2” (the time bins for the spectra are as shown in Fig. 1) and model the pn, MOS and RGS X-ray spectra. We specifically determine the temperatures, emission measures and abundances relative to solar values (Grevesse & Sauval 1998) with simultaneous iterative global XSPEC fits to the combination of EPIC and RGS (RGS+PN or RGS+MOS) spectra with variable-APEC (VAPEC; Smith et al. 2001) plasma models. As is often observed (Güdel et al. 2001; Robrade & Schmitt 2005; Lalitha et al. 2013), we require multi-temperature components to achieve an adequate description of the observed coronal spectra. We use combinations of two, three and four temperature components and find that a three temperature component model leads to an adequate description of the data. We fit each of these spectra in the full 0.2–10 keV energy range. For fitting the RGS spectra, the temperature and the abundances of elements like carbon, nitrogen, oxygen, neon and iron are allowed to vary freely and independently, however, the abundances are fixed among the different APEC temperature components. For fitting EPIC-MOS or pn spectra we allow the magnesium, sulphur, and silicon abundances to vary along with the oxygen, neon and iron abundance. However, the carbon and nitrogen abundances are fixed to values obtained from the RGS, which is more sensitive to strong individual lines of these elements. In Table 1, we summarise the results of this fitting procedure along with the 90% confidence range errors. Table 1 shows that the quiescent state is characterised by dominant plasma components at ~3, ~7.5 and ~20 MK, while during the flare the coronal temperature bins increase to ~3.5, ~12 and ~32 MK. During the flare, a pronounced enhancement of the emission measure at 2.8 keV is present, indicating the rise of emission measure at a higher temperature. The quiescent bins (quiet 1 and quiet 2) does not show any significant difference in the coronal properties when compared to the overall quiescent time-bin; suggesting no changes in coronal properties with orbital variation.


WASP-43b is the most heavily scrutinized phase curve, with four analyses of this data set already published (Stevenson et al. 2017; Mendonça et al. 2018; Morello et al. 2019; May & Stevenson 2020). Our phase curve semi-amplitude, eclipse depth, and radius are consistent with all of these works. The more contentious issue is that of the phase curve’s phase offset and nightside temperature. Stevenson et al. (2017) initially reported only a 2σ upper limit on the nightside temperature of 650 K, while all subsequent reanalyses (including ours) favour a significantly detectable nightside temperature of ∼800 K. As for the planet’s phase offset, Stevenson et al. (2017) and May & Stevenson (2020) favour a larger phase offset (21 ± 2 °E) than Mendonça et al. (2018) and Morello et al. (2019) (12 ± 3 °E and 11 ± 2 °E). May & Stevenson (2020) claimed that the differences between the retrieved phase offsets is the result of temporal binning which was not used by Stevenson et al. (2017) and May & Stevenson (2020) but was used by Mendonça et al. (2018), Morello et al. (2019), and this work. Fitting the temporally binned photometry for all 17 phase curves with each of our detector models already required more than 2000 CPU hours, and expanding this to unbinned photometry for all phase curve fits would require more than 125 000 CPU hours (or 434 d using our 12× multithreading computer) optimistically assuming all of detector models scaled linearly with the number of input data. However, we did try fitting just the WASP-43b unbinned phase curve with our preferred detector model (BLISS) and found that our phase offset and nightside temperature was unchanged. Including a linear slope in time also did not affect our phase offset or nightside temperature. Instead, we find that the phase offset inferred by our models depends on the choice of phase curve model, as our 4-parameter (v2) phase curve models are consistent with those of Stevenson et al. (2017) and May & Stevenson (2020), while our 2-parameter phase curve models (v1) are consistent with Mendonça et al. (2018) and Morello et al. (2019). Ultimately, we cannot decide between these two discrepant offsets as the ΔBIC between the two phase curve models for our preferred BLISS detector model is only 3.7 (insignificantly favouring the 20.4 ± 3.6 offset from the v2 model). For reference, Stevenson et al. (2014b) found phase offsets ranging from roughly −6 to 17 deg east in the Hubble/WFC3 bandpass.


Various observational techniques, such as measuring the Gunn–Peterson optical depth from QSO spectra or the prevalence of Ly α emission in high-redshift galaxies, have placed very tight constraints on the volume filling fraction of neutral hydrogen in the intergalactic medium (IGM) towards the end of reionization at z∼ 6 (Becker et al. 2001; Fan et al. 2006; Totani et al. 2006; McQuinn et al. 2007; McQuinn et al. 2008; Ota et al. 2008; Ouchi et al. 2010; Bolton et al. 2011; Mortlock et al. 2011; Ono et al. 2012; Becker & Bolton 2013; Chornock et al. 2013; Robertson et al. 2013; Schroeder, Mesinger & Haiman 2013; Caruana et al. 2014; Pentericci et al. 2014; Schenker et al. 2014; Tilvi et al. 2014; McGreer, Mesinger & D’Odorico 2015; Mesinger et al. 2015; Mitra, Choudhury & Ferrara 2015, 2018; Sobacchi & Mesinger 2015; Greig & Mesinger 2017). While the timing of the end of reionization is rather well constrained by observations and modelling (e.g. Fan et al. 2006; Choudhury et al. 2015) as is the photoionization rate of neutral hydrogen in the post-reionization Universe (Bolton & Haehnelt 2007; Calverley et al. 2011; Wyithe & Bolton 2011; Becker & Bolton 2013), much remains uncertain about the onset and extent of the process. This uncertainty is primarily driven by the current lack of understanding of which sources reionized the Universe and the difficulty of observing these systems deep into the epoch of reionization. Various classes of objects have been proposed as the sources of reionization including dwarf galaxies, mini-haloes, massive galaxies, active galactic nuclei, accretion shocks, globular clusters, stellar mass black holes, and dark matter annihilation and decay (Couchman & Rees 1986; Shapiro & Giroux 1987; Haiman & Loeb 1998; Madau, Haardt & Rees 1999; Ricotti 2002; Madau et al. 2004; Ricotti & Ostriker 2004; Mapelli, Ferrara & Pierpaoli 2006; Dopita et al. 2011; Mirabel et al. 2011; Katz & Ricotti 2013, 2014; Madau & Haardt 2015).


Studies of the radial n-capture-to-iron abundance gradients are very scarce so far. We can only search for a broad agreement of our results with several studies of abundance gradients with galactocentric distances (Rgc). da Silva et al. (2016) studied n-capture elements across the Galactic thin disc based on Cepheid variables. Because the Cepheids are young stars, their Rgc may be rather close to their birthplaces and Rmean. da Silva et al. (2016) supplemented their sample of 111 Cepheids with 324 more stars from other studies and found that the [Y/Fe] distribution is flat throughout the entire disc. In our study, we confirm this finding not only based on the whole thin-disc sample of stars and on a subsample of younger ≤4 Gyr stars, but also add another light s-process dominated element strontium. Like in our study, da Silva et al. (2016) also obtained positive [El/Fe] radial gradients for La, Ce, Nd, and Eu. The slopes are rather similar. For [Eu/Fe], they differ just by 0.002 dex kpc−1. More recently, Luck (2018b) also investigated the gradients of n-capture element abundance-to-iron ratios with respect to Rgc for a sample of 435 Cepheids. It is interesting to note that the [Ba/Fe] versus Rgc slope according to this Cepheid sample is also negative, as in our study. [Ba/Fe] is the only n-capture element-to-iron ratio with a negative radial gradient in our sample of stars and in Luck (2018b). Overbeek et al. (2016) investigated trends of Pr, Nd, and Eu to Fe abundance ratios with respect to Rgc using 23 open clusters. As in our study, they found that these elements have positive linear trends with galactocentric radius (the linear regression slopes are of about +0.04 dex kpc−1). They also suggested that the [El/Fe] relation of Pr and Nd, but not Eu, with the galactocentric radius may not be linear because the [El/Fe] of these elements appears to be enhanced around 10 kpc and drop around 12 kpc. Because only a small number of stars lie at these large radial distances, we cannot address this question. For the thick-disc stars, the radial abundance-to-iron slopes are negligible, as was found for α-process elements by Li et al. (2018), even though the production sites of α-elements and s-processes dominated elements are quite different.


Observations are now probing galaxies in the middle of the reionization epoch, when the gas in the intergalactic medium was transformed from its initially neutral state into a hot, ionized plasma (e.g. McLure et al. 2011; Finkelstein et al. 2012; Bouwens et al. 2014). Most likely stars in galaxies are responsible for this transformation, although this heavily depends on the fraction of ionizing photons produced by the stars that make it into the intergalactic medium, the so-called escape fraction fesc. The escape fraction is a key parameter in studies of the contribution of the observed galaxy population to reionization (e.g. Bouwens et al. 2012; Robertson et al. 2013), semi-analytic modelling of reionization (e.g. Choudhury, Haehnelt & Regan 2009; Pritchard, Loeb & Wyithe 2010; Santos et al. 2010; Mesinger, Furlanetto & Cen 2011; Raskutti et al. 2012; Mitra, Ferrara & Choudhury 2013; Shull et al. 2012) and numerical simulations of reionization (e.g. Iliev et al. 2006; Trac & Cen 2007; Ciardi et al. 2012). A large effort is going into determining the escape fraction observationally. Except for two objects (Leitet et al. 2011, 2013), in the local Universe no ionizing radiation has been detected directly (Leitherer et al. 1995; Deharveng et al. 2001), although some objects show indirect evidence of photon leakage (Heckman et al. 2011; Zastrow et al. 2011). The lack of detections may be partly due to selection bias (Bergvall et al. 2013), but the objects from which radiation is detected have very low escape fractions, fesc  4 per cent. At z ∼ 1, no objects with leaking ionizing photons have been detected (Bridge et al. 2010; Siana et al. 2010), but at z ∼ 3, the highest redshift at which the opacity of the intergalactic medium for ionizing photons is approximately less than unity, ionizing photons have been detected in ∼10 per cent of the observed objects (Nestor et al. 2013). Attempts to constrain the escape fraction with numerical simulations find ranges between fesc  10 per cent (Razoumov & Sommer-Larsen 2006, 2007; Gnedin, Kravtsov & Chen 2008; Paardekooper et al. 2011; Kim et al. 2013) and fesc > 80 per cent (Wise & Cen 2009; Razoumov & Sommer-Larsen 2010), with likely a strong mass and redshift dependence (Yajima, Choi & Nagamine 2010; Wise et al. 2014). Due to the opacity of the intergalactic medium, we need to mostly rely on numerical simulations to learn about the escape fraction during the epoch of reionization.


Therefore, the kinetics characteristics of the star could be the only piece to judge whether or not the SM star is the surviving companion of SN 1006. If its space velocity is significantly different from the other stars in the remnant of SN 1006, the probability to be the surviving companion would become high. Otherwise, the probability becomes low. We check the proper motion of the stars within 5 arcmin of the remnant centre from Gaia DR2, as shown in Fig. 19. From the figure, it seems that there is not difference between the SM star and other stars in the remnant of SN 1006 in the aspect of proper motion, i.e. the proper motion of the SM star only slightly deviates from the median value of the proper motions of the stars at the direction of the SNR centre of SN 1006, and such a proper motion disfavours the SM star as the surviving companion of SN 1006 (Schweizer & Middleditch 1980; Burleigh et al. 2000). So, a 3D space velocity is helpful to judge the nature of the SM star. However, unfortunately, some data of the SM star in Gaia DR2 are so uncertain that we cannot use them to constrain its 3D space velocity, otherwise we could obtain a complete wrong conclusion.5 For example, the parallax of the SM star is ϖ = 0.0736 ± 0.1244, and then σϖ/ϖ = 1.69 which is much larger than the threshold value of 0.2 for distance estimation from GAIA DR2 data (Astraatmadja & Bailer-Jones 2016; Katz et al. 2018). The distance of the SM star from this parallax is much larger than all the previous measurements from spectrum by at least a factor of 2 (see summary in Burleigh et al. 2000). Considering that some other astrometric measurements of the SM star are also very uncertain, we applied the measurements in the previous literatures as the distance of the SM star. Based on a radial velocity of $-13\pm 17\, {\rm km^{\rm -1}}$ and a distance of 2.07 ± 0.18 kpc (Schweizer & Middleditch 1980; Winkler et al. 2003; Kerzendorf et al. 2018), we can calculate the UVW velocities of the SM star, i. e. $U=-5.2\pm 14\, {\rm km^{\rm -1}}$, $V=197\pm 10\, {\rm km^{\rm -1}}$, and $W=3.1\pm 5\, {\rm km^{\rm -1}}$. The V value of the SM star is smaller than that of a normal disc star. We then transform these velocities into the Galactic rotational velocity at a Galactocentric distance of ∼6.67 kpc, i.e. $V_{\rm c}=196\pm 12\, {\rm km^{\rm -1}}$, which is smaller than the Galactic rotational velocity of the disc stars at the Galactocentric distance by $50\pm 19\, {\rm km^{\rm -1}}$ (Huang et al. 2016). This velocity difference is marginally consistent with the predicted orbital velocity here (see Fig. 7). In addition, the smaller rotational velocity of the SM star may explain its small proper motion shown in Fig. 19. So, the SM star is still possible to be the surviving companion of SN 1006.


A more puzzling task was the resolution of the fine and hyperfine structure. First, the A–E split structure attributed to the methyl internal rotation motion can be generally used as a molecular “fingerprint” to search for a molecule in an astronomical line survey (Cernicharo et al. 2016; Belloche et al. 2017). Moreover, it is known that for interstellar searches using surveys that done at centimeter wavelengths (i.e., those conducted with telescopes such as GBT and Yebes 40m), the recognition of hyperfine patterns in the observed spectra significantly help in the proper identification of interstellar molecules (McCarthy & McGuire 2021). As an example, the analysis of the hyperfine structure of several N-bearing species, such as N-protonated isocyanic acid (H2NCO+, Rodríguez-Almeida et al. 2021b) which has been detected toward G+0693-0.027 along with ethyl isocyante (C2H5NCO, Kolesniková et al. 2018), was required for its conclusive line-by-line identification. In this context, sensitive data at centimeter wavelengths are crucial because in TMC-1 and in G+0.693-0.027 the excitation temperatures of the molecules are very low, and hence the brightest lines of this relatively complex species fall at those frequencies. These interstellar sources have recently been suggested to be among the best targets to search for large molecular systems (McGuire et al. 2021; Rivilla et al. 2021b), further supporting centimeter-wave studies of as-yet-undiscovered interstellar candidates. Hence, we employed our narrowband LA-MB-FTMW spectrometer (León et al. 2021) to completely resolve both fine and hyperfine structures. We initially used the SPFIT/SPCAT program package (Pickett 1991) to analyze hyperfine patterns for the previously measured A and E lines of Z-AHA (see Fig. 3). This scrutiny was followed by measuring additional hyperfine components of several a- and b-type R-branch lines. Once we completed the analysis, new R-branch transitions belonging to the E-conformer were identified.


The sudden brightening of NGC 2617 provides a good opportunity to investigate the properties of CL-AGNs. In general, the CL processes can be interpreted as changes in obscuration or accretion rate. The obscuration model can be well applied to some X-ray selected CL-AGNs (e.g., Bianchi et al. 2005). The crossing time for an intervening object orbiting outside a BLR can be estimated as (LaMassa et al. 2015)
2

where rorb is the orbital radius of the foreground object on a circular, Keplerian orbit around the central black hole, M8 is the black hole mass in units of 108M⊙, and rsrc is the true size of the BLR. The above equation is derived by evaluating the time needed for this object to travel the length of an arc that corresponds to the projected size of the BLR. The observational constraints of rdt and rdt/rBLR are discussed in estimating tcross for the double-peaked BEL CL-AGN NGC 3516, where rdt is a dust torus radius (Feng et al. 2021, and references therein). rdt/rBLR ∼ 4–5 is obtained for most reverberation-mapped AGNs with the Hβ BLR and dust torus lag measurements. NGC 3516 has rdt/rBLR = 7. Thus, it seems appropriate to use rdt/rBLR = 5 in the CL-AGN NGC 2617. NGC 2617 has averages of rBLR = 6.15 lt-day and M8 = 0.22 for Hα and Hβ, and we obtain tcross = 7 yr. NGC 2617 is Seyfert 2 in 1994 and on 2003 December 30, and Seyfert 1 on 2013 April 25 (see Figure 2 in Shappee et al. 2014). Our observations show a Seyfert 1 type of optical spectra from 2019 October to 2020 May. The poor sampling of long-term spectroscopic observations makes it impossible to give the reliable durations of the appearance and “disappearance” of BELs. A long-term monitoring with a good sampling, e.g., twice a year, may give a reliable duration of “disappearance” of BELs in the CL processes, especially, the continuous and complete process of changing of Seyfert 1 → Seyfert 2 → Seyfert 1. This will be important to test the obscuration model of CL-AGNs.


The majority of observational evidence based on studies of SN Ia populations thus points towards a DD scenario for most, if not all, SNe Ia. However, finding self-consistent progenitor and explosion models that recreate the observed luminosity function as well as correlations between luminosity, light-curve parameters, and host galaxy properties has proven difficult. In particular, simulations based around explosions of MCh WDs (linked strongly with the SD scenario but also with many DD scenarios) find difficulty in reproducing the light curves of ‘normal’ SNe Ia as well as ‘peculiar’ objects (Ropke et al. 2007; Sim et al. 2013; see Maoz et al. 2014; Blondin et al. 2017; Jha, Maguire & Sullivan 2019 for overviews). In recent years, attention directed towards explosions of sub-MCh WDs triggered by double detonations (primarily related to a DD scenario) has led to promising results (e.g. Shen, Toonen & Graur 2017; Shen et al. 2018; Townsley et al. 2019; Gronow et al. 2020; Shen et al. 2021) although they still struggle to match observations at late times in the light-curve evolution (Gronow et al. 2021; Shen et al. 2021). An additional factor in support of the sub-MCh model is that the SN luminosity is related to the mass of the primary WD, which itself is likely to be related to its age (although this relation is probably complicated by other factors such as accretion rate, metallicity, and the composition of the companion), thereby providing an explanation for observed relation between light-curve stretch and stellar age (Rigault et al. 2013, 2020; Rose, Garnavich & Berg 2019; Nicolas et al. 2021). Other proposed scenarios include hybrid models in which standard CO WDs merge with hybrid helium-CO WDs (Zenati, Toonen & Perets 2019). With many models showing promising similarities to observations but each subject to its own drawbacks, it is becoming accepted that more than one progenitor scenario may contribute significantly to the overall population of ‘normal’ SNe Ia; detailed observations are thus required in order to place constraints on the relative fractions of each possible progenitor channel.


Figure 15 shows the comparison between pairs of molecular abundances, HC(O)NH2 and HNCO, CH3NCO and HNCO, and CH3NCO and HC(O)NH2. It is already known from previous observations that there is a correlation between HNCO and HC(O)NH2 (López-Sepulcre et al. 2015, 2019; Allen et al. 2020). In the top-left panel of Fig. 15 the best power-law fits derived by López-Sepulcre et al. (2015), X[HC(O)NH2] = 0.04 × X[HNCO]0.93, and by Quénard et al. (2018), X[HC(O)NH2] = 32.14 × X[HNCO]1.29, are compared with the one derived here, X[HC(O)NH2] = 0.006 × X[HNCO]0.73 (with a Pearson coefficient of 0.99 and a P-value 0.05, indicating a strong positive correlation). Thus, the sample of sources discussed in this work, which also includes HMCs and a shock-dominated molecular cloud, is in agreement with the correlation found previously for low- and intermediate-mass pre-stellar and protostellar objects, which holds across several orders of magnitude in abundance. Based on this tight correlation, it has been proposed that the two species are chemically related and that the formation of HC(O)NH2 might occur through H-addition to solid-phase HNCO (e.g. Tielens & Hagen 1982; Charnley et al. 2004). Experimental works first suggested that this process is not efficient (Noble et al. 2015; Fedoseev et al. 2015), while recent works revised this possibility and found that a correlation between these two molecular species can be understood by H-abstraction and addition reactions (e.g. Nguyen et al. 2011; Haupa et al. 2019; Suhasaria & Mennella 2020). Moreover, hydrogenation of NO combined with UV-photon exposure and radical-radical reactions on grains has been suggested as the main formation pathways for both HNCO and HC(O)NH2 (e.g. Jones et al. 2011; Fedoseev et al. 2016; Ligterink et al. 2018; Dulieu et al. 2019). Coutens et al. (2016) found that the deuteration (D/H ratio) of HC(O)NH2 in IRAS 16293 B is similar to that of HNCO, in agreement with the hypothesis that both species are chemically related via grain-surface reactions. Gas-phase formation routes have also been proposed (see e.g. NH2 + H2CO, Barone et al. 2015; Skouteris et al. 2017). Laboratory experiments by Martín-Doménech et al. (2020) show that both HNCO and HC(O)NH2 could form upon UV photoprocessing or electron irradiation of ice samples, indicating that energetic processing (like UV photons and cosmic rays) of ISM CO-rich ices could form both species, without the need of a chemical link and/or a similar precursor between the two. This was predicted by the chemical modelling of Quénard et al. (2018), who showed that the formation of HC(O)NH2 at different temperature regimes is governed by different chemical processes. While at low temperatures the formation of HC(O)NH2 is driven by gas-phase formation via the reaction NH2 + H2CO → HC(O)NH2 + H, at high temperature its formation occurs on the surface of dust grains via radical-radical addition reactions. Moreover, they showed that for HNCO grain-surface and gas-phase reactions are equally efficient at low temperature, while at high temperatures the gas-phase formation predominates and the small fraction formed on grains is released into the gas phase via thermal desorption. Rimola et al. (2018) also showed via theoretical quantum chemical computations that HC(O)NH2 can form on grain surfaces starting from CN, which can quickly react with water-rich amorphous ices. Thus, the correlation between HNCO and HC(O)NH2 is mainly due to a similar response to the temperature of the two molecules, and not to a direct chemical link. In fact, the increase of the temperaturetriggers processes on the ice-mantle of grains, such as thermal evaporation. Moreover, as discussed above, other processes, like UV photons, cosmic rays, and shocks, could help both on the formation of these molecules on grain surfaces and on their desorption in the gas.


Associations between ULXs and star clusters have also been studied in interacting galaxies. The latter are known to host a higher average number (>5) of ULXs. Therefore, they are good candidates in which to examine the properties of the population of ULXs. Poutanen et al. (2013) extensively examined the significant associations between ULXs and stellar clusters in the Antennae galaxies. Using data from HST and the Very Large Telescope supplemented with theoretical stellar isochrones, they estimated the ages of these clusters as 6 Myr. It was discussed that these ULXs were probably ejected from the cluster in the evolutionary process; thus these sources might be high-mass X-ray binaries instead of intermediate-mass black holes. Another well-known interacting galaxy is NGC 4490/NGC 4485 at a distance of 7.8 Mpc (Tully 1988). NGC 4490 is a late-type spiral galaxy and NGC 4485 is an irregular galaxy. Their linear sizes are 15 kpc for NGC 4490 and 5.6 kpc for NGC 4485. Radio observations show that star formation in NGC 4490 has been ongoing at a constant rate of ∼4.7 M yr−1 (Clemens et al. 1999). Also, NGC 4490 has a giant H i envelope that probably originated from the star formation (Clemens & Alexander 2002). Our aim in this study is to identify the possible optical counterparts of ULXs in this galaxy pair and to investigate their associations with star groups or clusters. Previously, three ULXs in this pair were detected by ROSAT HRI observations (Roberts & Warwick 2000). Later, using a Chandra ACIS-S observation, three more ULXs were identified by Roberts et al. (2002). The calculated unabsorbed luminosities of six ULXs (in the 0.5–8 keV band) fall into the range (2.6–4.9) × 1039 erg s−1. In addition, Roberts et al. noted that these ULXs appear to be spatially coincident with the star formation regions in the pair. Further, Fridriksson et al. (2008) searched for long-term variability of 38 X-ray sources in this galaxy pair using three Chandra observations. Eight of these sources were classified as ULXs in the luminosity range (0.6–3) × 1039 erg s−1. One of them is a transient ULX detected in a single observation (ID 4726). Gladstone & Roberts (2009) investigated spectral and temporal features of seven ULXs (except for ULX X-5—this source was ignored because of its low luminosity of LX ∼ 6 × 1038 erg s−1, which was given in Table 5 of Fridriksson et al. 2008) using the same Chandra and XMM-Newton data sets. The LX values of these sources are given in the range (0.9–4) × 1039 erg s−1 within the 0.5−8 keV energy band. Six of these seven sources (except the transient one, which is X-7 in this paper) were classified as ULXs by Swartz et al. (2011).


Deriving the completeness limits of the WISE photometry is mandatory to assess the reliability of our catalogue of starless cores. We examined the histograms of the number of mid-infrared (MIR) sources versus magnitude; taking into account the effects of the cuts required to fulfil the criteria of Koenig et al. (2012), rough completeness limits are [3.6] ~ 14, [4.6] ~ 12, [12] ~ 9 and [22] ~ 7. These values are 1–3 mag brighter than the sensitivity limits quoted in the WISE Explanatory Supplement3 for the relevant sky region. Once converted into flux units and, for example, compared with the models of Class I and Class 0 sources of 0.5 M⊙ by Whitney et al. (2004), it can be seen that the completeness limits at 3.6 and 4.6μm are faint enough to detect such objects taking into account a distance of 700 pc and a further foreground reddening up to AV = 20. Even in the worst case of edge-on discs, these objects would be detectable at 3.6 and 22μm. Furthermore, the completeness limit at 22 μm is faint enough to allow detection of Class I and Class 0 sources of even-lower-mass central objects. Alternatively, one can compute the bolometric luminosity following Kryukova et al. (2012). Starting from our completeness limit at 22 μm, after conservatively dereddening it by AV = 20, we assumed a spectral index γ = −2 (see Table 3 for definition) to compute the MIR luminosity from Eq. (6) of Kryukova et al. (2012). Equation (7) of Kryukova et al. (2012) then yields Lbol ~ 1.7–2.8 L⊙, depending on whether the NIR flux is neglected (which may be the case) or extrapolated from γ = −2. A comparison with the birthline of Palla & Stahler (1993) indicates a mass of ~ 0.4–0.5 M⊙ for the central protostar. For the sake of comparison, we can roughly estimate the completeness limit in central masses of the Herschel protostellar cores in Giannini et al. (2012) using their quoted completeness limit at 70 μm of 0.21 Jy and following Dunham et al. (2008). By using Eq. (2) of Dunham et al. (2008), scaled to a distance of 700 pc, we found that the flux density at 70 μm translates into a bolometric luminosity of the central (proto)star Lbol ~ 0.28 L⊙ (we note that Dunham et al. 2008 indicate this luminosity as Lint). We highlight the fact that the 70 μm emission is in principle a more sensitive protostellar tracer than WISE. However, this contrasts with the much lower number of protostellar cores found by Giannini et al. (2012), which may be due to a poorer effective sensitivity because of their selection criteria.


Chandrasekhar & Fermi (1953) assumed that “turbulent motions are isotropic”, and they adopted

$f\,{=}\,1/\sqrt{3}$f = 1/3
. If the field strength is weak, turbulent motions will drag the field lines in random directions and turbulence will be isotropic (super-Alfvénic turbulence). However, there is overwhelming observational evidence that magnetic fields in the ISM have well-defined directions, indicating that turbulence is sub, trans-Alfvénic and hence turbulent properties are highly anisotropic (see, for example, Montgomery & Turner 1981; Shebalin et al. 1983; Higdon 1984; Sridhar & Goldreich 1994; Goldreich & Sridhar 1995, 1997). Heyer et al. (2008), using CO data, found that velocity structures in Taurus are highly anisotropic. In the same region, Goldsmith et al. (2008) reported the existence of highly anisotropic density structures, which are aligned parallel to the mean field, known as striations. Striations have also been observed in the Polaris Flare (Panopoulou et al. 2015) and Musca (Cox et al. 2016; Tritsis & Tassis 2018), and they are formed due to magnetosonic waves (Tritsis & Tassis 2016) in sub-Alfvénic turbulence (Beattie & Federrath 2020). More evidence for ordered magnetic fields in molecular clouds can be found in Franco et al. (2010), Franco & Alves (2015), Pillai et al. (2015), Hoq et al. (2017), and Tang et al. (2019). Stephens et al. (2011) explored the magnetic field properties of 52 star forming regions in our Galaxy and concluded that more than 80% of their targets exhibit ordered magnetic fields. The diffuse atomic clouds in our Galaxy are preferentially aligned with the magnetic field (Clark et al. 2014), implying the importance of the magnetic field in their formation. Planck Collaboration Int. XXXV (2016) studied a larger sample of molecular clouds in the Goult Belt and concluded that density structures align parallel or perpendicular to the local mean field direction. This is also consistent with sub, trans-Alfvénic turbulence (e.g., Soler et al. 2013). In addition, Mouschovias et al. (2006), using Zeeman data, concluded that turbulence in molecular clouds is slightly sub-Alfvénic as well. All these lines of evidence indicate that ISM turbulence is sub, trans-Alfvénic, and hence anisotropic.


Many factors can affect the prevalence of AGN activity. One important question is how gas is brought down to the galaxy center to fuel supermassive black holes (SMBHs). In the literature, two kinds of mechanisms are proposed. One is the internal secular evolution process. The torque induced by non-axisymmetric galactic structures can drive slow and significant inflow (Kormendy & Kennicutt 2004; Hopkins & Quataert 2011; Sellwood 2014; Fanali et al. 2015). The galactic bar is one of the most prominent non-axisymmetric structures and it exists in about 40% of spiral galaxies (Oh et al. 2012). In addition, there is evidence demonstrating that bars can enhance star formation in the central regions of galaxies (e.g. Oh et al. 2012; Chown et al. 2019). However, the question of whether galactic bars can significantly affect AGN activity is still under debate (Arsenault 1989; Mulchaey & Regan 1997; Oh et al. 2012; Galloway et al. 2015; Goulding et al. 2017; Alonso et al. 2018). Other mechanisms, such as galaxy merger and interaction, are also expected to displace the angular momentum of the gas and transport the gas inward (e.g. Hopkins et al. 2006; Di Matteo et al. 2008; Bhowmick et al. 2020). Similarly to studies of secular evolution, observational evidence for this scenario is also mixed. Some studies have found significant environmental dependence of AGN activity (e.g. Koulouridis et al. 2006; Koss et al. 2010; Ellison et al. 2011; Sabater et al. 2013; Khabiboulline et al. 2014; Lackner et al. 2014; Satyapal et al. 2014; Hong et al. 2015; Kocevski et al. 2015; Goulding et al. 2018; Gao et al. 2020), while others have found no or only weak environmental effects (e.g. Grogin et al. 2005; Li et al. 2006a, 2008; Pierce et al. 2007; Ellison et al. 2008; Gabor et al. 2009; Darg et al. 2010; Wang & Li 2019; Man et al. 2019). The contradictory results may be caused by the difference in AGN selection criterion, observational bias, control sample, and environmental indicator used. As we show below, understanding the environmental effects on AGNs also requires knowledge about the evolutionary status of their host galaxies, as it can help us to better understand how to construct control samples and to adopt appropriate environmental indicators.


An alternative possibility to coronal heating is that the release and dissipation of magnetic energy actually takes place in the chromosphere. In this scenario, the chromospheric plasma is directly heated to coronal temperatures, rather than by thermal conduction fronts that are driven into the lower atmosphere as a consequence of heating localized in the corona (Hansteen et al. 2010). One manifestation of this process might be the type II spicules (De Pontieu et al. 2007) that have been suggested to play a role in supplying mass and energy to the corona (De Pontieu et al. 2009, 2011; Moore et al. 2011). N. E. Raouafi et al. (2015, in preparation) have argued that type II spicules have much more in common with so-called “classical” spicules (Beckers 1968, 1972; Pasachoff et al. 2009) than do type I spicules. In particular, type II and classical spicules are both commonly observed in quiet Sun and coronal hole regions, whereas type I spicules appear to be exclusively confined to active regions. Furthermore, Pereira et al. (2013) artificially coarsened Hinode/SOT observations of type II spicules to demonstrate that their lifetimes and ejection speeds are consistent with the earlier, ground-based observations of classical spicules (∼5 minutes and 25 km s−1). (N. E. Raouafi et al. 2015, in preparation) suggest that the term “classical spicules” be used for the earlier objects (see Sterling 2000, for a review) and the terms type I and II spicules be reserved for spicular phenomena observed during the era of Hinode observations. The key properties of type II spicules are their faster velocities (30–110 km s−1) and shorter lifetimes (50–150 s) compared with type I spicules. Type II spicules are typically observed in Ca ii emission by SOT before fading out of that passband and appearing in the SDO/AIA 304 Å channel, indicating that some degree of heating takes place as they rise. There is some observational evidence for a transition region or coronal component of their emission, visible as a bright, moving front in the AIA 171 Å channel (e.g., De Pontieu et al. 2011). The two possibilities for producing this warmer emission are: (1) pre-existing coronal material is shock-heated as the upflowing spicular material rams into it (Klimchuk 2012; Petralia et al. 2014a); or (2) the tip of the spicule is heated by some in situ process, which must be impulsive because the cooler emission quickly disappears from view (De Pontieu et al. 2007).


The mass estimate for each cluster was obtained by fitting a reduced tangential shear profile predicted by a projected Navarro–Frenk–White (NFW) profile (e.g. Bartelmann 1996) to the observed ellipticities. We derive the best-fitting profile parameters R200 and c200 by minimizing the merit function
(4)
\begin{eqnarray*}
\chi ^{2}\!=\!\sum _{i=1}^{N}{\frac{\left|g_{i}(\theta _{i},\beta _i;R_{200},c_{\mathrm{NFW}})\!-\! \tilde{\varepsilon }_{\mathrm{t},i}(\theta _{i})\right|^{2}}{\tilde{\sigma }_{\!i}^{2}\left(1\!-\!\left| g_{i}(\theta _{i},\beta _i;R_{200},c_{\mathrm{NFW}})\right|^{2}\right)^{2}}}.
\end{eqnarray*}
Here gi(θi, Σcrit, i;; R200, cNFW) is the model prediction for galaxy i and $\tilde{\varepsilon }_{\mathrm{t},i}$ the observed ellipticity times 1.08 for the same galaxy. The factor 1.08 is the multiplicative shear calibration bias of the used KSB+ pipeline (Kaiser et al. 1995; Erben et al. 2001) to convert from measured to true ellipticity. This calibration bias has an uncertainty of ∼5 per cent. This uncertainty is a dominant source of systematic uncertainty in the mass measurements. Each shear profile was centred on the BCG, using distances in the range of 0.2–4.2 Mpc for the fitting procedure. We minimized the χ2 on a grid of R200 and c200. Finally, we used the mass–concentration relation described by Bhattacharya et al. (2013) to put priors on the concentration parameter to break the degeneracies in the profile models. The initial mass estimates from equation (4) are biased. In evaluating the NFW shear profile we make use of the ratio in equation (2) when averaging the value of β over the reference catalogue sources. However, $\frac{\gamma (\langle \beta \rangle)}{1-\kappa (\langle \beta \rangle)}\ne \left\langle \frac{\gamma (\beta)}{1-\kappa (\beta)}\right\rangle$. Given the finite width of the β distribution that are averaged over when calculating βi from a reference catalogue (equation 3), we find a biased point estimate for βi. Especially in the inner regions of the cluster, this would model the shear profile incorrectly. We estimate the final masses by correcting for the averaging over β in two subsequent iterations. We utilize the best-fitting mass estimate from the zeroth iteration to predict the reduced shear, g, at the projected distance θ from the cluster centre, and βk. We then introduce $\beta _i^{\prime }$, which satisfies the equation:
(5)
\begin{eqnarray*}
g(\beta _{i}^{\prime })=\!\frac{\sum _{k=1}^{N}w_kg(\theta _{i},\beta _k)}{\sum _{k=1}^{N}w_k}\frac{1}{v_{b}(c_{1},c_{2})}.
\end{eqnarray*}


One way to explain the observations is to postulate that the cores of planets are formed in the very first Myr of the protoplanetary disk evolution, or even in the embedded phase while the disk is still forming. The disks for which masses have been measured have ages >1 Myr, and a general trend of declining disk mass with ages older than 1 Myr has been observed (e.g., Barenfeld et al. 2016). Thus, it is possible that disks were massive enough to form the cores of planets at younger ages. This idea has been suggested by Greaves & Rice (2010), Williams (2012), and Najita & Kenyon (2014), among others. In this scenario, the vast majority of the material composing planets must already be in the form of planetesimals, for rocky planet formation, and of already-formed planetary cores. The latter condition is necessary as gas giant planets need to accrete gas from the gas-rich disk. Assuming a gas-to-dust ratio of 100, disks at ∼1–3 Myr have just the right amount of gas mass to explain the population of gas giants (see Fig. 1). Thus, cores must already be in place at this age. Scenarios have been proposed to explain that pebble accretion can form planetesimals very early (0.1 Myr) in disks, when these are massive and possibly gravitationally unstable (Booth & Clarke 2016). However, it is expected that the formation of planetary cores is highly inefficient, with ∼350 M⊕ of pebbles needed to grow the core of Jupiter from half a lunar mass to 20 M⊕ (e.g., Morbidelli et al. 2016). Thus, such an inefficiency would imply that disks were initially ∼10–100 times more massive than is observed at ages >1 Myr. This would also imply that the vast majority of disks were initially gravitationally unstable. One issue of this scenario is that, if early disks are ∼10–100 times more massive than observed for disks older than 1 Myr, an extremely efficient gas-removal mechanism has to be found, consistent with the observations of Class 0 outflows (Frank et al. 2014).


Cosmological hydro dynamical N-body simulations offer another possibility to investigate the origin of the bimodality in the ([Fe/H], [α/Fe]) plane. Earlier simulations, e.g. full N-body simulations by Loebman et al. (2011), Brook et al. (2012) or hybrid simulations in which a semi-analytic chemical evolution was added on top of a cosmological simulation (Minchev, Chiappini & Martig 2013, 2014), were able to show that the thin and thick discs lie along different tracks in the ([Fe/H], [α/Fe]) plane, with the thick disc being old metal poor and rich in [α/Fe] and the thin disc being young, metal-rich and poor in [α/Fe]. They also showed that migration was important to generate the two discs. However, a clear bimodality in the ([Fe/H], [α/Fe]) plane was not seen. In the past few years good progress has been made to improve the spatial resolution as well as the chemical enrichment prescriptions. The bimodality has now been observed in some simulations (Grand et al. 2018; Mackereth et al. 2018; Clarke et al. 2019), and some of the simulations, in addition to the bimodality, also reproduce the basic trends of the ([Fe/H], [α/Fe]) distribution with radius R (Buck 2020; Vincenzo & Kobayashi 2020). Unlike analytical models, such simulations cannot be fine tuned to reproduce the Milky Way data, hence, the focus of these simulations is to qualitatively reproduce the abundance trends seen in the Milky Way, to understand how frequently do we get the bimodality and what is the mechanism for it. However, there is a lack of consensus between the different studies. Clarke et al. (2019) and Buck (2020) suggest that bimodality should be common in disc galaxies, whereas Mackereth et al. (2018) suggest that it is rare. Each simulation suggests slightly different mechanisms for the existence of the bimodality. Clarke et al. (2019) attribute bimodality to vigorous star formation in clumps at high redshift. Grand et al. (2018) suggest two distinct pathways, a centralized starbust pathway induced by mergers and a shrinking gas disc pathway. Buck (2020) suggest that after the formation of the high-[α/Fe] sequence a gas-rich merger dilutes the metallicity of the ISM leading to the formation of the low-[α/Fe] sequence. Mackereth et al. (2018) attribute the bimodality to unusually rapid gas accretion at earlier times, which is also characterized by a short time-scale to convert gas to stars. While some simulations clearly identify migration as key process to shape the sequences, others do not. In spite of the differences, it seems that some of the simulations (e.g. Mackereth et al. 2018; Buck 2020; Vincenzo & Kobayashi 2020) are not inconsistent with the Schönrich & Binney (2009a) paradigm.


It is now largely understood that the dust-to-gas mass ratio ϵ in protoplanetary discs is unlikely to match the canonical value in the interstellar medium of 0.01 (Mathis, Rumpl & Nordsieck 1977). For example, recent observations of CO isotopologues and dust continuum emission have found disc-averaged ϵ values to be much higher (∼0.2; see Ansdell et al. 2016), and simulations have demonstrated that discs can be formed with significant dust enrichment (Lebreuilly, Commerçon & Laibe 2020). There is also an observed discrepancy between the radial extents of the gas and dust components of protoplanetary discs, with dust discs being significantly more compact (Andrews et al. 2012; Pérez et al. 2012, 2015b). In some cases, such as IM Lup, the gas disc may be 10 times larger in radial extent than the mm dust disc (e.g. Cleeves et al. 2016). This discrepancy can explained by a combination of grain growth and radial drift. Essentially, the radial velocity, vr, of dust particles has two components, namely drag, vdrag, and drift, vdrift, and is given by
(1)$$\begin{eqnarray*}
v_{\mathrm{r}}=v_{\mathrm{drag}}+v_{\mathrm{drift}}=\frac{v_{\mathrm{g}, \mathrm{r}}}{1+{St}^{2}}+\frac{1}{{St}+{St}^{-1}} \frac{1}{\rho _{\mathrm{g}} \Omega } \frac{\partial P}{\partial R},
\end{eqnarray*}$$where vg, r is the radial velocity of the gas, ρg is the gas mass surface density, Ω is the Keplerian angular velocity, and P is the pressure (Weidenschilling 1977). The Stokes number, St, determines the degree of coupling to the gas. For a vertically isothermal disc (as used here), this is expressed simply as
(2)$$\begin{eqnarray*}
St = \frac{\pi a\rho _\mathrm{s}}{2\Sigma _\mathrm{g}},
\end{eqnarray*}$$where a is grain size, ρs is intrinsic bulk grain density, and Σg is the gas surface density. Examining equations (1) and (2 ), we can see that the drag term decreases as grain size increases. However, the drift term peaks at St = 1, which means that the grain size for which radial drift is fastest depends on the surface density, and therefore location within the disc.