In order to achieve high photometric accuracy and be sensitive to low amplitude undulations, we adopted techniques from the exoplanet community, with the purpose of eliminating the systematic errors. When performing differential photometry (Sect. 3), accurate bias-subtraction and flat-fielding are of major importance. According to Irwin et al. (2007), the Poisson noise is 200 e− for a typical detector with a gain of a few e− ADU−1 and the flat illumination level is of 20 000 ADU pixel−1 = 40 000 e− pixel−1. Thus, a typical photometric aperture with a radius of 3 pixels contributes ∼1 mmag photon noise. For this reason, we obtained a considerable amount of biases (150−300 frames) and twilight flat-fields (25−100 frames) each night to reduce the Poisson noise to less than 0.2 mmag (Irwin et al. 2007). The bias frames were averaged together using the minmax in the reject option of the zerocombine task in IRAF with a view of keeping radiation events out of the master bias frame. The master flat frame was the result of combining all the frames using a median mode. The median value is an excellent way of removing the effects of hot pixels and cosmic rays, so these extreme values do not affect the calculation, as they would, if they would averaged. The reject option was set to avsigclip, in which case the “typical” sigma would have been determined from the data itself rather than an a priori knowledge of the noise characteristics of the CCD. Other related issues that can limit the photometric precision are: (i) the positioning of the telescope, (ii) fringing issues, and (iii) the differential variations on the quantum efficiency of the pixels. With the aim of minimizing the contribution of these effects, we repositioned each star almost on the same pixel of the detector using the autoguiding system of each telescope. The read-out-noise of the detectors are insignificant, as it can be as low as a few e− ( 10 e− for RISE2 and Andor Zyla cameras).


Semi-analytical disc models indicate that the frequency of giant planets must increase with the mass of the host star between 0.2–1.5 M⊙ (Ida & Lin 2005; Kennedy & Kenyon 2008). However, this trend is expected to decrease above 1.5 M⊙ due to a smaller growth rate, longer migration time-scale, and shorter lifetime of the protostellar disc (Reffert et al. 2015). Looking for planets around main sequence stars more massive than the sun can help shed some light on this aspect. These stars have few spectral lines for Doppler measurements and are often broadened by the rapid rotation of the star. This has been the reason for RV surveys to have traditionally targeted slow rotating FGK type stars. However, as rapidly rotating stars evolve off the main sequence they slow down considerably and become much cooler making it relatively easy to search for planets around them. This fact was exploited by dedicated planet searches around intermediate mass sub-giants leading to dozens of planet discoveries (Johnson et al. 2007, 2010a, 2011). An important result obtained from the survey of giant stars at the Lick observatory pointed out that the occurrence rate peaks at a stellar mass of $1.9^{+0.1}_{-0.5}$ M⊙. However, many of the discovered planets around evolved stars were found at large orbital separations (Hatzes et al. 2003; Fischer et al. 2007; Robinson et al. 2007; Johnson et al. 2008). This is not a surprise as star–planet interaction is largely governed by tidal forces. When the stellar rotational period is longer than the planet orbital period, the star experiences spinning up, leading to orbital decay. Synchronization and circularization of orbit occurs in systems where the total angular momentum exceeds a critical value. When this total angular momentum is small enough, the orbit of the planet can continue to shrink and be engulfed by the host star. This phenomenon entirely depends on the dissipation time-scales for the star (Mazeh 2008, and references therein). The role of tidal forces becomes increasingly important in the context of host stars being in an evolved state. There is a higher chance of the planet being destroyed by the evolved star (Kunitomo et al. 2011; Schlaufman & Winn 2013). However, there is no obvious way to estimate these tidal dissipation forces. The circularization time-scale for such planets can be used to quantify tidal dissipation inside planets (Hansen 2010; Socrates et al. 2012). Most of the discovered hot Jupiters with periods less than 3 d are found to be on circular orbits. We calculate the circularization time-scales for the orbit of TOI-1789 b, which is τcir  = 0.08 Gyr (for QP = 106, equation 3 of Adams & Laughlin 2006). This is less than the age of the star as calculated from our work (Section 3.3.1).


While gas cooling and stellar feedback can transform dark matter cusps to cores, it is energetically challenging for this process to create large dark matter cores (typically >500 pc) in the very smallest ‘ultra-faint’ dwarfs, since they form so few stars (M*  105 M⊙; Peñarrubia et al. 2012; Garrison-Kimmel et al. 2013; Di Cintio et al. 2014; Maxwell, Wadsley & Couchman 2015; Oñorbe et al. 2015; Tollet et al. 2016). However, smaller dark matter cores may still form inside the half-light radius (R1/2 ∼ 20–200 pc for UFDs2), where the gravitational potential fluctuations are strongest (e.g. Oñorbe et al. 2015; Read et al. 2016). Whether this is expected to happen in a ΛCDM cosmology remains an active area of debate. Most studies to date find that cusp-core transformations are challenging at the likely mass-scale of UFDs (M200c ∼ 109 M⊙; M* ∼ 105 M⊙; e.g. Chan et al. 2015; Wheeler et al. 2019a; Gutcke et al. 2022). However, there are some notable exceptions. In recent work, Orkney et al. (2021) studied cusp-core transformations for UFDs drawn from the ‘Engineering Dwarfs at Galaxy formation’s Edge’ (EDGE) simulation project (with a mass, baryonic mass, and spatial resolution of 120 M⊙, 20 M⊙, and 3 pc, respectively, sufficient to resolve dark matter cores in UFDs larger than ∼20 pc). They found that UFDs can lower their inner dark matter density by up to a factor ∼2 through a combination of early heating due to star formation, followed by late-time heating from minor mergers. While none of their simulated dwarfs formed a completely flat central core, their small sample size left open the possibility that this combination of mechanisms could form flatter cores for some rarer assembly histories. It is also important to note that dark matter core formation on these mass scales is very sensitive to small changes in the star formation and feedback modelling. Pontzen et al. (2021) showed that a small increase in variability of the star formation rate on time-scales shorter than the local dynamical time is sufficient to form a full dark matter core in an ultra-faint, without significantly altering its stellar mass. As such, the question of whether complete dark matter core formation is expected in some or all UFDs in ΛCDM remains open.


Ulysses was launched on 1990 October 6 and orbited the Sun with a latitude varying from −80° to 80° and a solar distance ranging from ∼1 au to ∼5 au (Heber et al. 2009). The Kiel Electron Telescope (KET) on board Ulysses measured electrons in the energy range from ∼3 MeV to above 300 MeV, and protons and helium nuclei in the energy range from ∼5 MeV/nuc to above 2 GeV/nuc (Simpson et al. 1992). The data of the KET coincidence channel K12, which measures protons with energy in 0.25–2.0 GeV, has been used to study the GCR modulation outside the solar ecliptic plane in many works (see, e.g., Ndiitwani et al. 2005; Vos & Potgieter 2016; Boschini et al. 2017a). However, different works used different mono-energetic bins to represent this channel, e.g., 1.08 GeV (Rastoin et al. 1996), 2.5 GV (i.e., 1.73 GeV, Ndiitwani et al. 2005; Heber et al. 2009; Manuel et al. 2014), and 2.2 GeV (Boschini et al. 2017a). As the KET observations are integrated over a large energy interval (de Simone et al. 2011), it is perhaps better to weight the model results of several energy bins with the Ulysses response function and then combine them (Boschini et al. 2017a). Heber et al. (2009) obtained the 1 au equivalent count rates for this channel by correcting the proton intensity for the global spatial gradients of GCR protons, and the 1 au equivalent GCR proton flux can be obtained with the corresponding response factor. In addition, the precise cosmic-ray spectra measured by the PAMELA instrument can help us to roughly estimate the effective energy of the KET coincidence channel K12. In Figure 8, the black solid line shows the monthly averaged 0.25–2.0 GeV proton flux observed by Ulysses. Note that the original daily count rates from the Ulysses Final Archive (ufa.esac.esa.int/ufa) are divided by the corresponding response factor to obtain the proton flux. The dash-dotted line represents the 1 au equivalent 0.25–2.0 GeV proton flux, and the relevant count rates are digitized from Figure 5 in Heber et al. (2009). The 1.2 GeV proton flux observed by SOHO/EPHIN (Kühl et al. 2016) and PAMELA (Adriani et al. 2013) is shown as magenta triangles and green circles, respectively. The 1 au equivalent GCR proton flux roughly matches the 1.2 GeV GCR proton observations, and 1.2 GeV can be used to represent the Ulysses/KET channel K12. Therefore, we compute the 1.2 GeV proton flux along the trajectory of Ulysses to compare it with the Ulysses K12 measurements.


The H α studies of Umeda et al. (2004) and Stroe et al. (2014a, 2015) are tracing instantaneous (averaged over 10 Myr) SF and little is known about SF on longer time-scales and the reservoir of gas that would enable future SF. An excellent test case for studying the gas content of galaxies within merging clusters with shocks is CIZA J2242.8+5301 (Kocevski et al. 2007). For this particular cluster unfortunately, its location in the Galactic plane, prohibits studies of the rest-frame UV or FIR tracing SF on longer time-scales, as the emission is dominated by Milky Way dust. However, the rich multiwavelength data available for the cluster give us an unprecedented detailed view on the interaction of their shock systems with the member galaxies. CIZA J2242.8+5301 is an extremely massive (M200 ∼ 2 × 1015 M⊙; Dawson et al. 2015; Jee et al. 2015) and X-ray disturbed cluster (Akamatsu & Kawahara 2013; Ogrean et al. 2013, 2014) which most likely resulted from a head-on collision of two, equal-mass systems (van Weeren et al. 2011; Dawson et al. 2015). The cluster merger induced relatively strong shocks, which travelled through the ICM, accelerated particles to produce relics towards the north and south of the cluster (van Weeren et al. 2010; Stroe et al. 2013). There is evidence for a few additional smaller shock fronts throughout the cluster volume (Stroe et al. 2013; Ogrean et al. 2014). Of particular interest is the northern relic, which earned the cluster the nickname ‘Sausage’. The relic, tracing a shock of Mach number M ∼ 3 (Stroe et al. 2014c), is detected over a spatial extent of ∼1.5 Mpc in length and up to ∼150 kpc in width and over a wide radio frequency range (150 MHz–16 GHz; Stroe et al. 2013, 2014b). There is evidence that the merger and the shocks shape the evolution of cluster galaxies. The radio jets are bent into a head–tail morphology aligned with the merger axis of the cluster. This is probably ram pressure caused by the relative motion of galaxies with respect to the ICM (Stroe et al. 2013). The cluster was also found to host a high fraction of H α emitting galaxies (Stroe et al. 2014a, 2015). The cluster galaxies not only exhibit increased SF and AGN activity compared to their field counterparts, but are also more massive, more metal rich and show evidence for outflows likely driven by SNe (Sobral et al. 2015). Stroe et al. (2015) and Sobral et al. (2015) suggest that these relative massive galaxies (stellar masses of up to ∼1010.0–10.7 M⊙) retained the metal-rich gas, which was triggered to collapse into dense star-forming clouds by the passage of the shocks, travelling at speeds up to ∼2500 km s−1 (Stroe et al. 2014c), in line with simulations by Roediger et al. (2014).


A growing body of work suggests that planet formation is strongly dependent on the birth environment of the host star. Stars preferentially form in groups (Lada & Lada 2003), and in sufficiently dense environments the evolution of a PPD can be significantly influenced by neighbours (de Juan Ovelar et al. 2012). Close star–disc encounters are one such environmental influence on PPDs that can result in enhanced accretion and hasten disc depletion (Clarke & Pringle 1993; Ostriker 1994; Pfalzner et al. 2005; Olczak, Pfalzner & Spurzem 2006; Bate 2018; Winter et al. 2018a; Cuello et al. 2019). However, the stellar number densities required for tidal truncation are high, and in practice few observed regions satisfy this condition (Winter et al. 2018b, 2019a). The influence of tidal truncation is therefore limited to stellar multiples, either in bound systems (Dai et al. 2015; Kurtovic et al. 2018) or during the decay of higher order multiplicity (Winter, Booth & Clarke 2018c). Since stellar multiplicity does not appear to be strongly dependent on environment (see Duchêne & Kraus 2013, for a review), this suggests that encounters are not an environmental influence, but may set disc initial conditions during the early phases of cluster evolution (Bate 2018). Discs can also be externally depleted via thermal winds driven by far-ultraviolet (FUV) and extreme ultraviolet (EUV) photons from neighbouring massive stars (Johnstone, Fabian & Taylor 1998; Störzer & Hollenbach 1999; Adams et al. 2004; Facchini, Clarke & Bisbas 2016; Haworth et al. 2018; Haworth & Clarke 2019). This process of external photoevaporation dominates over dynamical encounters in observed environments, and can deplete PPDs rapidly for many stars that are born in massive and dense clustered environments (Scally & Clarke 2001; Winter et al. 2018b). Many stars in the solar neighbourhood are born in regions where UV fields are sufficient to significantly shorten disc lifetimes (Fatuzzo & Adams 2008; Winter et al. 2018b), and the fraction of stars born in such environments may be much greater outside of this region, dependent on galactic environment (Winter et al. 2019a). From an observational perspective, Guarcello et al. (2016) report disc survival fractions that decrease with increasing FUV flux in Cygnus OB2 (see also Winter, Clarke & Rosotti 2019b), and Ansdell et al. 2017 find a correlation between the dust mass in PPDs and separation from σ Ori. However, Richert et al. (2015) find no correlation of disc fraction with distance from OB stars. Reconciling these contradictory findings may require appealing to the inefficiency of external photoevaporation at small radii within the disc, dynamical and projection effects, or the stellar age gradient apparent in many star forming regions (Getman et al. 2018).


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


Theoretically, coronal loops are made up of magnetically confined denser and hotter plasma, and can thus support modes of oscillations (Aschwanden 1987; Roberts 2008). These oscillations are closely related to the physical properties of their host coronal loops and may open a new window for detecting the inhomogeneous corona (Nakariakov & Verwichte 2005; Yuan & Van Doorsselaere 2016a; Li & Liu 2018). Theories of magneto-acoustic oscillations in coronal loops have indicated that the fast kink mode possesses both a unique dispersion relation and zero asymptotic dispersion for a long-wave approximation, and could provide a potential diagnostic tool for determining physical properties of the inhomogeneous corona (Edwin & Roberts 1983; Roberts et al. 1984). Due to the specific role of coronal loops’ fast kink oscillations in coronal seismology, the proposal of using the fast kink oscillations to diagnose the physical properties of their host coronal loops has attracted a great deal of attention since it was first introduced (Roberts et al. 1984). Along with an increasing number of observational cases, the study of fast kink oscillations in coronal loops has been significantly advanced (Aschwanden et al. 1999; Nakariakov et al. 1999; Verwichte et al. 2004; Aschwanden & Schrijver 2011; Wang et al. 2012; Jain et al. 2015; Yuan & Van Doorsselaere 2016b; Shen et al. 2017; Pascoe et al. 2018; Shen et al. 2018; Nechaeva et al. 2019; Anfinogentov & Nakariakov 2019). Numerous detailed observations, on the other hand, have also brought new challenges to the current theory (De Moortel & Brady 2007; Guo et al. 2015; Li et al. 2017; Su et al. 2018; Li et al. 2019). Among these challenges, a prominent one is the increasingly presented oscillating coronal loops whose frequencies show significant changes, which is also known as the frequency drift (Su et al. 2018). It indicates that the frequency drift for the oscillation in fast kink mode can occur in a quiet loop (Su et al. 2018) or a quiet fiber (Li et al. 2018). It also indicates that the brightness of the oscillating structures undergoes a significant change during the occurrence of the frequency drift, which may imply changes in the loop’s thermal properties. A detailed investigation present in Table 1 and Figure 5 of Su et al. (2018) indicates that the period of fast kink oscillation has an ≈25% increase corresponding to an ≈40% increase in the loop’s density. A decrease in the period of fast kink oscillation is also observed by Li et al. (2018). It is also worth noting that the oscillation reported by Li et al. (2018) shows a significant increase of the amplitude as the period decreases, which is very unusual.


The newly discovered arcs and new spectroscopic redshifts have been incorporated into updated HFF+ versions of the Abell 2744 and MACSJ0416.1-2403 lensing models (Table 5); many of these have

 (see Figure 8 for a comparison of the arc redshift distributions adopted by the pre-HFF and new HFF+ lensing models; Cypriano et al. 2004; Okabe & Umetsu 2008; Zitrin et al. 2009; 2013; Okabe et al. 2010a, 2010b; Merten et al. 2011; Christensen et al. 2012; Mann & Ebeling 2012; Jauzac et al. 2014; Lam et al. 2014; Richard et al. 2014; Balestra et al. 2015; Diego et al. 2015; Grillo et al. 2015; Jauzac et al. 2015; Rodney et al. 2015; Wang et al. 2015; Kawamata et al. 2016). The incorporation of these new multiple image systems often results in a reduction in the statistical uncertainty in the galaxy magnifications for a given model. All of the public HFF lensing models provide a range of possible realizations from which the statistical uncertainty of a given model set may be calculated (typically 100 but no fewer than 30). We plot the cumulative distribution of the galaxy magnification uncertainties σ(model)/

, for the galaxies and photometric redshifts provided by the ASTRODEEP catalogs (Merlin et al. 2016; Castellano et al. 2016a) for Abell 2744 (Figure 9) and MACSJ0416.1-2403 (Figure 10). Generally, the statistical uncertainties are reduced for the models computed with the new HFF data sets, with more dramatic reductions for the methods that rely strongly upon the strong-lensing constraints. The parametric methods (CATS, Sharon, Zitrin, GLAFIC) report median statistical magnification errors of 0.2%–5%, while the non-parametric methods (Bradac Williams, Diego) report median statistical magnification errors of 2%–11% for the post-HFF calculations (green curves), versus 2%–22% and 2%–17% respectively for pre-HFF models (blue curves). (We note that the statistical errors for the MACSJ0416.1-2403 Bradac post-HFF models (Hoag et al. 2016) included additional uncertainties due to the photometric redshift uncertainties of the multiple images. These were not included in the pre-HFF Bradac model, and thus may explain why the post-HFF statistical errors are larger for this model.)


For our dataset of absolute magnitudes, we used data collected at the Institute of Astronomy of V. N. Karazin Kharkiv National University within the long-term observational programme to study asteroid magnitude-phase curves (Shevchenko et al. 2010, 2012, 2014a, 2016; Slyusarev et al. 2012). We also used some observational data obtained within several other programmes (Belskaya et al. 2010; Chiorny et al. 2007, 2011; Dotto et al. 2009; Hahn et al. 1989; Kaasalainen et al. 2004; Lagerkvist et al. 1998; Michalowski et al. 1995; Mohamed et al. 1994, 1995; Oszkiewicz et al. 2021; Shevchenko et al. 1992, 2003, 2009, 2014b, 2021; Velichko et al. 1995; Wilawer et al. 2022). All magnitudes were measured in the Johnson V band and extrapolated to zero phase angle using the HG1G2 system proposed by Muinonen et al. (2010), with some modifications presented by Penttilä et al. (2016). For computations, the online calculator1 for the HG1G2 photometric system was used. Since we derived absolute magnitudes in our data from the light curve maxima, and the definition of H is based on the rotationally averaged brightness, we added a half of the light curve amplitude corrected to zero phase angle to our results. We used the average correction coefficients from Zappala et al. (1990) for low- and moderate-albedo asteroids. This correction is typically very small because our light curve observations covered small phase angles. Absolute magnitudes obtained at different aspects were averaged. In such a manner, we obtained a homogeneous dataset of absolute magnitudes of about 400 asteroids up to H = 16.5 mag. Our database includes the absolute magnitude data, the G1 and G2 parameters, and the albedo and diameter values from different databases (such as Tedesco et al. 2002; Masiero et al. 2011, 2012; Nugent et al. 2015; Usui et al. 2011). The database is available at the CDS. Figure 1 shows the correlations of the absolute magnitudes from the largest datasets (MPC (HMPC), Pan-STARRS (HPS), and ATLAS (HATLAS)) with those of the Kharkiv dataset (HKH). For the ATLAS dataset, we used the absolute magnitudes in a cyan filter, since this filter overlaps the Johnson V band (Mahlke et al. 2021).


Hydrodynamical simulations of evolving galaxies allow us to calibrate these diagnostics by measuring their observability given a set of formation scenarios and physical processes (e.g. Jonsson et al. 2006; Rocha et al. 2007; Lotz et al. 2008a; Bush et al. 2010; Narayanan et al. 2010; Hayward et al. 2013; Snyder et al. 2013; Lanz et al. 2014). The quality and breadth of these experiments are limited by the availability of computational resources and the fidelity of models for galaxy physics such as star formation, supernovae, and the interstellar medium (ISM). It has only recently become widespread to model the formation of galaxies ab initio (e.g. Governato et al. 2004; Agertz, Teyssier & Moore 2011; Guedes et al. 2011; Marinacci, Pakmor & Springel 2013; Ceverino et al. 2014), and the realism continues to improve (Stinson et al. 2012; Hopkins et al. 2014; Torrey et al. 2014), albeit with still widely varying physics models (e.g. Scannapieco et al. 2012; Kim et al. 2014). Prior to these advances, studies were limited to small numbers of isolated galaxies or mergers to inform common diagnostics of galaxy evolution, an approach with a significant limitation: they do not fully account for cosmological context, such as gas accretion and the breadth of assembly histories. In addition to mergers, models of high-redshift galaxy formation (e.g. Dekel, Sari & Ceverino 2009; Dekel et al. 2013) have recently appreciated the tight coupling between gas accretion and disc evolution (e.g. Cacciato, Dekel & Genel 2012; Danovich et al. 2012; Dekel & Krumholz 2013), as well as bulge and super-massive black hole (SMBH) growth mediated by turbulent motions or violent disc instability (e.g. Bournaud et al. 2011; Porter et al. 2014) and the evolution of giant clumps (Dekel & Burkert 2013). These important processes likely complicate interpretation of a given observation, and recent studies of galaxy morphology have begun to exploit simulations including them (e.g. Scannapieco et al. 2010; Pedrosa, Tissera & De Rossi 2014).


The stellar metallicity in the Universe evolves with redshift (Mannucci et al. 2010; Sommariva et al. 2012; Krumholz & Dekel 2012; Dayal, Ferrara & Dunlop 2013; Madau & Dickinson 2014). The metallicity at a high redshift (z > 2) is much smaller in comparison to the low redshift Universe z  2. The first-generation stars contaminate the interstellar medium and cause a chemical evolution of the Universe. We can treat the metallicity evolution with redshift by a relation
(2)$$\begin{eqnarray*}
\log _{10}(Z(z))= \gamma z +\zeta ,
\end{eqnarray*}$$where γ captures the redshift dependence and ζ captures the metallicity value at z = 0 (Mannucci et al. 2010; Madau & Dickinson 2014). This relation captures the metallicity of the parent star or the gas cloud from which a star has formed. It is written to express only a mean evolution of the metallicity. Along with the mean metallicity evolution of the Universe, there is going to be a scatter in the metallicity depending on the galaxy properties. Such a source of uncertainty brings additional stochasticity to the metallicity relation. Currently, a limited number of observations (Gallazzi et al. 2008; Mannucci et al. 2010; Krumholz & Dekel 2012) are available to explore the environment dependence of the metallicity, and most of our current understandings are based on simulations(Genel 2016; Torrey et al. 2019). These studies show that the overall median metallicity dependence of the galaxies at different redshifts can be explained by power form (Pei, Fall & Hauser 1999; Young & Fryer 2007; Torrey et al. 2019). Several studies of GW merger rates and mass distribution are performed (Belczynski et al. 2002; Dominik et al. 2012, 2015; Mapelli et al. 2017; Giacobbo, Mapelli & Spera 2018; Toffano et al. 2019; van Son et al. 2022) which are motivated by these studies and show that the black hole mass distribution can exhibit a redshift dependence. The existence of any stochasticity in the galaxy metallicity distribution will also influence the mass distribution but is currently not well known. However, as the relation given in equation (1) is in terms of the logarithm of metallicity, so the impact of fluctuation around the median value depending on the individual galaxy properties is going to be a small (logarithmic) change. As we are unable to measure the host of the BBH due to a large sky localization error of the BBH, we cannot directly associate the properties of galaxies with BBH source properties. So, we can only infer an ensemble average mass distribution from the GW data and the additional stochasticity (which will depend on the host properties) will appear as an additional uncertainty in the measurement of MPISN. As a result, we consider a median distribution of galaxy metallicity and the dependence of MPISN on it.


Efforts have been made to model the signals caused by different sources of stellar variability within the RV time series (e.g., Tuomi et al. 2013; Rajpaul et al. 2015; Davis et al. 2017; Simola et al. 2019). Several solutions have been successfully proposed in order to deal with stellar oscillations and granulation phenomena, such as: calculating stellar evolution sequences (e.g., Christensen-Dalsgaard et al. 1995); fitting a two-level structure tracking (TST) algorithm based on a two-level representation of granulation (Del Moro 2004); using daytime spectra of the Sun in order to measure the solar oscillations (e.g., Kjeldsen et al. 2008; Lefebvre et al. 2008); and characterizing the statistical properties of magnetic activity cycles focusing on HARPS observations (e.g., Pepe et al. 2011; Dumusque et al. 2011b). However, properly modeling the other sources of stellar activity remains extremely challenging (e.g., Nava et al. 2019). In the present work, we deal with the cross correlation function (CCF) that is derived from the stellar spectrum (e.g., Hatzes 1996; Hatzes & Cochran 2000; Fiorenzano et al. 2005). As it is well known, the CCF barycenter estimates the RV of the star. The asymmetry and the full width at half maximum (FWHM) of the CCF give a strong indication for stellar activity, meaning that variations in RV are caused by active regions rather than by an exoplanet (e.g., Hatzes 1996; Queloz et al. 2001; Boisse et al. 2011; Figueira et al. 2013; Simola et al. 2019). Several solutions have been successfully proposed for mitigating stellar activity perturbations when working with RV measurements, including: decorrelating RV data against activity indicators such as log ${{R'}_{{\rm{HK}}}}$R′HK (e.g., Wilson 1968; Noyes et al. 1984) or Hα (e.g., Robertson et al. 2014); modeling stellar activity by fitting Gaussian processes (GPs, Rasmussen & Williams 2005; Haywood et al. 2014; Rajpaul et al. 2015); or moving averages (e.g., Tuomi et al. 2013) to the RV data. A common statistic employed for identifying changes in the shape of the CCF is the bisector span (e.g., Hatzes 1996; Queloz et al. 2001).


The source shows some preferred tracks in its movement along the HID. Dips occur as the source is in the SUL regime, either from SUL2 or from SUL3 regions; ingress and egress times populate the D3 and D2 spectra, whereas the D1 spectrum comes from the time segments characterized by the lowest count rate (deep dip). We noted that during the longest dips, the source occasionally switched to harder flaring episodes in D2 state. Most dips show the following pattern: SUL2/SUL3 → D3 → D2 → D1 → D2 → D3 → SUL2/SUL3. The passage from the SSUL to SUL state is only occasionally observed. We selected seven regions on the HID and extracted the corresponding spectra. For the normal branch spectra, the continuum emission is well fitted with two thermal components: a soft blackbody and a disc multicolour blackbody. The blackbody emission represents the bulk of the emitted power in each spectrum. It is likely due to strong reprocessing in an optically thick environment formed at Rsph, where disc inflow is mainly inflated by internal radiation pressure. This picture is consistent with the observed low temperature, large radius, and super-Eddington luminosity (see Shen et al. 2015; Soria & Kong 2016; Urquhart & Soria 2016; Guo et al. 2019). The hotter component, which we fitted using a diskbb, dominates the emission above 2 keV. Although its origin is still debated, it might come from internal hard X-ray emission, which has been inefficiently reprocessed, or simply scattered along our line of sight. Alternatively, it can be continuum emission (bremsshtrahlung and/or Comptonization) from an extended optically thin plasma where the emission lines are produced, or a tail of the blackbody emission which has been Compton upscattered in a coronal environment around the photosphere. In addition to the continuum, we added multiple emission and absorption lines derived by the combined averaged PN / RGS analysis to mimic the emitting and absorbing plasmas found in Paper I. Their shifts suggest different Doppler motions in several states as a consequence of a velocity field which changes depending on the launching site and on the geometry of the system. This seems supported by correlations among the parameters of the emission lines and the underneath hard X-ray flux (see Table 3). However, given the limited energy resolution of the EPIC we are not able to distinguish between a varying ionization state of the plasma, the effect of a different line broadening for the different ionized species, a complex absorption/emission pattern. A thorough study of the lines is left to a dedicated forthcoming study. For consistency the same spectral model has been applied also to the dipping branch spectra, although the physical conditions in and out of the dips might be different.


xstar predicts O to be progressively ionized through all its possible ionization stages as the central UV-X-ray source is approached providing a natural explanation for the absence of broad forbidden ${[}{\rm O\, \small{III}}{]}$ emission lines. No $[{\rm O\, \small{II}}]\, {\lambda }\, {\lambda }$3727, 3729 emission lines appear in the HST spectra, consistent with the xstar model. Furthermore, both the observed reddening-insensitive ratio $[{\rm O\, \small{III}}]\, {\lambda }\, 5008/[{\rm O\, \small{III}}]\, {\lambda }$4960 and the value predicted by xstar are consistent with the theoretical value (Dimitrijevic et al. 2007). However, there are two notable discrepancies between the HST observations and the xstar model predictions. The first is that the $[{\rm O\, \small{III}}]\, {\lambda }$5008 emission line is observed to be 230 per cent brighter than predicted by xstar. This excess emission could be attributed to the extended source of $[{\rm O\, \small{III}}]\, {\lambda}$5008 seen in the nucleus of NGC 3327 (Arribas & Mediavilla 1994; Mundell et al. 1995; Delgado & Perez 1997; García-Lorenzo, Mediavilla & Arribas 2001; Walsh et al. 2008). However, the second discrepancy that xstar predicts the $[{\rm O\, \small{III}}]\, {\lambda }$4364 emission line to be ∼25 times brighter than the upper limit estimated in D13 is not as easily addressed as the first. On the one hand, the $[{\rm O\, \small{III}}]\, {\lambda }$5008/λ4364 ratio produced by xstar is entirely consistent with that expected (Osterbrock 1989), given the temperature ∼104 K and electron density ∼108 cm−3 in the O++ region. On the other hand, the observed $[{\rm O\, \small{III}}]\, {\lambda }$4364 emission line would have to be as bright as H γ in order to match the xstar prediction. Observationally, this seems unlikely, but the resolution of the ${\it {\it HST}}$ observations is insufficient to adequately resolve the two lines in question (D13). Equally disconcerting, however, is that contrary to commonly accepted wisdom, xstar predicts the $[{\rm O\, \small{III}}]\, {\lambda }$4364 emission line to be bright even though the electron density in the O++ region exceeds the critical density of the 1S0 level responsible for the transition by about one order of magnitude.


It is difficult to isolate the impact of mass and environment on the rate and timing of quenching. Mass quenching is more important at earlier times in the evolution of galaxies and may be more important in denser regions (e.g., Peng et al. 2010; Muzzin et al. 2012; Lee et al. 2015; Darvish et al. 2016, 2018; Kawinwanichakij et al. 2017). And in the case of powerful radio galaxies, which lie in over-dense environments, both gas-rich and gas-poor mergers likely play an important role in both the growth of the stellar mass and the black holes. Volonteri et al. (2015b) suggest that in the merger phase, the AGN dominates the bolometric luminosity but the accretion can be very stochastic (see also Gabor & Bournaud 2013; DeGraf et al. 2017). It appears that the galaxies in our sample with the highest star-formation rates all host very powerful AGN, and are potentially all advanced mergers, consistent with this picture. In fact, PKS 0529−549, which has one of the highest SFRs of all the galaxies in our sample, has a modest gas fraction of about 15%, a high star-formation efficiency (SFR/molecular gas mass), and has been transforming its gas into stars rapidly (Man et al., in prep.). The star formation efficiencies in the other radio galaxies with high SFRs also appear extreme (10–100 Gyr−1; Man et al., in prep.). But of course, that does not explain our results in themselves. Dubois et al. (2015), in a study using numerical simulations of the relative growth of SMBHs and their host galaxies, found that star formation may regulate the black hole accretion rate. During the most rapid, gas-rich phase of the growth of massive galaxies, it may be that a larger fraction of the gas in the ISM is not available to fuel the SMBHs, but is consumed via star formation (see DeGraf et al. 2017). As the gas fractions decline, the relative power of the AGN compared to that of the star formation increases, resulting in an increased star formation efficiency. Concomitantly, the increased star formation rate can then disperse the dense gas making it easier for the jets to drive vigorous and efficient outflows (Nesvadba et al. 2006, 2017).


The inversion of the Fourier transform from limited data is a well-known problem in several imaging domains like, for instance, medical imaging (McGibney et al. 1993; Bronstein et al. 2002; Sutton et al. 2003; Fessler 2007; Gallagher et al. 2008; Lustig et al. 2008), crystallography (Eisebitt et al. 2004; Marchesini et al. 2008; Brady et al. 2009), and geophysics (Brossier et al. 2009; Jin 2010). This image reconstruction problem inspired several computational approaches like nonuniform Fast Fourier Transform (FFT) (Bronstein et al. 2002; Fessler & Sutton 2003; Greengard & Lee 2004; Lee & Greengard 2005), compressed sensing (Donoho 2006; Lustig et al. 2008; Bigot et al. 2016), and machine learning (Wang et al. 2018; Ravishankar et al. 2019). In the case of astronomical imaging, the use of Fourier methods is mainly related to radio and optical interferometry (Le Besnerais et al. 2008; Thiébaut & Giovannelli 2009; Wiaux et al. 2009; Felli & Spencer 2012; Thompson et al. 2017; Ye et al. 2020), although a similar methodology also involves snapshot imaging spectroscopy (Culhane et al. 2007; Harra et al. 2017; Courrier & Kankelborg 2018; Winebarger et al. 2019). However, in the last three decades, this approach has been utilized also in the case of solar hard X-ray telescopes that have been conceived in order to provide spatial Fourier components of the photon flux emitted via either the bremsstrahlung or thermal processes during solar flares (Lin et al. 2002; Krucker et al. 2020). These Fourier components, named visibilities, are sampled by the hard X-ray instrument in the two-dimensional Fourier space, named the (u, v) plane, in a sparse way, according to a geometry dependent on the instrument design. For instance, NASA’s Reuven Ramaty High Energy Spectroscopic Imager (RHESSI) relies on the use of a set of nine Rotating Modulation Collimators (RMCs) whose FWHM is logarithmically spaced between 23 and 183″ (Hurford et al. 2002). Each RMC measures visibilities on a circle of points in the (u, v) space with a spatial frequency that corresponds to its angular resolution and a position angle that varies according to the spacecraft rotation (see Figure 1, left panel). On the other hand, the Spectrometer/Telescope for Imaging X-rays (STIX) on board ESA’s Solar Orbiter is based on the Moiré pattern technology (Giordano et al. 2015; Massa et al. 2019), and its 30 collimators sample the (u, v) plane over a set of six spirals for an FWHM resolution coarser than 7″ (see Figure 1, right panel).


Having eliminated calibration or observational effects as the cause of the spectral changes, it must be that either (1) the configuration of the sources themselves has changed or (2) the interstellar scintillation has caused time-variable focusing and defocusing of the polarized substructure in the radio jets (e.g. Rickett 2001; de Bruyn & Macquart 2015), which can generate spectropolarimetric variability (e.g. Kedziora-Chudczer 2006). Interstellar scintillation (ISS) is difficult to distinguish from intrinsic variability without fully time-resolved data (see e.g. Bignall et al. 2015 and references therein), and can coexist with it (Koay et al. 2018). Never the less, ISS does not easily explain our results: Sources located more than ∼25 degrees from the Galactic plane (3/4 of our polarized sources) and with line-of-sight H α intensities less than ∼ a few Rayleighs (7/8 of our polarized sources; see column 9 of Table 1) are typically not strongly scattered (Pushkarev & Kovalev 2015), and experience associated flux density modulations of typically less than a few per cent (Heeschen 1984; Quirrenbach et al. 1992; Rickett, Lazio & Ghigo 2006; Lovell et al. 2008). This is smaller than the changes observed in our integrated fractional polarization spectra, which should undergo less modulation than the Stokes I in any case. ISS modulation also has a distinct frequency and time dependence. At the mid-galactic latitudes inhabited by most of our sources (see column 8 of Table 1), its magnitude peaks between 4 and 6 GHz (λ2 between 0.0024 and 0.0056 m2), and drops to less than 50 per cent of this value at 1.4 and 10 GHz (i.e. λ2 of 0.0008 and 0.046 m2). Thus, changes due to ISS should ‘spike’ in this narrow λ2 window, which we see little evidence of (though see perhaps PKS B0517–726 and PKS B1903–802; see Figs 3 and 9). The characteristic time-scale of ISS is ∼hours to days (Rickett et al. 2006; Gabányi et al. 2007, and references therein), and over multiyear time-scales, intrinsic effects tend to dominate the observed variability (e.g. Lazio et al. 2001; Rickett et al. 2006; Mooley et al. 2016). We therefore claim that the spectral variability most likely reflects intrinsic changes in the sources themselves.


Figure 2 shows the geometry used within our model. The center of the stellar sphere is located at the origin of the three-dimensional spherical coordinate system. PyTranSpot does not take into account a fractional area correction, as used within the WD code (Wilson & Devinney 1971; Wilson 1979, 1990, 2008, 2012). We argue that this effect is negligible, as the resulting loss of accuracy is much smaller than the noise currently present in observations. However, to obtain precise photometric transit and spot parameters, we recommend the use of a planetary pixel radius between 15 and 50 pixels (Tregloan-Reed et al. 2015). On the stellar sphere, every point is described by the two angles (longitude θ, co-latitude φ) and the distance to the stellar center (stellar radius rs in pixels). The longitude θ varies between − 90° and 90°, with the center of the stellar disk corresponding to a value of 0°. The co-latitude φ ranges from 0° to 180°, with the stellar equator set at 90°. Figure 3 illustrates the projection of a spot on to the stellar sphere, as seen from a two-dimensional perspective. The observer is assumed to lie far along the z-axis. To determine the pixels on the stellar sphere, which correspond to the starspot, we implement the following boundary condition: If the angle Δσ between the pixel on the sphere and the spotcenter is greater than the angular radius of the spot α, then this pixel does not belong to the spot. The values for Δσ are derived by using the spherical law of cosines: (2)\begin{equation} \cos(\Delta\sigma) = \cos(\phi_{\rm{spot}}) \cdot \cos(\phi) + \sin(\phi_{\rm{spot}}) \cdot \sin(\phi) \cdot \cos(\Delta\theta),  \label{eq:slaw} \end{equation}cos(Δσ)=cos(φspot)·cos(φ)+sin(φspot)·sin(φ)·cos(Δθ),where φspot and φ are the co-latitudes of the spotcenter and the surrounding pixels, respectively. The value Δθ represents the absolute difference in longitude between the spotcenter and the pixel center.


We run forced photometry at these SN locations using a pipeline, hereafter known as the zuds pipeline1 (Dhawan et al. 2021), which performs aperture photometry using the astropy affiliated package PhotUtils (Bradley et al. 2019), using a 6-pixel diameter aperture on the difference images. The reference images for the difference images are constructed by co-adding exposures from epochs at least 30 d or more before the initial estimate of the time of maximum from the alert photometry, using the software swarp (Bertin 2010). In order to build the co-add, we only take epochs with seeing between 1.7 and 3 arcsec and a magnitude limit deeper than 19.2 mag. For consistency, we use the same reference image for both SNe. In the zuds pipeline, difference images are obtained using hotpants (Becker 2015), an implementation of the image subtraction algorithm (Alard & Lupton 1998). The zero points for each epoch are computed by the Infrared Processing and Analysis Center (IPAC), corrected for a 6-pixel diameter aperture. For the i band, we use the images corrected for an observed fringing pattern, using the fringez software (Medford et al. 2021). From the IPAC forced-photometry service (Masci et al. 2019) at the same locations, we obtain the metadata for each observation, including the magnitude limit mlim of the observation, the seeing of the observation, and the standard deviation σpix on the background at the pixel on which the SN is located. We combine this information with the zuds pipeline results for data quality assessment. Specifically, we only use those observations that satisfy the following conditions: $1.0 \lt \mathrm{seeing} \lt 4.0\,\mathrm{ arcsec}, \ m_{\mathrm{lim}} \lt 19.2 \mathrm{\, mag}, \ \mathrm{ and} \ \sigma _{\mathrm{pix}} \lt 14.0$, where σpix is the robust σ per pixel in the science image and is used as a metric to remove non-photometric data. We then use a maximum likelihood method to fit the salt2 model to each of these two SN light curves. The low seeing values are removed to protect against undersampling during image subtraction. We then remove the epochs that have 5σ flux outliers relative to the best-fitting salt2 model (discussed later and summarized in Table 2) and use the remaining selected points as the light curves of the individual SNe. The final photometry data sets used are included as Tables C1 and C2. The resulting light curves are shown in Fig. 3. As stated earlier, this light curve clearly shows the presence of two transients with no detections for a period of over 100 d in between. For the unclassified transient AT 2019lcj, we notice that AT 2019lcj has a shoulder in the redder bands (r- and i band) as seen in Fig. 3 strongly indicating that the SN is of Type Ia. We will verify this shortly after discussing its redshifts and host properties.


The second data release (DR2) of the ESA Gaia mission has provided the largest available 6D phase-space (positions and velocities) dataset for 7.2 million stars brighter than GRVS = 12 mag (Gaia Collaboration et al. 2018b), making possible precise studies of the Milky Way structure and kinematics on large scales. Gaia data have already revealed signatures of non-equilibrium and ongoing vertical phase mixing in the Milky Way disc (Antoja et al. 2018), likely induced by a previous pericentric passage of the Sagittarius dwarf galaxy (Laporte et al. 2019; Bland-Hawthorn et al. 2019; Haines et al. 2019) or by internally driven bending waves (Khoperskov et al. 2019; Darling & Widrow 2019). A large number of kinematic arches with various morphologies not known prior to Gaia were found (Ramos et al. 2018; Kushniruk & Bensby 2019; Monari et al. 2019) and large-scale wiggles were discovered in the Vϕ − R plane (Kawata et al. 2018; Antoja et al. 2018). These features can be interpreted as the signature of the impact of an external perturbation (D’Onghia et al. 2016; Laporte et al. 2019) or as evidence of the spiral structure and the bar of the Milky Way (Hunt et al. 2018; Fragkoudi et al. 2019). At the same time, in the solar vicinity the Galactic spiral structure is believed to generate various patterns in the phase-space (Siebert et al. 2012; Williams et al. 2013), but uncertainties on the location and strength of the spiral arms have so far prevented us from explaining the observed patterns. In this work, we use the high-quality Gaia DR2 sample of stars with radial velocities (hereafter GRV2), together with a new method to highlight the stellar density structures, to explore the Milky Way spiral arms without relying on any specific stellar tracer. The outline of the Letter is as follows: in Sect. 2 we describe the data and the method we used; in Sect. 3 we examine the phase-space structure of the Milky Way and compare its various features with Milky Way-type galaxy simulations; and in Sect. 4 we summarize the conclusions that can be drawn from our study.


Most of the recent observational efforts to understand galaxy evolution have been focused on determining the history of cosmic star formation, gas density evolution, metallicity evolution, and mass growth of the Universe (Daddi et al. 2004; Mannucci et al. 2010; Madau & Dickinson 2014; Tomczak et al. 2014; Bouwens et al. 2015). These multiwavelength observational constraints have usually been summarized as galaxy scaling relations that might or might not change with redshift (Mannucci et al. 2010; Elbaz et al. 2011; Bouwens et al. 2014; Troncoso et al. 2014), in high- or low-density environments, in extreme physical conditions (starburst, AGN galaxies), and in spatially resolved data due to internal variations of the galaxy properties (Sanchez et al. 2013). In parallel, theoretical works and simulations have tried to explain the physical mechanisms that reproduce the measured global properties  (Daddi et al. 2010; Davé et al. 2011; Lilly et al. 2013; Lagos et al. 2014; Padilla et al. 2014). Despite these efforts, the completeness and cleanness of the sample are still challenging problems that depend on the sample selection-method, instrument limits, and telescope time. These problems make the comparison between observational and theoretical works even more difficult. For example, Campbell et al. (2014) compared the stellar mass of GALFORM galaxies predicted by the model with those obtained through the fit of their predicted broad-band colors. They found that both quantities differ for an individual galaxy, hence the clustering of mass-selected samples can be affected by systematic biases. Therefore, mass-selected samples might provide erroneous conclusions regarding their progenitors and descendants. In addition, the evolution of scaling relations is constrained with observations of galaxy samples that are selected with luminosity or stellar-mass thresholds and are located at different redshifts, which does not necessarily constitute causally connected populations (i.e., they do not follow a progenitor-to-descendant relation). Clustering-selected samples overcome this problem because in a hierarchical clustering scenario, a correlation analysis allows us to estimate the bias and hence statistically determine the progenitors and descendants of galaxy samples. The bias parameter measures the clustering difference between the galaxy spatial distribution and underlying dark-matter distribution. Thus, it relates the typical mass of halos hosting the galaxies (Sheth et al. 2001). Hence, measuring it in galaxy samples at different redshifts determines whether we are following the evolution of baryonic processes occurring in halos of similar masses or not. This fact is of extreme importance because once it is determined, we can use the multiwavelength data to study the evolution of the baryonic processes at certain halo mass, establishing a direct link between observations and galaxy formation models. Padilla et al. (2011) selected early-type galaxies according to their clustering and luminosity function in the MUSYC survey. So far, no study that selects star-forming galaxies according their clustering and luminosity function has been reported.


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.


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

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

n

sw

u

sw

_

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

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

u

sw

=|

u

sw

_

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


In this subsection, we first use our measured CLFs to infer the conditional stellar mass functions and then use the results to study the stellar mass contents of dark matter haloes. To convert luminosity into stellar mass, one typically uses a mass-to-light relation based on galaxy colour (e.g. Bell et al. 2003). This requires robust colour estimates. In our case, galaxies with r ∼ 21 in the SDSS photometric sample have typical error in the (u − r) colour of about 1 mag, mostly due to uncertainty in the u-band photometry. This error will propagate into the stellar mass estimates and can bias the stellar mass function, leading to an overestimate at the high-mass end.7 To reduce such bias, we estimate stellar masses using the observed mean colour–magnitude relations for blue and red galaxies separately. The details of this procedure are described in Appendix C. As our final goal is to estimate the global baryon fractions in stars, the use of average values as opposed to full colour distributions is not a severe limitation. Following Bell et al. (2003), we convert the observed luminosity and colour into stellar mass using

(11)

\begin{eqnarray}
\log \bigg [\frac{M_{{\ast }}}{\mathrm{M}_{\odot }}\bigg ] = -0.223+0.299\,(u-r) -0.4\,(M_{\rm r}-4.64) -0.1,\nonumber\\
\end{eqnarray}

where (u − r) is the mean colour of a blue or red galaxy at a given absolute magnitude Mr. The constant, 4.64, is the r-band magnitude of the Sun in the AB system (Blanton & Roweis 2007) and the −0.1 offset corresponds to the choice of the Kroupa initial mass function (Kroupa 2001). Using this light-to-mass relation, we convert the global best-fitting luminosity functions into the corresponding stellar mass functions. The two left-hand panels in Fig. 10 show the estimated conditional stellar mass functions for blue and red satellites as a function of halo mass, respectively. Since a fixed $M^{{\ast }}_{{\rm b}}$ is applied to satellite galaxies for all halo masses, a slight overestimate of the stellar mass occurs at the massive ends for small haloes. As the stellar masses of central galaxies are obtained using individual observed (u − r) colours, the overestimate of the stellar mass of satellites can sometimes cause the stellar mass of a satellite galaxy to exceed that of the central. The dashed lines in the left-hand panels indicate the ranges where such situation is present. In order to estimate the total stellar mass in haloes of a given halo mass, we integrate the inferred conditional stellar mass functions down to low masses. We find that using 107 M⊙, which is about the minimum stellar mass reachable by the sample used here or zero lead to similar results. The results are shown in the right-hand panel of Fig. 10. The coloured dashed lines show the stellar mass to halo mass ratios for blue and red satellites, respectively. The grey dashed line is the total stellar mass of satellite galaxies to halo mass ratio, while the grey solid line is the stellar to dark matter mass ratio of central galaxies. The total ratio is shown as the black line. For haloes with M200  1013 M⊙, the total stellar mass is dominated by the central galaxies; in contrast, for more massive haloes, it is dominated by red satellites. The contributions from red and blue satellites are comparable for haloes with M200 ∼ 1012 M⊙, and the contribution from blue satellites appears to increase towards lower halo masses. Note that, although there are marked upturns in the stellar mass functions at the low-mass ends for red galaxies, the low-mass galaxies in the upturns (M*  108 M⊙) contribute little to the total stellar mass. Our results are qualitatively consistent with estimates based on data with more limited dynamical ranges (e.g. Leauthaud et al. 2012a,b; Kravtsov, Vikhlinin & Meshscheryakov 2014).


More recently, Long et al. (2018) performed an analysis on 32 discs in the Taurus star-forming region using ALMA. From this sample 12 discs containing axisymmetric structure were identified. This structure takes the form of dark band bright ring pairs, emission bumps and cavities. Overall 19 gap ring pairs were identified, indicating that a number of these systems contain multiple gaps. These gaps range in location from R = 10–120 au with no preferred distance. The majority of these gaps are narrow, but the weak correlation between gap location and gap width potentially implies formation via planet–disc interactions. In addition a significant number of these gaps cannot be explained by condensation fronts. Long et al. (2018) perform an analysis on the width of these gaps in order to determine possible masses of planets that could form them. Assuming the width of the gaps corresponds to 4RHill (Dodson-Robinson & Salyk 2011) they estimate the masses of the planets to be in the 0.1–0.5MJ (q = 1.0 × 10−4–5.0 × 10−4) range, however they stress that these masses have large uncertainties and that the gap widths may be as large as 7–10RHill (Pinilla, Benisty & Birnstiel 2012). Alternatively they compare the distance between the minimum of the gaps and the maximum of the rings to the results of hydrodynamic simulations (Rosotti et al. 2016) with an α = 10−4 (ν = 2.5 × 10−7), resulting in a predicted planet mass of 0.05MJ (q = 5.0 × 10−5) and an α = 10−2 (ν = 2.5 × 10−5), resulting in a predicted planet mass of 0.3MJ (q = 3.0 × 10−4). Using equation (7) and an estimated disc lifetime of 2 Myr [based on stellar age estimates for the spectral type of the target stars (Baraffe et al. 2015; Feiden 2016)] we can see that in the higher viscosity case planets of 0.3MJ (q = 3.0 × 10−4) can form at any of these radii without creating vortices. The lower viscosity case is more difficult to predict as it is significantly lower than the viscosities we have explored, however for this planet mass it seems unlikely from our results that the predicted planet could form without creating vortices. Instead, we expect the maximum mass planets that could be found here to be roughly half the mass they predict. In addition, from our results planets of mass 0.5MJ (q = 5.0 × 10−4) would require the disc viscosity to be ν ⪆ 3.0–5.0 × 10−6 to form without creating vortices, depending on the radius at which they are located. Conversely we find planets as small as 0.1MJ (q = 1.0 × 10−4) can even form at ν = 2.0 × 10−6 without creating vortices. This can be seen in Fig. 8. Hence our results show that these gaps could be opened by planets of the masses predicted by Long et al. (2018) without forming vortices.


Space missions have traditionally focused on performing spectropolarimetric observations measuring the four Stokes parameters in a narrow spectral window where one or two photospheric absorption lines of interest are present. For instance, see Hinode/SP (Tsuneta et al. 2008; Lites et al. 2013), SDO/HMI (Pesnell, Thompson & Chamberlin 2012; Schou et al. 2012), and Solar Orbiter/PHI (Gandorfer et al. 2011; Solanki et al. 2015). On the contrary, ground-based telescopes usually have instruments which can cover several spectral lines simultaneously, e.g. THEMIS/MTR (López Ariste, Rayrole & Semel 2000; Paletou & Molodij 2001), SST/CRISP (Scharmer et al. 2003, 2008), DST/IBIS (Cavallini 2006) and DST/SPINOR (Socas-Navarro et al. 2006), Gregor/GRIS (Collados et al. 2012; Schmidt et al. 2012), or ZIMPOL (Povel 2001), among others. In most of the mentioned cases, the light beam occupies almost the full length of the camera in one of its directions due to the larger spectral coverage which directly increases the amount of data generated. Although the data rate is not usually a crucial factor for ground-based telescopes, space-based missions have an extremely limited telemetry. Thus, unless there is a strong reason to expand the wavelength coverage it is highly recommendable to keep focusing on narrow spectral windows which contain a high density of useful lines. In this regard, we find it extremely helpful to perform theoretical studies and observations to define the optimum spectral window for the purposes of a given mission. For example, Hinode/SP was strongly supported by ASP (Elmore et al. 1992) observations and SDO/HMI benefited from ground-based observations but also from specific supporting works like Norton et al. (2006). We performed a similar study in Quintero Noda et al. (2016) aiming to support future missions with chromospheric polarimetry as the main target, for instance Solar-C (Katsukawa & Solar-C Working Groups 2011; Katsukawa et al. 2012; Watanabe 2014; Suematsu & Solar-C Working Group 2016). We concluded that the Ca ii 8542 Å is a unique spectral line which is sensitive to a large range of heights, from the photosphere to the chromosphere (see figs 4 and 6 of the mentioned work). However, its sensitivity to the magnetic field at photospheric layers is low which precludes examining quiet Sun magnetic fields at these heights. Therefore, there is still room for improvement and, for this reason, we decided to examine the solar spectrum at the vicinity of the Ca ii 8542 Å line. In this regard, if we observe additional spectral lines we will increase the number of spectral points with valuable information, particularly if these lines have different heights of formation, which will enhance the accuracy of the inferred atmospheric parameters (for example Asensio Ramos et al. 2007). However, in order to achieve this purpose we have to expand the spectral window which will increase the data rate if we maintain the same spectral sampling. Therefore, it is essential that these additional lines provide valuable information complementing the Ca ii 8542 Å spectral line.


We used the

 band high-resolution spectra of Arcturus and μ Leo, obtained with WINERED, to estimate the microturbulence and iron abundance with a precision similar to that of previous results from spectra at different wavelengths. Our lists of Fe i lines in the 0.91–1.33 μm range will be useful for obtaining the precise metallicities of stars obscured by severe interstellar extinction compared with the optical regime, for which the extinction is stronger. For many objects in the Galactic disk found in recent infrared surveys, this new wavelength window may be ideal for detailed abundance analyses. One of the major error sources is the uncertainty in ξ in various studies, including ours, based on spectra at different wavelengths from the optical (e.g., Table 3 of Jofré et al. 2014) to the H band (e.g., Table 7 of Smith et al. 2013). Furthermore, how to determine the microturbulence and its error is not established or straightforward. The bootstrap method that we demonstrated in this paper can give quantitative estimates of the microturbulence and its error. The error in microturbulence is 0.11–0.24

 for each combination of target and line list. The obtained microturbulences are consistent with those that were estimated or assumed in previous studies on the same targets. Note, however, that using different line lists (or different sets of lines) can result in slightly different microturbulences depending especially on the

 values of strong lines used in the analysis. The very strong lines (X > −6) were rejected because these lines are likely to introduce problems into a chemical abundance analysis due to severe saturation, non-LTE effects, contribution of EW from the damping wing, and so on. Considering the comparison of our estimates with previous ones in addition to the scatters of

, we adopt the measurements with the Fe i lines selected from MB99 as our best estimates:

 and

 for Arcturus and μ Leo, respectively.


In this article, I present an analytical model of resonant chains. Analytical models have already been proposed, in particular to study the dynamics of the Laplace resonance (1:2:4 chain) between Io, Europa, and Ganymede (e.g., Henrard 1983). However, while several numerical studies have been dedicated to the capture of planets in various resonant chains (e.g., Cresswell & Nelson 2006; Papaloizou & Terquem 2010; Libert & Tsiganis 2011; Papaloizou 2016), general analytical models have not yet been proposed. Recently, Papaloizou (2015) proposed a semi-analytical model of three-planet resonances taking into account only the interactions between consecutive planets in the chain, with a particular focus on the Kepler-60 system (12:15:20 resonant chain, see also Steffen et al. 2013; Goździewski et al. 2016). This model is very similar to the studies of the Laplace resonance between the Galilean moons, but is not well suited in the general case. For instance, four-planet (or more) resonances are not considered. Moreover, for some three-planet resonances, the interactions between non-consecutive planets cannot be neglected. For instance, in a 3:4:6 resonant chain, each planet is locked in a first-order resonance with each of the other planets. In particular, the innermost and outermost planets are involved in a 2/1 MMR that strongly influences the dynamics of the system. I describe here a general model of resonant chains, with any number of planets, valid for any resonance order. I particularly focus on finding the equilibrium configurations (eccentricities, resonant arguments, etc.) around which a resonant system should librate. While a real system may be observed with significant amplitude of libration around the equilibrium, or could even have some angles circulating, the position of the equilibria still provides useful insights into the dynamics of the system. In Sect. 2, I describe this analytical model, and the method I use to find the equilibrium configurations. In Sect. 3, I apply the model to Kepler-223. I show that six equilibrium configurations exist for this resonant chain, and that the system is observed to be librating around one of them. I also show that knowing the current configuration of the system allows for interesting constraints to be put on its migration scenario, and in particular on the order in which the planets have been captured in the chain.


The simulations presented in this work have been performed with the publicly available hydrodynamic code GIZMO (Hopkins 2015), which is a descendant of GADGET2 (Springel 2005). The code evolves the magneto-hydrodynamics equations for the gas including a constrained-gradient divergence-cleaning method (Hopkins & Raives 2016; Hopkins 2016), together with the gas self-gravity. For the purpose of this study, we equipped the code with an on-the-fly non-equilibrium chemical network, which was implemented via the public chemistry library KROME (Grassi et al. 2014), similarly to Bovino et al. (2019). In particular, in our simulations, we assumed an isothermal equation of state for the gas, with the temperature set to 10 K or 15 K. These temperatures are in line with kinetic temperatures obtained from NH3 for the same regions (Friesen et al. 2009, 2017). The initial conditions of our simulations consist of a collapsing filament, modelled as a cylinder with a typical observed (Arzoumanian et al. 2011) Plummer-like density profile

$n(R) = n_0/[1+(R/R_{\textrm{flat}}){}^2]^{p/2}$

n(R)=
n
0

/

[1+

(R/
R

flat

)
2

]

p/2

, where R is the cylindrical radius, n0 is the ridge volume density and is constant along the filament axis, Rflat is the characteristic radius of the flat inner part of the density profile, and p is the characteristic exponent. Following observed estimates (Arzoumanian et al. 2011), we set p = 2 and Rflat = 0.033 pc, which gives a mean filament width of 3 × Rflat ~ 0.1 pc. The setup follows previous works (Seifried & Walch 2015; Körtgen et al. 2018). To avoid any spurious effect at the edges of the filament along its axis, we embed the cylinder in an exponentially decaying background, with the decay scale length set to the filament length Lfil = 1.6 pc. The box is large Lbox = 2.4 pc. We initialised the filament in a turbulent state, assuming a Burgers-like power spectrum that grows as ∝ k10 up to λpeak = Lbox∕6 and then decays as ∝ k−2 (see also Körtgen et al. 2018). Finally, we assumed the box is permeated by a constant magnetic field B0 = 40 μG (Seifried & Walch 2015; Körtgen et al. 2018).


In Table 3, we list the physical parameters of our model (not including the normalizations for each telescope and each eclipse), and in Tables 4 and 5 we show the resulting best-fit model and the 16th and 84th percentiles (approximately 1σ) for each parameter for each season. We are able to fit our measured light curves equally well regardless of which star we place star spots. However, if we place the star-spot signal on the secondary component, the out-of-eclipse model parameters vary significantly between observing seasons, whereas if the star-spot signal is originating on the primary component, the parameters are stable between seasons. Particularly, F, the ratio between the orbital and rotational frequency has different values for each season if the secondary component is responsible for the star-spot modulation signal. Since the rotation period of the secondary star should not change (and the effect of differential rotation for star spots at different latitudes is small for M dwarfs; Davenport et al. 2015), we conclude that the star-spot signal cannot be originating on the secondary component. Since we only detect one rotational frequency, and this frequency differs from the orbital frequency of the system, we have assumed that it is originating solely on one component of the system (the primary component); though, in reality, there is likely to be some star spots on the surface of both components and that rotation of the secondary component may also be contributing somewhat to this signal (though we do not have a significant detection). We will utilize the model for which star spots are located on the primary component for the rest of this paper. We note, however, that this choice does not significantly affect the values of the masses and radii of the components but does change the uncertainty. The light curves themselves are most directly sensitive to the sum of the component radii and their ratio. The eclipse duration measures a combination of (

)/a (where R1 and R2 are the component radii and a is the semimajor axis) and the inclination of the orbit. In the case of grazing eclipse (where we cannot break this degeneracy with a measurement of the duration of the total phase), this degeneracy is instead broken by the eclipse depth, which also depends on the limb darkening of the stars and the star spots on the stellar surfaces.


Blazars are a peculiar class of active galactic nuclei (AGNs) that have their relativistic jets pointed close to the line of sight to the observer with angle ≤ 10° (Antonucci 1993; Urry & Padovani 1995). They are classified as flat-spectrum radio quasars (FSRQs) and BL Lacerate (BL Lac) objects based on the strength of the emission lines in their optical/infrared (IR) spectrum. Both classes of objects emit radiation over the entire accessible electromagnetic spectrum from low-energy radio to high-energy γ-rays. As blazars are aligned close to the observer, the emission is highly Doppler boosted, causing them to appear as bright sources in the extragalactic sky. They dominate the extragalactic γ-ray sky first hinted by the Energetic Gammma-ray Experiment Telescope (EGRET) observations onboard the Compton Gamma-Ray Observatory (CGRO; Hartman et al. 1999) and now made apparent by the Large Area Telescope (LAT) onboard the Fermi Gamma-ray Space Telescope (Atwood et al. 2009). The broad-band spectra of blazars are dominated by emission from the jet with weak or absent emission lines from the broad-line region (BLR). One of the defining characteristics of blazars is that they show flux variations (Wagner & Witzel 1995) over a wide range of wavelengths on time-scales ranging from months to days and minutes. In addition to flux variations they also show large optical and radio polarization as well as optical polarization variability. In the radio band they have flat spectra with the radio spectral index (αr)  0.5 ($S_{\nu } \propto \nu ^{-\alpha _r})$. The broad-band spectral energy distribution (SED) of blazars is characterized by a two-hump structure, one peaking at low energies in the optical/IR/X-ray region and the other one peaking at high energies in the X-ray/MeV region (Fossati et al. 1998; Mao et al. 2016). In the one-zone leptonic emission models, the low-energy hump is due to synchrotron emission processes and the high-energy hump is due to inverse Compton (IC) emission processes (Abdo et al. 2010b). The seed photons for the IC process can be either internal to the jet (synchrotron self-Compton or SSC; Konigl 1981; Marscher & Gear 1985; Ghisellini & Maraschi 1989) or external to the jet (external Compton or EC; Begelman et al. 1987). In the case of EC, the seed photons can be from the disc (Dermer & Schlickeiser 1993; Boettcher, Mause & Schlickeiser 1997), the BLR (Sikora, Begelman & Rees 1994; Ghisellini & Madau 1996), and the torus (Błaerrorzdotejowski et al. 2000; Ghisellini & Tavecchio 2008). Though leptonic models are found to fit the observed SED of a majority of blazars, for some blazars, their SEDs are also well fitted by either hadronic (Mücke et al. 2003; Böttcher et al. 2013) or lepto-hadronic models (Diltz & Böttcher 2016; Paliya et al. 2016). In the hadronic scenario, the γ-ray emission is due to synchrotron radiation from extremely relativisitic protons (Mücke et al. 2003) or the cascade process resulting from proton–proton or proton–photon interactions (Mannheim 1993). Even during different brightness/flaring states of a source, a single emission model is not able to fit the broad-band SED at all times. For example in the source 3C 279, while the flare during 2014 March–April is well fitted by a leptonic model (Paliya, Sahayanathan & Stalin 2015b), the flare in 2013 December with a hard γ-ray spectrum is well described by lepto-hadronic processes (Paliya et al. 2016). Thus, the recent availability of multiwavelength data coupled with studies of sources at different active states indicates that we still do not have a clear understanding of the physical processes happening close to the central regions of blazars.


If we consider for the bulk density the value 4500 kg m−3, which is one of the highest measured in the asteroid population out of those asteroids with good quality of data (see Carry 2012), it will strengthen the hypothesis that Psyche could be an exposed metal core of a differentiated asteroid (Elkins-Tanton et al. 2017). According to the models of asteroid differentiation, the process that led to the formation of Psyche happened very early. Considering Psyche's current diameter, Deff = 226 km (Shepard et al. 2017), the Psyche parent body (PPB) was supposed to be ∼500 km in diameter and have suffered severe ‘hit-and-run’ impact events capable of removing all crust and mantle, exposing the core (Elkins-Tanton et al. 2016). In addition, Psyche should have ∼40 per cent macroporosity, if we assume that it is made of blocks of iron/nickel with a density around 7500 kg m−3. In that case, the core itself was possibly destroyed and re-accumulated, implying a severe collisional history. When an asteroid is disrupted catastrophically, with a remaining mass ≤50 per cent of the initial one, after a collision with another body, an asteroid family is formed. If the collision happened in the Main Belt, a family of asteroid fragments should be in the region of Psyche; however, no family related to Psyche has been found yet (Davis, Farinella & Marzari 1999). One possibility to solve this issue is that the potential Psyche asteroid family was created at an early time, e.g. within the first 500 Myr of Solar system history (Davis et al. 1999). This would allow the family fragments to be ground down by collisional evolution and be unobservable today. The same models show that, even in this case, today there should be several surviving fragments having diameters around 20 km and above the detection limit. There is a lack of primordial asteroid families in the Main Belt (Brož et al. 2013; Spoto, Milani & Knežević 2015), very likely due to the classical methods that are used to identify them. The hierarchical clustering method (HCM) is not sensitive enough to find old and dispersed families, as it searches for asteroids forming compact groups in orbital element space (semi-major axis, eccentricity and inclination). A new approach has been proposed and implemented with success (Walsh et al. 2013; Delbo’ et al. 2017), as it is able to distinguish very old families, having eccentricities and inclinations dispersed in space. Therefore the possibility of the absence of a Psyche family could be due to searching biases. However, this may be an unlikely hypothesis, because A-type asteroids that could represent mantle material (almost pure olivine) from differentiated bodies do not exist extensively in the orbital space related to Psyche, but instead are distributed randomly in the Main Belt (Davis et al. 1999; DeMeo et al. 2015). In order to study this puzzling small body further, NASA is sending a new Discovery Mission to Psyche. The main goal is to get insight into whether it is a core of a parent body and understand the procedures of differentiation, making all the above questions more valid than ever. The alternative theory is that Psyche is a planetesimal that bears primitive unmelted material (Elkins-Tanton et al. 2016).


Since the age determination using asteroseismology relies on the mass-age relation that red giants follow, this means that the method is biased by any event that changes the stellar mass, such as mass accretion from a companion or stellar mergers (blue stragglers or stars rejuvenated by accretion, e.g. Boffin et al. 2015) or mass loss. One way to look for mass accretion events from a companion is to look for radial velocity, photometric variations, or chemical signs of accretion (e.g. high carbon and s-process enhancements; Beers & Christlieb 2005; Abate et al. 2015). The effect of mass loss can be minimised by looking at stars in the low-RGB phase, in which the effect of mass loss is smaller compared to red clump stars (Anders et al. 2017). The first study to determine masses for a sample of metal-poor halo giants with both seismic information (from Kepler; Borucki et al. 2010) and chemistry from high-resolution APOGEE (Majewski et al. 2017) spectra, was by Epstein et al. (2014). The authors used scaling relations at face value and reported masses larger (M >  1 M⊙) than what would be expected for a typical old population. Similar results were obtained by Casey et al. (2018), also using scaling relations for three metal-poor stars. These findings led to the need for further tests of the use of asteroseismology in the low metallicity regime. Miglio et al. (2016) analysed a group of red giants in the globular cluster M4 ([Fe/H] = −1.10 dex and [α/Fe] = 0.4 dex) with seismic data from K2 mission (Howell et al. 2014). These authors found low seismic masses compatible with the old age of the cluster, hence suggesting that seismic masses and radii estimates would be reliable in the metal-poor regime provided that a correction to the Δν scaling relation is taken into account for red giant branch (hereafter RGB) stars. The correction presented in Miglio et al. (2016) is a correction that is theoretically motivated based on the computation of radial mode frequencies of stellar modes.

Background Background Background Background Similarities Background


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


As a general remark, whether the locally calibrated metallicity diagnostics are applicable to high-redshift galaxies is still a matter of great debate. Diagnostics that are expected to be little affected by the ionization conditions of the gas (see e.g. Dopita et al. 2016) have been suggested to be valuable for high-redshift galaxies, where strong variations in ionization parameter and excitation conditions compared to local galaxies have been invoked to explain the observed evolution in the emission-line ratios (as seen, for example, from the offset of high-z sources in the classical BPT diagrams with respect to the local sequence (Kewley et al. 2013; Nakajima et al. 2013; Steidel et al. 2014; Kashino et al. 2017; Strom et al. 2017). However, since such diagnostics usually involve the [N ii]/[O ii] or the [N ii]/[S ii] line ratios, they are strongly dependent on the assumed relation between the N/O ratio as a function of the oxygen abundance O/H, which is affected by a large scatter and whose evolution with cosmic time and/or dependence on galaxy mass is also indicated as a possible origin of the observed evolution of the emission-line properties in high-zgalaxies (Masters et al. 2014, 2016; Shapley et al. 2015). Therefore, strong-line indicators based only on alpha elements (like, e.g. oxygen) have also been suggested as appropriate to high redshift studies, since galaxies at z ∼ 1.5–2.5 seem to show no appreciable offset from local trends in oxygen-based diagnostic diagrams (e.g. R23 versus O32, Shapley et al. 2015). However, the location on the abovementioned diagram could even be sensitive to a variation in the hardening of the radiation field at a fixed metallicity rather than a variation in abundances (Steidel et al. 2016; Strom et al. 2017). In any case, at redshifts ∼1.5 (where the majority of KLEVER galaxies considered in this work lie), the lack of the [O ii] doublet in the NIR bands observable from KMOS prevents us from using purely oxygen diagnostics, thus forcing us to exploit the nitrogen-based ones. When the survey will be complete, we will investigate the spatially resolved behaviour of z ∼ 2 galaxies on the R23 versus O32 diagram in a more statistically robust manner. Recently, Patrício et al. (2018) have shown that oxygen-based diagnostics z ∼ 2 provide metallicities comparable to those inferred from the electron temperature method; unfortunately, just a handful of robust auroral line detections have been reported so far in high-z sources (e.g. Jones, Martin & Cooper 2015b; Sanders et al. 2016; see also Patrício et al. 2018, and references therein), due to the intrinsic observational challenges in detecting the faint auroral lines with current instrumentation. Only the advent of new facilities like JWST or the MOONS spectrograph on the VLT will ultimately allow us to tackle this issue in the next few years, allowing us to properly calibrate the metallicity diagnostics against fully Te-based abundance determination at high redshifts and providing the key to overcome all these potential discrepancies.


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


In an effort to understand the character of RG encounters with ICM shocks and the observable consequences, we have initiated an MHD simulation study of such interactions. The simulations include passive, but energy-dependent transport of CRe, so that resulting radio synchrotron properties can be modeled appropriately. Nolting et al. (2019a, 2019b) explored interactions between ICM-strength shocks and lobed RGs. Here, we extend that work to include such shock interactions with so-called “narrow-angle tail” (NAT) RGs. NATs, which are especially common in clusters, (e.g., Blanton et al. 2001; Garon et al. 2019) result from sustained relative motion between an RG and its ambient ICM; that is, the RG effectively evolves in a wind that deflects the RG jets and their discharge downwind. The NATs can extend multiple hundreds of kpc from their AGN sources, and, so long as the AGN jets remain “powered on,” simulations suggest that NAT tails remain dynamic and highly inhomogeneous (O’Neill et al. 2019). Their considerable lengths and elongated morphologies make them interesting candidates to supply CRe at ICM shocks to form radio relics. We refer readers to O’Neill et al. (2019) and references therein for details of NAT formation dynamics. We do provide in Section 2 an outline of salient features of the simulated NAT presented in O’Neill et al. (2019) that are especially relevant to the present work. Our focus in this paper is on the interactions of shocks with such a previously formed NAT. Specifically, we use new three-dimensional (3D) MHD simulations to see what happens when plane shocks moving transverse to the NAT major axis collide with the NAT. That geometry is both relatively simple, and, on the face of it, perhaps the best able to form a radio relic in such a manner. Our study includes cases with shock Mach numbers,

, in order to span the range of shock strengths most often mentioned in this context. As in the aforementioned studies, we carry out synthetic, frequency-dependent radio synchrotron observations of our simulated objects in order to better understand the relationships between their dynamical and observable properties.


The galaxy merging process can cause enhanced accretion onto the central SMBHs and thus initiate activity. One or both of the dual SMBHs may be active or re-activated. Simulations (e.g., Van Wassenhove et al. 2012) suggest that simultaneous activity is mostly expected at the late phases of mergers, at or below 10 kpc scale separations. Additionally, the recent work of Fu et al. (2015b) indicates that mergers trigger and tend to synchronize activity at separations of a few kiloparsecs. Therefore dual AGNs are expected to be observed, but they are not easily resolvable with current observing facilities. The number of convincing dual AGN systems, mostly detected by X-ray and radio observations (e.g., Beswick et al. 2001; Junkkarinen et al. 2001; Komossa et al. 2003; Hudson et al. 2006; Bianchi et al. 2008; Fu et al. 2011b; Koss et al. 2011, 2012; Mazzarella et al. 2012; Liu et al. 2013; Comerford et al. 2015; Müller-Sánchez et al. 2015), are relatively few compared to the theoretically predicted abundance (see also, Komossa & Zensus 2016). While very long baseline interferometric (VLBI) radio observations currently provide the highest spatial resolutions, making them a promising tool for the detection of dual AGNs6

6
In fact, thanks to its superior resolution, the first binary AGN was discovered using VLBI technique (Rodriguez et al. 2006).
, only about 10% of AGNs are radio-loud, therefore dual radio-emitting active nuclei would be quite rare. Moreover, when trying to confirm the existence of dual AGNs in candidate sources, non-detection in the radio bands does not immediately falsify the dual AGN hypothesis, because radio-quiet nuclei may also be present. Burke-Spolaor (2011) searched the archival VLBI observations of 3114 radio-emitting AGNs for sources containing compact double sources. Only one source (B3 0402+379) was found with a double nucleus with separation of about 7 pc, which was already known from the observations of Rodriguez et al. (2006).


As a first approximation, we consider that most part of the accretion luminosity is emitted in the soft X-ray spectrum (10 eV–10 keV), thus, soft X-ray luminosity is simply estimated by using the mass accretion parameter, $\dot{m}$(1)$$\begin{eqnarray*}
L_{\rm AC}= \frac{GM\dot{m}}{R},
\end{eqnarray*}$$where M and R are the mass and radius of the object, respectively, which can be either a white dwarf, neutron star, or black hole. Mass–radius relation is employed to estimate radius in case of white dwarfs and neutron stars (see e.g. Barstow 1991, 1993; Lopes & Menezes 2012; Berti 2013; Carvalho, Marinho & Malheiro 2018; de Santi & Santarelli 2019; Carvalho et al. 2020), and Schwarzschild radius is taken for black holes. We reinforce that the model above is only a way to estimate the X-ray flux produced by compact objects due to accretion. The accretion rate, $\dot{m}$, is the parameter which defines the luminosity for a given system. However, in this work, we will not study any particular object, instead we will take fiducial values for mass and radius of the compact object along with standard values for snow line distances to estimate the time-scales ices need to reach chemical equilibrium. So, the model does not define if the compact object is isolated or in a binary system. We assume that accretion rate, $\dot{m}$, is constant on time, which means that the systems we are studying are well behaved, not presenting any sudden infall of matter, bursts, substantial outflows, or strong winds. The main aim, as stated, is to obtain an estimate of the time-scales for ices to reach chemical equilibrium. The assumption of constant accretion rate is feasible in most cases because the time-scale for ices close to compact systems to reach chemical equilibrium is smaller than the time-scale for changes on mass, as one can notice from power-law parametrizations (Chen et al. 2019), where we see that $\dot{m}$ scales with Myr or Gyr, while the time-scales for chemical equilibrium are at most 0.1 Myr for distances smaller than 100 LY, as we are going to show.