A key question that remains unanswered is how BBHs are formed. Viable formation channels include isolated binary evolution (e.g., Bethe & Brown 1998; Belczynski et al. 2002, 2014, 2016; Dominik et al. 2013; Mennekens & Vanbeveren 2014; Spera et al. 2015; Eldridge & Stanway 2016; Mandel & de Mink 2016; Marchant et al. 2016; Mapelli et al. 2017; Stevenson et al. 2017; Barrett et al. 2018; Giacobbo & Mapelli 2018; Kruckow et al. 2018; Mapelli & Giacobbo 2018) and dynamical encounters in dense stellar environments, such as globular clusters (e.g., Portegies Zwart & McMillan 2000; O’Leary et al. 2006; Sadowski et al. 2008; Downing et al. 2010, 2011; Rodriguez et al. 2015, 2016a, 2016b; Askar et al. 2017; Fragione & Kocsis 2018; Rodriguez & Loeb 2018; Samsing 2018; Samsing et al. 2018; Zevin et al. 2019), young star clusters (e.g., Banerjee et al. 2010; Ziosi et al. 2014; Mapelli 2016; Banerjee 2017, 2018; Di Carlo et al. 2019; Kumamoto et al. 2019), and galactic nuclei (e.g., O’Leary et al. 2009; Antonini & Perets 2012; Antonini & Rasio 2016; Petrovich & Antonini 2017; Stone et al. 2017a, 2017b; Rasskazov & Kocsis 2019). Moreover, the dynamical process known as Kozai–Lidov (KL) resonance (Kozai 1962; Lidov 1962) can trigger the merger of a BBH, even if the BBH has not been formed in a dense star cluster. In fact, if the BBH is orbited by a tertiary body (i.e., the BBH is the inner binary of a stable hierarchical triple system), the KL mechanism triggers oscillations of the BBH’s eccentricity, which might speed up the merger by gravitational-wave emission. Each channel is expected to produce black hole mergers with different mass and spin distributions (Mandel & O’Shaughnessy 2010; Abbott et al. 2016a; Rodriguez et al. 2016c; Farr et al. 2017; Abbott et al. 2019d). The limited statistics from the low number of systems detected through gravitational waves and model uncertainties so far do not allow strong constraints on the formation channels.


Ideally, however, one would want to go beyond the description of cosmic global history, and trace galaxy evolution on a galaxy-by-galaxy basis to understand the physical processes driving it. In this respect, great progress has been made by surveys at different redshifts that have established the existence of a strong dependence of galaxy histories on galaxy stellar mass. On average, more massive galaxies have formed their stars and completed their star formation activity at higher z than less massive galaxies (the so-called downsizing effect, Cowie et al. 1996; Gavazzi et al. 2006; De Lucia et al. 2007; Sánchez-Blázquez et al. 2009). The existence of relations between SFR and galaxy stellar mass (SFR–Mass) and specific star formation rate and mass (sSFR = SFR/Mass) have been established from z = 0 out to z > 2 (Brinchmann et al. 2004; Daddi et al. 2007; Noeske et al. 2007; Salim et al. 2007; Rodighiero et al. 2011; Whitaker et al. 2012; Sobral et al. 2014; Speagle et al. 2014), and many other galaxy properties have been found to be correlated with galaxy mass. Furthermore, a number of works have pointed out that galaxy properties are even more strongly correlated with a combination of galaxy mass and galaxy ‘size’, arguing for velocity dispersion (Bernardi et al. 2003; Franx et al. 2008; Smith, Lucey & Hudson 2009; Wake, van Dokkum & Franx 2012) or galaxy surface mass density (Brinchmann et al. 2004; Kauffmann et al. 2006) as principal drivers. The exact origin of these trends is still unknown, but evidence has accumulated for a dependence of galaxy stellar population ages on galaxy sizes at fixed mass (van der Wel et al. 2009; Cappellari et al. 2012; Poggianti et al. 2013), suggesting that also galaxy structure, and not just stellar mass, is relevant. In a recent paper, Omand, Balogh & Poggianti (2014) argue that the observed correlation of the quenched fraction with M/R1.5 is related to the dominance of the bulge component with respect to the disc, suggesting it might ultimately be linked with galaxy morphology (see also Driver et al. 2013). Even the sSFR–Mass relation might be due to the increase of the bulge mass fractions with galaxy stellar mass, as the ratio of SFR and stellar mass of the galaxy disc is virtually independent of total stellar mass (Abramson et al. 2014).


The data presented here comprise quasi-simultaneous observations during secondary eclipse of WASP-33 b around the V and Y bands. The predicted planet-star flux ratio in the V-band is 0.2 ppt, four times lower than the accuracy of our measurements. Therefore, we can neglect the planet imprint and use this band to measure the stellar pulsations, and most specifically to tune their current phases (see phase shifts in von Essen et al. 2014). Particularly, our model for the light contribution of the stellar pulsations consists of eight sinusoidal pulsation frequencies with corresponding amplitudes and phases. Hence, to reduce the number of 24 free parameters and the values they can take, we use prior knowledge about the pulsation spectrum of the star that was acquired during von Essen et al. (2014). As the frequency resolution is 1/ΔT (Kurtz 1983), 3.5 h of data are not sufficient to determine the pulsations frequencies. Therefore, during our fitting procedure we use the frequencies determined in von Essen et al. (2014) as starting values plus their derived errors as Gaussian priors. As pointed out in von Essen et al. (2014), we found clear evidences of pulsation phase variability with a maximum change of 2 × 10-3 c/d. In other words, as an example after one year time a phase-constant model would appear to have the correct shape with respect to the pulsation pattern of the star, but shifted several minutes in time. To account for this, the eight phases were considered as fitting parameters. The von Essen et al. (2014) photometric follow-up started in August, 2010, and ended in October, 2012, coinciding with these LBT data. We then used the phases determined in von Essen et al. (2014) during our last observing season as starting values, and we restricted them to the limiting cases derived in Sect. 3.5 of von Essen et al. (2014), rather than allowing them to take arbitrary values. The pulsation amplitudes in δ Scuti stars are expected to be wavelength-dependent (see e.g. Daszyńska-Daszkiewicz 2008). Our follow-up campaign and these data were acquired in the blue wavelength range. Therefore the amplitudes estimated in von Essen et al. (2014), listed in Table 1, are used in this work as fixed values. This approach would be incorrect if the pulsation amplitudes would be significantly variable (see e.g., Breger et al. 2005). Nonetheless, the short time span of LBT data, and the achieved photometric precision compared to the intrinsically low values of WASP-33’s amplitudes, make the detection of any amplitude variability impossible.


The second issue concerns the fact that inside a given region, coreshine is not detected in all the dense clouds observed by Paladini (2014) and Lefèvre et al. (2014) and that the proportion of clouds exhibiting coreshine varies from one region to another. For instance, 75% of the dense clouds detected in Taurus exhibit coreshine, whereas in most other regions the proportion is closer to 50% (such as Cepheus, Chamaeleon, and Musca)5. On the contrary, there are for instance very few detections in the Orion region. In THEMIS, most of the scattering efficiency originates in the accretion of an a-C:H mantle. This leads to three possible explanations for the absence of detectable coreshine. The first explanation is related to the amount of carbon available in the gas phase. The abundance used by Köhler et al. (2015) relies on the highest C depletion measurements made by Parvathi et al. (2012) towards regions with \hbox{$N_{\rm H} \geqslant 2 \times 10^{21}$}NH⩾ 2 × 1021 H/cm2. Parvathi et al. (2012) highlighted the variability in the carbon depletion in dust depending on the line of sight. Thus, there may be clouds were the amount of carbon available for a-C:H mantle formation is smaller or even close to zero: such regions would be populated with aggregates with a thinner H-rich carbon mantle or no second mantle at all and thus exhibit very little or no coreshine emission. A second explanation is related to the stability of H-rich carbon in the ISM, which depends strongly on the radiation field intensity to local density ratio (Godard et al. 2011; Jones et al. 2014). In low-density regions (according to Jones et al. 2014, \hbox{$A_{V} \leqslant 0.7$}AV⩽ 0.7 for the standard ISRF), UV photons are responsible for causing the photo-dissociation of CH bonds, a-C:H → a-C. In transition regions from diffuse ISM to dense clouds (Jones et al. 2014, \hbox{$0.7 \leqslant A_{V} \leqslant 1.2$}0.7 ⩽ AV⩽ 1.2 for the standard ISRF), better shielded from UV photons and where the amount of hydrogen is significantly higher, H-poor carbon can be transformed into H-rich carbon through H atom incorporation, a-C → a-C:H. Similarly, carbon accreted from the gas phase in these transition regions is likely to be and stay H-rich. Then, in the dense molecular clouds, most of the hydrogen is in molecular form and thus not available to produce a-C:H mantles on the grains. However, this approximately matches the density at which ice mantles start to accrete on the grains, which would partly protect a-C:H layers that had formed earlier (Godard et al. 2011, and references therein). The stability and hydrogenation degree of a-C:H, as well as the exact values of AV thresholds, are both dependent on the timescale and UV field intensity. The resulting a-C ↔ a-C:H delicate balance could explain why in a quiet region such as Taurus most of the clouds exhibit coreshine, whereas in Orion, where on average the radiation field intensity and hardness are much higher, most clouds do not. A third explanation is related to the age and/or density of the clouds. In a young cloud, where dust growth is not advanced, or in an intermediate density cloud (ρC ~ a few 103 H/cm3), the dust population may be dominated by CMM grains instead of AMM(I) dust. Such clouds would be as bright in the IRAC 8 μm band as in the two IRAC bands at 3.6 and 4.5 μm, thus not matching the selection criteria defined by Pagani et al. (2010) and Lefèvre et al. (2014) and would be classified as “no coreshine" clouds.


Gibson (2014) proposed that marginalization over many systematics is more robust than simple model selection, and that the BIC-based model selection could be the worst criterion in their experiments. To assess the impact of BIC-based model selection choices (hereafter Method 1) on our derived transmission spectrum, we also performed a separate analysis on the spectroscopic light curves employing the systematics marginalization approach (hereafter Method 2). We followed the implication of this approach described in Wakeford et al. (2016), and refer the reader to that work for more details. Instead of using the wavelet-based MCMC to account for the correlated noise (see Method 1), for simplicity, Method 2 employed the MPFIT package to fit the data and accounted for the correlated noise using the time-averaging β approach. We calculated the marginal likelihood for all the systematics models using the Akaike information criterion (AIC; Akaike 1973) as the approximation, that is, \hbox{$\ln\mathcal{P}(D|S_q)\approx-\mathrm{AIC}/2$}ln𝒫(D | Sq) ≈ −AIC/2, which provides more adequate fits and performs better than BIC as suggested by Gibson (2014). The resulting Rp/R⋆ in each spectroscopic channel was then calculated as the marginal-likelihood-weighted average of the best-fitting values from all the systematics models, whose uncertainty was propagated from both the deviation from the weighted average and the best-fitting error bar for each systematics model. The derived Rp/R⋆ values are also listed in Table 3. The middle and bottom panels of Fig. 5 show the transmission spectra derived by Method 2 and the comparison between these two methods, respectively. The great consistency confirms that the BIC-based model selection in this work does not bias the derived transmission spectrum. Since the two methods have almost the same transit-depth values in any given spectral channel, we decide to present the results from Method 2 in the following discussion, as they have smaller error bars.


Studies aiming at measuring and modeling solar radiation and its variability are strongly motivated by the impact that solar irradiance (that is, the electromagnetic energy emitted by the Sun received at the top of Earth’s atmosphere in units of area and time), especially in the UV, has on the chemistry and physical properties of Earth’s atmosphere and climate (e.g., Gray et al. 2010; Matthes et al. 2017). Studies of solar variability have been recently also driven by the necessity of improving our understanding of stellar variability (see Fabbian et al. 2017, for a recent review), which, in turn, is essential to characterize the habitable zones of stars and the atmospheres of their exoplanets. As for Earth, modeling of exoplanet atmospheres requires as fundamental input the spectral energy distribution of the hosting star, especially UV and shorter wavelengths (e.g., Tian et al. 2014; Ranjan et al. 2017; Rugheimer & Kaltenegger 2018). Unfortunately, measurements of UV radiation are strongly hampered by the interstellar medium absorption (up to 70%–90%), which is significant even for relatively close stars, so that estimates of stellar UV radiation strongly rely on modeling (see Linsky 2017, for a recent review). Moreover, because there is no mission scheduled in the near future to observe stellar spectra in the UV, after the Hubble Space Telescope ceases operations, the characterization of UV spectra of stars hosting exoplanets that will be discovered by current and future missions (e.g., TESS or James Webb Space Telescope) will necessarily rely on indirect estimates, performed, for instance, through the use of semi-empirical models (e.g., Mauas et al. 1997; Fontenla et al. 2016; Busá et al. 2017) or proxies (e.g., Stelzer et al. 2013; Shkolnik et al. 2014). Stellar irradiance variability also affects the detectability of exoplanets (see, e.g., the recent review by Oshagh 2018). The passage over the disk of spots and faculae may induce photometric variations of amplitude similar to or larger than photometric variations induced by planetary transits. Moreover, the presence of active regions may alter spectral line profiles, thus hindering exoplanet detections performed through radial velocity measurements. Similarly, spectroscopic techniques that allow us to estimate the physical properties of exoplanet atmospheres (see, e.g., Kreidberg 2017, for a recent view) require as fundamental input the spectra synthetized through models representing quiet and active regions (faculae and sunspots). Finally, stellar irradiance variability observed at different spectral ranges, especially in the UV, is a fundamental observable for the characterization of the magnetic activity of a star, and therefore for the understanding of dynamo processes in stellar objects (e.g., Reinhold et al. 2013; Basri 2016; Salabert et al. 2016). Because stellar photometric and spectral variability can be modeled using the semi-empirical approaches developed for the Sun described above (see, e.g., Shapiro et al. 2016; Witzke et al. 2018), understanding the limitations of current irradiance models is fundamental to improving our capability of modeling stellar variability.


In Figures 1 and 2 we show that the X-ray (1.7 keV5

5
This value corresponds to the geometric mean of the XRT energy band, at which the error of the estimated flux can be reasonably suppressed.
), optical (R-band), and radio (6 GHz) fluxes varied with the time of observation applied to the proper corrections if observed at a distance of 200 Mpc, motivated by the fact that the averaged sensitive range of the Advanced LIGO/Virgo detectors in their full-sensitivity run is about 210 Mpc, for the current samples. Due to the faintness of the SGRB afterglow emission, there are gaps of the data between the previous more distant events and GW170817/GRB 170817A (please note that for the latter we only consider the quick decline phase as the early part is significantly influenced by the beam effect of the off-axis outflow). Therefore we extrapolate the very late (t > 200 day) X-ray and optical afterglow data of GRB 170817A to t ∼ 2 day after the burst and then compare them to other events. The radio to X-ray spectrum of the forward shock afterglow emission of GW170817/GRB 170817A is fν ∝ ν−0.6, which yields a p = 2.2 in the slow-cooling synchrotron radiation scenario (Lamb et al. 2018; Troja et al. 2018). In the jet model, such a p can also reasonably account for the very late flux decline of

 (Lamb et al. 2018). The extrapolation function of the forward shock emission of GRB 170817A to early times is thus taken as f ∝ t−2.2. Surprisingly, the forward shock afterglow emission of GW170817/GRB 170817A, the first neutron star merger event detected by Advanced LIGO/Virgo, are among the brightest ones for all SGRBs detected so far. Just a few events have X-ray afterglow emission brighter than that of GRB 170817A, as demonstrated in the right panels of Figure 1. The same conclusion holds for the optical and radio afterglow data, as shown in Figure 2, though these two samples are rather limited. We have also compared the distribution of the isotropic gamma-ray energy Eiso, calculated in the rest-frame energy band of 1–104 keV, for the SGRBs with well-measured spectra, and found no significant difference for the SGRBs with and without “long-lasting” afterglow emission (see Figure 3; where the number of events for the X-ray sample are smaller than that presented in Figure 1 because some bursts lack reliable spectral measurements). GRB170817A and GRB 150101B (Troja et al. 2018), two short events with the weakest detected prompt emission, have “bright” late-time afterglow emission because of their off-axis nature.


Finally, we attempt to characterize the reflection component using the full 2–35 keV spectra with a sophisticated model [M4: ${\tt{\rm constant}}$*${\tt{\rm TBabs}}$*(${\tt{\rm simplr}}$*${\tt {\rm kerrbb2}}$+${\tt{\rm kerrconv}}$*(${\tt{\rm ireflect}}$*${\tt{\rm simplc}}$)), to evaluate the impact on the spin measurement and understand the changes of the accretion flow and the interaction between the disc and the corona. This model features a self-consistent treatment of the thermal, Compton scattering and the reflection component: ${\tt {\rm kerrbb2}}$ describes the thermal component and supplies the seed photons for ${\tt{\rm simplr}}$ (a modified version of ${\tt{\rm simpl}}$, Steiner et al. 2011) to generate the Compton component; while a portion of the Compton component will escape to reach an observer, the remains (refer as ${\tt{\rm simplc}}$, Steiner et al. 2011) will strike back to the disc to generate the reflected component. The reflection fraction Rref in ${\tt{\rm ireflect}}$ (Magdziarz & Zdziarski 1995), defined as the ratio of the Compton photons striking back to the disc to that escaping to infinity, is restricted to negative value thereby only the reflected component is returned by ${\tt{\rm ireflect}}$. It is linked to the reflection constant parameter x in ${\tt{\rm simplr}}$ via the relation x = 1 + |Rref| (Gou et al. 2011). We set the elemental abundance to unity and the iron abundance AFe to five times the solar abundance (Bharali et al. 2019; Buisson et al. 2019; Xu et al. 2020). The disc temperature Tin is fixed at the value returned by ${\tt{\rm diskbb}}$ (M1, refer to Gou et al. 2011). The ionization parameter ξ is fixed at 1000 (i.e. log(ξ) = 3, Xu et al. 2020; Buisson et al. 2019), as it is difficult to be constrained. Finally we use ${\tt{\rm kerrconv}}$ (Brenneman & Reynolds 2006) to apply relativistic effects assuming an unbroken emissivity profile with index q = 3. The key parameters in ${\tt {\rm kerrbb2}}$ and ${\tt{\rm kerrconv}}$ are linked together.


The fireball model remains the most popular scenario for the gamma-ray burst (GRB) phenomenon (Cavallo & Rees 1978; Goodman 1986; Paczynski 1986; Shemi & Piran 1990; Rees & Mészáros 1992, 1994; Mészáros & Rees 1993). In this model, the GRB central engine is a stellar-mass black hole or a rapidly spinning and highly magnetized neutron star formed by either the collapse of a supermassive star (collapsar; Woosley 1993; MacFadyen & Woosley 1999; Woosley & Heger 2006) or the merger of two compact objects (Paczynski 1986; Fryer et al. 1999; Rosswog 2003). In both cases, the original explosion creates a bipolar collimated jet composed mainly of photons, electrons, positrons, and a small fraction of baryons. The relativistic explosion ejecta within the jet are not homogeneous—they form multiple high density layers, which propagate at various velocities. When the fastest layers catch up with the slowest, the charged particles contained in the layers are accelerated through mildly relativistic collisionless shocks (internal shocks; Rees & Mészáros 1994; Kobayashi et al. 1997; Daigne & Mochkovitch 1998). The particles subsequently cool via emission processes such as synchrotron, Synchrotron Self Compton (SSC), and Inverse Compton (IC). The internal shock phase is usually associated with the so-called GRB prompt emission,17

17
See Pe’er (2015) for a recent review of GRB prompt emission.
 mainly observed in the keV−MeV energy range (see, e.g., the spectral catalogs by Gruber et al. 2014; von Kienlin et al. 2014) and usually lasting from a few ms up to several tens to hundreds of seconds. As the ejecta interact with the interstellar medium they slow down via relativistic collisionless shocks (external shocks; Rees & Mészáros 1992; Mészáros & Rees 1993), accelerating charged particles, which then emit non-thermal synchrotron photons. This external shock phase is usually associated with the so-called GRB afterglow emission observed at radio wavelengths up to X-rays and in some cases even up to the GeV regime hours after the prompt phase, and days and even years for the lowest frequencies. The detailed origin of the gamma-ray emission, however, is not fully understood and many theoretical difficulties remain, such as the composition of the jet, the energy dissipation mechanisms, as well as the radiation mechanisms (e.g., Zhang 2011).


Using the RADEX3 non local thermodynamic equilibrium (LTE) modeling program (van der Tak et al. 2007) with collisional rate coefficients from Wiesenfeld & Faure (2013), we modeled the relation between the gas kinetic temperature and the measured average of para-H2CO 0.5 × [(322–221 + 321–220)/303–202] ratios, adopting a 2.73 K background temperature, an average observational linewidth of 4.0 km s−1, and column densities N(para-H2CO) = 2.7 × 1012 and 3.7 × 1012 cm−2 for N113 and N159W, respectively. The results are shown in Fig. 5. The values of the para-H2CO column density were obtained with APEX data (beam size ~30″; Tang et al. 2017b), which cover similar regions. Different column densities of para-H2CO only weakly affect derived kinetic temperatures (see Fig. 3 in Tang et al. 2017b or Fig. 4 in Tang et al. 2018a; this was also shown in Fig. 13 and discussed in Sect. 4.3.1 of Mangum & Wootten 1993) as long as all lines are optically thin. Considering that the relation between the gas temperature and the para-H2CO line ratio may vary at different spatial densities (see Fig. 2 in Tang et al. 2017b), we modeled it at spatial densities 104, 105, and 106 cm−3 in Fig. 5. It appears that Tkin at n(H2) = 105 cm−3 is consistently lower than values at 104 and 106 cm−3 by ≲23% and ≲34%, respectively, for Tkin ≲ 100 K. Local thermodynamic equilibrium (LTE) is a good approximation for the H2CO level populations under optically thin and high-density conditions (Mangum & Wootten 1993; Tang et al. 2017a,b, 2018b). Following the method applied by Tang et al. (2017b) in their Eq. (2), we plot the relation between the LTE kinetic temperature, TLTE, and the para-H2CO (3–2) line ratio in Fig. 5. Apparently, TLTE agrees well with Tnon-LTE at volume densities n(H2) ~ 105 cm−3 as long as Tkin ≲ 100 K. Previous observations show that para-H2CO (3–2) is sensitive to gas temperature at density 105 cm−3 (Ginsburg et al. 2016; Immer et al. 2016; Tang et al. 2017b). The spatial density measured with para-H2CO (303–202) and C18O (2–1) in N113 and N159W is n(H2) ~ 105 cm−3 on a size of ~30″ (Tang et al. 2017b). Therefore, here we adopt 105 cm−3 as an averaged spatial gas density in the N113 and N159W regions.


Previous theorethical studies have outlined that the [C ii] emission originates from the cold (with temperatures of a few 100 K) neutral medium and from photo-dissociation regions (PDR, Vallini et al. 2013). This seems to suggest that its presence closely traces star formation sites, resulting in a linear relation, as found by De Looze et al. (2014) and Herrera-Camus et al. (2015). While at low-redshift and close to solar metallicity such a relation is well established, as shown by several observations (De Looze et al. 2014; Herrera-Camus et al. 2018) and also numerical simulations (see, e.g. Lupi & Bovino 2020), significant deviations can arise in different ISM conditions, like at lower metallicity or in presence of a strong ionizations field, that are more typically found in the high-redshift Universe. To address the impact of such conditions, several studies have analysed the [C ii] emission from typical high-redshift galaxies, by post-processing hydrodynamic zoom-in cosmological simulations with cloudy (Ferland et al. 2017; see, e.g. Olsen et al. 2017; Pallottini et al. 2017, 2019; Katz et al. 2019), or via ad-hoc methods, as in Arata et al. (2020), or also via on-the-fly non-equilibrium chemistry (Lupi et al. 2020). The main conclusion in all these studies is that a [C ii] deficit exists at high redshift, most likely due to the starbursting nature of these galaxies rather than their metallicity, since most of these systems are close to solar (see, e.g. Vallini et al. 2015; Lupi & Bovino 2020). Other studies have evidenced a weak dependence of [C ii] on metallicity. Harikane et al. (2020) showed that the L[C ii]/SFR ratio does not show a strong dependence on metallicity, which to first approximation was interpreted as the result of the proportionality between C abundance and metallicity Z and an inverse proportionality between PDR column density and Z in a dust-dominated shielding regime (Kaufman, Wolfir & Hollenbach 2006). In this framework, if PDR give a large conribution to the [C ii] emissivity, the [C ii] luminosity is not expected to strongly depend on Z (see also Ferrara et al. 2019; Pallottini et al. 2019).


Walton et al. (2017) suggested that the broad-band spectral variability seen in Holmberg IX X-1, similar to that reported here for NGC 1313 X-1, could potentially be related to the presence of the expected funnel-like geometry for the inner accretion flow. In such a scenario, the funnel is expected to geometrically collimate the emission from the innermost regions within the funnel (discussed further in Section 4.2). Regardless of the nature of the accretor (black hole or neutron star), the highest energy emission probed by NuSTAR is usually expected to arise from these regions, either powered by a centrally located Compton-scattering corona (e.g. Reis & Miller 2013), or a centrally located accretion column. The stability of this emission would therefore imply that any geometrical collimation it experiences remains roughly constant, despite the change in observed broad-band X-ray flux (which would suggest a change in accretion rate, $\dot{M}$). In principle, an increase in accretion rate would be expected to result in an increase in the scale height of the funnel (e.g. King 2008; Middleton et al. 2015a). However, while this must happen over some range of $\dot{M}$ in order for the disc structure to transition from the thin disc expected for standard sub-Eddington accretion to the funnel-like geometry expected for super-Eddington accretion, as discussed by Lasota et al. (2016), once the disc reaches the point of being fully advection-dominated the opening angle of the disc should tend to a constant (H/R ∼ 1, where H is the scale height of the disc at radius R). Walton et al. (2017) speculated that once this occurs, rather than closing the funnel further, an increase in $\dot{M}$ instead simply increases the characteristic radius within which geometric beaming occurs, such that emission that is already within this region (the highest energies probed) experiences no further collimation with an increase in $\dot{M}$, while emission from larger radii (i.e. from more intermediate energies) does still become progressively more focused, and would exhibit stronger variability. In essence, this idea invokes a radially dependent beaming factor in which the beaming of the innermost regions has saturated to explain (in only a qualitative sense) the unusual, energy-dependent broad-band spectral evolution seen from Holmberg IX X-I (and now NGC 1313 X-1).


In astrophysics, the number of studies that apply ML techniques has risen substantially in the last years. Unsupervised learning algorithms have been used to identify different kinematic components of simulated galaxies (Obreja et al. 2018, 2019), to compare stellar spectra (Traven et al. 2017), to classify pulsars (Lee et al. 2012), and to find high-redshift quasars (Polsterer, Zinn & Gieseke 2013). Supervised learning has been used to classify variable stars (Richards et al. 2011), to classify galaxies morphologically (Huertas-Company et al. 2008), and to determine the redshift of galaxies (Hoyle et al. 2015; Hoyle 2016; D’Isanto & Polsterer 2018). Recently, ML has also been used to connect the properties of galaxies and dark matter haloes using supervised learning techniques. Kamdar, Turk & Brunner (2016a), Kamdar, Turk & Brunner (2016b) use tree-based methods to predict several galaxy properties from a set of halo properties and train the models on galaxy catalogues obtained from semi-analytic models and the Illustris hydrodynamic simulation (Vogelsberger et al. 2014). Sullivan, Iliev & Dixon (2018) train a simple neural network with one hidden layer to predict the baryon fraction within a dark matter halo at high redshift, given several halo properties (features). As training data they use the results of a cosmological hydrodynamic simulation with Ramses-RT. Similarly, Agarwal, Davé & Bassett (2018) use several ML methods to link input halo properties to galaxy properties, training on the Mufasa cosmological hydrodynamical simulation. Taking a reverse approach, Calderon & Berlind (2019) train tree-based methods and a neural network to derive halo mass from galaxy properties, training on an SDSS group catalogue. The limitation of all these studies is the supervised training and the training data. As labelled galaxy-halo data is not available for observed systems, the data for supervised learning has to be taken from a model. Even if the ML algorithms learn to reproduce the training data perfectly, the connection between galaxy and halo properties is the same as in the simulations. If the simulations predict the true relations poorly, so will the ML method. Therefore ML algorithms should not be trained on simulated data, but on observed data directly.


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


Inspired by these works, we investigated the possibility of introducing a color diagram for the characterization of irradiated planets using their effective temperature instead of their absolute magnitude. The effective temperature can be used as a proxy for the luminosity/absolute magnitude because the reference radius is assumed to be constant; see Section 3. To take an even more practical approach, we chose a normalized color parameter based on the Spitzer Infrared Array Camera (IRAC; Allen et al. 2004; Fazio et al. 2004) as a commonly used photometer for the observation of exoplanets (see, e.g., Charbonneau et al. 2005; Deming et al. 2007; Todorov et al. 2009; Sing et al. 2016). The IRAC photometric channels 1 and 2 are centered at 3.6 and 4.5 μm, respectively. Channel 1 (3.6 μm) is more suited to studying CH4/H2O spectral features, while channel 2 (4.5 μm) is more sensitive to CO/CO2 features (see, e.g., Désert et al. 2009; Swain et al. 2009a, 2009b). Depending on the type of spectroscopy, i.e., transmission or emission, the ratio of the transit depth or the ratio of the secondary eclipse depth at these channels could potentially provide information regarding the relative presence of these molecules in the atmosphere of a planet. For transmission spectroscopy, we define this ratio as
15

where IRACλ is the transition depth observed at the wavelength λ (μm) channel. In transmission spectroscopy, absorption features appear as positive signals in the unit of transit depth. This is not the case for emission spectroscopy, where absorption features are negative signals with respect to a blackbody curve. As a result, we rearrange the terms and define this ratio of channels for emission spectroscopy as
16

where IRACλ is the secondary eclipse depth observed at the wavelength λ (μm) channel. By applying IRAC’s spectral response curves to our 56,448 synthetic spectra, we estimated these ratios for the two spectroscopy methods. Figure 10 shows the IRAC synthetic color–temperature diagrams for cloud-free atmospheres under equilibrium chemistry conditions.


Flows with

Rem≪1

 and

N∼(1)

 have the distinct property that the induced magnetic field is quickly diffused away, yet the Lorentz force is not negligible. This limit is referred to as the quasi-static approximation to MHD (which we call “QMHD” henceforth; Moffatt 1967; Sommeria & Moreau 1982; Davidson 1995; Knaepen & Moreau 2008; Davidson 2013), and has been studied mainly in metallurgy and in MHD experiments due to the typically low conductivity of liquid metals (Alemany et al. 1979; Sommeria 1988; Gallet et al. 2009; Klein & Pothérat 2010; Pothérat & Klein 2014; Baker et al. 2018), although recent numerical studies on its turbulent properties and anisotropy have been done as well (Zikanov & Thess 1998; Burattini et al. 2008; Favier et al. 2010, 2011; Reddy & Verma 2014; Verma 2017). After nondimensionalizing the equations of MHD using the uniform density ρ, ℓ, and u, and taking the limits above, one is left with a single dynamical equation for the velocity
2

∂v∂t+v·∇v=−∇p*−Ro−1xˆ∥Ω×v−N∇−2(xˆ∥B0·∇)2v+F,

where p
* is the total pressure modified by rotation and magnetic pressure, Ro
−1 ≡ 2Ωℓ/u is the inverse Rossby number (quantifying the relative strength of the Coriolis force),

xˆ∥Ω

 and

xˆ∥B0

 are unit vectors in the direction of rotation and the background magnetic field, respectively, and
F
 is a generic forcing term that can include dissipation such as viscosity and a body force (to be specified in Section 3). The background magnetic field is fixed in time and is uniform in space, such that

∇×B0=B0∇×xˆ∥B0=0

. Care must be taken if considering a spatially dependent background magnetic field
B

0
(
x
), as the resulting equation will not be the same. See the discussion in Section 5. This equation is accompanied with the incompressibility condition ∇ ·
v
 = 0. The induced magnetic field can be found using a diagnostic relation
3

b=−∇−2xˆ∥B0·∇v,

which would be

b=−∇−2B0·∇v/η

 in dimensional variables.


According to the Dst index reconstructed by Love, Hayakawa & Cliver (2019), the interval of the telegraphic glitches taking place between ∼13:35 ut and ∼17:20 ut corresponds to the storm main phase (Dst ∼ −320 nT to ∼ −570 nT). This interval also corresponds to that of the low-latitude aurorae witnessed at many points at ±40° MLAT. A large-amplitude of the GIC is induced by magnetospheric and/or ionospheric current system. One possible cause of the telegraphic disturbance is the storm-time ring current that developed between ∼11:40 ut and ∼17:40 ut. Kappenman (2004) has shown that the magnitude of GICs flowing in the Japanese power grid increases with the magnitude of the Dst index. Another possible cause is the substorm–current wedge system that consists of field-aligned current and the tail current (McPherron, Russell & Aubry 1973). Downward field-aligned current is connected to the dawnside ionosphere, and upward field-aligned current is connected to the duskside ionosphere. The pair of field-aligned currents causes magnetic disturbances at mid- and low- latitudes (Pytte, Mcpherron & Kokubun 1976). The magnetic disturbance recorded at Tokyo (Fig. 5) shows a decrease in the H-component and a positive excursion of the D-component during the interval of ∼22–23 LT (∼13–14 ut). It is probable that Tokyo would be located at southwest of the upward field-aligned current during this interval. The D-component variation shows a few negative excursions during ∼25:40–30:00 LT (∼16:40–21:00 ut). Although the disturbance of the H-component is unavailable during this interval, it can be speculated that Tokyo was located at southeast of the downward field-aligned current. In addition to the development of the ring current, the formation of the substorm current wedge may also cause the telegraphic disruption. By considering the above discussion, at mid-latitude, we suggest that there are two regions where GICs can be caused by field-aligned currents. One is southwest of the upward field-aligned current, and the other is southeast of the downward field-aligned current. In these regions, the H-component of the magnetic field is expected to decrease significantly because of the combination of the effects of the ring current and the current wedge. Tokyo was probably situated in such hazardous regions during the 25 September 1909 storm.


Gaia 1 is a star cluster that was recently discovered by Koposov et al. (2017) in the first Gaia data release (Gaia Collaboration 2016), alongside with another system of lower mass. Its observation and previous detections were seriously hampered by the nearby bright star Sirius, which emphasized the impressive discovery power of the Gaia mission. This object was first characterized as an intermediate-age (6.3 Gyr) and moderately metal-rich (−0.7 dex) system, based on isochrone fits to a comprehensive combination of Gaia, 2MASS (Cutri et al. 2003), WISE (Wright et al. 2010), and Pan-STARRS1 (Chambers et al. 2016) photometry. Hence, this object was characterized by Koposov et al. (2017) as a star cluster, most likely of the globular confession. Further investigation of Gaia 1 found a metallicity higher by more than 0.5 dex, which challenged the previous age measurement and rather characterized it as a young (3 Gyr), metal-rich (−0.1 dex) object, possibly of extragalactic origin given its orbit that leads it up to ~1.7 kpc above the disk (Simpson et al. 2017). Subsequently, Mucciarelli et al. (2017) measured chemical abundances of six stars in Gaia 1, suggesting an equally high metallicity, but based on their abundance study, the suggestion of an extragalactic origin was revoked. While a more metal-rich nature found by the latter authors conformed with the results by Simpson et al. (2017), the evolutionary diagrams of both studies are very dissimilar and could not be explained by one simple isochrone fit. In particular, it was noted that “the Simpson et al. (2017) stars do not define a red giant branch in the theoretical plane, suggesting that their parameters are not correct” (Fig. 1 of Mucciarelli et al. 2017). Such an inconsistency clearly emphasizes that a clear-cut chemical abundance scale is inevitable for fully characterising Gaia 1, and to further allow for tailored age determinations, even more so in the light of the seemingly well-determined orbital characteristics, Thus, this work focuses on a detailed chemical abundance analysis of four red giant members of Gaia 1, based on high-resolution spectroscopy, which we complement with an investigation of the orbital properties of this transition object. Combined with the red clump sample of Mucciarelli et al. (2017) and reaching down to the subgiant level (Simpson et al. 2017), stars in different evolutionary states in Gaia 1 are progressively being sampled.


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


The gamma-ray emission from the solar disk due to CR cascades in the solar atmosphere is denoted as a disk component. This secondary gamma-ray produced by the hadronic interaction of cosmic ray with the solar surface was first proposed by Dolan & Fazio (1965). While only upper limits were obtained by early measurements over the range 20 keV–10 MeV (Peterson et al. 1966). A detailed theoretical model for gamma-rays from the collision of cosmic ray with the solar atmosphere was presented by Seckel et al. (1991). The predicted gamma-ray flux at energies from 10 MeV to 10 GeV has a large uncertainty, being sensitive to the assumptions about the cosmic-ray transport in the magnetic field near the Sun. Gamma rays from the Sun were first detected by the Energetic Gamma-ray Experiment Telescope (Orlando & Strong 2008). The measured flux from 100 MeV to 2 GeV was within the range of the theoretical predictions. The Fermi collaboration (Abdo et al. 2011) reported the detection of high energy gamma-rays at 0.1–10 GeV from the quiescent Sun using the first 1.5 yr data. However, the measured solar disk emission flux was about a factor of seven higher than that predicted about this disk component by a “nominal” model (Seckel et al. 1991). This mismatch motivated Ng et al. (2016) to analyze 6 yr of public Fermi-LAT data. The obtained gamma-ray spectrum follows a simple power-law shape (α = −2.3) in 1–100 GeV without any evident high energy cutoff. For the flux in 1–10 GeV, a significant time variation of the solar disk gamma-ray flux that anticorrelates with solar activity was discovered, suggesting that the solar magnetic field would play an important role. An updated analysis with 9 yr of Fermi-LAT data, from 2008 August 7 to 2017 July 27, was performed, and Tang et al. (2018) confirmed these results and extended the gamma-ray spectrum up to >200 GeV. Notably, the bright gamma-ray flux above 100 GeV is dominant only during solar minimum at the end of Cycle 23 (Linden et al. 2018). The HAWC measurements in periods of high solar activity may support these findings (Albert et al. 2018a). Data collected from 2014 November to 2017 December, the second half of solar cycle 24, have been used to set strong upper limits on the flux of 1–100 TeV gamma-rays from the solar disk, about 10% of the maximum gamma-ray flux estimated by Linden et al. (2018). The HAWC 95% upper limit at 1 TeV is about 13% of the flux extrapolated from the solar minimum Fermi-LAT gamma-ray spectrum.


The heating due to the reprocessing of non-thermal photons produced in the nebula can be efficient even at late times. Here, we treat these processes in a simple way as follows. At early times, electromagnetic cascades proceed in the saturation regime, leading to a flat energy spectrum up to ∼1 MeV (Metzger et al. 2014). At later times, the spectrum depends on the seed photon spectra, but it can roughly be estimated to be a flat spectrum from ∼1 eV to ∼0.1 TeV, while the supernova emission continues, which is expected based on more detailed calculations (e.g., Murase et al. 2015; K. Murase et al. 2017, in preparation). High-energy γ-rays (≳1 MeV) heat up the ejecta through the Compton scattering and the pair production process. X-ray and UV photons are absorbed and heat up the ejecta through the photoelectric (bound-free) absorption unless the ejecta are fully ionized. Here, we describe the heating rate as
12

Q

˙

rad

(
t
)
≈

(

f

γ

+

f

X
−
UV

,
bf

)

L

sd

,

where fγ and

f

X
−
UV

,
bf

 are the heating efficiencies of γ-rays and X-ray and UV photons to the spin-down luminosity, respectively. We calculate the frequency dependent heating efficiency of γ-rays at each time:
13

f

γ

(
t
)
=

∫

ν

min

ν

max

d
ν

ν

min
(

K

γ
,
ν

τ

γ
,
ν

,
1
)

∫

1

eV

1

TeV

d
ν

ν

,

where the frequency range of γ-rays is

(
h

ν

min

,
h

ν

max

)

=
(
10

keV
,
1

TeV
)

, and h is the Planck constant. Here, τγ, ν is the optical depth of the ejecta to γ-rays and Kγ, ν is the photon inelasticity at a given frequency, where the Klein–Nishina cross section and the cross section for the Bethe–Heitler pair production in the field of a carbon nucleus are taken into account (Chodorowski et al. 1992; Murase et al. 2015). Note that the coefficient of the γ-ray optical depth depends on the density profile of the ejecta. Here, we simply assume a density profile to be constant with the radius. Adopting a realistic density profile may result in different ejecta mass and velocity estimates by a factor of a few.


We recorded the IRPD spectra of mass-selected H+MF and H+MF-Ln≤2 clusters (L = Ar/N2) in the 2950–3650 cm−1 spectral range in a tandem quadrupole mass spectrometer interfaced with an electron ionization source (Dopfer 2003, 2005), a setup used previously to record IR spectra of a variety of hydrocarbon cations and their clusters (Dopfer et al. 2002; Solcà & Dopfer 2002; Andrei et al. 2008; Patzer et al. 2010; Chatterjee & Dopfer 2017, 2018a, 2018b, 2020; Chatterjee et al. 2019). Briefly, the parent ions are produced in an ion source, which combines a pulsed supersonic expansion with electron (chemical) ionization close to the nozzle orifice. The expanding gas mixture is generated by passing a carrier gas mixture of Ar (N2) and 5% H2 in He in a ratio 5:1 at 10 bar through a reservoir containing liquid MF (Sigma-Aldrich, 99%, heated to 323 K). One possible reaction pathway begins with electron ionization of H2, followed by exothermic proton transfer reactions to form H+MF and subsequent three-body association to generate H+MF-Ln clusters (Harrison & Tsang 1976; Hopkinson et al. 1979; Dopfer et al. 1999; Lawson et al. 2012; Chatterjee & Dopfer 2018a), according to:
5

6

7

8

This route is reminiscent of the synthesis of interstellar protonated molecules (Oka 2006; Etim et al. 2017). An alternative pathway involves charge transfer from Ar+ (or

 or

) and subsequent self-protonation (Lawson et al. 2012; Chatterjee & Dopfer 2018a):
5a

6a

7a

The desired ions are mass-selected in the first quadrupole and irradiated in an adjacent octupole with a tunable IR laser pulse (νIR, 10 Hz, 2–5 mJ pulse−1, 1 cm−1 bandwidth) of a Nd:YAG-pumped optical parametric oscillator. Calibration of νIR to better than 1 cm−1 is achieved by a wavemeter. Resonant vibrational excitation upon single-photon absorption leads to the fragmentation of neutral ligands or molecules:
9a

9b

9c

Resulting fragment ions are mass-selected by the second quadrupole and monitored with a Daly detector as a function of νIR to derive the IRPD spectrum of the parent ions, which is linearly normalized for the energy of the laser pulse. The contribution from metastable decay is subtracted from the laser-induced dissociation signal by triggering the ion source at twice the laser repetition rate. The observed widths of the vibrational bands mainly originate from unresolved rotational structure, sequence hot bands involving inter- and intramolecular modes, lifetime broadening, and congestion produced from overlap of various structural isomers. Low-energy collision-induced dissociation (CID) mass spectra at ∼10 eV collision energy in the laboratory frame are recorded by introducing 10−5 mbar N2 into the octople to confirm the composition of the ions and their clusters and establish their fragmentation channels.


The stellar photospheric parameters we collected from literature for the benchmark stars are summarized in Table A.1. Although most benchmark stars have v sini  2 km s−1 (Reiners et al. 2018), there are two stars with larger values: J07558+833 (12.1 km s−1) and J13005+056 (16.4 km s−1). These stars are useful to investigate the performance of the algorithms when dealing with higher rotational velocities. The literature values were derived with different methods. These methods include: interferometry to estimate the stellar radius and Teff (Boyajian et al. 2012; Ségransan et al. 2003; von Braun et al. 2014; Berger et al. 2006; Newton et al. 2015), synthetic model fitting using BT-Settl models to determine Teff (Gaidos et al. 2014; Lépine et al. 2013; Gaidos & Mann 2014; Mann et al. 2015) and log g (Lépine et al. 2013), empirical relations to derive stellar mass in the form of mass-luminosity relations (Mann et al. 2015; Khata et al. 2020; Boyajian et al. 2012; Berger et al. 2006; Ségransan et al. 2003), along with the mass-magnitude relations (Maldonado et al. 2015), mass-radius relations (von Braun et al. 2014), mass–Teff relations (Gaidos & Mann 2014; Gaidos et al. 2014), empirical relations to derive the stellar radius in the form of mass-radius relations (Maldonado et al. 2015) and Teff–radius relations (Gaidos & Mann 2014; Gaidos et al. 2014; Houdebine et al. 2019), pEW measurements to determine Teff (Maldonado et al. 2015; Neves et al. 2014; Newton et al. 2015) and [Fe/H] (Maldonado et al. 2015; Neves et al. 2014; Gaidos et al. 2014; Mann et al. 2015), the definition of spectral indices such as the H2O-K2 index to estimate Teff (Rojas-Ayala et al. 2012), as well as the combination of the H2O-K2 index with pEWs to derive [Fe/H] (Rojas-Ayala et al. 2012; Khata et al. 2020), the stellar radius and Teff (Khata et al. 2020), and spectral curvature indices for the determination of Teff (Gaidos & Mann 2014). Additionally, [Fe/H] was derived by using color-magnitude metallicity relations (Dittmann et al. 2016), atomic line strength relations (Gaidos & Mann 2014), and spectral feature relations (Terrien et al. 2015). Terrien et al. (2015) used K-band magnitudes and the Dartmouth Stellar Evolution Program (Dotter et al. 2008) to derive the stellar radius, whereas Mann et al. (2015) employed the Boltzmann equation with Teff determined from synthetic model fits. Last, but not least, Houdebine et al. (2019) derived Teff from photometric colors. For more details on the individual methods, we refer to the descriptions in the corresponding works.


The consequences of a potential rainout for a planetary atmosphere can be manyfold. First of all the rainout removes metals from the atmosphere, relocating them to deeper layers. Hence the corresponding grain or droplet opacity will be missing from higher atmospheric layers. Because we do not include cloud opacities in our calculations we make the implicit assumption of a rainout of the condensed particles, although we do not model it, the net effect being the removal of metals from the higher layers. It has to be kept in mind, however, that the chemical equilibrium solution of the gas abundances in chemical contact with the condensed species is not necessarily the same as it would be when assuming a rainout. Our implicit assumption of a rainout is also applicable when considering the gaseous Na and K alkali abundances. In our models MgSiO3 condenses at temperatures below ∼1600 K. In principle this silicate material can further react with the alkali atoms to form alkali feldspars (such as albite and orthoclase), removing the gaseous alkalis from the gas for T ≲  1600 K (see, e.g., Lodders 2010). We do not consider these feldspars in our condensation model, such that the alkali atoms stay in the gas, as they would in a silicate rainout scenario. It has been found that alkali atoms are present in cool brown dwarf atmospheres, indicating that silicate rainout may occur in these objects (Marley et al. 2002; Morley et al. 2012). Another consequence of condensed material can be the formation of a cloud deck, close to and above the layers of the atmosphere hot enough the evaporate the in-falling cloud particles again. Such cloud decks can heat the atmosphere locally and in the layers below, by making the atmosphere more opaque to the planet’s intrinsic flux, effectively acting like a blanket covering the lower layers of the atmosphere (see, e.g., Helling & Casewell 2014; Morley et al. 2014). If the cloud layer is optically thick close to the planet’s photosphere it will leave an imprint on the planet’s spectral appearance and and may reduce the contrast of absorption features. The height of the cloud deck depends critically on the planets effective temperature and also on its surface gravity since the condensation temperature is pressure-dependent. The cooler an object is, the deeper in its interior the clouds will reside. Therefore the spectral imprint of clouds will vary with temperature, similar to the behavior in brown dwarf atmospheres. Silicate clouds with a high optical depth are thought to reside in the photospheres L4–L6 type brown dwarfs (

 ∼ 1500–1700 K) where they affect the spectra. For cooler objects the cloud deck lies below the photosphere and the clouds are no longer seen (see, e.g., Lodders & Fegley 2006). In our atmospheres we checked the possible locations of the cloud decks (i.e., the layers below which the condensates evaporate). We found that the silicate evaporation layer of planets with

 = 1000 K  and

 K is always located at pressures far higher than that of the photosphere, such that we do not expect any spectral impact of a cloud layer. For effective temperatures between 1500 and 1750 K the evaporation layer lies close to and above the photosphere (in altitude), such that a cloud deck could potentially affect the spectrum. For increasing log(g) the photosphere shifts to layers of deeper pressure, but so does the evaporation layer, as condensation is pressure dependent. Note that this temperature range is close to the effective temperature where L4–L6 dwarfs are thought to be most strongly affected by silicate clouds. For higher temperatures the evaporation layer is far above the photosphere such that we do not expect clouds to be of importance.


We detected radio emission for six sources, but while the morphology of radio emission in four over six cases is compact on $\le \,$arcseconds scales, predominantly unresolved, for NGC 3185 and NGC 3941 we find a more complex morphology. The estimated radio luminosities at this frequency are L$\, \sim \, 5\, \times \, 10^{20}$ and ${\sim }\, 6\, \times \, 10^{18}$ W Hz−1 for NGC 3185 and NGC 3941, respectively, well below the radio-loud/radio-quiet threshold of L$\, \sim \, 10^{23}$ W Hz−1 defined by Condon (1992). Considering NGC 3185, the structure observed in L band has a size of $5\, \times \,$3.8 arcsec, which translates into a linear scale of $0.5\, \times \,$0.4 kpc.6 Analogous considerations can be made for the C and X Bands, leading to linear scales of $0.38\, \times \,$0.36 kpc. There is evidence for radio emission spread over the host galaxy scale for a number of Seyferts when observed with adequate angular resolution and sensitivity (Orienti et al. 2015). In particular, circumnuclear starburst rings with knots of star formation are observed. Orienti & Prieto (2010) observed diffuse radio emission with knots of star formation for a number of Seyferts, on scales smaller than 1 kpc (NGC 5506, NGC 7469, and NGC 7582). Analogously, the morphology of the radio emission in the case of NGC 3185 as observed in our radio maps may be consistent with emission from circumnuclear rings of star formation. In order to check this hypothesis, we overlapped L band and C band radio contours to an archivial HST image7 for NGC 3185, as shown in Fig. 4 . The radio contours overlap with optical emission, from which a nearly circular, ring-like structure emerges. However, further work is needed to understand the link between radio emission and star formation in the form of circumnuclear rings in this source. In particular, intermediate angular resolution scales radio observations (such as those of e-MERLIN) combined with H α maps would allow us to confirm the star formation hypothesis. If we consider the parent sample with our new data, then we find that the average spectral slope is compatible with flat (0.30 ± 0.10), with a nearly equal number of flat and steep slopes. If we consider the two sub-populations of type-1 and type-2 Seyferts, then no significant differences are found with respect to the average spectral index and the average radio-loudness parameter, the only difference being that type-1 sources are slightly more luminous. Considering the X-ray radio loudness parameter, the black hole mass and the Eddington ratio, we do not find significant differences between the type-1 and type-2 sub-classes. We note that, even though the sources in the Reference sample have an Eddington ratio nearly an order of magnitude smaller than the average for the Parent sample, the X-ray radio-loudness parameter does not exhibit anomalous values.


Concerning case (1), the first explanation that has been proposed is an increasing relative velocity among the building blocks with decreasing distance from the planet leading to substantial water loss in the case of the most energetic impacts (Estrada & Mosqueira 2006), which occurred closer to Jupiter. Nonetheless, this scenario has been discarded by a detailed study showing that Io and Europa analogs exhibit an overabundance of water when they are formed via an N-body code simulating imperfect accretion and water loss during collisions (Dwyer et al. 2013). A second explanation is that the observed water gradient among the satellites results from an outwardly decreasing temperature of the CPD, leading to the existence of a snowline at a given radial distance from Jupiter (see, e.g., Lunine & Stevenson 1982). In this case, bodies that formed inward of the snowline (Io) accreted from essentially water-poor building blocks, whereas bodies that formed outward of the snowline (Ganymede, Callisto) formed from a primordial mixture of water ice and silicates (e.g., Canup & Ward 2002; Mosqueira & Estrada 2003a, 2003b; Mousis & Gautier 2004). Within this scenario, the low water content of Europa is puzzling. So far, Europa’s water content has been mostly attributed to its formation both outward and inward of the snowline due to either (i) its migration inward of the snowline during formation (i.e., growth), (ii) the progressive cooling of the disk and thus inward migration of the snowline during its formation, or (iii) an interplay between the two mechanisms (Alibert et al. 2005; Canup & Ward 2009). However, the evolution of the CPD has been systematically modeled using an ad hoc parametrization of the turbulent viscous disk (the so-called α-viscosity, Shakura & Sunyaev 1973) which governs the temperature evolution and lifetime of the disk. While providing a good starting point for evolutionary disk models, this kind of parametrization has been highly questioned in recent years (Bai & Stone 2013; Simon et al. 2013; Gressel et al. 2015). Hence, using a predefined α-viscosity prescription to describe the CPD’s evolution and provide hints on Europa’s formation remains questionable. The same remark holds for planet (or satellite) migration, which has also been extensively studied within recent years (see, e.g., Paardekooper et al. 2010; Bitsch et al. 2014). These studies have shown that in realistic disk conditions, migrating planets can behave significantly differently from what was previously thought, i.e., a persistent inward motion (e.g., Tanaka et al. 2002), due to the existence of regions where the migration is halted and even reversed. Because the studies of satellite formation have been based so far on the migration formulation of Tanaka et al. (2002; e.g., Canup & Ward 2002, 2006; Alibert et al. 2005; Sasaki et al. 2010) their proposed growth/migration scenario is questionable.


(1a) Work is underway for an updated ExoMol line list for SiO which will extend into the ultraviolet. The current line list only considers vibration-rotation transitions and so the current maximum wavenumber was set at 6049 cm−1. (1b) The HITEMP line list for NO includes data from the ExoMol NOname line list (Wong et al. 2017). (1c) The Ames line list (Huang et al. 2017) and the CDSD-4000 databank (Tashkun & Perevalov 2011) are also available for CO2, as well as the HITEMP compilation (Rothman et al. 2010). (1d) The previous ExoMol line list for H2O, BT2 (Barber et al. 2006), is only complete up to temperatures of 3000 K, whereas the more accurate ExoMol POKAZATEL line list Polyansky et al. (2018) is complete up to 4000 K. (1e) There is also a line list for MgH from ExoMol Yadin (Yadin et al. 2012). However, since it only covers the ground electronic X2Σ+ state, and so is less complete than the more recent MoLLIST line list of Gharib-Nezhad et al. (2013), we use the latter. (1f) Previous to the ExoMol aCeTY line list of Chubb et al. (2020b), the main sources of data for acetylene were from HITRAN (Gordon et al. 2017) and ASD-1000 (Lyulin & Perevalov 2017). The data from HITRAN are only applicable for studies performed at room temperature, and were shown in Chubb et al. (2020b) to be inadequate for high-temperature applications. ASD-1000 was a vast improvement, although there does seem to be opacity missing from some of the hot bands when compared to ExoMol aCeTY in Chubb et al. (2020b). (1g) The previous ExoMol line list for CH4, called 10–10 (Yurchenko & Tennyson 2014), is only complete up to 1500 K. The updated 34–10 line list is therefore recommended instead. Future updates of the database will investigate using data for methane based on recent line lists from either TheoReTs (Rey et al. 2017) or HITEMP (Hargreaves et al. 2020); these are currently expected to be more accurate when considering high-resolution applications. For low-resolution applications, we expect the quality of the ExoMol line list used here to be sufficient, particularly because completeness is more important than accuracy at lower resolutions (Yurchenko et al. 2014). (1h) The energy states from Coppola et al. (2011) are used in the Amaral et al. (2019) line list for HD+. (1i) The energy states from Engel et al. (2005) are used in the Amaral et al. (2019) line list for HeH+. (1j) The pressure and temperature broadened profiles for the resonance doublets of Na and K are computed using Allard et al. (2016, 2019). See Sect. 3.2.3 for a discussion on the broadening profiles of these atoms.


Using the high-level ab initio calculations implemented in the MOLPRO 2015 software package (Werner et al. 2015, 2020), the electronic structures of CO have been determined. In our calculations, the molecular orbitals (MOs) and ground-state energies are computed by the HF method. Then, the CASSCF method (Knowles & Werner 1985; Werner & Knowles 1985) is applied to perform the state-averaged calculation to generate multi-configuration wave functions by utilizing the HF MOs as the starting orbitals. Finally, based on the CASSCF wave functions, the internally contracted multi-reference configuration interaction method with the Davidson correction (icMRCI+Q) (Knowles & Werner 1988; Werner et al. 1988; Knowles & Werner 1992; Shamasundar et al. 2011) is performed to consider the dynamic correlation and size-consistency error. The augmented correlation consistent polarized weighted core valence quintuplet aug-cc-pwCV5Z-DK Gaussian basis set is selected to describe the carbon and oxygen atoms, which is found to give an excellent production of the potential energy and dipole moments for electronic states as the CO molecule dissociates, as mentioned in previous publications (Dunning 1989; De Jong et al. 2001; Peterson & Dunning 2002). The scalar relativistic effect is considered by the third-order Douglas–Kroll Hamiltonian approximation (Reiher & Wolf 2004, 2004). The PECs, PDMs, and TDMs for the singlet and triplet states were computed at the internuclear distances from 0.8–7.5 Å with step sizes of 0.05 Å for 0.8–0.9 Å, 0.02 Å for 0.9–1.5 Å, 0.05 Å for 1.5–2.6 Å, 0.1 Å for 2.6–6 Å, and 0.5 Å for 6–7.5 Å, and those for the quintet states were computed at the internuclear distances from 0.8–15 Å with step sizes of 0.05 Å for 0.8–0.9 Å, 0.02 Å for 0.9–1.5 Å, 0.05 Å for 1.5–2.6 Å, 0.1 Å for 2.6–6 Å, and 0.5 Å for 6–15 Å. The obtained PECs can be also used to determine the dissociation energy D

e
, the electronic excitation energy relative to the ground state T

e
, the internuclear separation R

e
, the harmonic frequency ω

e
, the first-order anharmonic constant ω

e

χ

e
, the rotational constant B

e
, and the vibrational coupling constant α

e
.


The photoevaporation model successfully explains the ‘two-time-scale’ nature of protoplanetary disc evolution, where the inner regions of protoplanetary discs appear to evolve slowly on Myr time-scales, before dispersing on a much more rapid time-scale (e.g. Kenyon & Hartmann 1995; Ercolano, Clarke & Hall 2011; Koepferl et al. 2013; Ercolano et al. 2014). Furthermore, slow-moving (∼5–10 km s−1) ionized winds are observed to be occurring in many nearby discs hosting young stars (e.g. Hartigan, Edwards & Ghandour 1995; Pascucci & Sterzik 2009; Rigliaco et al. 2013) and are consistent with the photoevaporation model (Alexander 2008; Ercolano & Owen 2010; Pascucci et al. 2011; Owen, Scaife & Ercolano 2013a; Ercolano & Owen 2016). The photoevaporation model can also explain a large fraction of observed ‘transition discs’ (e.g. Owen & Clarke 2012; Espaillat et al. 2014), specifically those with holes ≲10 au and accretion rates ≲10−9 M⊙ yr−1 (Owen et al. 2011b) and even those with larger holes and higher accretion rates in more recent models that incorporate CO depletion in the outer disc (Ercolano, Weber & Owen 2018). Transition discs are protoplanetary discs with evidence for a large hole or cavity in their discs (e.g. Espaillat et al. 2014), but they are known to be a heterogeneous class of objects (e.g. Owen & Clarke 2012; van der Marel et al. 2016) and their origins are not always clear. However, a specific prediction of the standard photoevaporation scenario is that there should be a large number of transition discs with hole sizes ≳10 au but that are no longer accreting. This final long-lived stage of disc dispersal gives rise to transition discs which have lifetimes between 105 and 106 yr, but remain optically thick – ‘relic discs’ (Owen et al. 2011b). The long disc lifetimes emerge from the simple fact that discs store most of their mass at large radii, but photoevaporative clearing proceeds from the inside out, so it will always take longer to remove the larger disc mass that resides at larger distance. While several discs satisfy this criterion (Dong et al. 2017), the number of observed non-accreting transition discs with large holes falls far below the theoretical expectations (Owen et al. 2011b; Owen & Clarke 2012). Studies by Cieza et al. (2013) and Hardy et al. (2015) showed that optically thick relic discs are rare and many non-accreting stars that show evidence for a circumstellar disc are more consistent with young, radially optically thin, debris discs.


In the line cores of Q/I and U/I profiles, we see depolarization and rotation for fields in the range

 G. These are due to the Hanle effect. For

 G, we see the signatures of level-crossings in the line cores of (Q/I, U/I) profiles, namely they tend toward the non-magnetic value (see Figures 1(b) and 2(b)). We recall that, traditionally the loops in the polarization diagram (namely, a plot of Q/I versus U/I for a given wavelength and for a range of magnetic field strength or orientation values) are identified to be due to the level-crossings in the incomplete PBE regime (see, e.g., Bommier 1980; Landi Degl’Innocenti & Landolfi 2004, see also Sowmya et al. 2014). When a given curve in the polarization diagram forms a loop the Q/I and U/I values tend toward the non-magnetic value. Based on this we identify the above noted behavior in the line cores of (Q/I, U/I) profiles for the mentioned field-strength regime as to be the signatures of level-crossings in the incomplete PBE regime. Polarization diagrams require the use of very fine grids of magnetic field strength or orientation. With the radiative transfer calculations presented in this paper, it is computationally difficult to produce such diagrams. For

 G, transverse Zeeman effect like signatures are seen in the line core of (Q/I, U/I) profiles (see Figures 1(c) and 2(c)). The Faraday rotation (del Pino Alemán et al. 2016; Alsina Ballester et al. 2017; Sampoorna et al. 2017), which results in depolarization in the wings of Q/I and generation of U/I in the wings, strongly influences the wings of U/I profiles for the entire field-strength regime considered here, while it shows up in Q/I for

 G. For the cases of theoretical model line and the isothermal model atmosphere considered in this section, the Voigt effect starts to show up in U/I for

 G and in Q/I for

 G, and its signatures are similar to those discussed in Sampoorna et al. (2019a). Also we see the signatures of incomplete PBE in the V/I profiles, which are now asymmetric about the line center for fields up to 30 G.


Achondritic meteorites are fragments of differentiated asteroids or planetary bodies of the solar system. Ureilites are coarse-grained ultramafic (olivine–pyroxene) achondrites. They include accessory minerals of metal and sulfide associated with high abundances of carbon phases (on average 3 vol% and up to ∼7 vol%; Goodrich et al. 2015), including graphite and high-pressure diamond (Goodrich 1992; Mittlefehldt et al. 1998; Nabiei et al. 2018). According to their petrology, ureilites are further divided into main group ureilites (formerly referred to as monomict or unbrecciated ureilites; accounting for 95%) and rare polymict ureilites (or brecciated ureilites). The main group ureilites represent the mantle residues after the extraction of feldspar-rich magmas (Cohen et al. 2004; Bischoff et al. 2014; Barrat et al. 2016) and a sulfur-rich iron melt (Goodrich et al. 2004; Warren et al. 2006; Goodrich et al. 2007; Rankenburg et al. 2008; Barrat et al. 2015), whereas polymict ureilites are breccias containing fragments of main group ureilites as well as non-ureilite clasts (Goodrich et al. 2004, 2015). Unlike samples from other differentiated planetary bodies (e.g., terrestrial and lunar samples, Martian meteorites, angrites), some primitive isotopic geochemical features (e.g., O isotope heterogeneities; Greenwood et al. 2005, 2006, 2017) have been preserved in ureilites, which are considered incompatible with a magma ocean event (e.g., Goodrich 1992; Goodrich et al. 2004, 2015). Therefore, the geochemical signatures of ureilite meteorites can provide valuable information about the origin of the ureilite parent body (UPB) and the early evolution of the solar system. For instance, olivine cores from individual ureilite meteorites cover a range of Fe/Mn ratios from 3 to 57 (Goodrich 1992; Goodrich et al. 2004, 2007; Downes et al. 2008) and Δ17O values (mass-independent O isotopic variations) from −2.5‰ to −0.2‰ (Clayton & Mayeda 1988, 1996; Greenwood et al. 2017). The whole rock Δ17O values further correlate with both the Fe/Mn ratios and magnesium number (Mg#: molar ratio of Mg/Mg+Fe) of their olivine cores (Goodrich et al. 2004, 2015). The origin of these covariations is debated and multiple scenarios have been proposed to explain these features, including (1) a “smelting” process which causes redox reactions between C and FeO during UPB differentiation (Singletary & Grove 2003; Goodrich et al. 2007); (2) oxidation of metal due to the presence of water prior to igneous differentiation (Sanders et al. 2017); (3) inherited nebular redox variability from the precursor materials that were not homogenized during partial melting (Warren & Huber 2006; Warren 2012); (4) UPB accretion from the mixing of two different chemical and isotopic reservoirs (Barrat et al. 2017). As such, ureilite genesis still remains unclear. Understanding the origin of these geochemical correlations in ureilites is further complicated by the fact that the timing of formation and early evolution of the UPB is poorly constrained.


In Fig. 1, we investigate the dust grain size distributions at the periastron and apastron of debris disks a belt eccentricity of eb = 0.4 (with dynamical excitation Δeb = 0.1) for different material strengths. Since the radiation pressure has a strong influence on the cutoff in the grain size distribution at smallest sizes, the wavy patterns of the grain size distributions start around the smallest bound grains. We note that the blowout size can be increased with particle porosity and increasing stellar temperature (Burns et al. 1979; Kirchschlager & Wolf 2013; Brunngräber et al. 2017). We find different characteristic wavy patterns in the grain size distributions starting with the depletion of grains with radii below the blowout radius abo, which are caused by the lack of β > 0.5 dust grains (Thébault et al. 2003), depending on different collisional evolutions (Figs. 1 and 2). For grains with radii ~3 μm at the apastron side and grains with radii ~6 μm at the periastron side, a strong wavy pattern develops. This depletion leads to an over-density of slightly larger grains (“first peak”) because grains with radii a abo are depleted and thus can no longer contribute efficiently to the destruction and erosion processes anymore. The overabundance of grains with radii around the first peak (~1.5 abo) in turn induces another depletion of grains with radii around the “second depletion” (~4–40 abo) that is caused by small high-β grains originating inside the disks. Thus, an efficient destruction is responsible for the deep depletion of objects with radii of up to ~4−40 abo. Qualitatively, this first wavy pattern is less pronounced in the size distribution of higher material strengths, where the impact velocities and thus their rate of destructive collisions is significantly lower. A strong depletion for lower material strengths is found for grains with radii ~60 μm, while the depletion in the case of higher material strengths is valid for radii ≤10 μm (Fig. 1). This depletion eventually leads to an over-density of grains with radii around the “second peak”. The overabundance of these grains is shifted from ~100 μm (high material strength) to ~1000 μm (very low material strength).


Based on these results, a series of 3D numerical simulations solving the simplified reduced magnetohydrodynamic (RMHD) equations, introduced by Strauss (1976), in Cartesian geometry were performed. The goal of these simulations was twofold: (1) to determine how a coronal loop responds to different photospheric velocity patterns, and (2) to investigate how the electric current sheets are formed, as well as the details of the heating that occurs through the dissipation of magnetic energy (Rappazzo et al. 2007, 2008, 2010; Rappazzo & Velli 2011; Rappazzo & Parker 2013; Rappazzo 2015). The results detailed in these papers confirmed the 2D results that the energy flux entering the corona because of photospheric motions causes a turbulent cascade of energy toward small scales, with electric current sheets continuously being created and destroyed throughout the coronal loop. The turbulence that develops is highly intermittent. The dissipation of energy occurs in current sheets, which are localized structures. Hence, the heating also occurs on small spatial scales. (Note that there is also particle acceleration, although that is beyond the scope of the present model.) When the loop is fully turbulent, it achieves a statistically steady state in which, on average, the Poynting flux induced at the boundaries by footpoint convection is balanced by the dissipation of energy in the electric current sheets. In this steady state, saturation occurs for the fluctuating magnetic energy, kinetic energy, mean square electric current, enstrophy, and other quantities that are then seen to fluctuate around their mean values. When the system becomes nonlinear, its behavior is highly dynamical and chaotic. This state occurs independently of the detailed form of the boundary velocity. A statistically steady state is achieved in which, although the magnetic field footpoints are convected continuously by the boundary flows, the resulting topology of the total magnetic field is not simply a mapping of those flows. By the same token, the turbulent dynamics that occur are due to the inherent nonlinear nature of the system, rather than being a consequence of the complexity of the magnetic field footpoint configuration.


While different studies devoted to the near-IR spectra of Be stars show low-resolution data, many of them are restricted to a small sample, and some others analyse reduced spectral ranges. For instance, there are only a few studies done in the J band, and they focus mainly on a particular object or a specific spectral line or element (Mathew et al. 2012a,b; Štefl et al. 2009). Also, individual spectral ranges have already been studied for large samples of Be stars. Steele & Clark (2001) presented H-band spectroscopy of Be stars with a spectral resolution of R ≃ 3000. They reported Brackett and Fe ii lines in emission and, from the analysis of the strength ratio of the higher Brackett lines to Brγ, were able to distinguish early- from late-type Be stars. Later, Chojnowski et al. (2015) published high-resolution H-band spectroscopy for a great number of Be stars observed with APOGEE. They found that the Br11 emission line is formed preferentially in a circumstellar disc at an average distance of ~2.2R*, while the higher Brackett lines seem to originate in an innermost region. Several emission lines have been identified for the first time, such as C i λ 1.6895 μm, which is also formed in the inner region of the discs. In a later work, Chojnowski et al. (2017) analysed the variation of the emission strength, peak intensity ratio, and peak separation. Their analysis revealed a variety of temporal variability, including the disappearance and appearance of the line emission on different timescales. In the K band, Hanson et al. (1996), Clark & Steele (2000) and Granada et al. (2010) reported Brγ, Brδ, and Pfund lines in emission together with lines of He i in emission or absorption, and Mg ii, Fe ii and Na i lines in emission. Clark & Steele (2000) related the infrared characteristics to the underlying properties of the stars: objects that present He i features in emission or absorption are B3 or earlier; if the star presents Mg ii in emission but no He i, it is between B2 and b4; objects with Brγ emission but no evidence of He i or Mg ii are B5 or later. Lenorzer et al. (2002b) provided an extensive atlas of early type stars, including a number of Be stars, covering the K and L bands, while Lenorzer et al. (2002a) analysed the H recombination lines of those stars and constructed a diagram of flux ratios of some selected recombination lines: Hu14/Brα and Hu14/Pfγ. In this diagram, the location of the objects gives information about the density of the emitting gas. After that, Mennickent et al. (2009) presented a classification scheme for Be stars based on the intensity of the L-band hydrogen-emission lines. The objects in each group fall in different regions of Lenorzer’s diagram; thus, this classification scheme is probably connected to the density of the disc. Granada et al. (2010) analysed a sample of eight Be stars and classified them with Mennickent’s criterion. They found that for group I objects, the equivalent widths (EW) of Brα and Brγ lines are similar, while for stars in group II the EW(Brγ) is much larger (more than five times) than the EW(Brα). Besides this, Mennickent et al. (2009) and Granada et al. (2010) reported emission lines not only in Brα, Pfγ, and the Humphreys series but also in He i λ4.038 μm and He i λ4.041 μm. Sabogal et al. (2017) showed a sample of L-band Be-star spectra and correlated the infrared features with the optical Hα line behaviour.


A sky survey at multiple frequencies, carried out with the Square Kilometre Array (SKA) could be used for an independent investigation of the controversial dipole anisotropy with a much superior sensitivity and thereby settle the question of the CP, hopefully, in a more decisive manner. In fact it was argued by Crawford (2009) that it is not possible to detect a radio dipole at more than 1σ level (for a presumed radio dipole amplitude equal to the CMBR dipole, i.e. p = 1), in a survey like the NVSS as the latter does not have sufficient number of sources. The conclusion drawn instead was that in order to make a positive detection of a radio dipole we may have to wait for the SKA data, going to sub-µJy flux-density levels, and thus having much larger number of sources, to get a better signal to noise. In spite of this deterrent prediction, a radio dipole at statistically significant level was detected from the NVSS data itself (Singal 2011) which became possible only because the radio dipole amplitude turned out to be actually a factor of ∼4 larger than the CMBR dipole. Although SKA might provide number counts at sub-µJy levels (Schwarz et al. 2015; Bengaly et al. 2019), however, one may need to be wary of possible caveats in using radio source number counts at these flux-density levels as one might start seeing at sub-mJy levels, in addition to the powerful distant radio sources, a substantially increasing fraction of very different populations of radio sources, e.g. nearby normal galaxies, starburst galaxies, and even galactic sources (Windhorst 2003; Padovani 2011; Luchsinger et al. 2015). Instead what would be important is to get surveys at different frequencies from SKA, at a few mJy levels or above where the radio source population may comprise mostly powerful radio galaxies and quasars, and then investigate the dipoles to see how genuine is the difference in dipoles from surveys at widely separated frequency bands like that seen in the NVSS and TGSS dipoles. The multiple frequency flux-density measurements should also allow for the chosen sample a direct estimate of an optimum value of the spectral index, that enters in the expression for the dipole amplitude. The question of CP could be resolved in a positive manner if it is found that multiple-frequency radio source surveys yield dipoles consistent with the CMBR dipole, though it would still remain to be explained why the presently determined dipoles are not consistent with that. However, in case it does turn out that the SKA surveys with better statistical accuracies also yield dipole magnitudes which are significantly different from the CMBR dipole, even though might be pointing along the CMBR dipole direction, as is seen in the presently determined dipoles, then it will certainly be a big problem for the CP, and consequently all conventional cosmological models, including the ones dealing with the question of dark energy, could be in serious jeopardy.


The filtered MHD equations read
11

12

where we sum over repeated indices, and
13

14

15

16

denote the inertial (I), Maxwell (M), advective (A), and dynamo (D) subfilter-scale stresses, respectively. Despite their common origin through the electric field in the induction equation, we here treat

 and

 separately, in order to disentangle the effects of magnetic-field-line advection, encoded in

, and magnetic-field-line stretching, encoded in

. Usually, the magnetic subscale stress refers to the difference

 (Aluie 2017; Offermans et al. 2018). Equations (11) and (12) differ from expressions for the filtered MHD equations found elsewhere by an additional projection of the coupling terms. The latter ensures that the dynamics defined by Equations (11) and (12) are confined to the same finite-dimensional subspace Ωℓ of the original domain Ω (Buzzicotti et al. 2018; Offermans et al. 2018). At first sight, this formulation suggests that the corresponding evolution equations for kinetic and magnetic energy feature terms are not Galilean invariant, which ought to be avoided as the measured subfilter-scale energy transfers otherwise include unphysical fluctuations (Aluie & Eyink 2009a, 2009b; Buzzicotti et al. 2018). However, the energy balance equations can be expressed in an alternative way by including terms that vanish under spatial averaging and ensure Galilean invariance of all terms (Buzzicotti et al. 2018; Offermans et al. 2018). For a statistically stationary evolution, the spatiotemporally averaged energy budget can then be written as
17

18

where

 and

 are the filtered kinetic and magnetic dissipation rates, respectively, and

 are terms that convert kinetic to magnetic energy

 and vice versa

, and
19

20

21

22

denote the four proper energy fluxes, in the sense that they vanish in the limit ℓ → 0, as can be seen from Equations (13)–(16). If positive, the inertial and Maxwell fluxes,

 and

 transfer kinetic energy from scales larger than or equal to ℓ to scales smaller than ℓ and vice versa if negative, while the advective and dynamo fluxes,

 and

, do so with magnetic energy. Note that there is no interscale energy conversion as the conversion terms

 and

 only involve filtered fields; as such they are known as resolved-scale conversion terms (Aluie 2017). The total energy flux is then given by the sum
23


The simplest two component model (power law + disk) is a phenomenological model often used to describe the spectra of ULXs as an empirical description of a disk plus corona geometry. In the presence of a cool (kT ~ 0.1−0.4 keV) and luminous (L ~ 1039−1040 erg/s) disk, it allows inferring the presence of intermediate-mass black holes (e.g., Makishima et al. 2000). This is not the case for M33 X-8, where the disk component describes the high-energy part of the spectrum well and appears to be hot (kT ~ 1.15 keV), leaving a soft excess that is accounted for by the power law. The overall disk parameters are then inconsistent with a massive black hole, but instead are more typical of an ordinary stellar mass black hole: using the relationship between mass, temperature, and luminosity in a standard disk (see, e.g., Makishima et al. 2000), we derive a mass of ~10 M⊙ for a nonrotating black hole, consistent with the estimation obtained by data from other satellites (e.g., Foschini et al. 2006; Weng et al. 2009; Isobe et al. 2012). Sutton et al. (2013) developed a classification scheme based on a disk+power law fit, to be applied to ULX spectra, according to which the spectral state of an ULX source can be defined by the disk temperature, the power-law slope, and the ratio between the flux contribution of the two spectral components in the 0.3−1 keV band. Our result is consistent with that found by Sutton et al. (2013) using XMM-Newton data, and, according to their classification, it identifies M33 X-8 as a broadened disk source, or in other words, as a source whose spectrum is dominated by emission from a hot disk (see Table 2) and where the additional soft component may be the effect of an unrealistic description of the disk spectrum by the diskbb model. In fact, such hot-disk/soft power-law spectra are difficult to explain in the context of the analogy of ULXs with GBHs: the thermal state of GBHs is indeed characterized by a hot disk, but the presence of a soft power-law-like component in addition to the disk is unusual, and its physical interpretation is not simple: if this component is due to the presence of a Comptonized corona, we do not expect it to be dominant at energies lower than the temperature of the seed photons that come from the disk.


We present the photometry of the companion in Fig. 4 in a color-magnitude diagram. The corresponding numerical values are reported in Table 2. YSES 2b is consistent with a late L to early T spectral type when comparing it to colors of field brown dwarfs from the NIRSPEC Brown Dwarf Spectroscopic Survey (McLean et al. 2003, 2007), the IRTF spectral library (Rayner et al. 2009; Cushing et al. 2005), the L and T dwarf data archive (Knapp et al. 2004; Golimowski et al. 2004; Chiu et al. 2006), and the SpeX Prism Libraries (Burgasser et al. 2004, 2008, 2010; Gelino & Burgasser 2010; Burgasser 2007; Siegler et al. 2007; Reid et al. 2006; Kirkpatrick et al. 2006, 2010; Cruz et al. 2004; Burgasser & McElwain 2006; McElwain & Burgasser 2006; Sheppard & Cushing 2009; Looper et al. 2007, 2010; Muench et al. 2007; Dhital et al. 2011). Object distances were derived from Gaia EDR3 (Gaia Collaboration 2021), the Brown Dwarf Kinematics Project (Faherty et al. 2009), and the Pan-STARRS1 3π Survey (Best et al. 2018). In color-magnitude space, YSES 2b is very close to the innermost three planets of the HR 8799 multi-planetary system (Marois et al. 2008, 2010). These three planets are classified as mid to late L type dwarfs (e.g., Greenbaum et al. 2018), which agrees well with the sequence evolution of the adjacent field brown dwarfs from L to T spectral types3. A similar spectral type in this domain, therefore, seems very likely for YSES 2b, requiring confirmation by measurements at higher spectral resolution. Whereas the masses of the spectrally similar trio of HR 8799 c, d, and e are in the range 7–12 MJup (Wang et al. 2018; Marois et al. 2008, 2010), it is likely that YSES 2b has an even lower mass as the system age of (13.9 ± 2.3) Myr is significantly younger than the age of HR 8799, which is claimed to be member of the Columba association with an age of 30–50 Myr (Zuckerman et al. 2011; Bell et al. 2015). This is supported by the AMES-COND and AMES-dusty models (Allard et al. 2001; Chabrier et al. 2000) that we present in Fig. 4 for a system age of 13.9 Myr. An individual evaluation of these isochrones yielded masses from 5.3 MJup to 8.0 MJup as presented in Table 2. The uncertainties originate from the errors in the system age and planet magnitude that were propagated by a bootstrapping approach with 1000 randomly drawn samples from Gaussian distributions around both parameters. When combining the posterior distributions for the different models and filters we derived a final mass estimate of

$6.3^{1.6}_{-0.9}\,M_{\mathrm{Jup}}$6.3−0.9+1.6 MJup
 as the 68% confidence interval around the median of the sample. This estimate is based on broadband photometric measurements alone; further spectral coverage of the planetary SED will be important to constrain its effective temperature, luminosity, surface gravity, and mass.


Large spectroscopic and photometric surveys, such as the Sloan Digital Sky Survey (SDSS, York et al. 2000), have revolutionized astrophysics in many fields, but can only deliver a limited view of the star formation activity in the local universe, given that instruments have a small field of view (FoV) in the case of spectroscopic surveys, and a low spectral resolution in the case of photometric ones. In recent years, integral field spectroscopic (IFS) surveys such as the Calar Alto Legacy Integral Field spectroscopy Area (CALIFA, Sánchez et al. 2012a) survey used in this work, have overcome these problems with the use of instruments with larger FoVs and a fully spectral coverage (e.g SAURON, Bacon et al. 2001; ATLAS3D, Cappellari et al. 2011; SAMI, Croom et al. 2012; VENGA, Blanc et al. 2013; and MaNGA, Bundy et al. 2015). However, these surveys still have limitations, such as the lack of a large contiguous observed area to trace the environment of nearby galaxies. They also suffer from selection biases due to the exclusion of galaxies with angular sizes that do not fit in the FoV of the integral field units (IFUs) that need to be considered (Walcher et al. 2014). These problems can be circumvented with multi-filter photometric surveys, which use a set of intermediate and narrow-band filters designed to provide the required spectral information while still covering a large contiguous area. The Javalambre Photometric Local Universe Survey (J-PLUS1, Cenarro et al. 2019) is currently operating to observe thousands of square degrees of the northern sky from the Observatorio Astrofísico de Javalambre (OAJ2) in Teruel, Spain. The survey is being carried out with the 0.83 m JAST/T80 telescope and the panoramic camera T80Cam (Marin-Franch et al. 2015), with a 2 deg2 FoV. A set of twelve broad, intermediate, and narrow-band optical filters is used (Fig. 1 and Table 1), optimized to provide an adequate sampling of the spectral energy distribution (SED) of millions of stars in our galaxy. These SEDs will be required for the photometric calibration of the Javalambre Physics of the accelerating universe Astrophysical Survey (J-PAS3, Benitez et al. 2014). In addition, the position of the filters, the exposure times, and the survey strategy, are suitable to perform science that will expand our knowledge in many fields of astrophysics. Further details on the OAJ, instrumentation, filter set, J-PLUS photometric calibration process, strategy, and several science applications can be found in the J-PLUS presentation paper (Cenarro et al. 2019).