In Sect. 4.2 we see that the Q.S. decreases with both the stellar mass and the local density. The Q.S. provides us with a glimpse of quenching in the past. It significantly decreases with stellar mass at the low-mass end (similarly for the cluster candidates and the field), showing that more massive galaxies are at a much later stage of quenching. This is consistent with the downsizing scenario (e.g. Cowie et al. 1996; Cattaneo et al. 2008; Webb et al. 2020) that massive galaxies form and quench earlier, and hence they are at a later, more advanced stage of evolution compared to low-mass galaxies. The mass dependence of the quenching stage is strongly affected by the local density. The trend is only significant in high-density environments. For sparse environments, the errorbars are too large for us to say anything. The scenario is consistent with Hatch et al. (2011), where faster evolution in protoclusters is found. This can also be due to the migration of galaxies from the low-density cluster outskirts to the high-density cluster cores where the quenching happens. The Q.S. also shows a stable decreasing trend with the local density, indicating that galaxies in denser environments (cluster cores) are at a later, more advanced stage of quenching. The earlier Q.S. of field galaxies also supports this scenario. This is consistent with the inside-out quenching in clusters, where galaxies in cluster cores quench early, while the galaxies in the outer parts quench progressively later, which is consistent with the scenario in Koyama et al. (2013) and Shimakawa et al. (2018). Another possibility is that during the in-falling process their gas will be stripped off, which directly leads to their quenching (Bekki et al. 2002). In this case the effect should be stronger for low-mass galaxies since their gas components are easier to strip. This environmental dependence is not strongly affected by the stellar mass, which supports the inside-out quenching that has an impact on low- and high-mass galaxies equally. In McNab et al. (2021) the authors use three types of transitional populations: green valley (GV) selected by rest-frame (NUV−V) and (V − J) colours; blue quiescent (BQ) selected by rest-frame (U − V) and (V − J) colours; and post-starburst (PSB) selected by galaxy spectra. They connect the quenching timescale to the transitional population fraction excess in clusters. They found that the lowest mass systems ( 1010.5 M⊙) have short quenching timescales ( 1 Gyr), which agrees with our result that low-mass galaxies are dominated by fast quenching ( 1 Gyr).


A challenge with empirical methods is that with growing numbers of input parameters, it becomes prohibitive in terms of CPU time to use all of them. It can also be counterproductive to feed the machine learning tool with all of these parameters because some of them might either be too noisy or not bring any relevant information to the specific problem being tackled. Moreover, high-dimensional problems suffer from being overfit by machine learning methods (Cawley & Talbot 2010), thereby yielding high-dimensional nonoptimal solutions. This requires subselection of relevant variables from a large N-dimensional space (with N potentially close to 1000). This task itself can also be achieved using machine learning tools. Here we present, to our knowledge, the first application to astronomy of the combination of two machine learning techniques: genetic algorithms (GA; e.g., Steeb 2014) for selecting relevant features, followed by SVMs to build a decision–reward function. GAs alone have already been used in astronomy, for instance, in the study of orbits of exoplanets and the SEDs of young stellar objects (Cantó et al. 2009), the analysis of SN Ia data (Nesseris 2011), the study of star-formation and metal-enrichment histories of a resolved stellar system (Small et al. 2013), the detection of globular clusters from Hubble Space Telescope (HST) imaging (Cavuoti et al. 2014), and photometric redshift estimation (Hogan et al. 2015). At the same time, SVMs have been extensively used to solve a number of problems, such as object classification (Zhang & Zhao 2004), the identification of red variable sources (Woźniak et al. 2004), photometric redshift estimation (Wadadekar 2005), morphological classification (Huertas-Company et al. 2011), and parameter estimation for Gaia spectrophotometry (Liu et al. 2012). We note also that the combination of GA and SVM has already been used in a number of fields, such as cancer classification (e.g., Huerta et al. 2006; Albda et al. 2007), chemistry (e.g., Fatemi & Gharaghani 2007), and bankruptcy prediction (e.g., Min et al. 2006). We do not attempt here to provide the most optimized results from this combination of methods. Rather, we present a proof of concept that shows that GA and SVM yield remarkable results when combined, as opposed to using the SVM as a standalone tool.


On 2017 November 24 the MMS orbit allowed us to collect measurements in the pristine solar wind, well outside the Earth's magnetosheath and the bow shock, for a long period (i.e., a few times longer than the typical correlation scale) of approximately 1 hour from 01:10 to 02:10 UT. Figure 1 (upper panel) displays an overview of the magnetic field measurements collected by the FIELDS instrument suite (Torbert et al. 2016) on board of MMS1 with a temporal resolution Δt = 128 samples s−1 (Russell et al. 2016). The period of interest is a typical example of slow solar wind stream (V ∼ 377 km s−1), with an average magnetic field 〈B〉 ∼ 6.6 nT and a mean plasma density 〈n〉 ∼ 9 cm−3 (Roberts et al. 2020a, 2020b). This means that the average Alfvén speed is VA ∼ 50 km s−1, while the ion inertial length and gyroradius are di ∼ 76 km and ρi ∼ 96 km, respectively (Chhiber et al. 2018), with the corresponding timescales τd ∼ 1.3 s and τρ ∼ 1.6 s, respectively. As reported in previous works (Bandyopadhyay et al. 2018; Chhiber et al. 2018; Roberts et al. 2020a, 2020b) this interval is characterized by two different spectral scalings: a typical inertial range ∼ τ5/3 is found at large scales (i.e., τ > τb), while a steeper scaling ∼ τ7/3 is found at small scales (i.e., τ τb), with τb ∼ 2.4 s (Roberts et al. 2020a). Furthermore, the magnetic field spectrum flattens near τnoise ∼ 0.2 s, due to the instrumental noise floor near ∼5 Hz (Russell et al. 2016). Finally, a decrease at shorter timescales (e.g., τ ∼ 0.1 s) is due to an anti-aliasing filter of nonphysical origin (Russell et al. 2016; Roberts et al. 2020a). Taken together, this interval is particularly suitable for testing our formalism with respect to processes of both physical and nonphysical origin. The presence of an instrumental noise floor allows us indeed to assess our formalism with respect to purely stochastic processes, while the existence of two spectral regimes (i.e., the MHD/inertial and the kinetic/dissipative) allows us to investigate small- versus large-scale processes and their possible coupling in a dynamical system framework.


H2O ice on Pluto has long escaped spectroscopic detection, and based on initial New Horizons data appears to be exposed only in a number of specific locations, usually associated with red color, suggestive of water ice/tholin mix (Grundy et al. 2015; Cook et al. 2015). Nonetheless, water ice is likely to be ubiquitous in Pluto’s near subsurface, given its cosmogonical abundance, Pluto’s density, and its presence on Charon’s surface6. Absorption coefficients for pure water ice (kH2O) at sub-mm-to-cm wavelengths are discussed extensively by Mätzler (1998), who also provides several analytic formulations to estimate them as a function of frequency and temperature along with illustrative plots. We use the Mishima et al. (1983) formulation (see Appendix of Mätzler 1998). Its applicability is normally restricted to temperatures above 100 K, but Fig. 2 of Mätzler (1998) indicates the trend with temperature. Absorption coefficients extrapolated to 50 K (estimated as half the values at 100 K) are shown in Fig. 5. At 500 μm, our best estimate is kH2O = 0.25 cm-1, comparable to the above values for CH4 and N2 ices. The corresponding penetration length is therefore comparable to the diurnal skin depth but remains negligible compared to the seasonal skin depth, even for seasonal Γ = 25 MKS. According to these calculations, the seasonal layer would be probed only at a wavelength of ~4 mm and beyond. We also remark that the expression from Mishima et al. (1983) would give a penetration depth of 56 m at 2.2 cm, which is an order of magnitude larger than indicated by the laboratory measurements of Paillou et al. (2008). In addition, small concentrations of impurities can dramatically reduce the microwave transparency of water ice (e.g., Chyba et al. 1998 and references therein). Therefore, the above calculations likely indicate upper limits to the actual penetration depth of radiation in a H2O ice layer, from which we conclude that the seasonal layer is not reached at the Herschel wavelengths.


As an additional constraint we have to make sure that our MCMax models are consistent with the observed CO snowline location. Therefore, we analyse the mid-plane temperature profile Tmid-plane(r) for all our models that match the observed SED, which we plot in Fig. 4. As mentioned above, models of the same series have the same temperature structure. We find that all of them have mid-plane temperatures between ∼20and25 K at the observed snowline radius of $R_{\rm sl} \approx 90$ au (Qi et al. 2015). These are well within the range of values generally assumed and observed for the freeze-out temperature of CO: The freeze-out temperature can vary between ∼20 and ∼30 K depending on whether CO is binding to pure CO ice or a mixture with water ice (Collings et al. 2004), which is, in turn, also dependent on the chemical history of the ice (Garrod & Pauly 2011). In general, the CO freeze-out temperature is not known unambiguously and might vary from system to system (Hersant et al. 2009; Qi et al. 2015): Qi et al. (2013a) found a freeze-out temperature of CO of 17 K from their modelling of TW Hya, whereas Jørgensen et al. (2015) obtain temperatures of about 30 K in their study of embedded protostars. Qi et al. (2011) assume a freeze-out temperature for CO of T ≈ 19 K (pure CO ice) for HD 163296. However, in Qi et al. (2015), they perform a new analysis with higher resolution observational data and use a temperature in the mid-plane at Rsl of T ≈ 25 K (mixed CO/H2O ice). Thus, all our models have temperatures in the disc mid-plane at the location of the snowline radius that are well within the plausible range. Our exploration of self-consistent models confirms that all the freeze-out temperatures assumed in these previous literature references fall within the plausible range of temperatures for HD 163296. If the freeze-out temperature of CO was known unambiguously, this would, in combination with an observationally determined CO snowline location, be a powerful model discriminant and we might be able to exclude models based on this constraint. Since, however, it is unclear what exactly the relevant freeze-out temperature is, we find that all the models can match the observed snowline location of 90 au. This weak model discrimination also means that it is impossible to predict the CO snowline radius from SED model fitting alone or even from fitting the molecular line emission together with the SED (Qi et al. 2011): given the uncertainty in the sublimation temperature of CO, our viable SED fits imply predicted radii in the range ∼40–135 au as denoted by the red asterisks in Fig. 4. In general, we find that the location of the CO snowline radius does not further discriminate between models in comparison to the criterion given by the SED; however, it sets the radial location inwards of which no freeze-out is taking place in our models, and which is therefore important for the interpretation of the C18O emission. It is important to note that an SED fit does not determine the CO snowline location and that, vice versa, a CO snowline observation does not discriminate amongst possible SED models.


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

 to

, and with a mean value of

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

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


The GMC associated with G305 is one of the most massive and luminous clouds in the Milky Way (Fig. 1). It is located in the Galactic plane at l ~ 305°, b ~ 0° and at a kinematic distance of 4 kpc (derived from a combinationof radio and Hα observationsby Clark & Porter (2004); Davies et al. (2012) measured its spectrophotometric distance to be 3.8 ± 0.6 kpc and most recently Borissova et al. (2019) measured the Gaia DR2 average distance to be 3.7 ± 1.2 kpc); this places it in the Scutum-Crux spiral arm. Given this distance, the complex has a diameter of ~ 30 pc (Clark & Porter 2004) and a molecular mass of ~6 × 105 M⊙ (Hindson et al. 2010). The G305 complex consists of a large central cavity that has been cleared by the winds from massive stars belonging to two visible central clusters (Danks 1 and 2) and the Wolf-Rayet star (WR48a; Clark & Porter 2004; Davies et al. 2012). The cavity is surrounded by a thick layer of molecular gas (traced by CO and NH3 emission; Hindson et al. 2010, 2013). Radio continuum observations by Hindson et al. (2012) have revealed that the cavity is filled with ionized gas and identified six ultra-compact HII (UC HII) regions and also one bright rimmed cloud (BRC) at the periphery of the cavity, indicating molecular gas irradiated by UV radiation (Sugitani & Ogura 1994; Thompson et al. 2004), which may cause implosion (Bertoldi 1989) or evaporation. A number of studies havereported star formation tracers (water and methanol masers, HII regions and massive young stellar objects, MYSOs; Clark & Porter 2004; Lumsden et al. 2013; Urquhart et al. 2014; Green et al. 2009, 2012). Furthermore, Hindson et al. (2010) found the concentration of star formation tracers to be enhanced inside a clump of NH3 bearing molecular gas that faces the ionizing sources, which is consistent with the hypothesis that the star formation has been triggered. Analysis of the stellar clusters in the complex reveals them to have ages of 1.5 Myr for Danks 1 and 3 Myr for Danks 2,with the former possibly being triggered by the latter (Davies et al. 2012). Additionally, a diffuse population of evolved massive stars was also found to exist within the confines of the G305 complex that had formed around the same time as the two clusters (Leistra et al. 2005; Shara et al. 2009; Mauerhan et al. 2011; Davies et al. 2012; Faimali et al. 2012; Borissova et al. 2019).


The mean temperature and pressure profiles, along with their associated intrinsic scatters, are also shown in Fig. 7. Overall, at larger radii, the mean temperatures are relatively flat, and we do not detect the clear decrease found in other studies (see Fig. 8; e.g. Vikhlinin et al. 2006; Leccardi & Molendi 2008; Arnaud et al. 2010; Eckert et al. 2013b; McDonald et al. 2014). Specifically, we do not see a temperature increase at small radii ∼0.2r500 before a subsequent decrease at large radii. However, our temperature profile is compatible with the results of Leccardi & Molendi (2008) in that region, and only 1–2σ lower than the profiles obtained by Vikhlinin et al. (2006) and McDonald et al. (2014). While this difference is not statistically significant, it may be due to the selection effects given that the Leccardi & Molendi (2008) sample is most similar to ours in mass and redshift. Given the modest statistical significance of this difference, it may simply be due to noise fluctuations. However, inaccurate subtraction of the X-ray background may also play a role. For example, oversubtraction of the hard background would tend to bias spectroscopic X-ray temperatures low while biasing our derived temperatures high (via the reduction in X-ray-derived density). The difference could also be related to cluster physics. For instance, clumping within the ICM, which is expected to increase with radius, will tend to bias spectroscopically derived temperatures low compared to the X-ray/SZ values derived in our analysis (e.g. Mazzotta et al. 2004; Rasia et al. 2005; Vazza et al. 2013). Elongation of the cluster along the line of sight, which will increase the SZ brightness compared to the X-ray brightness, could also artificially boost the temperatures recovered in our analysis (e.g. Cooray 2000). Another possibility for the slightly higher than expected temperatures at large radii may be biases in the SZ data. Indirect evidence for such an effect can be found by comparing the pressure profiles obtained by Sayers et al. (2013b), based solely on Bolocam data, to those obtained by Sayers et al. (2016) based on a joint analysis of Bolocam and Planck for a nearly identical set of clusters. Beyond ≃0.5r500, the latter work found a lower value for the pressure profile, with the difference increasing to a factor of ≃1.5 at r500. This implies that the Bolocam data alone may be overestimating the pressure at large radii, which would bias our temperature profiles high in that region. This can be seen in the mean pressure profile plot. However there is good agreement in the radial range of interest in this study when compared with Arnaud et al. (2010) and Planck Collaboration V (2013). In addition, the mean temperature profiles recovered for the CC and NCC subsets in the innermost shell are not different at a statistically significant level (i.e. the CC subset does not show a significant drop towards the cluster centre). This is likely a result of the coarse binning required by the SZ data. Specifically, the innermost shell extends to 0.15r500, which is generally not small enough to resolve the cool core. All of the potential biases and physical effects noted in this paragraph apply to the individual cluster temperature profiles as well, and therefore may explain differences compared to other studies (e.g. ACCEPT) that appear for some clusters.


A third limitation, which is probably the most urgently in need of investigation, is the lack of a gaseous component both in the Milky Way disc and in the satellite(s). It is not easy to anticipate how the inclusion of gas in the simulations can impact the results. It has been shown (Moster et al. 2010; Qu et al. 2011) that the presence of a thin gaseous disc can limit the amount of disc heating: for gas fractions of the order of 20% (40%), the heating may be reduced by 25% (40%). For accretions occurred in the early history of the Galaxy, typically before redshift z ~ 1, the fractions of gas in the Milky Way disc may have been significantly higher (with fgas ≥ 50%) than those simulated in the above cited works. Moreover, in those early phases of the Galactic evolution it is not even clear how thin the gaseous disc may have been. While in nearby disc galaxies gaseous discs indeed have scale heights between a few tens and 100 pc and velocity dispersions of the order of ~10 km s-1. At higher redshift gaseous discs of approximately 1 kpc (corresponding to velocity dispersions of the order of 100 km s-1) have been observed in the continuum and in the gas component (Elmegreen & Elmegreen 2006; Epinat et al. 2012). In the N-body models cited above, the typical scale heights employed for the gaseous component are between 200 and 400 pc. It is thus crucial to quantify the heating of stellar discs and the efficiency in forming an in-situ halo also in more extreme conditions than those modeled so far, also because galactic stellar archeology seems to suggest that the Milky Way may have experienced an intense phase of star formation and significant gas turbulence at those epochs (Haywood et al. 2013; Snaith et al. 2014; Lehnert et al. 2014). If the inclusion of a gaseous component in the Milky Way disc seems inevitable for the simulation of accretion episodes that occurred at early times, the same is valid for modeling the accreted satellites. In the case of gas-rich satellites, the stellar fraction of the baryonic mass would be lower than 100%, as assumed in this paper and a certain fraction of the gaseous mass may be lost by tidal effects/ram pressure stripping before being accreted and converted into new stars. This would naturally lead the accretions to be less “stellar-rich” than those simulated in the present paper, thus effectively reducing the amount of stars of extra-galactic origin that a satellite of a given mass can bring into the inner halo (i.e., inside 20 kpc) of a Milky Way-type galaxy. Finally, it is worth emphasizing that we are using idealized simulations of local mergers to quantify the response of a stellar disc to merger events that may have occurred several Gyr ago, when both the stellar masses of the Milky Way and of its satellite(s) were significantly different from those employed here. Because the properties of the Milky Way at higher z are still largely unknown (in terms of mass and effective radius, etc.) and similarly, those of the satellite galaxies, idealized simulations of local mergers are currently still one of the only viable ways to quantify the response of a stellar disc to accretion events of a given mass ratio, even for those occurring at higher z (with the limitations previously discussed, such as the lack of a gaseous component). Some N-body models similar to those analyzed in this paper have tried to mimic mergers at higher redshift, finding that the evolution and thickening of the disc, and its orbital parameters, do not depend on the redshift, but only on the mass-ratio of the merger (cf., for example, Figs 10 and 14 in Villalobos & Helmi 2008). This is robust evidence of the fact that what matters is the relative mass ratio of the interacting galaxies (see also Quinn et al. 1993; Bournaud et al. 2005, 2009; Qu et al. 2010), and the relative variation of their parameters, rather than the absolute values. As a consequence, at first approximation, local mergers can be re-scaled to also mimic mergers at higher z. This, we suggest caution to be taken due to the limitations of these models, such as, for example, the lack of gas, that can play an important role in the process.


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


Due to their non-axisymmetry, bars can cause the gas to flow inwards (e.g., Athanassoula 1992; Regan et al. 1999; Sheth et al. 2000), thus enhancing star formation in the central regions of their host galaxies (Sérsic & Pastoriza 1967; Hawarden et al. 1986; Ho et al. 1997; Sheth et al. 2005; Coelho & Gadotti 2011; Ellison et al. 2011). As a result, barred galaxies have various stellar structures, such as nuclear rings, nuclear disks, inner rings, outer rings, and boxy peanut bulges (e.g., Combes & Gerin 1985; Athanassoula 1992; Sellwood & Wilkinson 1993; Knapen et al. 2002; Kormendy & Kennicutt 2004; Comerón et al. 2010; Kim et al. 2012; Erwin & Debattista 2013; Buta et al. 2015; Emsellem et al. 2015, and references therein). These are dense regions in terms of stellar density. However, bars also develop sparse regions around themselves, usually producing a “Θ” shaped region. These sparse regions are thought to be produced by the bar-driven secular evolution in a way that the bar sweeps out materials around it. Such sparse regions are called by different names, such as “light deficit”(Kim et al. 2016), “star formation desert” (James & Percival 2015, 2016), and “dark spacer” (Buta 2017). In this respect, some barred galaxies have been found to be accompanied by a very faint disk or almost no disk around the bar (Gadotti & de Souza 2003; Gadotti 2008; Łokas 2021). Using Hα imaging, James et al. (2009) found that star formation is suppressed in the immediate vicinity of the bar (James & Percival 2016, 2018). The bar effectively transports gas into the central region once it is formed. Therefore, the star formation is truncated in the star formation desert. James & Percival (2016, 2018) measured the age of stellar populations and put constraints on the bar formation epoch. With zoom-in cosmological simulations, Donohoe-Keyes et al. (2019) found a truncated star formation and a lack of young stellar populations. However, they stressed that the interpretation can be complicated due to the radial migration of stars. Kim et al. (2016) found that the light deficit is more pronounced among galaxies with a longer and stronger bar. Later, Buta (2017) found that these sparse regions occur not only inside the inner ring, but also between the bar and the outer ring. He also found that the degree of the light deficit is a strong function of the bar strength, A
2. Therefore, the bar-driven secular evolution is recorded in the light deficit and how it changes with redshift is worthy of investigation.


Solar flares occur because of the explosive release of magnetic energy via the reconnection process in the solar atmosphere. Similar energetic events have been observed in other stars, especially M dwarfs like YZ CMi (dM4.5e), EVLac (dM3.5e), and AD Leo (Hawley & Pettersen 1991; Kowalski et al. 2010). The general idea is that for low-mass stars, the flare activities would be more frequent if the stellar masses are smaller. The level of flare effects depends also on the rotation periods (P) of the stars For example, the M-type dwarfs with P  10 days have been found to exhibit far more flare activity than those with P > 10 days, according to the Kepler observation (Lin et al. 2019). As P ∼ 1/

, with t being the stellar age on the basis of the gyrochronology relation (Skumanich 1972; Barnes 2010; van Saders et al. 2016), it is expected that the flare activity should be more frequent and powerful for young and fast-rotating stars (Davenport 2016; Stelzer et al. 2016; Davenport et al. 2019). Such time evolution of the stellar activities is important to the study of habitability of exoplanets orbiting around low-mass stars because of the potential impacts on the atmospheric loss and biological damage (Tarter et al. 2007; West et al. 2008; Segura et al. 2010; Armstrong et al. 2016). The large amount of high-precision photometric light curves produced by the Kepler mission (Borucki et al. 2010) is therefore ideal for statistical studies of stellar flares (Walkowicz et al. 2011). Following the discovery of superflares of solar-type stars by Maehara et al. (2015), there are increasing interests in topics related to exospace weather effects across a wide range of spectral types from A-type (Balona et al. 2015), G-type (Maehara et al. 2012, 2015; Wu et al. 2015), to M-type stars (Hawley & Pettersen 1991; Kowalski et al. 2010; Chang et al. 2017). There are two types of exoplanets of binary stars: the S-type for those in orbit around one of the stellar component, and the P-type for those orbiting around both components (Kaltenegger & Haghighipour 2013; Pilat-Lohinger et al. 2019). Their surface temperatures (and hence the condition of habitability) would be determined by the total radiative fluxes and magnetic activity of the binary systems. From this point of view, the binary systems are no less interesting because of the possible presence of the P-type or S-type habitable exoplanets.


Now, we must consider a specific distribution of electrons. Ideally, with a well-constructed background-subtracted image, only recently injected coronal material should be visible in excess total brightness; hence, ideally, ne should be identically zero outside the CME. However, reality is not so kind as to clearly delineate between CME and non-CME material. The explosive eruption and ejection of coronal material may rearrange previously quiescent material. If such material is pushed into a line of sight that passes through the CME, then, due to the optically thin nature of the corona, it will be impossible to distinguish newly ejected material from newly arranged material. A further issue that must be confronted when choosing a functional form for ne is the lack of observation or direct measurement on the internal mass distribution of a CME, as well as imprecise knowledge on the morphology of the CME. For example, is a CME balloon-shaped with a circular cross section (Millward et al. 2013) or croissant-shaped with an elliptical cross section (Thernisien et al. 2006, 2009)? Are there one or more cavities in the CME, and if so, where are the cavities located, how wide are they relative to the CME, and how low is the cavity density relative to the edge density? Is the mass distributed symmetrically relative to the central axis of the CME? Does the mass distribution change with time, either by pileup at the CME leading edge or by continuous mass inflow from the lower atmosphere (Bein et al. 2013; DeForest et al. 2013a)? Nevertheless, in spite of such epistemic uncertainty on the internal mass distribution, if the shape of the CME is known—either directly through polarimetry (de Koning & Pizzo 2011) or by assuming a shape (Thernisien et al. 2006; Millward et al. 2013)—and hence the start and end points of the line-of-sight integral are known, one might choose a particularly simple distribution, namely,

 (Feng et al. 2013b). On the other hand, if both the CME mass distribution and morphology are poorly known, as was the case in the pre-STEREO era, then one might choose an even simpler distribution, that is, a point source,
12

where δ is the Dirac delta function and n0 is a constant. To enable direct comparison of our three-view mass determination with the two-view mass determination of CV09, we employ the point-source distribution.


The crucial aspect we want to test in this work is whether the CR-IGIMF scenario, once embedded in a realistic galaxy formation context, can match the observed trends. To this purpose, we use mean star formation histories (SFHs) predicted by the GAEA semi-analytic model (Hirschmann et al. 2016) for $z$ = 0 galaxies in four different stellar mass bins, namely M⋆ ∼ 1012, 1011.5, 1010.5, and $10^{9.25} \, {\rm M}_\odot$. These SFHs have been extracted from the reference GAEA realization and from runs implementing variable IMF approaches (F17 and F18). Galaxies more massive than ∼1010.5 are typically characterized by an early peak of SFR, followed by a smooth decay. The epoch, height, and width of the peak depend on the final galaxy stellar mass, with more massive galaxies having an earlier, narrower, and higher peak (see also De Lucia et al. 2006). Lower mass galaxies have almost constant SFHs. For the mean SFH in each mass bin, we compute the mass-weighted global IMF using our CR-IGIMF grid and then the corresponding value of fdg. It is worth noting that in our estimate for fdg we only consider the $\lt 1 \, \mathrm{M}_\odot$ mass range, where the mass-weighted IMF coincides with the present-day mass function. Moreover, observational constraints are closer to luminosity-weighted IMFs. However, for very old stellar populations (i.e. massive ETGs), we do not expect this difference to change our conclusions significantly. In Fig. 3, we compare these fdg for UCR/UMW = 1 (blue stars – for each mass bin, we plot separately the values corresponding to the mean SFHs extracted from the three GAEA realizations considered), with the observed values. We correct the observed values of fdg from LB13 to an aperture of 1 effective radius, whose properties we consider to be comparable to SAM predictions. To this aim, we assume an IMF radial profile with the same shape as that recently derived for one massive ETG by La Barbera et al. (2017). For each mass bin, the profile is rescaled, in the central region, in order to match the fdg value within the SDSS fibre aperture, as detailed in LB13. The correction, which is larger at the highest mass and negligible at the lowest mass,4 brings all fdg values from LB13 in the range from ∼0.72 to ∼0.8, as illustrated in Fig. 3 (see red dots with error bars, corresponding to the 18 stacked spectra of LB13). Remarkably, the aperture correction brings the observed fdg values within the range predicted by the CR-IGIMF.


To further test the possible role of mass in driving the high emission-line velocity-widths observed in our targets, in Fig. 14 we plot W80,Hα as a function of the emission-line ratio log ([N ii]/Hα). This emission-line ratio is a tracer of the metallicity of star-forming galaxies (e.g. Alloin et al. 1979; Denicoló, Terlevich & Terlevich 2002; Kewley & Dopita 2002), as well as an indicator for the source of ionizing radiation (e.g. Kewley et al. 2006; Rich et al. 2014). Furthermore, there is an observed relationship between mass and metallicity and therefore an expected relationship between this emission-line ratio and stellar mass (e.g. Lequeux et al. 1979; Tremonti et al. 2004; Maiolino et al. 2008; Stott et al. 2013). We can also make a crude prediction for the relationship between W80,Hα and mass, under the assumption that the line width is a tracer of the stellar velocity dispersion. Therefore, for a given stellar mass, we predict the position galaxies would be located in Fig. 14 by combining: (1) the observed z = 0.7 mass–metallicity relation (following Maiolino et al. 2008) and (2) the observed mass–velocity dispersion relationship for massive galaxies (following Bezanson, Franx & van Dokkum 2015). The majority of the star-forming galaxies appear to broadly follow the expected trend. Furthermore, the measurements from the stacked average emission-line profile (Fig. 11) are in agreement with the rough mass-driven prediction for the average mass of these galaxies [i.e. log (M⋆/M⊙) = 10.3; see Fig. 14]. In contrast, the AGN typically have higher log ([N ii]/Hα) emission-line ratios and higher velocity-widths than the star-forming galaxy sample (also visible in the stacked profiles; Fig. 11) and a positive correlation is observed between these two quantities. Such a positive correlation has been shown to be a tracer of shocks and outflows in the ISM through IFS observations of AGN and star-forming galaxies (e.g. Ho et al. 2014; McElroy et al. 2015). Interestingly, the small number of star-forming galaxies with high line widths (i.e. W80 ≳ 400 km s−1) appear to follow the same relationship as the KASHz AGN, which may indicate that these galaxies also have a contribution from shocks and/or host AGN that were not detected in the X-ray surveys. We clarify that some of the AGN targets have log ([N ii]/Hα) emission-line ratios that could also be photoionized by H ii regions (see Fig. 14) and we will explore these ideas further when exploring the spatially resolved outflow kinematics and emission-line flux ratios of the KASHz AGN in future papers.


The close proximity in the sky of M 16 and M 17, two of the nearest giant HII regions of our galactic neighborhood lying at a similar distance from the Sun, naturally leads to the question of whether they are physically related, and whether they may share a common origin (Moriguchi et al. 2002; Oliveira 2008; Nishimura et al. 2017). Both giant HII regions are projected on the contour of a giant bubble-shaped structure, outlined in the distribution of HI and CO emission as first noted by Moriguchi et al. (2002). Evidence for triggered star formation in M 16 has been examined in detail by Guarcello et al. (2010), who concluded it had been induced externally, and not by the activity of its associated cluster NGC 6611. This suggests that the formation of M 16 and M 17 could have been triggered by the expansion of the bubble, powered by a previous generation of massive stars near its center, thus representing an example of triggered star formation on the scale of several tens of parsecs (Elmegreen 1998). Given the ages of the giant HII regions, the timescale of expansion of a wind-blown bubble, and the short lifetimes of massive stars, it is to be expected that the most massive members of that previous generation may have exploded as supernovae several Myr ago. The spatial dispersion of the members of the association that must have taken place progressively during its existence, combined with the distance of 2 kpc to the M 16–M 17 complex and the large number of unrelated foreground and background stars in that general direction, would make it extremely difficult to identify even its currently hottest members still remaining on the main sequence. Moriguchi et al. (2002) noted the presence of O and early B stars in the area and proposed that they were part of a massive star population responsible for having caused the bubble, but a review of their properties shows them to be generally too bright to be at the distance of the bubble and the giant HII regions, and instead are more likely members of a foreground population.


Cold gas kinematics of radio AGNs can tell us about the nature of feedback to their host galaxies. Both, radiative winds from central optical AGN, and radio jets can affect the gas kinematics in host galaxies. In this section, in order to understand the effect of both radiation and jet on gas kinematics, we compare the radio luminosity at 1.4 GHz and [O iii] λ5007 line luminosity (using the line fluxes from MPA-JHU group) for LERGs and HERGs. While radio luminosity at 1.4 GHz can be used as tracer of jet power (Cavagnolo et al. 2010), [O iii] λ5007 line luminosity can be used as a tracer for AGN bolometric luminosity (LaMassa et al. 2010). We find that there exists a weak but significant correlation (Kendall’s tau=0.4, p=2.4 × 10−16) between the radio luminosities and the [O iii] λ5007 line luminosities of LERGs (Fig. 9), which is consistent with earlier studies (Baum & Heckman 1989; Tadhunter et al. 1998), implying a common source of both luminosities. A similar correlation is noticed for HERGs but with higher [O iii] λ5007 luminosity than LERGs for a particular value of radio luminosity, which could mean the extra energy in form of wind-driven by radiation from accretion disc to cause the turbulence in host galaxy. However, in our sample of radio AGNs, while for low radio power ($P_{1.4 \rm GHz}\, \lt $ 1024.3 W Hz−1) LERGs and HERGs, there is almost no difference in distribution of centroid shifts in the absorption profiles relative to the systemic velocity, with all but one within ±200 km s−1, a larger number of intermediate radio power ($P_{1.4 \rm GHz}\, \sim$ 1024.3−1026.0 W Hz−1) LERGs show centroid velocity shifts greater than 200 km s−1 compared to HERGs. Also the range of centroid velocity shift for LERGs is wider (−479 to +356 km s−1) than HERGs. Although, we have doubled the number of detections compared to our previous analysis (Chandola & Saikia 2017), the overall number of sources with H i absorption detections for HERGs used for kinematic analysis is still small. Hence there are large statistical uncertainties to draw a firm conclusion about H i gas kinematics in HERGs as a population.


Let us first define some terminology before describing our results. “Outflow” means the flow with a positive radial velocity vr, including both “turbulent outflow” and “real outflow.” In the former case, the test particle will first move outward but will eventually return after moving outward for some distance. In the latter case, the test particle continues to flow outward and eventually escapes the outer boundary of the simulation domain. “Real outflow” consists of two components, i.e., jet and wind. The jet region is defined as the region occupied by the time-averaged magnetic field lines connected to the ergosphere (described by

r

erg

≡

r

g

+

1
−

a

2

cos

2

θ

r

g

;

 Visser 2007) of the black hole. We note that this definition coincides with other notions of the jet based on velocity and magnetization, as seen even in early two-dimensional simulations (McKinney & Gammie 2004). Moreover, turbulence tends not to have a strong effect on these field lines, so that in both individual snapshots and a time-averaged sense, the field lines connecting to the ergosphere coincide with β  2 and σ > 1 (McKinney et al. 2012, see Figures 3 and 6). Thus, the jet region is bounded by the magnetic field line whose foot point is rooted at the black hole ergosphere with θ = 90°, i.e., the boundary between the black hole ergosphere and the accretion flow (refer to the red lines in Figure 5). In this case, all magnetic field lines in the jet region are anchored to the black hole ergosphere and thus can extract the spin energy of the black hole via the Blandford & Znajek mechanism (Blandford & Znajek 1977; hereafter BZ77) to power the jet (“BZ-jet”). Real outflows outside of this boundary are powered by the rotation energy of the accretion flow, and we call them wind. Note that our definition of wind adopted here is different from that adopted in some literature, where they require that the Bernoulli parameter of wind must satisfy Be > 0. We do not add this requirement because we find that for a nonsteady accretion flow, Be is not constant along the trajectories but usually increases outward, at least to the radius within which turbulence is well developed (Yuan et al. 2015). We find that even though Be is negative at a small radius, it can become positive when it propagates outward.


The choice of κ has some bearing on the value of Mej as calculated in Eq. (2). Although taken as a constant in various model light curves, the actual optical opacity varies with time (e.g. Chugai 2000; Nagy 2018), but tests have shown that that a constant opacity can be a reasonable assumption at early times (see Mazzali et al. 2000; Taddia et al. 2018). SN 2019bkc is a H/He-deficient SN, so to select an appropriate value for κ, we search the literature literature and consider only SNe of this type. For SNe Ia, where the large abundance of Fe-group elements is a source of significant opacity, Cappellaro et al. (1997) used κ = 0.15 cm2 g−1, while Arnett (1982) used κ = 0.08 cm2 g−1. The light curve of the broad lined SNe Ic 1997ef was modelled in Mazzali et al. (2000) using the same code as Cappellaro et al. (1997), this time a lower constant opacity of 0.08 cm2 g−1 was used owing to the lower Fe abundance in this SN type. The average opacity of model CC-SNe light curves was investigated by Nagy (2018), where it was found that κ = 0.1 cm2 g−1 was suitable for their H/He-deficient models. Taddia et al. (2018) demonstrated that fitting the light curves of H-deficient CC-SNe with a simple analytical model and a constant opacity κ = 0.07 cm2 g−1 returned physical parameters consistent with more complex hydrodynamic light curve models. Prentice et al. (2019) also found that using κ = 0.07 cm2 g−1 gave comparable ejecta masses to both photospheric phase and nebular phase spectroscopic modelling of H-deficient CC-SNe, with the exception of some gamma-ray burst SNe. From Sect. 5 we find that the outer ejecta is not rich in Fe-group elements, and there is no indication of helium. From the early-nebular spectra in Sect. 4.2 we see no indication of strong Fe II or Fe III line emission, demonstrating that the ejecta is poor in Fe-group elements relative to normal SNe Ia and is more like H/He-deficient CC-SNe. This justifies the use of κ = 0.07 cm2 g−1, but to show the range of possible Mej, we consider the range 0.07–0.1 cm2 g−1.


The Planck cosmic microwave background (CMB) mission (Planck Collaboration I 2011) has for the first time allowed us to retrieve all-sky maps (Hill & Spergel 2014; Planck Collaboration XXII 2015; Khatri 2016) of the Sunyaev-Zeldovich (SZ) effect (Zeldovich & Sunyaev 1969). The chief advantage of Planck over other past and current satellite and ground-based missions is its multiple frequency channels covering the low-frequency Rayleigh–Jeans as well as the higher frequency Wien region of the CMB spectrum making the separation of the thermal SZ from CMB and foregrounds feasible. As the blackbody photons from the CMB interact with hot intergalactic/intracluster medium (ICM) travelling from the last scattering surface (Peebles & Yu 1970; Sunyaev & Zeldovich 1970) to us, Compton scattering upscatters a fraction of photons to higher energy creating a distortion from the Planck spectrum $I_{\nu }^{\rm Planck}$ (Sunyaev & Zeldovich 1972). The change in the intensity $\Delta I_{\nu }=I_{\nu }-I_{\nu }^{\rm Planck}$ of the CMB radiation is given by (Zeldovich & Sunyaev 1969)

(1)

\begin{eqnarray}
\Delta I_{\nu }=y\frac{2 h\nu ^3}{c^2}\frac{x e^x}{(e^x-1)^2}\left[x\left(\frac{e^x+1}{e^x-1}\right)-4\right],
\end{eqnarray}

where $x=\frac{h\nu }{{{k_{\rm B}}}T}$, T = 2.725(1 + z) is the CMB temperature at redshift z, ν = ν0(1 + z) is the frequency of CMB photon at redshift z, ν0 is the observed frequency today (z = 0), h is the Planck constant, kB is Boltzmann constant and c is the speed of light. The amplitude of the distortion, y, is proportional to the integral of the pressure P along the line of sight,

(2)

\begin{eqnarray}
y=\frac{{{\sigma _{\rm T}}}}{{{m_{\rm e}}}c^2} \int {{\rm d}}s\, {{n_{\rm e}}}{{k_{\rm B}}}{{T_{\rm e}}},
\end{eqnarray}

where Te and ne are the electron temperature and electron number density, respectively, in the ICM plasma, me is the mass of the electron, σT is the Thomson scattering cross-section, and s is the distance coordinate along the line of sight.


As expected, the orbital parameters obtained from this fit are fully consistent with those reported in Table 1, since the long baseline of the data set guarantees to clearly disentangle orbital phase modulation from and phase variation due to the NS spin frequency changes. From the best-fitting parameter of each frequency phase component we infer the dipolar magnetic moment μF ≃ 4.1(4) × 1026 and μ1h ≃ 4.1(5) × 1026 G cm3, for the fundamental and the first harmonic, respectively. Adopting the Friedman-Pandharipande-Skyrme (FPS) equation of state (see e.g. Friedman & Pandharipande 1981; Pandharipande & Ravenhall 1989) for a 1.4 M⊙ NS, we estimate an NS radius of R = 1.14 × 106 cm, and a moment of inertia I ≃ 1.45 × 1045 g cm2. This corresponds to an equatorial magnetic field of Beq = μ/R3 = 2.8(3) × 108 ≃ 2.8(3) × 108 G. This value is consistent both with the estimation reported in Sanna et al. (2018d) from spin frequency equilibrium considerations for the X-ray pulsar, and the average magnetic field of known AMXPs (Mukherjee et al. 2015). It is noteworthy that the value of Beq obtained here is likely overestimated due to a non-accurate estimation of mass accretion rate in case of spin-down regime. In fact, as discussed by Kluźniak & Rappaport (2007), in this regime the angular momentum deposited in the disc by the pulsar torques leads to a substantial additional dissipation of energy in the disc, hence, the mass accretion rate estimated from equation (17) results on an upper limit of the quantity. However, since it is not quite clear what fraction of this additional dissipation of energy is released in non-thermal process and what is kept inside the disc, it is complicated to quantify the discrepancy. We started approaching the problem considering the worst case scenario at which the whole spin-down luminosity of the pulsar $I\omega \dot{\omega }$ is transferred and released by the accretion disc. With this hypothesis, we subtract the rotation luminosity from observed luminosity in equation (17) and we then fitted the frequency phase delays. We obtained that, taking into account the correction on the mass accretion rate, the NS magnetic field decreases roughly by 15 per cent, reaching the value Beq = 2.4(4) × 108 G. Both the properties of the source during the outburst and the magnetic field estimation obtained from the studies of the spin-down like behaviour of the phase delays do not seem to suggest IGR J17591–2342 as an exception among the AMXPs.


A current topic of active debate is to what extent galaxies are affected by the assembly history of their host halos. The stochasticity in the complex baryonic physics may act to erase the record of halo assembly history. If, however, the galaxy properties closely correlate with the halo formation history, this would lead to a dependence of the galaxy content on large-scale environment and a corresponding clustering signature. This effect has commonly been referred to as galaxy assembly bias both colloquially and in the literature, and we adopt this distinction here. We stress, however, that what is referred to here is the manifestation of halo assembly bias in the galaxy distribution. The predictions for galaxy assembly bias have been explored with simulated galaxies (Zhu et al. 2006; Croton et al. 2007; Reed et al. 2007; Zu et al. 2008; Zentner et al. 2014; Chaves-Montero et al. 2015; Bray et al. 2016; Romano-Diaz et al. 2017). Detecting (galaxy) assembly bias is much more challenging since halo properties are not directly observed. Observational studies of assembly bias have generally produced mixed results. There have been several suggestive detections in observations (Berlind et al. 2006; Yang et al. 2006; Tinker et al. 2008b, 2017b; Wang et al. 2008, 2013b; Cooper et al. 2010; Lacerna et al. 2014a; Hearin et al. 2015; Watson et al. 2015; Miyatake et al. 2016; Saito et al. 2016; Zentner et al. 2016; Montero-Dorta et al. 2017; Tojeiro et al. 2017), while numerous other studies indicate the impact of assembly bias to be small (Abbas & Sheth 2006; Blanton & Berlind 2007; Croton & Farrar 2008; Tinker et al. 2008a, 2011; Deason et al. 2013; Lacerna et al. 2014b; Lin et al. 2016; Vakili & Hahn 2016; Zu & Mandelbaum 2016; Dvornik et al. 2017). The situation is further complicated as various systematic effects can mimic the effects of assembly bias (e.g., Campbell et al. 2015; Zu et al. 2016; Busch & White 2017; Lacerna et al. 2017; Sin et al. 2017; Tinker et al. 2017a; Zu & Mandelbaum 2017) and the evidence for assembly bias to date remains inconclusive and controversial.


In order to separate the role of different physical mechanisms in galaxy evolution, a number of studies have constrained stellar-to-halo mass (SHM) relations and ratios as a function of time using the abundance matching technique (e.g. Behroozi, Conroy & Wechsler 2010a; Moster et al. 2010; Behroozi, Conroy & Wechsler 2010b), the conditional luminosity function technique proposed by Yang, Mo & Van Den Bosch (2003), the halo occupation distribution (HOD) formalism (e.g. Berlind & Weinberg 2002; Kravtsov et al. 2004; Moster et al. 2010), and by combining the HOD, N-body simulations, galaxy clustering, and galaxy–galaxy lensing techniques (e.g. Leauthaud et al. 2012; Coupon et al. 2015). Distinguishing the properties of central galaxies from those of satellite galaxies in studies based only on the distribution of luminosity or stellar mass is challenging (e.g. George et al. 2011). By combining several observables and techniques (e.g. HOD, galaxy–galaxy lensing, and galaxy clustering) one can probe a global SHM relation for central galaxies and satellite galaxies (e.g. Leauthaud et al. 2012; Coupon et al. 2015). Coupon et al. (2015), for example, used multiwavelength data of ∼60 000 galaxies with spectroscopic redshifts in the Canada France Hawaii Telescope Lensing Survey (CFHTLenS) and Vimos Public Extragalactic Redshift Survey (VIPERS) field to constrain the relationship between central/satellite mass and halo mass, characterizing the contributions from central and satellite galaxies in the SHM relation. In this paper, we directly identify the BGGs using their precise redshifts and estimate stellar masses using the broad-band spectral energy distribution (SED) fitting technique (Ilbert et al. 2010) as used by Coupon et al. (2015). We utilize the advantages of the X-ray selection of galaxy groups and a wealth of multiwavelength, high signal-to-noise ratio observations such as the UltraVISTA survey in the COSMOS field (Laigle, Capak & Scoville 2016) to investigate the SHM relation for the central galaxies over 9 billion years. We aim to quantify the intrinsic (lognormal) scatter in stellar mass at fixed redshift in observations and compare them to the recently implemented semi-analytic model (SAM) by Henriques et al. (2015).


The nonaxisymmetric potential of a bar induces large-scale streaming motions in stars and gas into the central part of the galaxy (e.g., Athanassoula 1992a, 1992b; Sellwood & Wilkinson 1993). Being dissipative, the gas loses angular momentum and energy and flows inward toward the galactic center (Knapen etÂ al. 1995; Regan etÂ al. 1999; Sheth etÂ al. 2000, 2002), accumulating in the central â¼1Â kpc of galaxies (e.g., Sakamoto etÂ al. 1999; Sheth etÂ al. 2005). The accumulation of gas in the central parts leads to high levels of circumnuclear star formation activity (SÃ©rsic & Pastoriza 1965; Hawarden etÂ al. 1986; Devereux 1987; Martin 1995; Ho etÂ al. 1997; Sheth etÂ al. 2000, 2005; Gadotti & dos Anjos 2001; Ellison etÂ al. 2011; Coelho & Gadotti 2011; Wang etÂ al. 2012); this circumnuclear star formation is often in the shape of nuclear rings (Knapen etÂ al. 2002; ComerÃ³n etÂ al. 2010; Kim etÂ al. 2012; Seo & Kim 2013) and nuclear star clusters (BÃ¶ker etÂ al. 2002, 2004, 2011). Such star formation activities may help to create disky pseudobulges (Kormendy & Kennicutt 2004; Sheth etÂ al. 2005; Athanassoula 2005; Debattista etÂ al. 2006). Bars are the primary mechanism for transporting gas from a few kiloparsec scale to the central kiloparsec. However, there have been mixed answers to the question of whether the presence of a bar and active galactic nucleus (AGN) activity are connected. Some studies find weak statistical links among AGN activity and the presence of bars (e.g., Arsenault 1989; Knapen etÂ al. 2000; Laine etÂ al. 2002; Laurikainen etÂ al. 2004a; Coelho & Gadotti 2011), whereas others find little or no link (e.g., Moles etÂ al. 1995; McLeod & Rieke 1995; Mulchaey & Regan 1997; Ho etÂ al. 1997; Hunt & Malkan 1999; Martini etÂ al. 2003; Lee etÂ al. 2012; Cisternas etÂ al. 2013). While bar torques drive gas inside the bar corotation inward, they push the gas between the corotation and outer Lindblad resonance (OLR) outward (Combes 2008; Kubryk etÂ al. 2013).


Cygnus A, at z = 0.0562, is 10 times closer than the next radio galaxy of similar radio luminosity.4

4
Radio luminosity >1045 erg s−1.
 The nuclear regions in Cygnus A have been observed extensively at radio through X-ray wavelengths (Carilli & Barthel 1996). The inner few arcseconds is a complex mix of optically obscuring dust clouds (Vestergaard & Barthel 1993; Whysong & Antonucci 2004; Lopez-Rodriguez et al. 2014; Merlo et al. 2014), atomic gas seen in narrow line emission (Stockton et al. 1994; Taylor et al. 2003), H i 21 cm absorption toward the inner radio jets, with a neutral atomic column density >1023 cm−2, depending on H i excitation temperature (Struve & Conway 2010), polarized, broad optical emission lines due to scattering by dust (Antonnuci et al. 1994; Ogle et al. 1997), and a highly absorbed hard X-ray spectrum with a total gas column density of ∼3 × 1023 cm−2 (Ueno et al. 1994; Reynolds et al. 2015). VLBI radio observations at 0.05 mas resolution reveal highly collimated jets originating on scales ∼200 times the Schwarzschild radius (Boccardi et al. 2016). Tadhunter et al. (2003), derive a black hole mass of 2.5 ± 0.7 × 109 M⊙ from HST and Keck spectroscopy of Pa-α and [O iii], and conclude that Cygnus A contains an AGN with a bolometric luminosity of order 1046 erg s−1, comparable to high redshift quasars (Runnoe et al. 2012). This AGN is highly obscured in the optical due to dust along our line of sight, with Av > 50 magnitudes, based on near-IR spectroscopy (Imanishi & Ueno 2000). Studies of the mid- to far-IR spectral and polarization properties have led to a model of a clumpy, dusty torus obscuring the AGN in Cygnus A, with a radius of at least 130 pc, although these conclusions are based on spatially integrated properties; these observations did not have the spatial resolution to resolve the torus, and hence are partially contaminated by emission from the radio core-jet (Privon et al. 2012; Lopez-Rodriguez et al. 2018).


The mass accretion onto the black hole is important for a better understanding of AGN evolution. The Eddington ratio, the ratio between the AGN bolometric luminosity and the Eddington luminosity (Lbol/LEdd), provides insight into the black hole growth because the bolometric luminosity reflects the mass accretion rate. We show AGN bolometric luminosity versus black hole mass for our sample of broad-line AGNs in the different redshift bins in the left panel of Figure 5. The different X-ray surveys are shown with different symbols as labeled. The dotted reference lines indicate constant Eddington ratios of 1, 0.1, 0.01, and 0.001. Our sample of broad-line AGNs covers the black hole mass range 7.0  log MBH/M⊙  9.5 and the bolometric luminosity range 43  log Lbol  47 with a wide dispersion in the Eddington ratio distribution. For comparison, we show published observations in the same redshift range from the literature in the right panel of Figure 5 (Gavignaud et al. 2008; Merloni et al. 2010; Shen et al. 2011; Nobuta et al. 2012; Matsuoka et al. 2013). The SDSS quasar sample (gray points; Shen et al. 2011) is limited to the high-mass and high-luminosity regime because the SDSS detection limit corresponds to a luminosity of log Lbol ∼ 46 at z ∼ 1. Compared to the SDSS quasar sample, our sample of broad-line AGNs shows a wider dispersion in the black hole mass, AGN bolometric luminosity, and Eddington ratio distribution, consistent with previous studies on deep AGN samples (Gavignaud et al. 2008; Merloni et al. 2010; Nobuta et al. 2012; Matsuoka et al. 2013), which fill in the low-mass and low-luminosity region. The figure shows contours at the 1σ level, together with the literature data, except the SDSS quasar sample. The figure also reveals that only a small number of AGNs exceed the Eddington limit by a small amount. AGNs with similar black hole masses show a broad range of bolometric luminosities spanning about two orders of magnitude, indicating that the accretion rate of black holes is widely distributed. This suggests that the AGN cosmic downsizing phenomenon could be explained by some more-massive black holes with low accretion rates, which are relatively fainter than less-massive black holes with efficient accretion. Lusso et al. (2012) suggest that AGNs show higher Eddington ratios at higher redshift at any given MBH, and the Eddington ratio increases with bolometric luminosity. We confirm that there is a tendency for low-luminosity AGNs (log Lbol ≲ 45.5) with less-massive black holes (log MBH/M⊙ ≲ 8) to have lower Eddington ratios than high-luminosity AGNs (log Lbol ≳ 45.5) with massive black holes (log MBH/M⊙ ≳ 8), consistent with Lusso et al. (2012). It is important to note that, when comparing with results in the literature, one should take into account the different methods of spectral line fitting and correction for bolometric luminosities. Nevertheless, they show similar distributions of the accretion rate of black holes over a wide range, consistent with previous studies.


Recently, rotationally supported disks have been found not only in Class I sources but also in some Class 0 sources (e.g., Murillo et al. 2013; Yen et al. 2013, 2017; Ohashi et al. 2014; Tobin et al. 2015, 2016b, 2016a; Seifried et al. 2016; Aso et al. 2017; Lee et al. 2017; Okoda et al. 2018). In spite of these extensive studies, there is still controversy regarding when and how a disk structure is formed around a newly born protostar. Moreover, the disk formation process has been revealed to be much more complicated for binary and multiple cases, both in observations (Dutrey et al. 2014; Tokuda et al. 2014; Takakuwa et al. 2014, 2017; Tobin et al. 2016b, 2016a; Boehler et al. 2017; Artur de la Villarmois et al. 2018; Alves et al. 2019) and in numerical simulations (e.g., Bate & Bonnell 1997; Kratter et al. 2008; Fateeva et al. 2011; Shi et al. 2012; Ragusa et al. 2017; Satsuka et al. 2017; Price et al. 2018; Matsumoto et al. 2019). For instance, circumbinary/circummultiple disk structures with a spiral structure as well as a circumstellar disk for each component are reported (e.g., Tobin et al. 2016a; Takakuwa et al. 2017; Artur de la Villarmois et al. 2018; Matsumoto et al. 2019; Alves et al. 2019). In addition, it is not clear how molecules are processed during the disk formation process and what kinds of molecules are finally inherited by protoplanetary disks and potentially by planets. Understanding these processes is crucial, as they will provide important constraints on the initial physical and chemical conditions for the planetary system formation study. In this context, physical and chemical structures and their mutual relation for disk-forming regions of low-mass protostellar sources have been investigated with the Atacama Large Millimeter/submillimeter Array (ALMA; e.g., Sakai et al. 2014b, 2014a; Oya et al. 2016, 2017, 2018, 2019; Imai et al. 2016, 2019; Jacobsen et al. 2019). These studies reveal that infalling envelopes and rotationally supported disks are not smoothly connected to each other either in physical structure or in chemical composition, unlike previous expectations.


For confined flares, the key question is the factor determining their confined character. Wang & Zhang (2007) analyzed eight X-class flares and found that confined events occur closer to the magnetic center and eruptive events tend to occur close to the edge of active regions (ARs), implying that the strong external field overlying the AR core is probably the main reason for the confinement. Similar results have been found by Baumgartner et al. (2018) based on a statistical analysis of 44 flares during 2011–2015. Amari et al. (2018) suggested that the role of the magnetic cage crucially affects the class of eruption—either confined or eruptive. To date, many studies have drawn the consistent conclusion that the decay index of the potential strapping field determines the likelihood of ejective/confined eruptions (Green et al. 2002; Shen et al. 2011; Yang et al. 2014; Chen et al. 2015; Thalmann et al. 2015; Li et al. 2018a). Previous studies showed that the torus instability of a magnetic FR occurs when the critical decay index reaches 1.5 (Bateman 1978; Kliem & Török 2006). Zuccarello et al. (2015) performed a series of numerical magnetohydrodynamics (MHD) simulations of FR eruptions and found that the critical decay index for the onset of the torus instability lies in the range 1.3–1.5. Another factor determining whether a flare event is CME-eruptive or not is the non-potentiality of ARs including the free magnetic energy, relative helicity, and magnetic twists (Falconer et al. 2002, 2006; Nindos & Andrews 2004; Tziotziou et al. 2012). Sun et al. (2015) suggested that AR eruptiveness is related to the relative value of magnetic non-potentiality over the constraint of a background field. However, in the statistical study of Jing et al. (2018), the unsigned twist number of a magnetic FR plays little role in differentiating between confined and ejective flares, and the decay index of the potential strapping field above the FR discriminates them well.


The bolometric luminosity is then computed as the sum of the disc luminosity and the 2–10 keV X-ray luminosity. The λEdd, given by λEdd = Lbol/LEdd, as a function of the MBH is plotted on the central panel of Fig. 5, while the λEdd distribution is shown in the horizontal histogram. Fig. 12 shows the 2–10 keV X-ray bolometric correction ($\kappa _{\rm 2{\rm -}10\,keV}=L_{\rm bol}/L_{\rm 2{\rm -}10\,keV}$) versus Lbol (left-hand panel) and the λEdd (right-hand panel). Tight correlations between the $\kappa _{\rm 2{\rm -}10\,keV}$ and Lbol (Pearson correlation coefficient r = 0.71) as well as the λEdd (Pearson correlation coefficient r = 0.78) are found in our sample as clearly shown in Fig. 12. A similar trend, that the sources with higher bolometric luminosities have higher bolometric corrections, was found in Lusso et al. (2012). A relation between the $\kappa _{\rm 2{\rm -}10\,keV}$ and λEdd is also found in several previous works (Vasudevan & Fabian 2007, 2009; Vasudevan et al. 2009; Lusso et al. 2012). The tight $\kappa _{\rm 2{\rm -}10\,keV}{\rm -}L_{\rm bol}$ relation shown in Fig. 12 as well as the correlation between $\kappa _{\rm 2{\rm -}10\,keV}$ and λEdd, rather than intrinsic, can however be a natural outcome of our flux-limited sample, which will lead to a correlation between the monochromatic optical luminosity Lmon,opt and the X-ray luminosity $L_{\rm 2{\rm -}10\,keV}$. We tested the significance of the correlation by means of simulations. We generated a sample which the log N − log S of both the X-ray and optical flux follows a power-law form, and has a redshift distribution similar to our AGN sample. We then applied the flux cut-off, f0.5–10 keV > 1 × 10−15 erg s−1 cm−2 and R4681  22 mag, on the simulated sources. Using the Lmon,opt and $L_{\rm 2{\rm -}10\,keV}$ of the simulated data we obtain a Pearson correlation coefficient value r of ∼0.57, which is smaller than the correlation coefficient found in the observed data (r ∼ 0.71). Thus the observed correlations in our sample should not be purely due to the selection bias. This result is also consistent with the conclusion that the strong correlation between the monochromatic UV luminosity at 2500Å and the X-ray luminosity at 2 keV is independent of redshift (Risaliti & Lusso 2015). The distributions of the Lbol and $\kappa _{\rm 2{\rm -}10\,keV}$ are shown in the left-hand panel of Fig. 12 (top panel: Lbol, right-hand panel: $\kappa _{\rm 2{\rm -}10\,keV}$). The $\kappa _{\rm 2{\rm -}10\,keV}$ found in our sample, with a mean value of ∼18, are consistent with the values found in previous works (e.g. Vasudevan & Fabian 2007; Lusso et al. 2012).


The deconvolution of large galaxy survey images requires that the spatial variation of the point spread function (PSF) across the field of view is taken into account. The PSF field is usually estimated beforehand through parametric models and simulations as in Krist et al. (2011) or is directly estimated from the (noisy) observations of stars in the field of view (Bertin 2011; Kuijken et al. 2015; Zuntz et al. 2018; Mboula et al. 2016; Schmitz et al. 2020). Even when the PSF is known perfectly, this ill-posed deconvolution problem is challenging, in particular because of the size of the image that is to be processed. Starck et al. (2000) proposed an object-oriented deconvolution that consists of first detecting galaxies and then deconvolving each object independently, taking the PSF at the position of the center of the galaxy into account (but not the variation in the PSF field at the galaxy scale). Following this idea, Farrens et al. (2017) introduced a space-variant deconvolution approach for galaxy images that is based on two regularization strategies: using either a sparse prior in a transformed domain (Starck et al. 2015a), or trying to learn without supervision a low-dimensional subspace for galaxy representation using a low-rank prior on the recovered galaxy images. When a sufficient number of galaxies were processed jointly (more than 1000), the authors found that the low-rank approach provided significantly lower ellipticity errors than sparsity. This illustrates the importance of learning adequate representations for galaxies. To proceed in learning, supervised deep-learning techniques that use databases of galaxy images might be employed to learn complex mappings that might regularize our deconvolution problem. Deep convolutional architectures have also proved to be computationally efficient in processing large numbers of images when the model has been learned. They are therefore promising in the context of modern galaxy surveys.


Major differences between our approach and a full re-calculation of the hydrodynamics were not expected since the changes in the 14N and 22Ne abundances at the different metallicities do not alter the energy release in the hydrodynamic simulations significantly. The situation is different for deflagrations where the buoyancy, and therefore the Rayleigh-Taylor instabilities, depend on Ye. In contrast to detonations, the propagation of a deflagration front is thus affected by the metallicity (e.g., Meakin et al. 2009). The assumption we made here is confirmed by the comparison of the models presented in Table 1. Model M2a is taken from Gronow et al. (2020). The model was calculated at zero metallicity and has a total mass of 1.05 M⊙ with a He shell of 0.07 M⊙ at He ignition. Model M10_05_1, on the other hand, has a similar mass configuration, though it was calculated at solar metallicity (Model M10_05 in Gronow et al. 2021). Model M2a_pp is the same model as Model M2a, but the postprocessing step was calculated with solar metallicity instead of zero metallicity. An inspection of the abundances of Models M2a_pp and M10_05_1 at t = 100 s after He detonation ignition shows that the results of the postprocessing step with varying metallicities are in reasonably good agreement with a full re-calculation of the hydrodynamic model. The maximum difference in the yields produced in the core detonation is only 10%, while the maximum difference is 50% in the He detonation (excluding 12C in both). However, differences in the yields produced in the He detonation can in part be attributed to the slightly different setups of Model M2a (and therefore Model M2a_pp) and Model M10_05_1 at the beginning of the relaxation simulation, with the differences in the total and shell masses being less than 1% (see Gronow et al. 2021 for an explanation of the difference). Generally, the contribution of the yields from the He detonation to the total nucleosynthetic yields are small compared to those of the core detonation. Our approach is thus sufficient to derive nucleosynthetic yields for GCE studies. It saves significant computational costs as additional 3D hydrodynamical simulations of the explosion do not need to be carried out. Nevertheless, there might be slight differences visible in the observables because they are sensitive to the products of the He shell detonation (Höflich et al. 1996; Nugent et al. 1997; Kromer et al. 2010).


The coronal rain plasma can be distinguished from the prominence material by looking at their trajectories and average speeds. The timescale on which the coronal rain forms following the heating onset is much shorter than for the quiescent scenario; in the studied event condensations appear 10 min after the reconnection event, whereas observations of quiescent rain suggests it recurs in the same loop of the order of hours (Antolin & Rouppe van der Voort 2012; Kohutova & Verwichte 2016). The period of the loop heating-condensation cycle in the quiescent scenario is equivalent to the time it takes for the sustained footpoint heating to refill the loop sufficiently with evaporated plasma to reach the thermally unstable regime, after the loop has been evacuated by the previous coronal rain event. This short timescale for coronal rain formation is likely a consequence of the heating input being much greater than in the quiescent case and of the short length of the studied loop. The 1D numerical simulations suggest that although the loop length is a contributing factor, the heating input is the main factor affecting the coronal rain formation timescale (Froment et al. 2018). The thermal instability in the case associated with magnetic reconnection is also more concentrated spatially and only a certain fraction of the loop with a cross section of around 5 Mm width becomes unstable. This implies that the heating that triggers the thermal instability is more localised and only affects a small number of field lines in the loop. As the thermal conduction acts predominantly along the magnetic field, most of the matter and energy transport occurs along the affected field lines. Comparing this to the quiescent scenario, the typical width of the loop bundles observed to undergo condensation formation is around 10−15 Mm (Antolin & Rouppe van der Voort 2012; Kohutova & Verwichte 2016), and in some cases, reaching 40 Mm (Auchère et al. 2018; Froment et al. 2019).


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.


One of the most intriguing results from RV surveys is the observed scarcity of relatively close-in (a ≲ 0.5 AU) planets around post-MS stars. This observational trend has been attributed to the strong tidal torque exerted by the star as its radius grows during the giant phase. As a result, planets are expected to lose orbital angular momentum, thus moving inward until they are evaporated in the stellar atmosphere (Livio & Soker 1983; Sato et al. 2008; Villaver & Livio 2009; Kunitomo et al. 2011). On the other hand, the majority of the giant stars targeted by RV surveys are intermediate-mass stars (M⋆ ~ 1.5–3.0 M⊙), thus they are the post-MS counterpart of A and early F main-sequence stars. Therefore, their companions should not be directly compared to those orbiting solar-type stars. Based on this analysis, known planets orbiting field giant stars are expected to be born in different conditions from those around low-mass stars. In particular, these planets are formed in more massive disks (since Md ∝ M⋆; Andrews et al. 2013), from which they can efficiently accrete a significant amount of gas, becoming gas giants (e.g., Kennedy & Kenyon 2008). In addition, due to the higher gas accretion rate (Muzerolle et al. 2005) and higher irradiation, these disks have shorter dissipation timescales (Currie 2009; Kennedy & Kenyon 2009) and the snow line is located at a greater distance from the central star (Kennedy & Kenyon 2008). As a consequence, these planets are most likely formed at greater orbital distances and, due to the shorter disk timescale, inward migration is halted; they thus reach their final position at a relatively large distance from the parent star. For comparison, Currie (2009) predicted that only ~1.5% of intermediate-mass stars host giant planets with a ≲ 0.5 AU, while ≳7.5% of them host at least one gas giant at a ≳ 0.5 AU. Fig. 9 shows the mass versus the orbital distance of planets detected around giant stars (log g ≲ 3.5), via RV measurements (black dots) and by the transit method (red open circles). We note that values of the RV detected systems correspond to the minimum planet mass (Mp sini). The dotted line represents a radial velocity semi-amplitude of K = 30 m s−1 for a 1.5 M⊙ star, (corresponding to a 3-σ detection; e.g., Hekker et al. 2006). As can be seen, there is only one companion detected via RVs interior to 0.1 AU, and the rest of them reside at an orbital distance a ≳ 0.4 AU. As discussed above, this observational result might be explained by the engulfment of the innermost planets as the parent star evolves off the MS and becomes a giant star. However, since a similar trend is observed in less evolved subgiants whose radii have not yet reached a value where tidal interactions are strong enough to affect the orbits of their companions, Johnson et al. (2007) argued that this is probably explained by a different formation scenario between planets around low-mass stars and those formed in more massive disks. From Fig. 9 it is also evident that planets residing interior to ~0.1 AU are significantly less massive (Mp ≲ 1 MJ) than those orbiting at a greater distance. In fact, two of these transiting planets are well below the 3-σ detection threshold, thus they are not detectable via radial velocities. A similar trend is also observed in MS stars (Zucker & Mazeh 2002), which might be caused by a decrease in the type II migration speed with increasing planetary mass, i.e., d a∕dt ∝ M

$_P^{-1}$
P−1
 (Mordasini et al. 2009). This theoretical prediction naturally explains why the most massive planets are found at a ≳ 0.4 AU. On the other hand, the mass distribution of the parent stars of these two populations of planets are different. While the mean stellar mass of the RV detected planets is 1.78 M⊙, this value is only 1.38 M⊙ for the transiting systems and thus two distinct planet mass distributions are expected to be found. Moreover, a similar result is observed between the mass of planets orbiting subgiant and giant stars (planets around giant stars being significantly more massive than those around subgiants; see Jones et al. 2014). In fact, the mean mass of the subgiant parent stars is 1.5 M⊙, significantly lower than giant host stars. These results provide further observational support of a different formation and migration scenario for planets at different host star mass. This result suggest that the observed lack of planet around giant stars is mainly due to the primordial distinct formation scenario proposed by Johnson et al. (Johnson et al. (2007)).


The dynamical interaction with a companion is proposed to be the driving force behind most features seen in transition discs including the formations of dust traps. For our RC-TDs, van der Marel et al. (2015a, 2016a, 2018) showed gas cavities inside dust cavities for SR21, HD135344B, DoAr44, J1604, Sz111, J16083070. van der Plas et al. (2019) utilized SPH and radiative transfer codes to show some disc features seen in HD100453 can be attributed to an undetected, low mass close companion within the disc’s cavity. The study of HD100453 is further refined by Gonzalez et al. (2020) and Nealon et al. (2020), who show that while the outer disc morphology can be caused by a companion star on an inclined orbit exterior to the disc, the inner cavity can be explained by a $\rm \lesssim 5$ MJ planet, less massive than previously suggested (van der Plas et al. 2019), at 15–20 au. Using similar 1D radial brightness profiles for the majority of our sources (HD135344B, RY Lup, J1608, Sz111, SR24S, and DoAr44), Pinilla et al. (2017, 2018) suggest that the clearing of the inner cavity could be attributed to the dynamical interaction with an embedded planet. For HD169142, Fedele et al. (2017) uses a thermo-chemical code to model the gas and dust distribution. Their results suggest that dynamical interaction between the disc and two giant embedded planets results in the depletion of the inner disc and creates two pressure bumps that aid in the trapping of dust at each observable ring position. It still remains unclear for the majority of transition discs if a companion is indeed responsible for the formation of the cavity, whether this companion is an embedded planet or a binary star. What is notable about our sample is that for the RC-TDs the 8.8 mm and sub-mm grains share a similar cavity size ($\rm R_{peak}$ value). This is also seen in SR24S and HD142527 (included in Fig. 4). Pinilla et al. (2019) present a planet-disc model for SR24S that predicts both mm and sub-mm grains will share a similar radial peak in the dust density. Price et al. (2018) extensively modelled HD142527 with 3D hydrodynamical simulations considering several possible orbits for the M-dwarf binary companion presented in Lacour et al. (2016). They conclude that all the observable disc features can be attributed to the tidal truncation of the disc from the binary companion. Given that our RC-TDs and HD142527 follow the one-to-one correlation shown in Fig. 4, we suggest similar physical mechanisms affecting the grain evolution for these discs may have occurred.


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).


However, the intrinsic effects caused by the unknown emission and acceleration mechanisms in the source could mitigate or enhance the LIV-induced time delay, which would impact the accuracy of the resulting constraints on LIV. A key challenge is then to distinguish an intrinsic time lag at the source from a delay induced by LIV. Long GRBs usually have significantly positive or negative intrinsic spectral lags and should not be used for LIV searches until reasonable progress is made on the modeling of the emission and acceleration mechanisms (Chen et al. 2005; Ukwatta et al. 2012; Bernardini et al. 2015), while short GRBs are consistent with null or negligible intrinsic spectral lag and are therefore an ideal tool to measure the LIV effect (Norris & Bonnell 2006; Bernardini et al. 2015, 2017; Xiao et al. 2022). Currently, in addition to short GRBs, active galactic nucleus (AGN) flares and gamma-ray pulsars are two other classes of astrophysical sources that have no significant intrinsic lag in general and are often used for LIV tests (Biller et al. 1999; Kaaret 1999; Aharonian et al. 2008; MAGIC Collaboration et al. 2017). It should be noted, however, that there is also evidence of intrinsic lags in some cases of AGN flares and pulsars. For example, MAGIC Collaboration during an observational campaign regarding Mkn 501 blazar found an indication of about 4 minutes time delay between the peaks at E  0.25 TeV and E > 1.2 TeV (MAGIC Collaboration et al. 2008), which may indicate a progressive acceleration of electrons in the emitting plasma blob. A robust method to study the correlations between arrival times and energy, based on a likelihood function built from the physical picture assumed for the emission, propagation, and detection of the photons was proposed by Martínez & Errando (2009). In the case of pulsars, there are some lags if the energy range is extended too much toward low energies (e.g., radio versus TeV). No real progress on the topic of intrinsic effects will be made without accurate models for production and acceleration mechanisms for each type of source. Perennes et al. (2020) first attempted to gain knowledge on source-intrinsic spectral lags of flaring AGNs at high and very high energies and on short timescales relevant for LIV searches, using leptonic AGN flare modeling. Concerning GRBs, some ways have been proposed to reduce the impact of intrinsic effects, e.g., fitting the observed spectral lags of statistical samples of GRBs at a range of different redshifts (Ellis et al. 2006; Bernardini et al. 2017; Xiao et al. 2022), or using only a limited observer-frame energy bands range corresponding to the fixed source-frame energy bands (Wei & Wu 2017). Anyway, there is no reason to think that the low and high-energy photons should be emitted simultaneously at the source, and while detecting distinct signals at different energy channels, we have no idea which one was sent first. Previous studies usually assumed that the intrinsic time delays are either an unknown constant for all GRBs considered or scale with the photon energy E according to some power-law function (Ellis et al. 2006; Biesiada & Piórkowska 2009a; Zhang & Ma 2015; Wei et al. 2017a; Acciari et al. 2020; Pan et al. 2020; Du et al. 2021).


Diffusion plays a significant role in the transport of charged, energetic particles in the heliosphere, whether these be galactic cosmic rays (e.g., Engelbrecht 2019; Shen et al. 2019; Moloto & Engelbrecht 2020), solar energetic particles (e.g., Strauss et al. 2017; van den Berg et al. 2021), or Jovian electrons (e.g., Ferreira et al. 2001; Vogt et al. 2020). As such, the diffusion of such particles parallel and perpendicular to the heliospheric magnetic field (HMF) has attracted considerable interest over the years, with various theoretical models for these quantities being proposed, ranging from the quasilinear theory (QLT) of Jokipii (1966), to the nonlinear guiding center (NLGC) theory of Matthaeus et al. (2003) and various recent theories (see, e.g., Shalchi 2010; Ruffolo et al. 2012; Qin & Zhang 2014), which have in turn been applied in various particle transport studies (e.g., Florinski & Pogorelov 2009; Engelbrecht & Burger 2015; Qin & Shen 2017; Moloto et al. 2018; Engelbrecht & Moloto 2021). These theoretical advances have benefited from new insights into particle diffusion via two separate avenues of research, both involving numerical simulations, as particle diffusion coefficients cannot be directly observed. One avenue of research involves numerical test particle simulations of particle diffusion coefficients in the presence of synthetically generated magnetic turbulence, in the process of gaining new insights as to the behavior of these particles, in particular, turbulence scenarios corresponding to a greater or lesser degree with what is observed in the solar wind (see, e.g., Minnie et al. 2007a; Ruffolo et al. 2008; Tautz & Shalchi 2011; Dalena et al.2012; Kong et al. 2017; Mertsch 2020). The other avenue for insights into the diffusion coefficients of charged particles involves the simulation of their transport in the heliosphere. Such studies report on the transport parameters needed as inputs for transport models to ensure agreement between computed particle intensities and various in situ spacecraft observations of the same. These approaches are by no means incompatible, as results from numerical test particle simulations have been shown to be in agreement with those yielded by transport modeling studies (Tautz & Shalchi 2013). The present study follows the latter avenue of inquiry, focusing in particular on the transport of Jovian electrons. In a sense, these particles are the ideal candidates for such a study, as the transport of low-energy electrons in the inner heliosphere has long been known to be negligibly influenced by drift effects (see, e.g., Ferreira et al. 2001; Engelbrecht & Burger 2010; Engelbrecht et al. 2017). Furthermore, the relative orbital motions of the Earth and Jupiter across the Parker (1958) HMF, coupled with the relative abundance of electron observations at 1 au as well as the Jovian source, allows one to compare computed intensities with observations taken during periods of good and bad magnetic connectivity with the source. This, then, allows for the simultaneous study of the transport coefficients of these electrons both parallel and perpendicular to the HMF, which is the aim of this study.


Ultra-fast outflows (UFOs) of highly ionised gas observed at sub-parsec scales (Reeves et al. 2003; Tombesi et al. 2012) have been proposed as the likely origin of galaxy-wide outflows, interpreted as the result of the impact of UFOs on the ISM (King & Pounds 2015, and references therein). Furthermore, both models and observations of kiloparsec-scale outflows seem to indicate a UFO-ISM interaction in an energy-conserving regime, whereby the swept-up gas expands adiabatically. So far, the co-existence of a massive molecular outflow with a nuclear UFO has been confirmed in a handful of AGNs with LBol  ∼  1044 − 1046 erg s−1 (Tombesi et al. 2015; Feruglio et al. 2015; Longinotti et al. 2015) and in APM 08279+5255 (Feruglio et al. 2017), which is a gravitationally lensed QSO at z  ∼  4 with an estimated intrinsic LBol of a few times 1047 erg s−1 (Saturni et al. 2018). In all these sources the momentum boost (i.e. the momentum flux of the wind normalised to the AGN radiative momentum output, LBol/c) of the UFO is ∼1, while the momentum rate of the molecular outflow is usually ≫1, in qualitative agreement with the theoretical predictions for an energy-conserving expansion (Faucher-Giguère & Quataert 2012; Costa et al. 2014). However, these results are still limited to a very small sample and suffer from large observational uncertainties, mostly due to the relatively low signal-to-noise ratio of the UFO- or outflow-related features confirmed in spectra, or to the limited spatial resolution of sub-millimetre observations. Recent studies increasing the statistics of sources with detection of molecular outflows have widened the range of measured energetics (e.g. García-Burillo et al. 2014; Veilleux et al. 2017; Feruglio et al. 2017; Brusa et al. 2018; Barcos-Muñoz et al. 2018; Fluetsch et al. 2019). These outflows are consistent with driving mechanisms alternative to the energy-conserving expansion, such as direct radiation pressure onto the host-galaxy ISM (e.g. Ishibashi & Fabian 2014; Ishibashi et al. 2018; Costa et al. 2018).


This additional heating effect would raise the temperature of the inflowing gases to a level where they cannot drive star formation effectively and begin to evaporate. We may use the virial theorem to estimate the time-scale over which filamentary inflows may halted in this manner: the virial temperature is the temperature above which gravitational collapse of gas is halted and, presumably, any heating to temperatures above this level would lead to evaporation. If assuming inflows persist over filaments of lengths of up to 50 kpc (Dekel et al. 2009; Stewart et al. 2013; Goerdt & Ceverino 2015; Dayal & Ferrara 2018) and that they are the sole driver of the star-formation activity arising at a rate of $\mathcal {R}_{\rm SF} \approx 16~\text{M}_{\odot }~\text{yr}^{-1}$ with a 30 per cent mass conversion efficiency (Meier, Turner & Beck 2002; Turner et al. 2015; Behroozi & Silk 2015; Sun & Furlanetto 2016) with an inflow velocity of 400 km s−1 (from the velocity offset of the Lyman-α line in MACS1149-JD1 – see Hashimoto et al. 2018), the steady-state mass of these inflows would be around 6.7 × 107 M⊙. If the typical diameter of these flows is similar to the galaxy which they feed, i.e. 1 kpc, this would give a virial temperature of Tvir ≈ 5000 K (Binney & Tremaine 2008). If adopting a number density of 10 cm−3 for the filamentary inflows (i.e. comparable to the mean density of the ISM in the host galaxy), the estimated CR heating rate of 10−25erg cm−3 s−1 would suggest it would take of order only a few Myrs for the virial temperature of the inflows to be exceeded. At this point, the supply of gas to the galaxy would be strangulated, halting star-formation within a dynamical time-scale τdyn (being the time required for the system to respond to the strangulation and internal heating). Since the strangulation and ISM quenching time-scales are comparatively short, the magnetic saturation and dynamical time-scales alone specify the time-scale over which star-formation would be quenched.