To confirm the importance of VO, water and an inversion layer (Evans et al. 2018; Mikal-Evans et al. 2019, 2020) obtained repeated HST observations of the transmission spectrum and the secondary eclipse using the STIS and WFC 3 instruments. The optical transmission spectrum displays rich variation, with multiple features consistent with VO absorption that Evans et al. (2018) could reproduce by assuming an isothermal T-P profile at 1500 K and a metallicity equivalent to 10× to 30× solar. Absorption bands of TiO appeared to be muted in the transmission spectrum, which was explained by Evans et al. (2018) as evidence of condensation of Ti-bearing species, which commences at higher temperatures than condensation of V-bearing species, producing for example, calcium titanates (Lodders 2002) while VO remains in the gas phase. Mikal-Evans et al. (2019) observed the day side emission spectrum with the G102 grism of WFC3 (0.8–1.1 μm), augmenting their earlier observations with the G141 grism. The G102 spectrum does not show the VO bands expected to be present there, and this led Mikal-Evans et al. (2019) to question the interpretation that the 1.2 μm feature is caused by VO emission. The secondary eclipse was observed at 2 μm (Kovács & Kovács 2019) and at optical wavelengths with the TESS instrument. These were analysed together with the preceding Hubble, Spitzer, and ground-based observations to yield tighter constraints on the atmospheric structure, composition and overall system parameters (Bourrier et al. 2020a; Daylan et al. 2019). These studies found that the hottest point on the day side exceeds a temperature of 3000 K, that the atmosphere is inverted on the day side, and a metallicity that is consistent with solar (Bourrier et al. 2020a) or slightly elevated (Daylan et al. 2019). Although the chemical retrievals follow different strategies (equilibriumversus free-chemistry), both indicate that a depletion of TiO relative to VO is needed to explain the observed emission spectrum, supporting the earlier findings by Mikal-Evans et al. (2019). Recently, Mikal-Evans et al. (2020) obtained new secondary-eclipse observations using the G141 grism of WFC3. Although confirming the presence of emission by H2O, a joint analysis with their previous WFC3 observations did not reproduce the emission feature at 1.2 μm, prompting the authors to entirely discard their previous interpretation of emission caused by VO.


MAXI J1820 is a BHT that was observed for the first time in the optical band by the All-Sky Automated Search for SuperNovae ASSAS-SN (Shappee et al. 2014) on 2018 March 3 (Tucker et al. 2018), and one week later by MAXI in X-rays (Kawamuro et al. 2018). Detailed studies of the optical counterpart revealed that the system hosts a stellar-mass black hole (∼8.5 M⊙) accreting from a ∼0.4 M⊙ companion star (Torres et al. 2019, 2020). Since its discovery, the source has undergone a long (approximately one year) and bright outburst, becoming at its peak the second brightest object in the X-ray sky. Due to its brightness, the system was the object of an impressive multi-wavelength observing campaign (see, e.g., Shidatsu et al. 2018; Paice et al. 2019; Hoang et al. 2019; Trushkin et al. 2018; Bright et al. 2020; Tetarenko et al. 2021) and of a large number of studies. The most recent and precise measure of the distance, determined via radio parallax, is 3.0 ± 0.3 kpc (Atri et al. 2020). Furthermore, the system shows X-ray dips (Kajava et al. 2019) but not eclipses, suggesting an inclination between 60° and 80°. Other evidence of the high inclination of the system are provided by optical spectroscopy (Torres et al. 2019) and by the estimate of the inclination of the jet axis (Atri et al. 2020; Wood et al. 2021), which is about 63°. The orbital period of the system has also been estimated to be around 0.68 days (Patterson et al. 2018; Torres et al. 2020). In X-rays, the outburst was studied in detail in HS (see, e.g., Bharali et al. 2019; Buisson et al. 2019; Zdziarski et al. 2021), SS (see, e.g., Fabian et al. 2020) and in its final phase (see, e.g., Xu et al. 2020). The truncation of the disk during the HS is one of the most controversial aspects of the system. On the one hand, a number of spectral-timing works have pointed out that the disk reaches the ISCO already in HS, while a contracting lamppost corona is responsible for the hard X-ray emission (Kara et al. 2019; Buisson et al. 2019; You et al. 2021; Wang et al. 2021). On the other hand, a truncated disk scenario has also been proposed on the basis of further spectral-timing analyses, even on the same sets of data (Zdziarski et al. 2021; De Marco et al. 2021; Axelsson & Veledina 2021).


In the modelling, it is assumed that the low-energy peak (from radio to optical–UV) is due to synchrotron emission from ultrarelativistic electrons in the jet with an energy distribution as given by equation (2). Instead, the HE peak is due to the IC scattering of internal (SSC; Ghisellini et al. 1985; Maraschi et al. 1992; Bloom & Marscher 1996) or external photons (EIC; Sikora et al. 1994; Błażejowski et al. 2000; Ghisellini & Tavecchio 2009). The IC scattering of external photons is considered, since the SEDs of FSRQS are better explained by EIC, as shown by the previous studies (e.g. Abeysekara et al. 2015; Ahnen et al. 2015; Hayashida et al. 2015b; Gasparyan et al. 2018; MAGIC Collaboration 2018), and the CD is evident in the SEDs of the considered sources (Fig. 6). Localization of the emission region in the jet is an open question and along the jet, depending on the distance from the central black hole, different photon fields can be dominant for the IC scattering (Sikora et al. 2009). In this paper, we assume that the emitting region is outside the broad-line region (BLR) where the dominant photon field is the IR emission from the dusty torus. Sikora et al. (2002) showed that in MeV blazar SEDs the shift of the peak of the HE component to lower energies is most likely due to the Comptonization of IR photons from the dusty torus. The IR radiation from the dusty torus is assumed to have a blackbody spectrum with a luminosity of LIR = 0.6 Ldisc (see Ahnen et al. 2015) where Ldisc is the accretion disc luminosity, which fills a volume that for simplicity is approximated as a spherical shell with a radius of RIR = 2.5 × 1018 (Ld/1045)1/2 cm (Nenkova et al. 2008) with the energy density of $u_{\rm IR}=0.6\:L_{\rm d}/4 \pi R_{\rm IR}^2\:\delta ^2$ in the co-moving frame of the jet. In Ghisellini et al. (2011) and Marcotulli et al. (2017), the HE component in the SED of distant blazars was modelled by IC scattering of BLR reflected photons, adopting a smooth broken power-law shape of the emitting electrons. We refer the reader to these papers for details on the modelling when BLR reflected photons are considered.


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


Close to the end of their formation, stars are surrounded by a gas and dust disk, from which planets form. Magnetic fields are known to play a key role in the star-disk system (Johns-Krull 2014). It is believed that the inner regions of the disk are significantly ionized by the stellar radiation and that accreting material flows along magnetic channels that connect the disk to the star (Koenigl 1991). Very long and intense X-ray flares in star-forming regions might occur in such long channels (Favata et al. 2005), but this is highly debated (Getman et al. 2008). These flux tubes might resemble those observed in the solar corona and diagnosed in the stellar coronae, but on a much larger scale. On the Sun we see the so-called coronal loops on the scale of several thousand kilometers in active regions, but some faint large-scale structures can extend up to ∼1 R⊙ (Reale 2014). Most solar flares occur in active region loops, but the long-lasting ones can involve more and more loops aligned in arcades. The other stars are so distant that we cannot resolve the flaring regions, but it is supposed that they occur in loops and even in arcades. Whereas the duration of solar flares typically ranges from a few minutes to several hours, stellar flares can be very intense, more than the solar bolometric luminosity, and long-lasting, including longer than one day, in very active stars. Several such gigantic coronal flares have been surveyed in star-forming regions (Favata et al. 2005) and where they occur is a big question. Magnetic instabilities in flux tubes were proposed to be the origin of the flaring activity also in T Tauri stars (Birk 1998; Birk et al. 2000), and long-lasting stellar flares might be expected to involve loop arcades (Getman et al. 2008), like those on the Sun. In long-lasting solar flares, the duration is mainly due to the progressive involvement of more and similar loops, therefore duration is not directly linked to the size of the flaring structures. This might also be the case for giant stellar flares. However, if a single stellar loop were flaring, the cooling time of the confined plasma would be proportional to the loop length (Serio et al. 1991; Reale 2014), and day-long flares would correspond to giant loops, as long as they possibly connected the star with the disk (Hartmann et al. 2016). There are ways to distinguish between a pure cooling in a single loop and a decay only due to progressive reduction of the energy release in a loop arcade (Reale et al. 1997), but the explanations are contested and the uncertainties are large (Getman et al. 2008). Several studies (Favata et al. 2005; Giardino et al. 2007) find results compatible with long magnetic channels in pre-main sequence (PMS) stars, but the derivation of the loop length is based on the assumption of a flare occurring in a single loop (Reale 2007).


The CO emission, tracking the bulk of the gas, reveals an almost face-on one-armed spiral, of which almost two full windings can be traced. What could be the origin of this spiral structure? As the majority of AGB stars are in binary systems, and perhaps all host planets, interaction between the outflow and a sufficiently massive and nearby companion may be the explanation of the observed CO morphology. The intricate emission features in the inner 2″ of the central CO emission maps is strongly reminiscent of hydrodynamical simulations of wind–binary interaction by Mastrodemos & Morris (1998) and Mohamed & Podsiadlowski (2012), where the latter authors performed tailored simulations for the Mira AB system in which the outflow of the AGB star Mira A is perturbed by the presence of its close companion Mira B. The wind–binary interaction that ensues leads to what is known as wind Roche-lobe overflow (WRLOF), where the slow AGB wind is confined to the star’s Roche lobe, while overflowing through the L1 Lagrange point. Gravitational interaction of the overflowing material with the companion produces an intricate feedback system where the stellar outflow material is ejected into the surrounding CSE through two distinct streams (through L2 and the stagnation point3) which combine to form an annular stream. As this stream travels outwards, it creates the larger scale spiral observed in the wind. The morphology resulting from this particular type of wind–binary interaction is shown in Fig. 3 in Mohamed & Podsiadlowski (2012). In Fig. 11 we show the emission pattern seen in the central regions of the CO channel at υ*. We compare this image with the bottom left panel of Fig. 3 in Mohamed & Podsiadlowski (2012), an opacity map of the interaction zone. Though the two properties that are compared differ in nature, they likely still trace the same global morphological structure. Indeed, several of the predicted morphological features can be identified in the data of EP Aqr. The bright central region with a north and southward hook-like extension are strikingly similar, as are the eastern and western crescent-shaped “voids”, the overall shape, and the morphological properties of the small-scale instabilities.


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


In the expectation of a relationship between the observed IRX and the rest-frame UV slope there is the assumption that the stars and dust are well mixed, which leads to the coupling of any observed reddening in the UV to the FIR emission detected (e.g. Meurer et al. 1999; Charlot & Fall 2000; Calzetti 2001). If instead the galaxy consists of regions of significantly different obscuration, then the relationship will break down for the galaxy as a whole. Indeed, geometric effects have been put forward as an explanation of the discrepant results at z > 5 (Faisst et al. 2017; Popping, Somerville & Galametz 2017). In local starburst galaxies, the existence of an IRX–β relation and a clear morphological similarity, indicates that the rest-frame UV emission from young stars is being attenuated from dust that is tracing broadly the same star-forming regions of the galaxy (e.g. in the spiral arms; Kennicutt et al. 2003; Gil de Paz et al. 2007). In the high-redshift Universe, however, where galaxies become more turbulent and irregular (e.g. Förster Schreiber et al. 2011; Buitrago et al. 2013; Guo et al. 2015) the expected morphology of the dust relative to the observed UV emission is not clear. Evidence for offset dust continuum emission relative to the rest-UV has been identified in several high-redshift Lyman-break galaxies (LBGs; Koprowski et al. 2016; Faisst et al. 2017; Laporte et al. 2017; Bowler et al. 2018), and similar trends have been found when comparing the [C ii] FIR line and the rest-UV continuum (e.g. Maiolino et al. 2015; Carniani et al. 2017). Although some of these offsets have been attributed to astrometric systematics (e.g. Dunlop et al. 2017) there is a growing consensus that FIR continuum and line emission are frequently physically offset as compared to the observed rest-UV emission (see Carniani et al. 2018). Whether high-redshift galaxies show large and distinct regions of obscured and unobscured star formation has implications for the use of the IRX–β relation in deriving the cosmic SFR density (e.g. Bouwens et al. 2016b), as the assumed energy balance will break down (Buat et al. 2019) and the global β measurement will not be representative of the full source.


Galaxies seem to retain a memory of their spin orientation with respect to the cosmic web filaments and walls, as suggested by the results from large-scale cosmological hydrodynamical simulations (Dubois et al. 2014; Codis et al. 2018; Wang et al. 2018; Ganeshaiah Veena et al. 2019; Kraljic, Davé & Pichon 2020b). The mass dependence of the spin alignment signal is however debated. While some works confirmed the existence of a galaxy spin transition from parallel to perpendicular with respect to the filament’s direction (Dubois et al. 2014; Codis et al. 2018; Kraljic et al. 2020b), and analogously with respect to walls (Codis et al. 2018; Kraljic et al. 2020b), others (Ganeshaiah Veena et al. 2019; Krolewski et al. 2019) found preferential perpendicular orientation with respect to filaments at all masses with no sign of a spin transition. A possible interpretation of this lack of detection of a clear transition is the nature of the filaments, with galaxies in thinner filaments having their spins more likely perpendicular to the filament’s axis, compared to galaxies of similar mass in thicker filaments (Ganeshaiah Veena et al. 2019). This can be in turn understood recalling the multiscale nature of the problem and the conditional TTT (Codis et al. 2015) predicting larger transition mass for denser, thus thicker, filaments. Further support for this interpretation was provided by the findings of stronger impact of large-scale tides on the galaxy spin orientation in denser filaments (Kraljic et al. 2020b, using filament density as a proxy for the thickness of filaments). In addition to the stellar mass, the spin-filament alignment was shown to depend on other internal properties of galaxies. Blue or rotation-supported galaxies were found to dominate the alignment signal at low stellar mass, while red or dispersion-dominated galaxies tend to show a preferential perpendicular alignment (Codis et al. 2018; Wang et al. 2018; Kraljic et al. 2020b).


SEP events with gigaelectronvolt particles are generally rare. Typically about a dozen events occur during each solar cycle, although only two GLEs were reported in cycle 24, probably due to the change in the state of the heliosphere (Gopalswamy et al. 2013a, 2014a; Thakur et al. 2014). It appears that the 2012 July 23 event would have been another GLE event if it had occurred on the front side of the Sun. The purpose of this paper is to examine the event from the perspectives of CME kinematics, SEP intensity and spectrum, and radio-burst association to see if the 2012 July 23 event can be considered as an extreme particle event. The reason for considering these properties is clear from the following facts. Particles up to gigaelectronvolt energies are accelerated by strong shocks driven by CMEs of very high speeds (∼2000 km s−1) and intense, soft X-ray flares (see Gopalswamy et al. 2010, 2012b). The high speed is typically attained very close to the Sun, so the density and magnetic field in the corona are high for efficient particle acceleration (e.g., Mewaldt et al. 2012; Gopalswamy et al. 2014a). The high CME speed implies that a fast-mode MHD shock forms close to the Sun, as indicated by the onset of metric type II radio bursts, typically at heights 1.5 solar radii (Rs). CMEs attaining high speeds near the Sun have to accelerate impulsively, so these events are characterized by high initial acceleration (∼2 km s−2, see Gopalswamy et al. 2012b). This is in contrast to slowly accelerating CMEs (from filament regions outside active regions) that form shocks at large distances from the Sun and do not accelerate particles to energies more than a few tens of megaelectronvolts (Gopalswamy et al. 2015a, 2015d). Accordingly, the SEP spectra of such events are very soft, as opposed to the hard spectra of GLE events. Whether an event has a soft or hard spectrum is important information because the hard-spectrum events have stronger space weather impacts (see, e.g., Reames 2013). SEP events with gigaelectronvolt components are accompanied by type II radio bursts from meter (m) wavelengths to kilometer (km) wavelengths (Gopalswamy et al. 2005b, 2010). Type II bursts occurring at such wide-ranging wavelengths imply strong shocks throughout the inner heliosphere (Gopalswamy et al. 2005a).


It is much harder to localize and track the formation of current sheets in realistic black hole accretion flows in a larger domain and for a longer period because of the effects of the more complicated global dynamics governed by the central object, and due to the turbulence induced by the MRI. Both the evolution of accretion flows and the formation of current sheets therein strongly depend on the magnetic field geometry. We model an accretion disk around a rotating black hole, varying the initial conditions to study current sheet formation in different scenarios of magnetic field geometry. In the magnetically arrested disk (MAD; Igumenshchev et al. 2003; Narayan et al. 2003) scenario, the MRI and subsequent turbulence in the inner accretion disk are suppressed due to large-scale magnetic flux (see, e.g., White et al. 2019). In axisymmetric simulations as considered here, the arrested inflow is regularly broken by frequent bursts of accretion, allowing for a macroscopic equatorial current sheet to form and break in a periodic fashion. In a full 3D setup, magnetically buoyant structures are interchanged with less-magnetized dense fluid (Igumenshchev 2008; White et al. 2019), resulting in a magnetic Rayleigh–Taylor instability (Kruskal & Schwarzschild 1954) potentially sourcing interchange-type magnetic reconnection. In the Standard And Normal Evolution (SANE; Narayan et al. 2012; Sadowski et al. 2013) state, a fully turbulent accretion disk can develop due to a smaller magnetic flux (see, e.g., Porth et al. 2019), and current sheets can ubiquitously form and interact with the turbulent flow. Polarized synchrotron radiation observed by the Event Horizon Telescope (Event Horizon Telescope Collaboration et al. 2019a) can probe the field-line structure at event-horizon scales and put tighter constraints on the magnetization and address whether the accretion is in a SANE or a MAD state (Event Horizon Telescope Collaboration et al. 2019b).


Astrophysical processes involving radiative energy transfer are calculated by the balance between compressional heating and adiabatic cooling (Blondin et al. 1990; Taam, Fu & Fryxell 1991). Analytical prescriptions for the heating and cooling rates in complex environments are only possible under certain limits. However, the increasing computer power available today is allowing to model complex astrophysical scenarios efficiently and at a relatively low cost, including the dynamical update of the microphysics and chemistry. For instance, thermal instabilities, non-axisymmetric rotating objects, the relationships between ionization, molecular states, level populations, and kinetic temperatures of low-density environments are some of the ingredients that have no analytical counterparts and that can be calculated with highly efficient numerical algorithms. A particularly interesting question is related to the accretion of angular momentum, when the flow contains a density or velocity gradient perpendicular to the flow direction (Davies & Pringle 1980; Ruffert & Anzer 1995; Ruffert 1997, 1999). In particular, Proga & Begelman (2003) performed two-dimensional (2D) axisymmetric simulations of the accretion of slowly rotating gas on to a black hole. They found that for low angular momentum, the flow is Bondi-like, while for intermediate total angular momentum, the gas with higher angular momentum does not accrete and forms a dense torus about the black hole and, as a result, the accretion rate is substantially below the Bondi rate. For even higher total angular momentum, a dense torus coupled to a centrifugal barrier sets in, which further reduces the accretion rate. Proga & Begelman (2003) have argued that rotation may explain the difference between accretion rates estimated from observations and those predicted by the Bondi flow. Moreover, Perna et al. (2003) suggested that combining rotation and magnetic fields results in accretion rates on to isolated neutron stars that are much lower than those estimated using the Bondi formula. Later on, Krumholz, McKee & Klein (2005) considered the three-dimensional (3D) accretion of gas with constant vorticity and found that the resulting flow field is highly non-axisymmetric and time-dependent and that even a small amount of vorticity can substantially change the accretion rate. Considerable progress has been made over the past 20 yr in developing advanced numerical models to understand the physics of accretion on to compact objects. A thorough review of Bondi accretion theory and related earlier numerical simulations is given by Edgar (2004).


We used the publicly available code AROME (Boué et al. 2013) to analytically compute the RM RV anomaly as measured with the CCF method. This code, written in C, was given the orbital planetary and stellar parameters (the projected rotation velocity Vsin(i), the semi-major axis a, the radius of the star Rstar, expressed in solar radii units, the inclination angle i, the mutual inclination angle λ, and the planet orbital period P, all taken from Triaud et al. 2009, see Table 1), and the times of observation, which it subsequently used to calculate the CCFs and the expected RV measurements from a Gaussian fit to these. The fraction of flux blocked by a planet crossing the surface of its host star depends on the limb darkening of the star. For the calculation with AROME we chose the non-linear law of Claret (2000) to match those used in the analysis of Pont et al. (2008) and Sing et al. (2011b), that is, (3)\begin{equation} \frac{I \left( \mu \right)}{I \left( 1 \right)} \ = \ 1 - \sum_{k=1}^{4} a_{k} \left( 1 - \mu^{k/2} \right) \label{claret2000}. \end{equation}IμI(1)=1−∑k=14ak(1−μk/2).For the white-light RV time series we used the quadratic limb-darkening law coefficients as in Triaud et al. (2009), who studied the RM effect for this planet using the same data set. All the limb-darkening coefficients used in our analysis are given in Table 2. Since we are interested in the dependence of the RM effect on the planet effective size, for each passband we selected the limb-darkening law corresponding to those wavelengths and calculated the anomaly for 5000 values of the planet-star radius ratio (Rp/Rstar), between 0.105 and 0.205 with a step of 2 × 10-5. These boundaries were chosen arbitrarily with the purpose of including the measured planet-star radius ratio for this planet using the same HARPS data as Triaud et al. (2009) (0.1581 ± 0.0005). All other parameters were kept fixed. We note that for the analysis we are only interested in the relative change of the Rp/Rstar as function of wavelength, not in absolute values. Therefore it is not relevant to fit for parameters such as the projected rotation velocity Vsini, the mutual inclination angle λ, the macroturbulence z, and the scaled semi-major axis a/Rstar separately for each passband. These should be independent of wavelength and therefore can only result in a small vertical offset in the transmission spectrum, not in a change of slope.


Here, we relate the observed morphology of the dust continuum emission to the physical processes taking place within star-forming galaxies around the peak of cosmic star formation. As discussed by Cheng et al. (2020), the extended dust continuum emission observed in the less-FIR luminous SHiZELS galaxies suggests a dominant component of extended, disc-wide star formation; in contrast, the emission from sub-millimetre selected galaxies appears to be dominated by a compact, nuclear starburst. SHiZELS-14 is an outlier in the sense that it has both a submillimetre bright compact core and very extended emission. Tadaki et al. (2020) show that the most compact galaxies in their sample tend to have high gas fractions (derived via $S_{870\mu \rm {m}}$), and argue that this reflects efficient radial gas inflows. Numerical simulations have long shown that galaxy mergers are capable of triggering tidally driven gas inflows (Hernquist 1989; Barnes & Hernquist 1991), which can cause strong nuclear starbursts (e.g. Mihos & Hernquist 1994, 1996; Hopkins et al. 2013; Moreno et al. 2015). However, observations of local galaxies such as the Antennae system demonstrate that galaxy interactions can also trigger widespread star formation that is not limited to a compact, nuclear region (Wang et al. 2004). More recent, high resolution simulations show that these observations can be explained via merger-driven injections of turbulence into the ISM: extended compression results in fragmentation into dense, star-forming gas, and spatially extended starburst activity (Renaud et al. 2014; Renaud, Bournaud & Duc 2015). Renaud et al. (2015) argue that this process is particularly important in the early and mid-stages of a galaxy merger: during the first two simulated pericentre passages, star clusters form kiloparsecs from the galactic nucleus, with the central starburst dominating only from the beginning of the final coalescence. This progression of star formation from extended to compact as the merger unfolds is also consistent with observations of local galaxies (Pan et al. 2019). The extended star formation observed in SHiZELS-14 may therefore suggest that we are viewing the short-lived mid-stages of a merger; this would be consistent with its complex, irregular morphology and dispersion-dominated $\rm {H}\,\alpha$ kinematics. The similarly TIR-luminous but more compact sources within the AS2UDS samples may comprise galaxies experiencing a wider range of evolutionary stages, including some later-stage mergers.


An important reason for modeling the THS plasma is identifying the pathways of chemical growth. Tables 3 and 4 list the dominant production and loss reactions, respectively, for a set of species. The neutral versions of these species have each been identified in Titan's upper atmosphere (Waite et al. 2007; Cui et al. 2009). The values of the calculated reaction rates are listed if larger than 1 × 10−6 mol m−3 s−1. For the experimental conditions considered, the model predicts that neutral C2H2 production is only appreciable in the mixture that already contains an acetylene precursor through the reaction of C4H2 with C4H3+, which are themselves reaction products that, at Titan, might be derived through other chemical pathways. C2H2 is destroyed mainly by reactions with C2H2+ ions or CHx+ fragments. Neutral C2H4 exhibits large production rates for all the precursor mixtures since its formation pathway involves CH4 and the CH fragment, which are both abundant. Nitrogen incorporation is an important part of the haze chemistry of Titan (Imanaka & Smith 2010). HCN has been detected in Cassini Composite Infrared Spectrometer observations at 713 cm−1 (Coustenis et al. 2008). Although its abundance is seasonal, modeled concentrations of HCN nominally peak near the mesopause at around 108 cm−3 (Liang et al. 2007), and HCN mixing ratios are highest in the ionosphere where they are between 0.1% and 1% (Hébrard et al. 2012). According to Hébrard et al.'s network, the dominant pathways for HCN production in the upper atmosphere are HCNH+H

HCN+H2 and N+CH3

HCN+2H. In the THS plasma, various paths for nitrogen incorporation are included in the chemical network including N+ reactions with CH and CH4 leading to CN+ and HCNH+ as well as the dominant neutral mechanisms highlighted by Hébrard et al. The model suggests that the neutral pathway, N+CH3, is a dominant source of HCN for each of the N2/CH4/CxHy mixtures. The reason is that atomic nitrogen and CH3 are abundant products from the precursor fragmentation. The HCNH+H pathway is less productive since HCNH must first be formed from the fragments. The model also suggests that once formed, HCN is stable, subject only to small rates of charge transfer with N2(X, v = 0)+ or reaction with the C2H5+ ion.


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


The fact that all massive ETGs fall into a single FP, coupled with the segregation of the highest ranked objects from lesser galaxies, entails that any non-edge-on projection of this flat surface must also lead to segregated 2D scaling laws. To investigate this issue we now use M⋆ to represent scale, shifting to the (logarithmic) RVM coordinate system defined by the three most basic global parameters connected by the standard plane. In this manner we set the framework for the study of two of the most firmly established empirical scaling relations of elliptical galaxies: the Kormendy-like RM relation (Shen et al. 2003) and the VM relation, a mass analogue of the classical FJR. In good agreement with observational studies of BCG/BGGs (Bernardi et al. 2007; Lauer et al. 2007; Bernardi 2009; Méndez-Abreu et al. 2012), we find that our simulated first-ranked galaxies lie off the standard 2D scaling relations defined by the bulk of the ETG population. In particular, as shown in Fig. 3, BGGs are larger and have lower effective velocity dispersions than ordinary ellipticals of the same stellar mass. The combination of this latter result with the fact that light appears to be similarly concentrated for BGGs than for non-BGGs (Paper I), tells us that the total mass-to-light fraction interior to Re is lower for the former than for the latter. Our numerical experiments, however, do not seem to support claims of the steepening of the R ∝ Mα relation for CGs towards values α ≳ 1 (Lauer et al. 2007; Bernardi 2009). We find instead that our first-ranked objects, which occupy a locus moderately offset from the central axis of the observational data in Fig. 3A, are well fitted by a model with α = 0.60 ± 0.03. This value of the power-law index agrees well with the slope α ∼ 0.65 found for non-BCG galaxies in the Sloan r-band (Shen et al. 2003; Bernardi et al. 2007), while a plain orthogonal fit to the general elliptical population data included in Fig. 3A (green dots and small grey circles) also gives α ∼ 0.6. Approaching closer to our findings, Liu et al. (2008) obtain α ∼ 0.9 from surface measurements up an isophotal limit of 25 r-mag arcsec−2, which reduces to ∼0.8 when their magnitudes are transformed into mass in old stars, whereas they get α ∼ 0.75 for a control sample of non-BCGs. Differences in the photometry, the waveband of the observations, sample construction (i.e. incompletenesses and selection biases), and fitting methods would help explain the lack of a closer agreement between these results about the most robust of the 2D relationships.


In general, a precise measurement of the instrumental line-spread function can only be obtained from the LFC lines since only these are truly unresolved. Unfortunately, the LFC covers only 57% of the ESPRESSO spectral range. So even if a proper modeling of the line-spread function would resolve some of the discovered discrepancies, it might only be available for a limited wavelength range. The transitions used to constrain the fine-structure constant are, however, distributed over a wide range in wavelengths. The exact location of the lines depends of course on the absorber redshift, but restricting the range to the region covered by the LFC (approximately 5000 Å–7000 Å, see Fig. 8) would render many well-studied absorption systems basically unobservable with ESPRESSO. For example, for the zabs = 1.69 systems along the HE 2217-1818 sightline (Molaro et al. 2013a), the Mg II lines would not be covered anymore, leaving only the Fe II lines around ≃ 2500 Å for a constraint of the fine-structure constant (compare to Fig. 1). However, these five lines have a limited spread in sensitivity with respect to α. In addition, relying only on the LFC wavelength range will make it at any redshift impossible to observe the Fe II 1608 Å line together with the other Fe II lines at λrest > 2300 Å. Usually, this is a very valuable combination of transitions, since the Fe II 1608 Å line shifts in opposite direction compared to the other Fe II lines and using only transitions originating from the same ion avoids possible systematics related to different velocity structures and isotopic abundances. For many absorption systems, it is thus crucial to use the full spectral range of ESPRESSO and a restriction to the limited range covered by the currently installed laser frequency comb would substantially diminish the scientific return. Therefore, it is important that future improvements of the ESPRESSO wavelength calibration are applicable to the full spectral range of ESPRESSO.


Recently, forms of feedback that are fundamentally different from SNe have been shown to be essential to galaxy formation. Murray, Quataert & Thompson (2010) analysed the dynamical effects of several forms of stellar feedback on parent molecular clouds. In their models they include momentum input from ionized gas in H ii regions, shocked stellar winds, hot gas pressure, protostellar jets and cosmic rays. Murray et al. (2010) conclude that radiation pressure (RP) on dust grains is likely to be the dominant form of feedback in star-forming galaxies. A variety of other studies have reached the same conclusions, placing the combination of RP and photoionization of gas by massive stars as the dominant mechanism for disruption of molecular clouds and internal regulation of the SF process (Indebetouw et al. 2009; Krumholz & Matzner 2009; Murray et al. 2010; Andrews & Thompson 2011; Hopkins, Quataert & Murray 2011; Lopez et al. 2011; Pellegrini, Baldwin & Ferland 2011). RP alone might also be the only mechanism that explains galactic fountains and the warm gas outflows observed in absorption in high-redshift galaxies (Murray, Ménard & Thompson 2011). In addition, recent numerical work by Krumholz & Thompson (2012) shows that radiation feedback fully accounts for the large gas velocity dispersions measured in young star clusters in the MW. There are at least three reasons why radiative feedback is an essential ingredient of the galaxy formation process. First, observations show that molecular clouds begin to disperse shortly after the O stars form and before the first SNe explode and deposit their energy into the gas (Kawamura et al. 2009). Secondly, the total energy output of a stellar cluster is dominated by radiation. The rate of radiative energy output by O and B stars is ∼200 times larger than the average power injected by SNe and stellar winds during the lifetime of the most massive stars. Thirdly, it is difficult to explain the large gas turbulence values observed in star-forming regions without including the momentum input by radiation (Murray et al. 2010).


The mirror mode is a fundamental process in magnetized plasma environments. It plays many important roles in solar physics, interplanetary, planetary, astrophysical, and laboratory plasma environments, for example, it converts electromagnetic energy and particle kinetic energy (Kivelson & Southwood 1996), excites plasma waves and instabilities (Smith et al. 1969), modulates particle distributions (Yao et al. 2018b), and is suggested as a significant source of turbulent energy (Pokhotelov et al. 2003) and serves as messengers of solar corona (Russell et al. 2008). The most common mirror mode is in space, for example, it is observed to be full of Earth magnetosheath and can exist in the Earth magnetosphere for a long time. These structures are generally suggested to be magnetohydrodynamics (MHD) scale and static in the plasma frame. They display anticorrelation between magnetic and plasma pressures. The spatiotemporal scales and three-dimensional (3D) structures, evolution processes, and other important effects (e.g., drift, finite Larmor radius effect, non-Maxwellian ion distribution, and electron temperature influence) have been extensively studied in the past half century (e.g., Hasegawa 1969; Southwood & Kivelson 1993; Chisham et al. 1998; Pokhotelov et al. 2000, 2013; Gary & Karimabadi 2006; Genot et al. 2009; Hellinger et al. 2009). The studies on the mirror mode were mostly confined to the MHD scale. Numerical simulations and theoretical studies further revealed their kinetic effects, although the fundamental theoretical framework is still at MHD scale and lacks support from observations. If the electron distribution is anisotropic (with perpendicular temperature exceeding the parallel), the electrons become unstable and would excite the electron mirror-mode instability to remove the free energy. This instability was first discovered by Basu & Coppi (1982), and subsequently detailed by Basu & Coppi (1984), Migliuolo (1986), Marchenko et al. (1988), and more recently by Gary & Karimabadi (2006), Pokhotelov et al. (2013), and Hellinger & Štverák (2018). This electron mirror-mode instability condition is similar to the MHD-scale mirror mode and can be expressed as

, where βe⊥, Te⊥, and Te∥ denote electron perpendicular plasma beta and perpendicular and parallel electron temperature, respectively. This has been theoretically predicted using a linear calculation (Pokhotelov et al. 2000) and also found in more precise numerical simulations (for example, including the effect of off-diagonal terms in dielectric tensor elements for the mirror instability) by Noreen et al. (2017). The contribution of electrons in the mirror instability in the quasilinear regime was then also discussed by Noreen et al. (2017). Historically, the electron mirror mode has been studied in theories and numerical simulations. But so far there have been few unambiguous observations of their existence because the capability to resolve electron-scale structures has been strongly limited by the insufficient measurement resolution of satellite-borne instrumentation. Using magnetic field data obtained from the spacecraft AMPTE-IRM and Equator-S, Treumann & Baumjohann (2018) presented observational evidence for the electron mirror mode in the Earth's magnetosheath. Low-frequency whistler waves were also observed and were used to diagnose the effect of anisotropic electron temperature on the mirror mode. These observations suggest that the whistler waves were probably related to the trapped electrons for which the trapping condition was provided by the magnetic depressions caused by the electron mirror branch. The study also pointed out that high temporal resolution observations are required for the confirmation of the electron mirror mode and its responsibility for electron trapping and wave excitation. In the recent Magnetospheric Multiscale (MMS; Burch et al. 2016) studies, similar low-frequency whistler waves were observed inside mirror-mode structures by Ahmadi et al. (2018) with a detailed in-depth investigation. The electron temperature anisotropy was suggested to provide a favorable environment for the growth of whistler waves. This result indicates the possible existence of localized electrons that were trapped by the electron mirror branch. Similar observations can be found in Breuillard et al. (2018), which observed whistler waves in mirror-mode structures with perpendicular electron temperature anisotropy.


Previous observations of AGN that investigate correlations between αOX and Eddington ratio have revealed some similarities with X-ray binary outbursts at high Lbol/LEdd, but these comparisons have not been possible below the critical Lbol/LEdd ≲ 10−2, where an inversion in this correlation is predicted to occur. At higher Eddington ratios of Lbol/LEdd ≳ 10−2, single-epoch X-ray and UV observations of large samples of AGN have previously revealed a hardening of αOX as Lbol/LEdd drops from ∼1 to ∼10−2 (e.g., Vignali et al. 2003; Strateva et al. 2005; Steffen et al. 2006; Just et al. 2007; Grupe et al. 2010; Jin et al. 2012; Wu et al. 2012; Trichas et al. 2013; Vagnetti et al. 2013). This correlation was also observed in multi-epoch UV/X-ray observations of the fading of Mrk 1018 (Noda & Done 2018), which confirms this behavior in an individual AGN. However, the predicted softening of αOX below Lbol/LEdd ≲ 10−2 (thus causing an inversion in the correlation between αOX and Lbol/LEdd) has not been previously observed. This is primarily due to the difficulty of robustly measuring both αOX and Lbol/LEdd for AGN below Lbol/LEdd ≲ 10−2, for three main reasons. First, at low Eddington ratios, AGN are often dust-obscured (Fabian et al. 2008), and thus measuring their intrinsic UV luminosities (and αOX) is difficult. Second, broad emission lines often disappear in low-luminosity AGN below Lbol/LEdd ≲ 10−2, making it difficult to measure MBH (and LEdd). Third, using a sample of AGN with a wide range of Eddington ratios to trace how αOX changes as a function of Lbol/LEdd can be hampered by the

 scaling of the thin disk temperature with MBH at a fixed Eddington ratio. If the AGN sample has a large range in MBH, this can cause an additional scatter in αOX. Thus, we would ideally use a sample of AGN with a narrow range in MBH, but the difficulty of measuring MBH at Lbol/LEdd ≲ 10−2 also hampers the construction of such a sample. In this paper, we will use a new method to bypass all of these issues, with the goal of extending this spectral comparison between X-ray binaries and AGN to Lbol/LEdd ≲ 10−2.


For the purpose of this study, we adopt the general concept that the global solar wind is generally composed of relatively steady high-speed solar winds from long-lived high latitude open coronal field regions. The high-speed solar winds from the northern and southern hemispheres are separated by a layer of—on average—slower, denser, more complicated, and variable outflows and structures (Gosling 1996; McComas et al. 2008). This boundary layer between the polar outflows has a latitudinal extent that is roughly defined by the heliospheric current sheet (HCS) maximum excursion. In the solar wind, there also exist various anomalous episodes, as consequences of transient and/or energetic activities that may be remote (in the corona) or heliospheric in origin. The following phenomena or transients relating to anomalous solar wind parameters have been studied and have inspired our study. (1) False magnetic field polarity reversals—evoking images of switchbacks—that have been argued as being interchange reconnection debris (Owens et al. 2013, 2017, 2020), and recently also observed much closer to the Sun by the Parker Solar Probe mission (Laker et al. 2021), and the origin is being debated. (2) Heliospheric magnetic field (HMF) departures from the Parker spiral to nearly radial field at 1 au (Murphy et al. 2002; Watari et al. 2005). The great majority of the initial mass function orientation statistics fall in the vicinity of Parker spiral fields for typical solar wind speeds. However, blocks of time occasionally stand out when the HMF is nearly radial. (3) Interplanetary coronal mass ejections (ICMEs), magnetic clouds (MCs), and other flux ropes, whose structures are foreign to the ambient solar wind and whose plasma differs from the background plasma, often bring anomalously low temperatures and plasma beta (Burlaga et al. 1981; Klein & Burlaga 1982; Burlaga 1988; Richardson & Cane 1995; Kilpua et al. 2009). (4) The intervals of counterstreaming suprathermal electrons (CSEs), which are often interpreted as closed loops of magnetic fields with both ends being connected to a hot electron source within the corona (Bame et al. 1981; Gosling et al. 1987, 1992). (5) Heat flux dropouts, suggesting complete disconnection from hot electron sources (McComas et al. 1989). Many studies have been devoted to these phenomena, including their relationship to the location of the HCS/coronal streamer belt and their solar cycle variations (McComas et al. 1989; Fitzenreiter & Ogilvie 1992; Gosling et al. 1992, 1993; Shodhan et al. 2000; Murphy et al. 2002; Watari et al. 2005; Lavraud et al. 2010; Yu et al. 2014, 2016; Owens et al. 2017, 2020). Weaker solar cycles and advanced imaging and modeling capabilities have raised the profile of pseudostreamers and their boundaries as contributors to the outflows within this slow wind layer (Wang et al. 2012; Owens et al. 2013, 2014). Similarly, the density blobs that are released from the ends of the coronal streamers are another source of slow solar wind (Sheeley & Wang 2007; Rouillard et al. 2010a, 2010b) that belong to this collection of features. These have been associated with in situ observations of small flux rope-like structures in the solar wind at 1 au (Kilpua et al. 2009; Rouillard et al. 2010a, 2010b; Viall & Vourlidas 2015; Sanchez-Diaz et al. 2017; Lavraud et al. 2020). Clearly, there are many reasons and sources of evidence for the occurrence of anomalous characteristics that differ from the typical ambient solar wind. The question is whether they occur in organized ways that provide insights into their origins.


To study this, one must represent the dynamics in coordinates that focus on the mechanism. Action-angle expansions do this very well and are useful for systems which do not evolve with time (Binney & Tremaine 2008). However, we know that galaxies do evolve in time, and this time dependence influences the evolution itself. The nature of galactic dynamics requires analysis that can accurately treat multiple time-scales. For example, interesting evolution takes place on time-scales longer than the characteristic period, largely driven by resonant exchange and phase mixing. To do this efficiently, one may follow the gravitational field in evolving systems using basis-function expansions (BFE). BFE represents the potential and density of near-equilibrium galaxies in basis functions: pairs of biorthogonal functions that satisfy the Poisson equation and are mutually orthogonal (Clutton-Brock 1972, 1973; Kalnajs 1976; Fridman & Polyachenko 1984; Hernquist & Ostriker 1992; Weinberg 1999; Lilley et al. 2018a; Lilley, Sanders & Evans 2018b). Each of these basis sets (op. cit.) share the same properties but differ in the dimensionality, node location, profile shape, and method of construction. Most of these use integral transform methods following Clutton–Brock and Kalnajs. Alternatively, Weinberg (1999) solves radial part of the Poisson equation directly to best represent the underlying galaxy density profile. We adopt this method here. In effect, this windows the length scales to particular ones of interest based on the equilibrium model. We describe the relationship between these methods in the next section. Additionally useful, one can take any set of biorthogonal functions and create a new biorthogonal set of functions by a vector-space rotation. In particular, one may select the rotation by diagonalizing the variance matrix of the expansion coefficients given the particle distribution; this generates a new set of orthogonal functions that looks like the particle distribution (Petersen, Weinberg & Katz 2021). This new data-motivated basis is sometimes called empirical orthogonal functions (EOFs) after Lorenz (1956).


We only recall here the main features of this model. Heavy elements are produced through three main enrichment channels, namely by SNIa, SNII, and AGB stars, depending on their typical lifetimes and yields. To this purpose, we assume the initial mass function by Chabrier (2003) as a distribution of initial masses for the population of stars, and the mass-dependent lifetimes by Padovani & Matteucci (1993) to account for the different time-scales of stars of different masses. The abundance of the various metal species produced during the evolution of a stellar particle is then estimated by considering different sets of stellar yields for SNIa, SNII, and AGB (namely Thielemann et al. 2003, for SNIa; Woosley & Weaver 1995 combined with those by Romano et al. 2010, for SNII; Karakas 2010, for AGB stars). Once metals are produced, they are distributed from stars to surrounding gas particles by smoothing them on the SPH kernel, consistently with the other thermodynamical quantities, while no process of metal diffusion is explicitly included in the simulations. Previous studies in the literature have investigated the influence of changing the details of the metal spreading on the final enrichment pattern in simulated clusters (e.g. Tornatore et al. 2007; Wiersma et al. 2009b). From various tests presented in Tornatore et al. 2007 for the same chemical evolution model used in the current simulations, we conclude that changes in the numerical details of the metal injection scheme (e.g. number of neighbouring particles or weighting scheme for the metal diffusion to the gas) have only a minor impact on the resulting star formation history, stellar population, and chemical enrichment pattern. The differences, in particular, are smaller than the scatter from cluster to cluster. Moreover, for a given scheme of metal spreading, the final enrichment level of the simulated clusters is more strongly influenced by the physical processes included in the simulations, such as the energy feedback (see Fabjan et al. 2010; Planelles et al. 2014; Biffi et al. 2017).


Besides AGN feedback, additional clues on the SMBH–galaxy connection can be obtained from constraints on AGN obscuration, which can also occur on a range of physical scales (see review by Ramos Almeida & Ricci 2017). The most basic AGN unification model predicts that the obscuring medium is a small (parsec-scale) nuclear torus surrounding the active black hole (BH), and the degree of obscuration simply depends on the viewing angle (Antonucci 1993; Urry & Padovani 1995). However, there is compelling evidence for AGN obscuration being closely related to their host galaxies. For example, previous work has revealed different hosts and dust structures between Seyfert 1’s and 2’s down to fine angular scales, strongly disfavoring the conventional torus orientation picture (e.g., Malkan et al. 1998; Prieto et al. 2021). Furthermore, spatially resolved mid-IR or hard-X-ray studies of nearby heavily absorbed systems found that the obscuration is fully consistent with moderate- to large-scale dust lanes and features with a range of hydrogen column densities (Bianchi et al. 2007; Arévalo et al. 2014; Bauer et al. 2015), and with AGN ionization cone collimation taking place at distances well beyond the inner torus (Prieto et al. 2014; Mezcua et al. 2016). Additionally, the observed relationship between the 9.7 μm silicate absorption depth and the inclination of the host galaxies of heavily absorbed AGNs support large-scale obscuration (Goulding et al. 2012), and an intriguing trend for intermediate redshift star-forming galaxies points to an increasing fraction of heavily absorbed AGNs with increasing galaxy-wide specific star formation rate (= SFR/stellar mass, a tracer of galaxy gas fractions; Juneau et al. 2013). The latter suggests either a direct role of host galaxies gas in the absorption of X-rays from the AGN or a true physical link between the small-scale torus and the multiscale interstellar medium. Some studies find cases with high X-ray absorption (i.e., Compton-thick regime), which are consistent with small-scale torus absorption (e.g., Baloković et al. 2014; Markowitz et al. 2014; Ricci et al. 2014; Koss et al. 2017), or evidence for both nuclear and possible host galaxy contributions, where the latter might be dependent on galaxy mass and redshift (Brightman et al. 2014; Buchner et al. 2015; Buchner & Bauer 2017). Therefore, assessing AGN feedback, AGN obscuration, and the possible interplay with host galaxy properties and substructure can shed light on the SMBH–galaxy connection.


The observed two-point correlation function ωobs(θ) is corrected for an underestimation due to a finite coverage of the observation data. The correction is conducted by adding an integral constraint (IC; Groth & Peebles 1977) as follows:
(6)$$\begin{eqnarray}
\omega (\theta) = \omega _{\rm obs}(\theta) + \rm {IC}.
\end{eqnarray}$$With the assumption of a single power-law correlation function ω(θ) = Aωθ−δ, IC is expressed by the formalism in Roche et al. (1999) as
(7)$$\begin{eqnarray}
\mathrm{IC} = \frac{\Sigma _{i}[RR(\theta _{i})\omega (\theta _{i})]}{\Sigma _{i} RR(\theta _{i})},
\end{eqnarray}$$where RR(θi) is the non-normalized number of random–random pairs. Combined with equation (7), equation (6) becomes
(8)$$\begin{eqnarray}
\omega _{\rm obs}(\theta) = A_{\omega }\biggl [\theta ^{-\delta } - \frac{\Sigma _{i}[RR(\theta _{i})\theta _{i}^{-\delta }]}{\Sigma _{i} RR(\theta _{i})}\biggr ].
\end{eqnarray}$$The observed two-point correlation function ωobs(θ) is fitted by equation (8) to obtain the corrected two-point correlation function ω(θ). We conducted the fit by fixing a slope parameter δ to 0.8. Since δ is sensitive to the sample size, constraining the slope δ is not effective because of the small number of sgzK galaxies. The result with fixed δ is useful for direct comparison with previous studies since many studies assumed the slope parameter δ fixed to 0.8 (Kong et al. 2006; Hayashi et al. 2007; Blanc et al. 2008; Hartley et al. 2008; Ishikawa et al. 2015). The least-squares fit procedure in mpfit1 (Markwardt 2009) was used to determine Aω. The two-point correlation functions for sgzKs with Ks  21.1 and 21.5 are presented in Fig. 4. Ishikawa et al. (2015) reported that the two-point correlation function of sgzKs at small angular scale (θ ≲ 0${_{.}^{\circ}}$01) has a steeper slope compared to that at large angular scale, which represents the difference of contributions from the one-halo term (pairs of sgzKs in the same halo) and the two-halo term (pairs of sgzKs in different haloes) as predicted from the analysis by the dark matter halo model. However, such characteristic is unclear in Fig. 4 due to the small number of sgzK galaxies. The results of clustering analysis for the two magnitude-limited sgzKs are listed in Table 1. In Fig. 5, the amplitudes of two-point correlation functions for sgzKs are presented together with the results in the literature. For the estimation of the error, we considered the effect of cosmic variance. For this, we used four sub-regions presented in Fig. 1. Two-point correlation functions were estimated four times separately after excluding each of the sub-regions in turn. A standard deviation of the four two-point correlation functions can be treated as the uncertainty of two-point correlation function due to cosmic variance. It was added quadratically in the estimation of the error of two-point correlation function. As shown in Fig. 5, our result is comparable to the previous studies. In addition to the results in the literature, our result shows Ks-band magnitude dependence of the clustering strength.


NGC1068 is a nearby (D = 14 Mpc Bland-Hawthorn et al. 1997, 1″ ∼ 70 pc) Seyfert 2 galaxy and is considered to be the archetype of a composite AGN-starburst system. The proximity of this composite galaxy makes it an ideal laboratory for resolving the feedback from the starburst regions that are spatially distinct from the AGN activity. NGC 1068 has been extensively investigated by many single-dish and interferometric campaigns focused on the study of how its central region is fueled and the related feedback activity, using molecular line observations (e.g., Usero et al. 2004; Israel 2009; Kamenetzky et al. 2011; Hailey-Dunsheath et al. 2012; Aladro et al. 2013; García-Burillo et al. 2014, 2017, 2019; Viti et al. 2014; Impellizzeri et al. 2019; Imanishi et al. 2020). The available CO Observations of NGC 1068 by Schinnerer et al. (2000) reveal the molecular gas distributing over three regions, which has also been confirmed by, for instance, García-Burillo et al. (2014, 2019) and Sánchez-García et al. (2022): a starburst ring (SB ring) with a radius ∼1.5 kpc, a circumnuclear disk (CND) of radius ∼200 pc, and a ∼2 kpc stellar bar running north east, along PA ∼48° (Scoville et al. 1988), from the CND. In García-Burillo et al. (2014) and Viti et al. (2014), five chemically distinct regions were found to be present within the CND: the AGN, the East Knot, West Knot, and regions to the north and south of the AGN (CND-N and CND-S) using data from the Atacama Large Millimeter/submillimeter Array (ALMA). Viti et al. (2014) combined these ALMA data with Plateau de Bure Interferometer (PdBI) data and determined the physical and chemical properties of each region. It was found that a pronounced chemical differentiation is present across the CND and that each sub-region could be characterized by a three-phase component interstellar medium, where one of the components is comprised of shocked gas. In fact, García-Burillo et al. (2010) used the PdBI to map NGC 1068 and found strong emission of SiO(2–1) to the east and west of CND. The SiO kinematics of the CND point to an overall rotating structure and is distorted by non-circular or non-coplanar motions, or a combination of both. The authors have concluded that this could be due to large scale shocks through cloud-cloud collisions or through a jet-ISM interaction. Such shock-related non-circular kinematics of gas was also identified by Krips et al. (2011) using several molecular ratios of CO, 13CO, HCN, and HCO+. However, due to strong CN emission that is not easily explained by shock models nor photon-dominated region (PDR) chemistry, these authors also suggested that the CND could actually be one large X-ray dominated region (XDR).


There are some indications that available models of the post-AGB and CSPN phases are not accurate enough. First, the two available grids of post-AGB models (Vassiliadis & Wood 1994; Blöcker 1995a) do not agree with each other on the predicted timescales (Zijlstra et al. 2008). Second, consistency between the masses of white dwarfs and those of CSPNe seems to require faster evolutionary speeds than predicted by both sets of models (Gesicki et al. 2014). Third, present models of the CSPNe phase are unable to explain why the cut-off of the PNe luminosity function is constant in most galaxies (Marigo et al. 2001, 2004). Lastly, post-AGB stellar evolution models, computed with updated physics in a reduced mass range (Kitsikis 2008; Weiss & Ferguson 2009), show a strong disagreement with the previous grids. This is not a surprise since many improvements have been carried out in the field of stellar physics in recent decades. Most importantly, available grids have been computed with opacities, which are now 45 years old (Cox & Stewart 1970b,a) before the big changes introduced by the OPAL (Iglesias & Rogers 1996), and Opacity Project (Seaton 2007) redeterminations. Similarly, nuclear reaction rates, equation of states, conductive opacities, and neutrino emission rates adopted in the models date from the early eighties and even earlier. In addition, Herwig et al. (1997) showed that the existence of carbon stars at low luminosities can be explained by the addition of mixing beyond the formal convective boundaries during the thermal pulses (TP) on the AGB. Finally, Marigo (2002) showed that C-rich molecular opacities are essential to predict the correct effective temperatures once the AGB models become carbon rich (NC/NO> 1, by number fractions). This is particularly important because of the impact of effective temperatures on the mass loss rates. While all these improvements in stellar modeling have been implemented in AGB stellar models, and very detailed and exhaustive grids and models are available (Weiss & Ferguson 2009; Cristallo et al. 2009, 2011; Ventura & Marigo 2010; Karakas 2010; Lugaro et al. 2012; Constantino et al. 2014; Doherty et al. 2015), the inclusion of these improvements in post-AGB stellar models is still missing. It is time for a recomputation of the post-AGB models in the light of all these advances.


Recently, another explosion mechanism has gained more attention in the context of both the explosion dynamics and formation process of neutron stars composed of exotic matter at their interiors (see Fischer et al. 2018; Zha et al. 2020). When the energy density becomes sufficiently high, then nuclear—in general, hadronic—matter undergoes a phase transition to the deconfined quark–gluon plasma. Therefore, the solution of quantum chromodynamics (QCD)—the theory for strong interactions with quarks and gluons as the degrees of freedom—predicts a smooth crossover transition at a pseudocritical temperature in the range of 150–160 MeV (Bazavov et al. 2014; Borsányi et al. 2014; Bazavov et al. 2019). However, this is the case only at vanishing baryon density, and hence cannot be applied to astrophysical applications of compact stellar objects such as neutron stars and supernovae. At high density, phenomenological quark matter models have long been employed in astrophysical studies, based on the common two-phase approach with separate hadronic and quark matter phases. Such phase transition construction results not only in the transition to the third family of compact stars, known as hybrid stars, as an extension to the neutron stars second family, but also in the as-yet incompletely understood question of the nature of the QCD phase transition at high baryon density (see Annala et al. 2020, and references therein). It is likely that low- and intermediate-mass NSs, having masses of ∼1.4 M
⊙, can be explained solely by hadronic equations of state (EOS). More massive NSs with ∼2 M
⊙, the presence of which has been observationally confirmed at high accuracy (see. Demorest et al. 2010; Antoniadis et al. 2013; Cromartie et al. 2020), feature the highest baryon densities encountered in the universe. It is a valid question to ask if a QCD transition occurs at the densities encountered at the interior of such massive pulsars (see Kurkela et al. 2014, and references therein). Furthermore, if confirmed, this is likely to affect our understanding of the core-collapse supernova phenomenology.


The magnetic field configuration at the deep photosphere shows a low twist in most of the umbra (Fig. 4b). Only some penumbral regions exhibit a certain twist, which is generally below 30°. On the contrary, the twist measured at the height of the Si I 10 827 Å line shows high values at the bottom right quarter, which reach values up to −90° around the umbra-penumbra boundary. This twist contrasts with that found inside the umbra at the bottom left quarter, which is mainly positive. Socas-Navarro (2005) found that the magnetic twist can change the sign from the photosphere to the chromosphere. Our observations indicate that the twist can change from the deep photosphere (where it is almost negligible) to higher photospheric layers (where negative and positive twists coexist). This variation takes place over a height difference of around 130 km (Felipe et al. 2018). However, the degree of the twist may be sensitive to the choice of the center of the sunspot. In this context, it can be more meaningful to discuss the magnetic field torsion. Figure 4e shows that the bottom part of the penumbra has a slightly negative torsion, with stronger values near the umbra-penumbra boundary (in the same region where the twist from the Si I 10 827 Å line was higher). Since the magnetic field at the formation height of the Ca I 10 839 Å line is approximately pointing towards the center, a negative torsion indicates that at the formation height of the Si I 10 827 Å line the horizontal component of the magnetic field is shifted clockwise from the radial direction (see Fig. 5 for a vectorial representation of the horizontal magnetic field). A positive torsion, such as that measured at the left and bottom part of the umbra, means that the magnetic field is shifted counterclockwise. The position on the horizontal plane of the wavefront of a slow magnetoacoustic wave propagating along magnetic field lines from the deep photosphere to the high photosphere will rotate according to the direction of the torsion. As discussed in Sect. 3.1, the bottom arm of the spiral wavefront initially appears at the left side of the umbra and moves counterclockwise towards the center of the sunspot. This movement is in agreement with the positive torsion measured at that region from the analysis of the spectropolarimetric map. On the contrary, at the regions where the measured torsion is negative, we do not detect clockwise motions of the spiral wavefront. In that part we only find a radially outward movement.


The mergers of double neutron star systems or the neutron star-black hole binaries generate strong gravitational wave (GW) radiation as well as short-duration gamma-ray bursts (SGRBs; including the so-called long-short GRBs that have a duration longer than 2 s but are unaccompanied by supernova emission down to very stringent limits; Eichler et al. 1989; Piran 2004; Della Valle et al. 2006; Fynbo et al. 2006; Berger 2014). Before 2017, it was widely believed that the GW/SGRB association rate is low because the SGRB outflows are highly collimated with a typical half-opening angle of ∼0.1 rad (Clark et al. 2015; Li et al. 2016). Surprisingly, on 2017 August 17, the gamma-ray monitor on board the Fermi γ-ray space telescope and INTEGRAL had successfully detected a weak-short GRB 170817A (Goldstein et al. 2017; Savchenko et al. 2017) that is spatially and temporally correlated with GW170817, the first neutron star merger event detected by Advanced LIGO/Virgo (Abbott et al. 2017). The GW/SGRB association has been formally established. However, considering the relatively small event distance (D ∼ 40 Mpc), the isotropic-equivalent gamma-ray radiation energy of GRB 170817A is just ∼3 × 1046 erg, which is at least 100 times dimmer than that of the typical SGRBs. An underluminous SGRB could either result from the breakout of the mildly relativistic shock from the leading edge of the merger-driven quasi-isotropic sub-relativistic ejecta (Kasliwal et al. 2017), or be the faint prompt emission of a highly structured relativistic ejecta viewed at a large polar angle (Jin et al. 2018). The puzzling fact that GRB 170817A and the long-duration GRB 980425 (at a distance of D ∼ 36 Mpc, and that has been suggested to be the shock breakout signal; Kulkarni et al. 1998), the two close events with remarkably different progenitors, have rather similar luminosity and spectral peak energy (Wang et al. 2017), may favor the shock breakout model. It is thus unclear whether or not GW170817-like mergers are indeed the sources of the bright SGRBs. The forward shock afterglow observations of GW170817/GRB 170817A are helpful in answering such a question. Though the “early” rising X-ray and radio afterglow emission could be reproduced by a cocoon-like mildly relativistic ejecta (Kasliwal et al. 2017), the late-time afterglow data modelings strongly favor the presence of an off-axis relativistic (structured) outflow component (D’Avanzo et al. 2018; Lamb et al. 2018; Mooley et al. 2018b; Yue et al. 2018). Particularly, the off-axis relativistic outflow component at a viewing angle of θv ∼ 0.35 rad has been convincingly identified/measured in the radio image (Mooley et al. 2018a; Ghirlanda et al. 2019). Nevertheless, a direct “observational” link between GW170817/GRB 170817A and bright SGRBs is still lacking. In this Letter, we carry out statistical studies of the SGRB afterglow data and aim to establish such a connection.


In the coupled ADAF-jet model, the accretion flow ADAF and the jet are connected by a defined parameter, $\eta \equiv \dot{M}_{\rm jet}/\dot{M}$, and $\dot{M}_{\rm jet}$ is input by assuming a value of, η, which is free parameter in the present model. The half-opening angle ϕ of the jet in the low/hard state of NS-LMXBs is uncertain. In this paper, we fix ϕ = 0.1 as assumed by several other authors for modelling the SED of the BH-LMXBs (e.g. Yuan et al. 2005; Zhang et al. 2010). Observationally, the bulk Lorentz factor of the jet in the low/hard state of X-ray binaries can be restricted in a relatively narrow range and the velocity of the jet is mildly relativistic, i.e. Γjet ≲ 2. More strictly, the bulk Lorentz factor is restricted to be as Γjet ≲ 1.67 (Gallo et al. 2003), and Γjet ≲ 1.2 (Fender 2006). In the internal shock model, the energy density of the internal shock increases with increasing Γjet, which finally will result in an increase of both the radio emission and X-ray emission (Yuan et al. 2005). However, since Γjet is restricted in a very narrow range by observations, we expect that a slight change of Γjet will result in a slight change of the jet emission. In this paper, we fix Γjet = 1.2 corresponding the bulk velocity of the jet 0.55c (Fender 2006). The value of ϵe and ϵB describing the fraction of the internal energy of the internal shock stored in the accelerated electrons and the magnetic field, and the index, pjet, describing the power-law distribution of the electrons in the jet after the acceleration by the shock are uncertain. Qiao & Liu (2015) tested the effect of ϵe and ϵB on the emergent spectrum of the jet in an observationally inferred range of 0.01  ϵe  0.1 and 0.01  ϵB  0.1. It was found that a change of ϵB in the range of 0.01–0.1, the emergent spectrum of the jet nearly does not change (see the right-hand panel of fig. 3 of Qiao & Liu 2015). A change of ϵe in the range of 0.01–0.1, the radio spectrum nearly does not change. However, the X-ray luminosity changes obviously by changing the value of ϵe from 0.01 to 0.1 (see the left-hand panel of fig. 3 of Qiao & Liu 2015). As shown in the left-hand panel of fig. 2 of Qiao & Liu (2015), the X-ray emission is completely dominated by the accretion flow (corona) in the luminous X-ray state, which is also true in this paper, i.e. the X-ray emission from the ADAF completely dominates the X-ray emission from the jet. In this paper, we fix ϵe = 0.04 and ϵB = 0.02, respectively, throughout the paper as (Qiao & Liu 2015). The value of the power-law index pjet of the electron distribution in the jet predicted by the shock acceleration is 2  pjet  3. By modelling the SEDs of three BH-LMXBs, the value of the power-law index pjet of the electron distribution is constrained to be 2.1 (Zhang et al. 2010). Meanwhile, a change of pjet in the range of 2  pjet  3 has very minor effect on the X-ray spectrum. In this paper, we fix the power-law index pjet = 2.1 throughout the paper.


Another important sink for CO2 is the loss of CO2 by weathering of the surface. We neglected this effect in the present study as in Tosi et al. (2017). Foley & Smye (2018) study the potential impact of weathering for stagnant-lid planets. They find that for large enough planetary carbon reservoirs and radiogenic heating, weathering and outgassing can balance each other for 1000–5000 Myr, thus enabling habitable surface conditions. On the one hand, for large carbon reservoirs they show that weathering is supply-limited, i.e. the supply of fresh surface material is likely too small such that CO2 would accumulate in the atmosphere, which leads to a Venus-like, uninhabitable hot climate. On the other hand, for low outgassing rates limited by the carbon reservoir, the planet would likely exist in a snowball state. For the snowball state limit, they use outgassing values determined by Haqq-Misra et al. (2016) and Kadoya & Tajika (2014) as lower limits, which are equal to 10 and 100% of present Earth’s outgassing, respectively; 10% of Earth’s CO2 outgassing flux, as adopted by Foley & Smye (2018), corresponds to ~2.6 ⋅ 1010 kg yr−1. In our models the rate of CO2 outgassing depends on the initial water concentration and on the assumed redox state. For 62 ppm water in the mantle and

$f_{\mathrm{O}_2}$

f

O
2

 at the IW buffer, the outgassing rate during the phase of melt production peaks at about 2.5 ⋅109 kg yr−1, while for

$f_{O_2}$

f

O
2

 at IW+1 it is one order of magnitude higher, and hence comparable with the lower limit mentioned above. Foley & Smye (2018) discuss weathering for Earth-like water reservoirs. In our scenarios, the weathering of the surface could be limited by the smaller surface water reservoir and lower precipitation rates. Therefore, although our outgassing rates are close to the lower limits adopted by Foley & Smye (2018) that might lead to snowball states, the overall impact of weathering on our findings is not easily predictable and will require further study. Furthermore, Foley & Smye (2018) consider metamorphic outgassing as an additional source of CO2, which could increase CO2 outgassing rates. Metamorphic outgassing refers to the release of CO2 associated with the decarbonation of buried carbonated crust. On Earth, the contribution of this mechanism to the planet’s long-termcarbon cycle is thought to be potentially important, but is still poorly understood (Evans 2011). Furthermore, the release of carbon due to metamorphic processes is generally associated with partial melting in subduction zones (e.g. Dasgupta & Hirschmann 2010) and deformation in active orogenic regions (e.g. Evans et al. 2008), two settings that are intimately related to plate tectonics and hence absent in a stagnant-lid planet. Whether metamorphic outgassing on such bodies can be as relevant as on a planet with plate tectonics is therefore unclear and deserves more investigation.


The hydrodynamic equations (1–5) are solved in this paper using total variation diminishing (TVD) scheme, introduced and developed by Harten (1983). The scheme (or the modified version of it) is applicable to hydrodynamic problems and has been used extensively in relevant astrophysical applications (Ryu 1993; Ryu et al. 1995a; Ryu, Jones & Frank 1995b; Lee, Ryu & Chattopadhyay 2011; Chattopadhyay et al. 2012; Lee et al. 2016). TVD scheme is an Eulerian, second-order accurate, non-linear, finite difference scheme, which accurately captures shock. The temporal and spatial evolution of the conserved quantities ρ, ρvi, and ${\cal E}$ is computed using approximate Roe type Riemann solver to solve the differential equations, followed by application of a non-oscillatory first-order accurate scheme to the modified flux functions to achieve second-order accuracy (see Roe 1981; Harten 1983; Ryu 1993). Equations of motion (1–5) are similar to those solved in Chattopadhyay et al. (2012). In Chattopadhyay et al. (2012), the galactic outflow was powered by the radiation from the galactic disc, while being decelerated by the gravity of the galactic disc, the halo, and the bulge matter. In contrast, in this paper, the accretion disc outflow is powered by the radiative fluxes and the centrifugal force from the KD, and is decelerated by the radiative drag terms as well as the gravity of the central black hole. To solve the equations of motion (1–5), we considered the TVD scheme (see Chattopadhyay et al. 2012, for details) for the resolution 512 × 512. A schematic representation of the computational arrangement is presented in Fig. 2, which marks the ghost cells where the boundary conditions are implemented and also the computational domain. We employed continuous boundary condition at z = 0 boundary, and outflow boundary condition at the outer r and z boundaries (i.e. no inflow but continuous if v > 0). At r = 0, or the axis of symmetry, reflection boundary condition has been employed. The type of boundary conditions employed are also mentioned in Fig. 2. We simulate a region of 512 from the black hole, each in r and z direction, therefore the dimension of each cell is equivalent to 1. The gravity of the black hole is described by Paczyński and Wiita potential (Paczyński & Wiita 1980). In order to avoid the coordinate singularity on the horizon, the black hole is covered by a sink region of radius 3 around the origin, which do not affect the physics since the inner edge of KD is 3.


The CMEs are solar eruptions caused by magnetic reconnections in the star corona (Low 2001; Howard 2006). They expel a large amount of fast charged particles and a magnetic cloud that evolves into an interplanetary coronal mass ejection (ICME; Sheeley Jr. et al. 1985; Neugebauer & Goldstein 1997; Cane & Richardson 2003; Gosling 1990). If the ICME impacts the Earth, the measured SW dynamic pressure increases to 10−100 nPa and the IMF intensity to 100–300 nT (Gosling et al. 1991; Huttunen et al. 2002; Manchester IV et al. 2004; Schwenn et al. 2005; Riley 2012; Howard 2014; Mays et al. 2015; Kay et al. 2017; Savani et al. 2017; Salman et al. 2018; Kilpua et al. 2019; Hapgood 2019). The Disturbance Storm Time Index (Dst) indicates the magnetic activity derived from a network of near-equatorial geomagnetic observatories that measures the intensity of the globally symmetrical equatorial electrojet (the ring current), which is widely used to identify extreme SW and IMF space weather conditions (Sugiura & Chapman 1960; Loewe & Prölss 1997; Siscoe et al. 2006; Borovsky & Shprits, Yuri 2017). A negative Dst value means that Earth’s magnetic field is weakened due to the IMF erosion, particularly during solar storms. The strongest event observed so far is the Carrington event that occurred in 1859 (Carrington 1859). An unusual large number of sunspots on the solar disk and a wide active region was registered, and an extremely fast ICME was launched from it toward the Earth. Several authors studied the Carrington event and suggested that it was a shock that traveled at about 2000 km s−1 (Cliver et al. 1990) that generated the strongest geomagnetic storm with Dst ≈−1700 nT (Tsurutani et al. 2003). This was later revised to Dst ≈−850 nT by Siscoe et al. (2006). The most recent strongest event, called the Bastille Day event (14–16 July 2000), reached a Dst ≈−300 nT for an SW velocity of 1000 km s−1 and an IMF intensity of ≈45 nT (Rastatter et al. 2002). On the other hand, typical ICMEs impacting the Earth show an averaged plasma velocity of 350–500 km s−1 and IMF intensities between 9–13 nT, leading to geomagnetic storms with Dst  −50 nT (Cane & Richardson 2003).


Ring systems are a ubiquitous feature in planetary systems – all the gas giants in the Solar System have ring systems around them of varying optical depths (see, e.g., Tiscareno 2013; Charnoz et al. 2018), and ring systems have been detected around minor planets (e.g., Chariklo; Braga-Ribas et al. 2014), so it is reasonable that exoplanets and substellar objects host ring systems as well. Long-period eclipsing binary star systems, where one star is surrounded by an extended dark disk-like structure that periodically eclipses the other component, have already been observed, such as EE Cep (Mikolajewski & Graczyk 1999), ϵ Aurigae (Guinan & Dewarf 2002), and TYC 2505-672-1, with a companion period of 69 yr (Lipunov et al. 2016; Rodriguez et al. 2016). A large ring-like structure around a substellar companion was proposed to explain observations from 2007 from the J1407 system (Mamajek et al. 2012). 1SWASP J140747.93-394 542.6 (V1400 Cen; hereafter called “J1407”) is a young, pre-main-sequence star in the Sco-Cen OB association (Mamajek et al. 2012) with spectral type K5 IV(e) Li and is similar in size and mass to the Sun. In 2007, it displayed a complex symmetric dimming pattern of up to ~ 3 magnitudes during a 56 day eclipse. This has been attributed to the transit of a substellar companion (called “J1407 b”) with a mass of 60–100 MJup (Rieder & Kenworthy 2016) surrounded by an exoring system consisting of at least 37 rings and extending out to 0.6 au in radius (Kenworthy & Mamajek 2015). For these rings to show detectable transit signatures, they must be significantly misaligned with respect to the orbital plane of J1407 b (Zanazzi & Lai 2017). This potential ring system would be considerably larger than the ring system of Saturn, which is located within the planet’s tidal disruption radius. The proposed rings around J1407 b would even cover a significant fraction of the companion’s Hill sphere and would not be expected to be stable over gigayear timescales. If the candidate ringed companion is in a bound orbit around the star, this orbit must be moderately eccentric in order for no othereclipses to have been detected to date (Kenworthy et al. 2015), raising the possibility that there might be a second as yet undetected companion in the system that causes the implied orbital eccentricity for J1407 b. Radial velocity measurements are overwhelmed by the chromospheric noise of the star and do not place strong constraints on other substellar companions (Kenworthy et al. 2015). The transit of J1407 suggests that its orbital plane has a high inclination to our line of sight – if there are other planets inside the orbit of J1407 b, their orbits may well be coplanar with J1407 b and there is a high chance that these companions may transit J1407.


The X-ray luminosity of CG X-1 is variable by a factor of ≈10 (Bianchi et al. 2002; Weisskopf et al. 2004). The highest flux reported in the literature (5.2 × 10−12 erg cm−2 s−1 for a power-law fit or 5 × 10−12 erg cm−2 s−1 for an MCD fit, in the 0.5–8 keV band; Weisskopf et al. 2004) would imply, for a distance of 4.2 Mpc, a 0.5–10 keV luminosity of LX = (1.5–2) × 1040 erg s−1. If the system is Eddington-limited, the lower limit on the mass of the accreting BH is MBH ≳ 75 M⊙ for an He or C/O donor. For the system to shine in X-rays, the velocity of the WR star wind has to be slow enough to allow the formation of an accretion disc. This condition corresponds for CG X-1 to the requirement MBH ≳ 1.5 vw, 10004δ2 M⊙, where MBH is the BH mass, vw, 1000 is the wind velocity in units of 1000 km s−1, and δ ≈ 1 is a dimensionless parameter (adapted from Carpano et al. 2007b, see also Illarionov & Sunyaev 1975). In the simplest wind-accretion case (e.g. Edgar 2004), the luminosity can be estimated as

(1)

\begin{equation}
L_{\rm{X}}\approx \eta \frac{\dot{M}_{\rm{w}} c^2G^2M_{\rm{BH}}^2}{a^2 (v_{\rm{orb}}^2+v_{\rm{w}}^2)^2},
\end{equation}

where η is the efficiency, $\dot{M}_{\rm{w}}$ is the wind mass-loss rate, a is the orbital separation, vorb is the orbital velocity, and vw is the wind velocity at the BH orbit. Assuming $\dot{M}_{\rm{w}} = 10^{-5}$ M⊙ yr−1 and vw = 1000 km s−1 for the WR star (e.g. Crowther 2007), a = 5.8 × 1011 cm (for a 10 M⊙ companion), MBH = 75 M⊙, and the formation of a disc with η = 0.1, the corresponding luminosity is LX ≃ 2 × 1040 erg s−1. More in general, for MBH > 10 M⊙ and all the other things being equal, one finds LX ≳ 3 × 1039 erg s−1. In case of Roche lobe overflow, even higher X-ray luminosity could be achieved. However, we note that if CG X-1 is indeed a WR–BH binary, the WR star is probably not filling its Roche lobe [unless it is very massive; see for example the discussion of the case of Cyg X-3, where the orbital period is much shorter, in Szostek & Zdziarski (2008)]. An X-ray luminosity of ∼2 × 1040 erg s−1 can be therefore accounted for. We finally notice that, although we do not regard the question as crucial, the problem of the lifetime of the system discussed by Weisskopf et al. (2004) would be significantly attenuated, since the WR phase of a massive O-type star is thought to last a few ×105 yr (Meynet & Maeder 2005).


Both Nel (2016) and Zhao et al. (2018) report that these parallel mean free paths are smaller during periods of high solar activity and larger during solar minima, with the opposite being true for the resulting perpendicular mean free paths. Zhao et al. (2018) also show that such solar cycle dependences would not be fully accounted for if only the solar cycle changes in the HMF were taken into consideration. These mean free paths also display complicated spatial dependences if turbulence quantities beyond 1 au, yielded by various turbulence transport models (see, e.g., Oughton et al. 2011; Usmanov et al. 2016; Wiengarten et al. 2016; Zank et al. 2017), taking into account observed latitudinal variations of turbulence quantities in the heliosphere (Forsyth et al. 1996; Bavassono et al. 2000a, 2000b; Erdös & Balogh 2005), were used as inputs for the turbulence quantities (e.g., Engelbrecht & Burger 2013a, 2015b; Chhiber et al. 2017; Moloto et al. 2018). Furthermore, mean free paths such as those discussed have, when used in conjunction with turbulence-reduced drift coefficients (see, e.g., Minnie et al. 2007b; Engelbrecht et al. 2017) in 3D stochastic modulation codes, led to computed galactic intensities in reasonable agreement with spacecraft observations at Earth (see, e.g., Engelbrecht & Burger 2013a, 2013b; Qin & Shen 2017) and even for several different solar minima (Moloto et al. 2018). The necessity of taking cosmic-ray drift effects into account, combined with the complicated spatial dependences and the fact that none of the diffusion coefficients described above display a P1 rigidity dependence, implies that a convection–diffusion or force-field approach would not be ideal to describe long-term modulation, and that the assumptions implicit to the effective diffusion coefficient used in these formulations are unrealistic. This latter point would call into question any conclusions drawn as to historic solar parameters from quantities such as the modulation potential.


Rather than AGN feedback, it is possible that the effects we are seeing are from a different process coeval or prior to the onset of AGN accretion. Several works have pointed out that AGN activity coincides with a recent starburst, with the AGN having significant accretion events at least ∼200 Myr after the starburst has occurred (Davies et al. 2007; Wild et al. 2007; Wild, Heckman & Charlot 2010; Yesuf et al. 2014) giving the neutral material time to propagate out to the impact parameters probed by COS-AGN (Heckman et al. 2017). With a sample of QSO sightlines probing the CGM around 17 low-redshift starburst and post-starburst galaxies, Heckman et al. (2017) have observed a similar signature of enhanced EWs of Ly α, Si iii, and C iv (the latter of which is not measured in our control sample) relative to a control-matched sample (matched in stellar mass and impact parameter). In the range of impact parameters and stellar masses probed by COS-AGN, the strength of our enhanced EW signature is consistent with the values probed by Heckman et al. (2017). However, the results of Heckman et al. (2017) show strong offsets in the kinematics of the gas from the host galaxy (≈100 km s−1; see fig. 5 from Heckman et al. 2017), whereas the COS-AGN sightlines do not (bottom panel of Fig. 6). Assuming that the AGN activity was triggered by the starburst, a minimum delay time of 200 Myr could allow for any starburst-driven winds to dissipate and kinematic offsets to no longer be present at the impact parameters of the COS-AGN sample. Although this starburst picture provides a possible explanation of our observations, we caution that starbursts are not the only astrophysical event linked to AGN accretion activity. For example, mergers that trigger the AGN (Ellison et al. 2011, 2013; Satyapal et al. 2014; Silverman et al. 2014; Goulding et al. 2018) could potentially affect the surrounding CGM gas. Past and future work focusing on the CGM of galaxy mergers can further test this result (Johnson et al. 2014; Hani et al. 2017; Bordoloi et al. in preparation).


The largest fragment in this cluster, (525) Adelaide, is the only asteroid with some physical characterisation available. Masiero et al. (2014) analysed WISE/NEOWISE infrared observations and reported Adelaide’s size D = 9.33 ± 0.24 km and geometric albedo pV = 0.22 ± 0.05. These results assume an absolute magnitude H = 12.4 mag in the visible band. More up-to-date absolute magnitude determinations across all standard databases (such as MPC, JPL, or AstDyS) indicate a slightly smaller value of absolute magnitude: H ≃ 12.1. The difference of about 0.3 magnitude is a characteristic scatter in this parameter reported by Pravec et al. (2012), who also noted that near H ≃ 12 mag the systematic offset of the database-reported values should be small (becoming as large as − 0.5 mag for smaller objects). It is therefore possible that the true size of (525) Adelaide is slightly larger, its geometric albedo slightly higher, or a combination of both. The answer will be found when photometrically calibrated data of this asteroid are taken. Luckily, this issue is not critical for our analysis. With a safe margin we can assume Adelaide’s size to be between 9 and 11.5 km, and the geometric albedo between 0.22 and 0.29. This albedo range closely matches the characteristic value in the Flora family region of the inner main belt. Nesvorný et al. (2015) identified (525) Adelaide as a member in the Flora family despite the proper inclination value of its orbit being at the high end of the Flora family members. Nevertheless, whether Adelaide is a fragment from the Flora-family formation event, which took part more than 1 Gyr ago (e.g. Vokrouhlický et al. 2017b), is again not a crucial issue for our study. The confirmation of this albedo value also comes from broad-band photometry of (525) Adelaide taken by the Sloan Digital Sky Survey (SDSS) project. Considering the methodology in Parker et al. (2008), we used the SDSS-based observations to infer its colour indexes a* = 0.108 and i − z = −0.08. Given the information in Fig. 3 of Parker et al. (2008) we concluded that these values are characteristic of S-complex asteroids. This is a prevalent spectral type in the Flora zone, and the characteristic albedo values of these objects very closely match those given for (525) Adelaide.