The solar corona is still enigmatic from a scientific point of view, with important unsolved questions about its nature, such as solar wind acceleration and coronal heating (McComas et al. 2007; Parnell & De Moortel 2012). Although finding solutions to these questions is important on its own, it is also expected to have major implications for related fields, such as space weather (Singh et al. 2010), which is set to grow in importance as we make advances in technology and space exploration. One impediment toward solving coronal mysteries is the notorious difficulty in determining its key physical parameters, such as the magnetic field, by direct spectroscopic or polarimetric measurements. Early observational evidence of waves in coronal structures using SOHO/TRACE (Aschwanden et al. 1999; Berghmans & Clette 1999) paved the way for the previously theorized coronal seismology (Uchida 1970; Roberts et al. 1984) to be a tool for coronal plasma diagnostics. The first attempt to seismologically determine the magnetic field of transversely oscillating coronal loops was applied to the first such event observed by Nakariakov & Ofman (2001). Since then, coronal seismology has successfully been applied to numerous oscillation events (for reviews, see, e.g., De Moortel 2005; De Moortel & Nakariakov 2012; Stepanov et al. 2012). A common feature of all previously diagnosed events is their localization in time, i.e., single events. This obviously limits the applicability of seismology to the brief duration of the oscillation event. Moreover, these single-oscillation events tend to be rare, as they are mostly related to flaring events or eruptions, meaning that seismology is restricted to brief diagnostics highly localized in time, or in time and space for non-global oscillations. However, the discovery of ubiquitous propagating transverse oscillations with CoMP (Tomczyk et al. 2007; Tomczyk & McIntosh 2009) and SDO (McIntosh et al. 2011) or the more recently identified nearly ubiquitous, decay-less low-amplitude kink coronal loop oscillations (Anfinogentov et al. 2013, 2015; Nisticò et al. 2013), as well as oscillations in plumes (Thurgood et al. 2014), led to the possibility of continuous diagnostics in time, i.e., dynamic coronal seismology. Consequently, very recently, the first seismologic “magnetic field image” was obtained, based on the ubiquitous transverse waves (Long et al. 2017), using a methodology put forth by Morton et al. (2015). In this study, the authors use the magnetohydrodynamic (MHD) kink phase speed of a flux tube (Edwin & Roberts 1983) as the inversion tool for the magnetic field. These ubiquitous propagating transverse waves are now widely regarded as Alfvénic waves (Goossens et al. 2012), although this reinterpretation of the nature of the waves does not modify the phase speed formula used in the inversion. However, it is still assumed that the observed ubiquitous waves are transverse oscillations of flux tubes, and while the fine structure in the corona is still unknown (Peter et al. 2013; Reale 2014; Aschwanden & Peter 2017), it is unlikely that the magnetic cylinder model is satisfactory. Structuring across the magnetic field, among other factors (De Moortel & Pascoe 2009; Pascoe & De Moortel 2014), is an important detail for seismology, as it can greatly influence the nature and propagation of MHD waves (Luna et al. 2010; Terradas et al. 2010; Verth et al. 2010), altering the dependence of the observed phase speed on physical properties such as the magnetic field or mass density (e.g., Verth et al. 2007; Arregui et al. 2013), which might lead to erroneous inversions if not considered. Some light was shed recently on the weaknesses of modeling the corona as a bundle of independent thin magnetic strands by Magyar & Van Doorsselaere (2016). In their simulations, a loop consisting of packed strands is quickly deformed and mixed when disturbed by propagating transverse waves, leading to a turbulent cross-section (Magyar et al. 2017). This result reiterates the above-mentioned need to move away from rigid cylindrical models in favor of more realistic descriptions that account for nonlinearities.


The distance between the peak of the main source and the transient source (blue POSS I) is ≈6 pixels or ≈6 arcsec (≈0.3 kpc) towards the North, at an angle of ≈− 10° (Fig. 2; left-hand column; rows 4–5). From the PSF characteristics of the blue POSS I and blue subtracted POSS images (Section 2.1.1), the transient source is slightly resolved ( 2 × PSF FWHM). Because of the faintness of the transient and its proximity to the larger, brighter main source, an automated detection algorithm such as SExtractor (Bertin & Arnouts 1996), implemented in GAIA36 2016A, was unsuccessful in deblending the two sources. Therefore, a more rudimentary method was employed to determine the magnitude of the transient: using ds9, the transient and the brightest North-western source (Sections 2.2 and 2.3; Fig. 2; left-hand column; rows 4–5; Fig. 3) were fitted with ellipses to perform relative aperture photometry on the photometrically calibrated unconvolved POSS images, after sky subtraction (see below). This procedure shows that the transient source corresponds to ≳96 per cent of the flux of the North-western source (m ≈ 20.9 mag; USNO B1.0; Monet et al. 2003), which is equivalent to the transient being Δm ≲ 0.05 mag fainter than the North-western source (Fig. 2; left-hand column; rows 4–5). Similarly, the flux ratio between the main source and the transient is approximately a factor of 6 (Section 2.1.4). Given this very simplistic procedure to obtain the transient photometry, the magnitude of the transient is quite uncertain. A magnitude of m ≈ 21.0±0.2 mag will be adopted in the following discussion (Section 3), with the confidence interval provided assuming a 20 per cent error in the flux (detection at a 5σ level; see below), corresponding to the estimated photometric error at the maximum intensity extended to the full source, and neglecting unquantifiable systematics errors; the error estimation is included in AppendixA. Favourably, changes in the magnitude as large as Δm ≈ 1.5 will not significantly alter the conclusions of this work (Section 3).


Throughout their short lifetimes, high-mass stars (>8 M⊙) inject large amounts of energy and momentum into their host environments through a variety of feedback processes (e.g. Krumholz et al. 2014). The most potentially disruptive of these feedback mechanisms occurs when the stars eventually die, exploding as supernovae (SNe). Indeed, SNe are thought to play a major role in the self-regulation of star formation in galaxies through their contribution to the total energy and momentum budget of the interstellar medium (ISM; McKee & Ostriker 1977; Mac Low & Klessen 2004; Klessen & Glover 2016). As the rate of cooling in the ISM is proportional to the gas density squared, the efficiency with which SNe inject energy and momentum into the local galactic environment strongly depends on the density distribution of the gas into which they explode (see Girichidis et al. 2016 and references therein). For example, SNe that explode within dense molecular clouds may be limited to disrupting their natal gas clouds, whilst SNe that explode into lower density environments can drive hot expanding bubbles to much larger distances (tens to hundreds of pc) and influence galactic scale processes (e.g. kpc-scale galactic outflows; Veilleux, Cecil & Bland-Hawthorn 2005; Agertz et al. 2013; Stinson et al. 2013; Keller, Kruijssen & Wadsley 2020; Veilleux et al. 2020). Feedback from the pre-SNe stages of high-mass stars plays a significant role in determining the environment into which SNe subsequently explode. Simulations have long predicted that this ‘pre-processing’ can potentially even destroy the host molecular cloud before the first SN explosion (e.g. Dale, Ercolano & Bonnell 2012, 2013), and observations of molecular clouds and H ii regions in nearby galaxies now show that pre-SN feedback is primarily responsible for the destruction of molecular clouds across the local galaxy population (Kruijssen et al. 2019b; Chevance et al. 2020b,c). Studying the effects of these earliest stages of stellar feedback on their environment is then crucial to quantifying the contribution of SNe in driving the galaxy-scale energy and momentum cycle of the ISM in galaxies. In light of this, significant observational effort has been invested to better disentangle and quantify the effect of various feedback mechanisms within young stellar systems (e.g. Oey 1996a,b; Pellegrini, Baldwin & Ferland 2010, 2011). More recent efforts have focused on measuring and comparing the internal pressure components from different feedback mechanisms in H ii regions located within the Small and Large Magellanic Clouds (SMC and LMC, respectively), such as the well-known 30 Doradus complex (e.g. Lopez et al. 2011, 2014; Chevance et al. 2016; McLeod et al. 2019), as well as other nearby galaxies (e.g. McLeod et al. 2020). These studies have provided important insights into early-stage feedback, but further work is needed to understand how pre-processing varies with environment, particularly to higher density, pressure, and metallicity regimes such as those in galactic nuclei and high-redshift galaxies.


We observed our full sample of all 24 candidate highly variable AGN with Swift (Gehrels et al. 2004) for ~2 ks each, between 2010 and 2014 as part of a fill-in programme. All XRT (Burrows et al. 2005) observations were made in photon counting mode with exposure times ranging from 1.6–3.7 ks. The Swift-XRT data were obtained from the UK Swift Science Data Centre1 and reduced following the procedures of Evans et al. (2009) using the Swift software and calibration database available within HEASOFT v.6.12. Simultaneous observations were made with the Swift BAT (Barthelmy et al. 2005) at 14–195 keV and the Swift UV/Optical Telescope (UVOT; Roming et al. 2005) with the u filter applied. For ten sources, additional archival Swift observations were available at the time of writing which we have included and analysed in an identical manner. Details of all the observations used in this paper are given in the appendix (see Table A.1). With the XRT we detected 16 (or two-thirds) of the sample sources in our fill-in observations. Widening our search, we looked at data stacks in the Swift XRT Point Source Catalogue (1SXPS; Evans et al. 2014) and other pointed XRT observations and found that a further five sources were detected. Two of the three XRT non-detected sources have only ever been detected in the XMM slew survey (Figs. 1b and f), and cannot be identified with any source detected in other wavelength surveys such as 2MASS, WISE, SDSS or 6dF in our searches. One of these, XMMSL1 J015510.9-140028, lies at the detection threshold of the slew survey. The other, XMMSL1 J113001.8+020007, has a higher significance, however the photons at the source location are aligned along a row which indicates that this might not be an astrophysical point source. We conclude therefore that those two detections in the slew survey are highly likely to be spurious. We discuss the spurious fraction further in Sect. 8. The remaining XRT-undetected source is XMMSL1 J193439.3+490922, which has three detections in XMM slews and is hence likely real. All XRT-detected sources are also detected with UVOT. Three sources (Mrk 352, ESO 362-G018, ESO 139-G012) can be found in the Swift BAT 70-month All-Sky Hard X-ray Survey Source Catalog (Baumgartner et al. 2013).


To calculate the boundaries of the HZ of a stagnant-lid Earth around M, K, G, and F dwarfs, we applied a 1D, cloud-free, radiative-convective climate model, which has been described in detail by von Paris et al. (2010) and von Paris et al. (2015), and is based on Kasting et al. (1984) and Segura et al. (2003). The radiative transfer is split into a stellar and a thermal wavelength regime. The short wavelength regime treats the absorption and scattering of stellar irradiation using a δ-two-stream method including Rayleigh scattering coefficients following the approach of Allen (1973) and four-term correlated-k exponential sums covering a wavelength regime from 273.5 nm to 4.545 μm. This wavelength coverage is optimized for solar irradiation. Especially for late M dwarfs the cut-off at 4.545 μm leads to non-negligible loss in incoming radiation of up to ≈5% (see also Wunderlich et al. 2019). Hence, HZ boundaries obtained with the models lie closer to the star than would be expected when accounting for this missing portion of irradiation. The long-wavelength regime treats the absorption by CO2 and H2O in the wavelength regime from 1 to 500 μm via correlated-ks computed based on HITEMP 1995 (Rothman et al. 1995). The ckd continuum (Clough et al. 1989), and the collision-induced absorption as described in Kasting et al. (1984) for CO2 and as described in von Paris et al. (2013) for N2 –N2 are included. Convection is treated by applying a convective adjustment when the adiabatic lapse exceeds the radiative lapse rate, including latent heat release from H2O or CO2 where applicable. The water mixing ratio profile (

$C_{\mathrm{H}_2\mathrm{O}}$

C

H
2

O

) is calculated from the temperature profile, the saturation vapour pressure (psat), and by assuming a relative humidity (RH):

$C_{\mathrm{H}_2\mathrm{O}}=\textrm{RH}\frac{p_{\mathrm{sat}}}{p}$

C

H
2

O

=RH

p

sat

p

, with p the pressure of the atmosphere. By making use of our 1D climate model we estimate global diurnal mean values without accounting for effects such as slow planetary rotation or an interactive hydrological cycle. A discussion on the potential influence of 3D processes is given in Sect. 4.


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).


Supermassive black holes (SMBHs) are believed to exist in the centres of all massive galaxies (Kormendy & Richstone 1995). A small proportion of these are growing, with gas accretion rates ranging from ∼10−4 to 10 M⊙ yr−1 and a proportionately wide range of bolometric luminosities (∼1042–1047 erg s−1). These are active galactic nuclei (AGNs) and may accrete large fractions of their mass in bursts of rapid accretion (Croton et al. 2006), requiring rapid inflow of gas from galaxy length-scales. Stripping the gas of enough angular momentum to allow for such rapid accretion, thereby powering the most luminous AGN, proves extremely challenging. Theoretical work suggests major mergers can provide the torque to displace such an overwhelming fraction of the angular momentum of the gas, allowing for the highest accretion rates on to the central black hole whilst transforming the galaxy morphology (Toomre & Toomre 1972; Barnes 1988; BarnesBarnes & Hernquist 1991; Di Matteo, Springel & Hernquist 2005; Cox et al. 2008). Gas rich mergers may trigger nuclear and global starbursts (Mihos & Hernquist 1994, 1996; Hopkins et al. 2006) and major mergers disrupt the morphologies of the colliding galaxies, often exhibiting long tidal tails or shells of expelled gas and stars soon after the merger has begun. Detecting this can be challenging however, since the single new galaxy has a relaxation time-scale after which morphological features of mergers fade (Tinsley 1978; Kennicutt et al. 1987; Ellison et al. 2013). Observational evidence suggesting a link between major mergers and SMBH accretion has been mixed (e.g. Gabor et al. 2009; Cisternas et al. 2011; Schawinski et al. 2011; Kocevski et al. 2012; Treister et al. 2012; Ellison et al. 2013; Villforth et al. 2014; Kocevski et al. 2015; Villforth et al. 2017). Alternatively, AGNs may be triggered secularly through, for example, disc instabilities (Bournaud et al. 2011), bars (Knapen, Shlosman & Peletier 2000; Oh, Oh & Yi 2012) or otherwise by minor mergers (Kaviraj 2013). It remains unclear whether alternatives to major merger triggering can drive several M⊙ yr−1 of gas to the central SMBHs, as is necessary to power the most luminous AGN.


Taking advantage of modern computer architecture, numerical simulations have become a powerful tool for investigating SNR dynamical evolution by means of testing various scenarios with specific purposes (Ferrand 2020). As relevant observational evidence is steadily growing, particular attention has been devoted to tackling with SNR temporal evolution in an inhomogeneous medium, aiming at deciphering the observed asymmetries of emission morphology or clarifying the effects on the synthetic radio polarization maps exerted by various configurations of the interstellar magnetic field (e.g., Orlando et al. 2007; Schneiter et al. 2015; Yang et al. 2015; Bandiera & Petruk 2016; Petruk et al. 2017). As a first attempt, magnetohydrodynamic (MHD) simulations of a benchmark type Ia SNR expanding into a turbulent background were carried out by Balsara et al. (2001), and several obtained results are different from those in a uniform medium: significant azimuthal variations observed in density and magnetic field profiles, a patchy and time-independent synchrotron shell which may in turn serve as a probe into the nature of ISM turbulence, and amplification of the magnetic field in the post-shock region due to interactions between the forward shock and the turbulent background. Under the assumption that both density and magnetic field fluctuations follow a Kolmogorov-like power spectrum, the temporal evolution of an SNR propagating into a turbulent medium was investigated by Guo et al. (2012), with a focus on the structures and amplification of the magnetic field in the shock downstream. Recently, two-dimensional cylindrical MHD simulations were implemented to investigate the dynamical properties of young type Ia SNRs undergoing shock acceleration in a turbulent medium by Peng et al. (2020), where an initial power-law density profile is adopted and the derived relative contact discontinuity positions are compared with the observed results of two typical type Ia SNRs: SN 1006 and Tycho.


The main RSG sample contains 1405 candidates from the SMC source catalog. However, targets with Rank 4 and 5 are selected only in one CMD by either the MIST models or the theoretical J − KS color cuts, and many of them reach down close to the tip of the red giant branch (TRGB) and AGB population (see also Figs. 13 and 14 of Yang et al. 2019). To be on the safe side we adopted only targets with ranks from 0 to 3 (targets identified in at least two CMDs) as our initial sample, which resulted in 1107 targets. Due to the photometric quality cuts and uncertainties of the Spitzer and Gaia data, the strict constraints on the astrometric solution, and the deblending applied during the construction of the source catalog, some of the spectroscopically confirmed RSGs were also rejected. In order to make the sample as complete as possible, we retrieved and added all known spectroscopic RSGs in both optical and mid-infrared (MIR) bands from Simbad (Wenger et al. 2000) and data taken by Spitzer Infrared Spectrograph (IRS; Houck et al. 2004), respectively. From Simbad, we selected 322 RSGs with RV ≥ 90 km s−1, spectral type later than G0, and luminosity class brighter than II by using criteria query (Levesque 2013; González-Fernández et al. 2015), for which 192 targets were matched with our initial sample within 1″. Additionally, a crossmatching with the main RSG sample of 1405 candidates indicated that three Rank 4 candidates were also matched within 1″. Surprisingly, there are two spectroscopic RSGs matched with the source catalog within 1″, but not selected as the RSG candidates by either the MIST models or the theoretical J − KS color cuts. Visual inspection of Gaia and 2MASS (Two Micron All Sky Survey; Skrutskie et al. 2006) CMDs (shown below) indicated that these two targets were slightly off the blue and red boundaries of the RSG region, respectively, which was likely due to the intrinsic variability of the RSGs (Kiss et al. 2006; Yang & Jiang 2011; Ren et al. 2019). Consequently, in total, there are 127 unselected spectroscopic RSGs from Simbad. For data taken by Spitzer/IRS, there were 22 RSGs from Ruffle et al. (2015), who classified 209 point sources observed by Spitzer/IRS using a decision tree method, based on IR spectral features, continuum and spectral energy distribution shape, bolometric luminosity, cluster membership, and variability information (all the targets from Kraemer et al. 2017 were also included). Of these 22 RSGs, 16 of them were matched with our initial sample within 1″, and 4 of them were matched with the previous unselected Simbad RSGs within 1″. Thus, there are only two unselected spectroscopic RSGs from Spitzer/IRS. In total, there are additional 129 spectroscopic RSGs from both Simbad and Spitzer/IRS, for which we give them Rank −1.


The EWs were measured with the methods described in Vásquez et al. (2015). As in Paper I, we used the sum of the EWs of the two strongest CaT lines (λ8542, λ8662) as a metallicity estimator, following the Ca II triplet method of Armandroff & Da Costa (1991). Different functions have been tested in the literature to measure the EWs of the CaT lines, depending on the metallicity regime. For metal-poor stars ([Fe/H] ≲ −0.7 dex) a Gaussian function was used with excellent results (Armandroff & Da Costa 1991), while a more general function (such as a Moffat function or the sum of a Gaussian and Lorentzian, G + L) is needed to fit the strong wings of the CaT lines observed in metal-rich stars (Rutledge et al. 1997; Cole et al. 2004). Following our previous work (Gullieuszik et al. 2009; Saviane et al. 2012) we have adopted here a G+L profile fit. To measure the EWs, each spectrum was normalised with a low-order polynomial using the IRAF continuum task, and set to the rest frame by correcting for the observed radial velocity. The two strongest CaT lines were fitted by a G+L profile using a non-linear least squares fitting routine part of the R programming language. Five clusters from the sample of Saviane et al. (2012) covering a wide metallicity range were re-reduced and analysed with our code to ensure that our EWs measurements are on the same scale as the template clusters used to define the metallicity calibration. Figure 5 shows the comparison between our EWs measurements and the line strengths measured by Saviane et al. (2012) (in both cases the sum of the two strongest lines) for the five calibration clusters. The observed scatter is consistent with the internal errors of the EW measurements, computed as in Vásquez et al. (2015). The measurements show a small deviation from the unity relation, which is more evident at low metallicity. A linear fit to this trend gives the relation: ΣEW(S12) = 0.97 ΣEW(this work) + 0.21, with an rms about the fit of 0.13 Å. This fit is shown in Fig. 5 as a dashed black line. For internal consistency, all EWs in this work have been adjusted to the measurement scale of Saviane et al. (2012) by using this relation. In Table 3 we provide the coordinates, radial velocities, and the sum of the equivalent widths for the cluster member stars, both measured (“m”) and corrected (“c”) to the system of Saviane et al. 2012.


Considering a BBH system resulting from a gas rich merger, the BBH is probably surrounded by a circumbinary disk, and each of the two SMBHs is associated with a mini-disk (see Figure 1). In between the circumbinary disk and the inner mini-disks, a gap (or hole) is opened by the secondary SMBH, which is probably the most distinct feature of a BBH–disk accretion system, in analogy to a system in which a gap or hole is opened by a planet migrating in the planetary disk around a star (Lin et al. 1996; Quanz et al. 2013). This type of geometric configurations for the BBH–disk accretion systems has been revealed by many numerical simulations and analysis (Artymowicz & Lubow 1996; Escala et al. 2005; Hayasaki et al. 2008; Cuadra et al. 2009; D’Orazio et al. 2013; Farris et al. 2014; Roedig et al. 2014).4

4
The width of the gap (or hole) is roughly determined by, but could be somewhat larger than, the Hill radius

. However, set a slightly large gap size, e.g.,

, does not affect the results presented in this paper significantly.
 The continuum emission from disk accretion onto a BBH may be much more complicated than that from disk accretion onto a single SMBH, since the dynamical interaction between the BBH and the accretion flow onto it changes the disk structure (Gültekin & Miller 2012; Sesana et al. 2012; Rafikov 2013; Roedig et al. 2014; Yan et al. 2014; Farris et al. 2015). Nevertheless, we adopt a simple model to approximate the continuum emission from a BBH–disk accretion system as the combination of the emissions from an outer circumbinary disk and an inner mini-disk around the secondary SMBH, each approximated by multicolor blackbody radiation in the standard thin disk model (Novikov & Thorne 1973; Shakura & Sunyaev 1973). The emission from the mini-disk around the primary SMBH is insignificant for a BBH system with a small mass ratio (roughly in the range of a few percent to 0.25) due to its low accretion rate as suggested by the state of the art numerical simulations (Roedig et al. 2012; Farris et al. 2014), thus its emission can be neglected. Our analysis suggests that a large q cannot lead to a good fit to the observations.


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


Similarly to the [α/Fe] ratio, the ratio of the slow (s-) neutron capture process elements to iron can be regarded as a cosmic clock. Ba, Sr, La, and Y are mainly s-process elements produced on long timescales by low mass AGB stars (Matteucci 2012). Since a low mass star must evolve to the AGB phase before the s-process can occur, the s-process elements are characterized by a delay in the production, much like the delay of iron production by SNe Ia relative to the α elements production by core collapse SNe. Among the four s-process elements mentioned above, GES provides the abundances of Y II (the first s-process peak element) and Ba II (the second s-process peak element) for all our sample stars. Their abundances behave differently in the Galactic thick and thin discs (Bensby et al. 2005, 2014; Israelian et al. 2014; Bisterzo et al. 2017; Delgado Mena et al. 2017). Unlike the Galactic thick disc stars, which show an almost constant [Ba/Fe] abundance close to the solar value, the Galactic thin disc stars have their [Ba/Fe] abundances increasing with [Fe/H] and reaching their maximum values around solar metallicity, after which a clear decline is seen (see also Cristallo et al. 2015a,b, for the most recent s-process calculation in AGB yields). The same trend is observed in our sample. In Fig. 13 we display the Li-[Ba/Fe], [Ba/Fe] as a function of [Fe/H], and the evolution of absolute Ba abundance A(Ba), as derived from Ba II lines. Similar figures are also plotted for yttrium (Y II). [Ba/Fe] and [Y/Fe] values here are derived from MCMC simulations, taking into account the measurement uncertainties of A(Ba II)/A(Y II) and [Fe/H]. By applying the same MCMC setups used for [α/Fe] (see Sect. 3.1), we calculate the mean values of [Ba/Fe] and [Y/Fe] for each star. These values, together with their corresponding 1σ uncertainties, are listed in Table 1. In the literature there are several theoretical works on the evolution of [Ba/Fe] and [Y/Fe] in the Galactic thin disc (e.g. Pagel & Tautvaisiene 1997; Travaglio et al. 1999, 2004; Cescutti et al. 2006; Maiorca et al. 2012; Bisterzo et al. 2017). For comparison, we show in Fig. 13 the predictions of the most recent one (Bisterzo et al. 2017) where the updated nuclear reaction network was used.


The properties of the persistent radio source associated with FRB 121102 may be constrained independently of the Faraday-rotating medium. We assume equipartition between the relativistic gas and magnetic field as is common in synchrotron sources3 (Readhead 1994). The source becomes self-absorbed at $1.5$ GHz for radius $R_{\rm per} < 0.05$ pc; this is thus the lower bound on the source size. European Very Long Baseline Interferometry (VLBI) Network observations of the source at 5 GHz set an upper bound on the source radius of Rper ≲ 0.35 pc (Marcote et al. 2017). This is consistent with the ${\approx } 30\, {{\rm per\, cent}}$ amplitude modulations observed in the source at 3 GHz (Chatterjee et al. 2017) being caused by refractive interstellar scintillation in the Milky Way interstellar medium (ISM; Walker 1998). For any radius within the allowed range (0.05  Rper/pc  0.35), we can determine the equipartition magnetic field, Beq, and the column of relativistic electrons, Nrel, using the standard expressions for synchrotron emissivity and absorption coefficients (Rybicki & Lightman 1979, their equations 6.36 and 6.53). We assume a power-law energy distribution of radiating electrons with somewhat shallow index of b = −1.5 that can account for the relatively flat spectrum of the source (Chatterjee et al. 2017). The peak Lorentz factor of the distribution, γmax, is chosen to correspond to the observed spectral break frequency of $\nu _{\rm max}=10$ GHz. If the lower Lorentz factor cut-off corresponds to emission at $\nu _{\rm min}=1$ GHz,4 then the equipartition magnetic field and electron column thus determined for minimum and maximum source sizes are $B_{\rm eq}\approx 140$ mG, $\gamma _{ \rm min}\approx 50$, γmax ≈ 160, $N_{\rm rel} \approx 0.95\, {\rm pc}\, {\rm cm}^{-3}$ for $R_{\rm per}=0.05$ pc, and $B_{\rm eq}\approx 27$ mG, $\gamma _{ \rm min}\approx 120$, γmax ≈ 370, $N_{\rm rel} \approx 0.1\, {\rm pc}\, {\rm cm}^{-3}$ for $R_{\rm per}=0.35$ pc. The reader can scale the equipartition field to other source sizes using Beq(R) ∝ R−6/7. The total energy contained in the relativistic electrons and the magnetic field (‘equipartition energy’) is ∼1049.1 and ∼1050.2 erg, respectively. If the relativistic electrons were injected in a one-off event, the synchrotron cooling rates at γmax yield source ages of $14$ yr for R = 0.05 pc and 60 yr for $R=0.35$ pc. The corresponding expansion velocities are $0.011\, c$ and $0.02\, c$, respectively.


There is significant scatter (larger than 1 dex) among the tdepl measurements in all redshift bins, even though we only consider MS galaxies with ΔMS = ±0.3 dex around the MS parametrization of Speagle et al. (2014). This scatter at a fixed redshift is believed to be a product of the multi-functional dependence of tdepl on many physical parameters, such as the offset from the MS, the star formation rate, the stellar mass, and possibly the environment (e.g., Dessauges-Zavadsky et al. 2015; Scoville et al. 2017; Noble et al. 2017; Silverman et al. 2018; Tacconi et al. 2018; Tadaki et al. 2019; Liu et al. 2019b). Given the strong anti-correlation found between tdepl and the offset from the MS (Genzel et al. 2015; Dessauges-Zavadsky et al. 2015; Tacconi et al. 2018), we still expect tdepl variations for galaxies on the MS while in their evolutionary process they are transiting up and down across the MS band (e.g., Sargent et al. 2014; Tacchella et al. 2016). The previously reported anti-correlation between tdepl and sSFR (Saintonge et al. 2011; Dessauges-Zavadsky et al. 2015) is also further supported by our galaxies at z = 4.4 − 5.9 (Fig. 6, middle panel). This highlights comparable timescales for gas consumption and stellar mass formation. We find a Spearman rank coefficient of −0.49 and p-value of 4.5 × 10−10 for the dependence of tdepl on sSFR when considering the MS SFGs at z ∼ 1 − 5.9. The observed offset of ALPINE galaxies with respect to the tdepl–sSFR relation of MS SFGs at z = 0 and to a smaller extent to the relations at z ∼ 1 and z ∼ 2 is compatible with the displacement of the z = 0 relation along the sSFR-axis by factors derived from the sSFR evolution with redshift of MS SFGs out to z ∼ 5 (Speagle et al. 2014). Nevertheless, a less steep sSFR redshift evolution toward z ∼ 5 than parametrized by Speagle et al. (2014) is suggested by the ALPINE sample, in line with the sSFR(z) results of Khusanova et al. (2020a). On the other hand, with tdepl measurements achieved down to Mstars ∼ 108.4 M⊙ for the ALPINE galaxies, we confirm that for MS SFGs at z ∼ 1 − 5.9 the tdepl dependence on Mstars, if any, must be weak as shown in Fig. 6 (right panel). This further supports the idea that the linear KS relation established for local galaxies (Kennicutt 1998b) might hold up to z ∼ 5.9 for MS SFGs.


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.


Our results appear to stand apart from similar studies in full spherical shells (e.g., Nelson et al. 2013; Hotta et al. 2016) in that the differential rotation is strongly quenched as a function of the magnetic Reynolds number. However, in Nelson et al. (2013) the values of Rm′ (=2πReM) correspond to a range of 8...32 in ReM in our units where the radial and latitudinal differential rotation decrease by about 30 per cent. This is roughly consistent with our results. On the other hand, Hotta et al. (2016) reached higher values of ReM than in the present study, but no strong quenching was reported. The reason might be that their models are rotating substantially slower than ours, leading to weaker magnetic fields and a weaker back-reaction to the flow. Furthermore, in these models, the differential rotation is strongly influenced by their SGS heat flux, which transports one third of the luminosity. Another obvious candidate for explaining the difference is the wedge geometry used in the current simulations. However, we note that earlier simulations with a similar setup did not show a marked trend in the energy of the differential rotation as the azimuthal extent of the domain was varied (see Table 1 of Käpylä et al. 2013). However, results of Boussinesq simulations of convective dynamos have shown a similar change as a function of the magnetic Prandtl number (Schrinner et al. 2012). The drop in the amplitude of the differential rotation was associated with a change in the dynamo mode from an oscillatory multipolar solution to a quasi-steady dipolar configuration (cf. Fig. 15 of Schrinner et al. 2012) that prevents strong differential rotation from developing. We do not find a strong dipole component in our simulations (see Sect. 4.2.3). However, the strong suppression of the differential rotation often coincides with the appearance of a small-scale dynamo (see Table 1 and the discussion in the Sect. 4.1.2) or a change in the large-scale dynamo mode as discussed above.


As discussed in Section 1, one of the primary motivations for this work is to attempt to understand the variations in apparent IMF that have been observed in early type galaxies (ETGs). While there are multiple lines of evidence for this variation, the most straightforward to extract from out simulations is the mass to light ratio of the stellar populations we produce. In this section we therefore look at the mass to light ratio in our simulations for the purpose of comparing to that in observed galaxies. We calculate this by using the slug stellar population synthesis code (da Silva, Fumagalli & Krumholz 2012; Krumholz et al. 2015) to generate isochrones at stellar population ages from 5 Gyr to 10 Gyr, using the MIST stellar evolution tracks (Choi et al. 2016) and Starburst99-style stellar atmosphere models (Leitherer et al. 1999). Each isochrone provides a prediction of present-day mass, bolometric luminosity, and luminosity in a range of photometric filters as a function of initial mass for stars with initial mass $\ge 0.1\, {\rm M}_{\odot }$; we assume that the luminosities of stars with initial masses less than 0.1 M⊙ are negligible, and that these stars also experience negligible mass loss. We further assume that all stars with initial mass $\lt 8\, {\rm M}_{\odot }$ (which are all the stars formed in our simulations) that reach the end of their lives leave behind 0.7 M⊙ white dwarf remnants. We use the isochrone to calculate the luminosity and present-day mass of all the stars formed in each of our simulations at ages from 5 − 10 Gyr, and from these we calculate the mass to light ratio of the stellar population as a function of age for each of our simulations. For comparison, we use the same isochrones to calculate the mass to light ratio of Chabrier (2005) and Salpeter (1955, truncated at a lower mass limit of $0.1\, {\rm M}_{\odot }$) IMFs at the same ages. We use the SDSS r band for this calculation, but results are qualitatively similar in other filters.


The large radiation field directly produced from young stellar objects can exert a significant pressure on the surrounding material. This radiation pressure, Prad, at a given position within an H ii region, is related to the bolometric luminosity, Lbol, of the stellar population and the distance, r, from each star to that position within the region:
(3)$$\begin{eqnarray*}
P_\mathrm{rad} = \sum {\frac{L_\mathrm{bol}}{4 \pi r^{2} c}},
\end{eqnarray*}$$where the summation is over all stars within the region. The volume-averaged direct radiation pressure, Pdir, is then given as (Lopez et al. 2014),
(4)$$\begin{eqnarray*}
P_\mathrm{dir} = \frac{3 L_\mathrm{bol}}{4 \pi R^{2} c},
\end{eqnarray*}$$where R is the radius of the H ii region (or effective radius, Reff, that we define later and use throughout the rest of the paper), and Lbol is the bolometric luminosity from the population of massive stars within the H ii region. This form differs by a factor of three from McLeod et al. (2019, equation 4), as these authors calculate the radiation surface pressure rather than the volume average pressure. This expression is appropriate to compute the force balance at the surface of an empty shell. However, as this work aims at understanding the large-scale dynamics of the Galactic Centre H ii regions (e.g. the total energy and pressure budget for each source), the inclusion of a factor of three in the numerator of the above equation is required. We also note here that the higher metallicity within the Galactic Centre, or increasing the amount of dust, has no effect on the Pdir calculation. Direct radiation pressure is limited by the momentum supplied by the stellar radiation field, and, as long as there is enough dust around to absorb all the radiation, the momentum per unit time delivered is the same. Lopez et al. (2011) determine the bolometric luminosity of the H ii regions within the LMC and SMC from H $\alpha$ emission. However, this is not possible for the H ii regions investigated here, due to the high optical extinction towards the Galactic Centre (Av >20 mag), which completely obscures any H $\alpha$ emission. We, therefore, adopt two alternative methods of calculating the bolometric luminosity using radio and infrared observations (i.e. wavelengths where the emission is much less affected by dust extinction). First, we can make the assumption that the bolometric luminosity is proportional to the flux of ionizing photons, $\mathcal {N}_\mathrm{LyC}$, such that $L_\mathrm{bol} = \mathcal {N}_\mathrm{LyC} \left\langle h \nu \right\rangle$, where 〈hν〉 ∼ 15  eV is the mean photon energy (Pellegrini et al. 2007). We use the $\mathcal {N}_\mathrm{LyC}$ for each H ii region as determined from the radio observations outlined in Table  2 (i.e. Gaume & Claussen 1990; Mehringer et al. 1992; Schmiedeke et al. 2016), and solve for the direct radiation pressure using equation (4). The second method assumes that the luminosity integrated over infrared wavelengths approximately corresponds to the total bolometric luminosity. This is a common assumption made for embedded star-forming regions, where the luminosity from massive stars produced at ultraviolet wavelengths is absorbed and remitted by the dust in the infrared. Barnes et al. (2017) have produced maps of the total infrared luminosity across the Galactic Centre. These authors fit a two-component modified blackbody function to extinction corrected 5.8–24 $\mu $m (Carey et al. 2009; Churchwell et al. 2009) and 160 –500 $\mu $m (Molinari et al. 2010) emission maps (referred to as the warm and cool component of the bolometric luminosity; see fig. 2 of Barnes et al. 2017). These infrared (i.e. bolometric) luminosity maps are used with the two methods outlined below to also determine the direct radiation pressure within each of the Galactic Centre H ii regions. In comparison with the first method for calculating the direct radiation pressure from radio observations, we choose to identify individual sources within the infrared maps. These can be considered as discrete H ii regions each with a single value of the direct radiation pressure. We choose to identify these H ii regions in the map of the warm component of the bolometric luminosity using a dendrogram analysis (Rosolowsky et al. 2008). We choose to use a structure finding algorithm, as opposed to by-eye identification, to give reproducibility within regions with particularly complex morphology (the warm bolometric luminosity map is given in fig. 2 from Barnes et al. 2017).3 We make use of the ‘leaves’ identified from the dendrogram analysis, which are the highest level (i.e. smallest) structures in the analysis and here represent distinct H ii regions. We take the mask of each H ii regions (dendrogram leaf), and apply this to both the warm and cool bolometric luminosity component maps, which we sum to then get the total bolometric luminosity. This is used with equation (4) to get the direct radiation pressure (Pdir) within each H ii region. The effective radius (Reff) of each H ii region is defined as the radius for a circle with the corresponding area (A) of each structure (i.e. $R_{\rm eff}=\sqrt{A/\pi }$). In addition to the dendrogram analysis, we also calculate the direct radiation pressure within apertures of increasing radius from the centre of each H ii region complex. To do so, we place circular masks for each source on to both the warm and cool bolometric luminosity component maps, and sum the enclosed values to then get the total bolometric luminosity. The circle is then increased in radius, and the process repeated. We again use equation (4) to determine the direct radiation pressure within these increasing circular apertures. This method differs from the dendrogram analysis, as it returns a continuous radial distribution from the source centre, as opposed to a distribution of distinct H ii region with various sizes.


Several molecules show a large discrepancy between the abundances derived from observations and calculated by chemical equilibrium, although it is not as severe as for the molecules discussed above. We refer to PN in O-rich stars and H2S in C-rich stars, which are indicated by hatched rectangles in Fig. 2. For PN in O-rich AGB atmospheres, the disagreement between the observed abundances, (1–2) × 10−8 (Ziurys et al. 2018), and the calculated maximum chemical equilibrium abundance is almost three orders of magnitude. However, uncertainties on the observational and theoretical sides mean that the true level of disagreement is unclear. For example, while Ziurys et al. (2018) derived a PN abundance of 10−8 relative to H2 in IK Tau, De Beck et al. (2013) and Velilla Prieto et al. (2017) derived higher abundances, (3–7) × 10−7, in this source. When we give preference to these latter abundances, the level of disagreement would be even higher. On the other hand, the formation enthalpy of PN is rather uncertain (see Lodders 1999), which directly translates into the calculated chemical equilibrium abundance. In this study we adopted the thermochemical data for PN from Lodders (1999), who gives preference to a formation enthalpy at 298.15 K of 171.5 kJ mol−1, while other compilations such as JANAF use lower values that would result in higher chemical equilibrium abundances for PN. This would reduce the level of disagreement. In the case of H2S in C-rich AGB stars, the calculated maximum chemical equilibrium abundance is 7 × 10−11, while the value derived from observations is ~50 times higher. In this case, the observed abundance is based on the detection of only one line in only one source (see Agúndez et al. 2012), and thus it has to be viewed with some caution. In summary, the main failures of chemical equilibrium to account for the observed abundances of parent molecules in circumstellar envelopes are NH3, HCN, CS, SO2, and possibly PN in M-type stars, H2O and NH3 in S-type stars, and the hydrides H2O, NH3, SiH4, PH3, and perhaps H2S as well in C-type stars. The large discrepancies between the abundances derived from observations and those calculated with chemical equilibrium necessarily imply that nonequilibrium chemical processes must be at work in AGB atmospheres. Any invoked nonequilibrium scenario must account for all these anomalously overabundant molecules, but must also reproduce the remaining molecular abundances that are reasonably well explained by chemical equilibrium. No scenario currently provides a fully satisfactory agreement with observations, although two mechanisms that can drive the chemical composition out of equilibrium have been proposed.


We now investigate relativistic reflection models with a primary Comptonisation continuum shape, which is more physical and has a sharper high-energy rollover compared to an exponential cutoff power law. In addition, such models have the advantage of having the hot corona temperature (kThot) as a physical parameter rather than a phenomenological exponential cutoff energy. We first apply the RELXILLCP model, which uses the NTHCOMP Comptonisation model (Zdziarski et al. 1996; Życki et al. 1999) as the incident spectrum. The other physical parameters are the same as those in the RELXILL model presented above. We find a good fit and infer similar hot corona temperatures of kThot ∼ 26 keV for all three epochs (Table 2). Then, we consider the REFLKERR where the hard X-ray Comptonisation spectrum is computed with the COMPPS model (Poutanen & Svensson 1996), which appears to be a better description of thermal Comptonisation when compared to Monte Carlo simulations (Zdziarski et al. 2020). Moreover, REFLKERR has, as physical parameter, either the Compton parameter (y) or the optical depth (τ). We choose to perform the fit with the optical depth as the direct inferred parameter. The temperature of the thermal seed photons (kTbb) Comptonised by the hot corona is an explicit physical parameter of this model. Here, we assume that the seed photons are provided by the cold disc, then kTbb was fixed at 10 eV corresponding to the expected maximum temperature of the accretion disc around a black hole mass of 1.4 × 108 M⊙ accreting at a ∼10% Eddington rate. In addition, REFLKERR allows us to choose either a slab or a spherical geometry for the hot corona. The latter corresponds to numerous active sphere regions above the disc surface. The hard X-ray shape of the reflected component is calculated using IREFLECT convolved with COMPPS rather than using XILLVERCP (see Niedźwiecki et al. 2019 for detailed explanations). Both models give good fits (Table 2, Fig. 3), though a larger χ2 value for the spherical geometry. Similar values of the hot corona temperature are measured for the three epochs: kThot ∼ 30−31 keV and kThot ∼ 21−22 keV for the slab and spherical geometries, respectively. From τ, we can infer the corresponding Compton-parameter of the hot corona (yhot) using the relation y = 4τ(kT/511 keV) (Beloborodov 1999). This correspond to yhot ∼ 0.5 and yhot ∼ 1.1 for the slab and spherical geometries, respectively.


We can compare Fig. 14 with the corresponding figure obtained by Mowlavi et al. (2019) in the Magellanic Clouds (see their Figs. 4 and 7 for the LMC and SMC, respectively) and in the Milky Way from DR2 data (their Fig. 10). Our conclusions here are similar: (i) There are far fewer C-rich than O-rich stars in the Galaxy than in the Clouds. The low number of carbon stars compared to O-rich stars between the Galaxy and the Clouds agrees with the decrease in TDU efficiency with increasing metallicity, and with a higher O abundance in the envelope of Galactic AGB stars on average. On the other hand, because some of the stars located in RGB and faint AGB region in Fig. 14 might be CH and/or R-hot type stars (i.e. C-rich objects, see previous sections), we could derive a lower limit for the ratio between carbon to M (O-rich) stars. It is well known that this ratio increases with the decreasing (average) metallicity of the galaxy. The primary reason for this correlation is that less C needs to be dredged-up in a metal-poor star to enable atmospheric carbon atoms to exceed those of oxygen. We derive a ratio ∼0.05, which is very similar to the average ratio derived in the disc of M 31 (see e.g. van den Bergh 2000; Hamren et al. 2015). (ii) Moreover, the distribution of O-rich stars of the Gaia-2MASS diagram covers at any given MKs magnitude a much wider range of WRP, BP − RP − WKs, J − Ks in the Galaxy than in the Clouds. The wider distribution in both axes of the O-rich zones in Fig. 14 compared with the corresponding feature in the Clouds would result from the combined effect of O-rich AGB stars turning much later into C-rich stars in the Galaxy, and the existence of a more ample range of stellar metallicities in the Galactic sample. Moreover, Fig. 14 clearly shows the high dispersion existing in MKs for the C-rich objects at a given WRP, BP − RP − WKs, J − Ks value. Part of this dispersion in MKs is compatible with the typical range in Teff (2500−3500 K) deduced for N-type stars (Bergeat et al. 2001), and to the circumstellar extinction (which we did not consider here) preferably for the objects in the extreme C-rich region. However, the mixing of carbon stars of different populations probably also contributes significantly to this dispersion in MKs (and also in Mbol). In fact, following the method outlined in Sect. 4, we have studied the kinematics of these stars and calculated the membership probability to the halo and to the thin and thick disc of the 2659 new carbon star candidates with a Vrad measurement according to EDR3 (∼40% of the sample, i.e. 1305 objects). Figure 15 shows the corresponding Toomre diagram for these carbon stars. Of this limited sample, roughly 50% belong to the thin disc (blue circles in Fig. 15), ∼30% to the thick disc or halo (blue crosses and triangles, respectively), and the rest (∼20%) have an ambiguous membership according to our membership criteria (open blue circles). Nevertheless, we note that assuming a less strict likelihood percentage to assign membership to a population (see Sect. 4), about 25% of the stars with ambiguous membership would be thick-disc and/or halo stars. Because thick-disc and halo stars are older than thin-disc stars on average, many of these C-rich objects are very probably not intrinsic AGB carbon stars, but extrinsic C-rich giants: stars with masses lower than ∼1.5 M⊙ that have become carbon rich through the mass transfer in a binary system. An alternative to this would be the possibility that the minimum mass for the formation of an intrinsic AGB stars could be as low as 1 M⊙. Some observational evidence for this can be found in the literature (Shetye et al. 2019). This conclusion is reinforced by the scale height onto the Galactic plane that can be estimated for all the C-rich stars in Fig. 14 similarly to what was done in Sect. 2: an exponential fit gives zo ∼ 600 pc, which is much larger that the scale height derived for the intrinsic N-type AGB carbon stars that clearly belong to the thin disc (see Sect. 2).


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


Low- and intermediate-mass stars are formed by the gravitational collapse of the parental giant molecular cloud (GMC), followed by the accretion process (Palla 1996). During the accretion phase, material is ejected as well via collimated bipolar jets. However, when a YSO reaches 8 M⊙, the radiative flux becomes so intense (using ϕ = L/4πd2, the ratio between the radiative fluxes of an O5 and a B3 star – masses of ∼40 and ∼8 M⊙, respectively – is ≈250) that it may interrupt the accretion flow. A process that constrains the outcoming radiation field to narrower angles may leave some room for the accretion process to continue in some directions. This seems to be the case for the outflows driven by young stars from a very broad mass range, as previous reported by several authors (Bachiller 1996; Bontemps et al. 1996; Shepherd & Churchwell 1996; Beuther et al. 2002; Wu et al. 2004). Outflows associated with high-mass objects are expected to be more energetic than the outflows observed in lower mass YSOs (Beuther et al. 2005; Zhang et al. 2005; López-Sepulcre et al. 2009), with velocities greater than ∼100 km s−1 (Martí, Rodríguez & Reipurth 1998). Some authors have found evidences that outflows associated with massive stars are scaled up versions of their low-mass counterparts (Vaidya et al. 2011; Codella et al. 2013) while other works have reported that no well-collimated outflows have been found towards MYSOs (Shepherd, Testi & Stark 2003; Sollins et al. 2004). Massive YSO outflows mapped in high-velocity CO lines have collimation factors R = length/width ∼2.05 ± 0.96 as compared to R ∼ 2.81 ± 2.16 for low-mass stars (Wu et al. 2004), indicating a weak tendency that outflows associated with massive stars are less collimated than those from low-mass stars as previously thought (Richer et al. 2000). Besides the degree of collimation, these massive outflows would work removing mass from the plane of the accretion disc, lowering the density on the plane and, therefore, facilitating the accretion flow to reach the stellar core as shown in the recent 3D simulations presented by Krumholz et al. (2009). Although these authors have not included the outflow activity on their simulations, they argue that the presence of outflows would decrease the star formation efficiency from 70 per cent (considering purely radiation effects) to 50 per cent.


LPVs are known to exist on sets of sequences in period–luminosity space (e.g. Wood et al. 1999; Wood 2000) depending on their variability type and pulsation mode. The primary periods of Mira-like variables lie on the commonly called C and C′ sequences (Ita et al. 2004; Spano et al. 2011) with C′ lying at a lower period than C. Sequences A and B lie at lower periods still and are populated by the so-called OGLE small amplitude red giants or OSARGs (Soszynski et al. 2004a). Sequences D and E are populated by long secondary pulsators, whose nature is still unclear, as well as ellipsoidal and eclipsing binary systems (Soszynski et al. 2004b), with the latter two contained in a separate CRTS catalogue not utilized in this work. Soszyński & Wood (2013) also found that there is a low-amplitude population of SRVs whose primary period lies between the C and C′ sequences. Given that the selections of Fig. 1 produce a CRTS sample with a wide range of visual amplitudes, it is uncertain on which sequence our CRTS sources lie and to which class of LPVs they belong. The left-hand panel of Fig. 2 shows sources from Gaia’s DR2 LPV catalogue (Gaia Collaboration et al. 2016, 2018; Mowlavi et al. 2018) chosen to lie within a 15° aperture of the LMC. Cross-matching with 2MASS reveals three distinct sequences existing in the Ks band, with the middle sequence corresponding to the Mira C sequence. Belokurov et al. (2017) defined a variability parameter (the ‘Gaia amplitude’) based on Gaia’s flux information as:
(1)
\begin{eqnarray*}
\mbox{Amp} = \mbox{log}_{10} \left(\sqrt{N_{\mbox{obs}}} \: \frac{\sigma _{\overline{I_{\mathrm{ G}}}}}{\overline{I_{\mathrm{ G}}}} \right)
\end{eqnarray*}
where $\sqrt{N_{\mbox{obs}}}$ is the number of observations, $\sigma _{\overline{I_{\mathrm{ G}}}}$ is the mean flux error in the G band, and $\overline{I_{\mathrm{ G}}}$ is the mean flux in the G band. Requiring a Gaia amplitude greater than −0.55 isolates a sample of LPVs lying on a single period–luminosity sequence, as evident in Fig. 2. We produce a secondary cleaned CRTS sample located on this middle sequence by cross-matching with the Gaia DR2 source catalogue and enforcing that the Gaia amplitude > −0.55. Further, we restrict the sample to visual amplitudes >1 to eliminate small amplitude variables. Application of these two cuts gives a cleaned CRTS sample with 225 members. We utilize this cleaned CRTS sample in Section 3.1, where we exploit the period–age correlation of LPVs, the interpretation of which may be muddied if low visual amplitude variables were inadvertently retained. For example, AGB variables residing in a common Magellanic Cloud globular cluster have been observed by Kamath et al. (2010) both at high and low amplitudes. They found stars with low amplitudes also had lower stellar periods, implying differing period–age relations.


The GALEX NUV observations span a wide wavelength range, from 1771 to 2831 Å. While these data provide no spectral information within that bandpass, we rely on solar and stellar flare studies to inform the likely contributors to the flare flux. The NUV spectral region has not had as many observational constraints as the far-UV region in flare studies. Few NUV stellar flare spectra exist at all, and the few that do were obtained either for solar flares or on nearby M dwarfs. Flares observed in the UV are often associated with the more impulsive phases of solar flares, starting with early observations showing a close temporal association between UV and hard X-ray emission (Cheng et al. 1981). Welsh et al. (2006) reported on high time-resolution NUV+FUV flares seen with GALEX on nearby M dwarfs, and Hawley et al. (2007) presented high spectral-resolution NUV flare measurements of an M-dwarf flare. From these two studies, the contribution of emission lines relative to continuum emission could be determined; the main emission lines in the flare NUV spectrum were Mg ii, Fe ii, Al iii, and C iii. However, the main emission component overall was a continuum component. Recent results from solar flares observed from space (Heinzel & Kleint 2014; Kleint et al. 2016) demonstrate an NUV spectrum originating largely from Hydrogen Balmer continuum emission. The formation of the NUV emission appears to originate from an impulsive thermal and nonthermal ionization caused by the precipitation of electron beams through the chromosphere. This explains the temporal correlation with solar flare hard X-ray emission observed previously. More recently, Kowalski et al. (2019) presented accurately calibrated NUV flare spectra at high time cadence on an M dwarf, again finding a large flux enhancement due to continuum radiation. They commented that the oft-used 9000 K blackbody used to describe blue-optical stellar flare emission (Hawley et al. 2003) under-predicts the NUV continuum flare flux by a factor of two. Based on general similarities in radiative properties between solar and stellar flares studied thus far (Osten 2016), it is likely that a combination of line and continuum emission enhancements are present in the NUV flare flux from the flares being considered, but we cannot speculate about the relative contribution of one versus the other. These sources originate from different layers of the stellar atmosphere: singly and doubly ionized emission lines likely originate in the chromosphere, and the Balmer continuum emission also originates from the chromosphere. Some lines, such as Mg ii, exhibit absorption components and self-reversals, indicating optical depth effects in the atmosphere, while other lines such as Fe ii appear to be optically thin. Any hot blackbody emission might originate further in the photosphere.


These new limits, in conjunction with the inconsistency of isotropic flux interpretations, leave no room for an astrophysical interpretation of AAEs in the context of the standard model for time windows as short as 103 s. However, it has been shown that these events can be explained using physics beyond the standard model, as many models suggest that AAEs lend support for axionic dark matter, sterile neutrinos, supersymmetry, or heavy dark matter (Anchordoqui et al. 2018; Connolly et al. 2018; Dudas et al. 2018; Fox et al. 2018; Huang 2018; Abdullah et al. 2019; Anchordoqui & Antoniadis 2019; Borah et al. 2019; Chauhan & Mohanty 2019; Cherry & Shoemaker 2019; Chipman et al. 2019; Cline et al. 2019; Collins et al. 2019; Esmaili & Farzan 2019; Esteban et al. 2019; Heurtier et al. 2019a, 2019b; Hooper et al. 2019). Many of these models, excluding the axionic dark matter explanation (Esteban et al. 2019) or those heavy dark matter scenarios that are tuned to prevent signatures in IceCube (Hooper et al. 2019), can be constrained by this nonobservation at IceCube. Dedicated tests to quantify these constraints are beyond the scope of this work and may be the focus of a future study. In addition to explanations that incite new physics, it has recently been suggested that AAEs could be explained by downward-going CR-induced EASs that reflected off of subsurface features in the Antarctic ice (Shoemaker et al. 2019). Another possible explanation could be coherent transition radiation from the geomagnetically induced air shower current, which could mimic an upgoing air shower (Motloch et al. 2017; de Vries & Prohira 2019). Explaining these anomalous events with systematic effects or confirming the need for new physics requires a deeper understanding of ANITA’s detection volume. Efforts such as the HiCal radio frequency pulser, which has flown alongside ANITA on the last two flights (Prohira et al. 2018), are already underway to try to characterize the various properties of the Antarctic ice surface.


Having constrained the estimated CME propagation by matching the observed and modeled fronts in this way, it was then possible to estimate the arrival time and velocity of each CME as it passed Venus and Earth. At Venus, the shock driven by CME-2 caught up with CME-1, showing a typical shock-ICME structure. According to observations from the Wind spacecraft, the shock driven by CME-2 had passed through CME-1 before arrival at Earth. By comparing the estimated and observed arrival times of each CME, our approach resulted in arrival time estimates within 2.5 hr of those observed at VEX and Wind. The longitudinal structure of the CMEs obtained by this approach has the potential to improve space weather forecasting. The accuracy of arrival times can be affected by uncertainties in the CME initial conditions, interaction between CMEs, distortion of the CME shape by solar wind structure, the presence of shocks, and the efficiency of solar wind drag on each CME. The relative importance of each such factor could be investigated through an ensemble approach. The drag-based ensemble model developed by Dumbović et al. (2018) is a possible option, but the method is not valid for CME–CME interaction events. In order to test the sensitivity of CME propagation direction and width to the predicted arrival time and velocity, we summarize the CME initial parameters from Srivastava et al. (2018), Kilpua et al. (2019), and Scolini et al. (2019) and two conditions from ours (the time at which the fastest velocity was estimated and the last observation by the coronagraphs). Table 2 shows the initial parameters from those studies and the errors in predicted velocity and arrival time. Note that the minimum value of the drag parameters we used here is 1 × 10−9 km s−1, which was revealed as the lowest possible value (Rollett et al. 2014, 2016; Temmer & Nitta 2015; Kubicka et al. 2016). Based on that, there may exist a residual between the predicted profile and the observations. The residual values of nose and ghost fronts are shown in the last two columns of Table 2. For an Earth-directed CME, the residual between model and observed elongations of the CME nose will reflect the accuracy of the predicted arrival time and in situ velocity of the CME at Earth. The residual value between model and observed elongations of the CME flank provides information about how well the model reproduces the shape of the CME front, which is important for predicting the time and in situ speed at Earth for those CMEs whose flank encounters the Earth. The model with the smallest residual values between model and observed elongations for both CME nose and flank provides the most creditable estimate of the in situ CME parameters at Earth, suggesting that the use of this technique can add to our forecast skill. In our analysis, the CME initial parameters estimated using the time and location of the fastest CME velocity observed in the coronagraph data produced the smallest residual between subsequent observed and model CME elongations. This should therefore be considered to be the best estimate of CME kinematics, and, if we were doing a weighted ensemble, this would be given a much higher weighting than the other runs. It should be noted that many of the other runs did not produce a minimum residual within the likely range of drag parameters, indicating that these runs are somehow not capturing the physics. Table 2 shows that different initial parameters change the predicted arrival time of CME-1 at Venus by 8.5 hr and at Earth by 14.6 hr in total. For CME-2, the prediction errors are found as 6 hr at Venus and 8 hr at Earth. The prediction errors are comparable to the mean absolute error obtained from the drag-based ensemble model (Dumbović et al. 2018). In future work, we will try to use the heliospheric upwind extrapolation model in large ensembles to efficiently investigate the effect on the CME transit time of the uncertainty in the initial CME parameters and ambient solar wind (Owens et al. 2020a). Our results indicate that CME-1 and CME-2 interacted with each other before they arrived at Venus, according to the propagation distances derived from our modeling. The in situ observation from Venus shows a typical shock-ICME complex structure, which provides confirmation of this interpretation. Our results also suggest that a CME–CME interaction is possibly involved in disrupting the propagation direction or geometry of each CME. Such a deflection and interaction is consistent with the fact that CME-1 (CME-2) reached VEX earlier (later) than expected (Shen et al. 2012, 2014; Wang et al. 2014, 2016). The difference between expected arrival time and observational arrival time is larger at Earth than at Venus. This implies that the interaction persisted between Venus and Earth.


From the X-ray point of view, old open clusters are interesting for a number of reasons. First, X-ray observations efficiently detect different classes of close, interacting binaries, enabling the study of processes such as tidal coupling and the link between X-rays and rotation. The X-ray luminosity of late-type stars strongly depends on stellar rotation. As single stars age, they spin down due to magnetic braking (Pallavicini 1989). As a result, their X-ray emission decreases accordingly. An old star like our Sun (∼4.5 Gyr) has an X-ray luminosity of about 1026 to 1027 erg s−1 (0.1–2.4 keV; Peres et al. 2000). Even with the deepest exposures of a sensitive X-ray telescope like the Chandra X-Ray Observatory, this is nearly impossible to detect except for the nearest stars. Nevertheless, an early ROSAT observation of the old open cluster M 67, which lies at ∼840 pc (Pasquini et al. 2008) and is about as old as the Sun (

; Dinescu et al. 1995), revealed a large number of X-ray sources among the cluster members (Belloni et al. 1993). Many of these turned out to be close, tidally interacting binaries, where the stellar rotation is locked to the orbital period and therefore kept at a level that can sustain magnetically active coronae. Subsequent XMM-Newton (Gondoin 2005; Giardino et al. 2008; Gosnell et al. 2012) and Chandra (van den Berg et al. 2004, 2013; Giardino et al. 2008) observations of old open clusters have detected many such active binaries (ABs). ABs can be binaries of two detached stars, or they can have a contact or semi-detached configuration such as in W UMa and Algol binaries, respectively. In terms of the number of sources, ABs are the most prominent X-ray source class in old open clusters, but other classes of interacting binaries are represented as well. In cataclysmic variables (CVs), the X-rays are the result of accretion from a late-type main-sequence donor onto a white dwarf. In fact, the first ROSAT observation of M 67 was aimed at studying the X-rays from a CV that was discovered in the optical (Gilliland et al. 1991). The origin of the X-ray emission from more exotic open-cluster binaries, like blue stragglers, is less understood, but in X-rays they are more similar to the ABs than to the mass-transfer sources (van den Berg 2013).


Comparison of apparent effective diameters of these sources to direct size measurements supports a similar conclusion. Simpson et al. (2015) present ALMA observations of 23 SCUBA-2-selected SMGs with a median physical half-light diameter of 2.4 ± 0.2 kpc, while Ikarashi et al. (2015) show ALMA observations of 13 AzTEC-selected SMGs with a median physical half-light diameter of $1.34^{+0.26}_{-0.28}$ kpc. ALMA observations of four SPT-selected lensed SMGs give a mean physical half-light diameter of 2.14 kpc (Hezaveh et al. 2013b). This measurement is consistent with a recent lensing analysis of a significantly expanded SPT-selected DSFG sample (Spilker et al. 2016). These high-resolution ALMA observations constrain the FIR sizes of the sources to be 1.0–2.5 kpc. Earlier observations of the physical sizes of SMGs by CO detection and 1.4 GHz imaging suggest larger sizes (e.g. Tacconi et al. 2006; Biggs & Ivison 2008; Younger et al. 2008). However, Simpson et al. (2015) point out that the submillimetre sizes are consistent with resolved 12CO detections, while the sizes derived from 1.4 GHz imaging are about two times larger because of the cosmic ray diffusion, which can explain the results before higher frequency observations at ALMA were possible (Chapman et al. 2004; Tacconi et al. 2006; Biggs & Ivison 2008; Younger et al. 2008). Similarly, Ikarashi et al. (2015) reveal that the 12CO detected sizes and the 1.4 GHz imaging sizes of similar sources are greater than their submillimetre sizes as well. Furthermore, observations of local galaxies also show the submillimetre sizes are smaller than the CO detected sizes (e.g. Sakamoto et al. 2006, 2008; Wilson et al. 2008) and the 1.4 GHz continuum sizes (e.g. Elbaz et al. 2011). Our photometrically derived $\sqrt{\mu }d$ is best compared to the submillimetre continuum sizes. With a median apparent effective diameter of $4.2^{+1.7}_{-1.0}$ kpc, the $\sqrt{\mu }d$ of our sample is one to six times the observed intrinsic diameters (1.0–2.5 kpc). Lensing (or multiplicity) increases the apparent effective size of a source, so this comparison favours a lensing (or multiplicity) interpretation for the ACT-selected sources.


The EW(λ8542)/EW(λ8498) values are obtained around ∼1.4 in the first observing night, which are somewhat smaller than the values around ∼1.6 derived in the second night, when a strong optical flare decay was detected (also see the Section 4.2). These low ratios are consistent with the values found for several other stars with strong chromospheric activity (e.g. Montes et al. 2000; Gu et al. 2002; López-Santiago et al. 2003; Zhang & Gu 2008; Gálvez et al. 2009; Cao & Gu 2014, 2015, 2017; Zhang et al. 2016), which suggests that the $\rm{Ca\,{\small II}}$ IRT line emission arises from plage-like regions. The EHα/EHβ ratios have also been usually used as a diagnostic for discriminating the presence of different structures on the stellar surface. As Huenemoerder & Ramsey (1987) discussed, the low ratios in RS CVn-type stars are caused by plage-like regions, while prominence-like structures have high values. Similar results have also been reported by Hall & Ramsey (1992) who found that low ratios (∼ 1–2) can be achieved both in plages and prominences viewed against the disc, but high values (∼ 3–15) can only be obtained in extended prominence-like structures viewed off the stellar limb. We obtain the ratios on SZ Psc during the flare decay phase change from 2.40 to 3.40, which are not especially high and anticorrelated with the variation of activity emission shown in Fig. 3, in which the EWs of Hα and Hβ line subtraction and the EHα/EHβ values are plotted as a function of orbital phase. Especially when the EWs have an increasing oscillation during the gradually decrease, which is resulted from flare ejection (see the discussion in Section 4.2), the ratios have a similar anticorrelation feature. These facts suggest that the low EHα/EHβ ratios and its variation might be dominantly associated with the flare decrease, and accompanied cool post-flare loops (see the Section 4.3) might play a part of role for the low ratios, which may have a state like absorbing prominence projected against the disc.


The young starburst inferred by the detections of high ionization emission line of He II λ4686 and the blue WR bump in this and previous works (Guseva et al. 2000; Brinchmann, Kunth & Durret 2008) is confirmed by the age estimates made here for the bright and faint regions in Mrk 22 as ∼4 and ∼10 Myr, respectively. Unlike previous works, we carried out abundance analysis for both the regions separately. We found an appreciable metallicity difference of ∼0.5 dex between the bright region [12 + log (O/H) ∼ 8] and the faint region [12 + log(O/H) ∼ 7.5]. The separation between two regions is ∼0.6 kpc. Typical metallicity gradients in normal spiral galaxies have been found between −0.009 and −0.231 dex kpc−1, with an average gradient of −0.06 dex kpc−1 (Zaritsky, Kennicutt & Huchra 1994). The observed metallicity difference between the two regions in Mrk 22 is too large to be explained as a normal galactic metallicity gradient. The chemical composition as measured from the gas-phase metallicity [12 + log(O/H)] shows various degree of spatial variations in different types of dwarf galaxies. For instance, shallow gradient in metallicity is seen in SBS 0335−052 (Papaderos et al. 2006) while no significant variations were seen in Mrk 35 (Cairós et al. 2007). A study on a large sample indicates that normal BCD galaxies are chemically homogeneous (Kobulnicky & Skillman 1996; Papaderos et al. 2006; Kehrig et al. 2008; Cairós et al. 2009; Pérez-Montero & Contini 2009; Pérez-Montero et al. 2011; Hägele et al. 2011; García-Benito & Pérez-Montero 2012; Lagos & Papaderos 2013). On the other hand, the metallicity of extremely metal-poor galaxies is usually not homogeneous within the galaxy, with the low metallicity seen in regions of intense star formation (Papaderos et al. 2006; Izotov & Thuan 2009; Levesque et al. 2011; Sánchez Almeida et al. 2013, 2014, 2015). However, large metallicity gradients are not common in dwarf galaxies. The simplest explanation for large metallicity difference in a single system is a recent merger of two galaxies with different metallicity. In a few cases, significantly large metallicity differences between star-forming regions in dwarf galaxies were seen and understood in terms of recent tidal interactions or mergers (López-Sánchez, Esteban & Rodríguez 2004a,b; López-Sánchez, Esteban & García-Rojas 2006; López-Sánchez & Esteban 2009, 2010). The evolution in terms of metallicities in interacting dwarf galaxies is fairly complex as it can depend on various factors such as mixing of metals with the interstellar medium (ISM), possible outflows of metals, and inflow of metal-poor gas in tidally interacting systems.


NLFFF extrapolation provides the reconstructed coronal magnetic field for AR 11158 from 2011 February 13 − 2011 February 15 (Figures 1(d)–(f)). The field lines (yellow lines) within the core of the AR have arcade-like structure with a relatively strong twist mainly near the PIL. These figures show that the magnetic field evolved during this period. Although we did not quantitatively compare the field lines with the observation, in general, the reconstructed coronal field morphologies match with the observations in Figures 1(a)–(c). The general morphologies and the locations of the high-twist fields are also in agreement with many previous studies (Jing et al. 2012; Sun et al. 2012; Dalmasse et al. 2013; Inoue et al. 2013, 2014a; Liu et al. 2013; Wang et al. 2013; Aschwanden et al. 2014; Malanushenko et al. 2014; Zhao et al. 2014). Unlike Zhao et al. (2014) who could identify the twisted flux rope from the topology of the reconstructed coronal field, we could not find an obvious topological signature of a flux rope existing in our NLFFF during our analysis time window. It might be due to the fact that there was little magnetic flux with twist higher than one turn in our NLFFF and it is difficult to topologically define it as a flux rope. However, our result is consistent with other NLFFF results (Jing et al. 2012; Sun et al. 2012; Liu et al. 2013; Wang et al. 2013; Inoue et al. 2014a; Malanushenko et al. 2014). The high-twist region in our result is also in agreement with the region with high helicity flux (Dalmasse et al. 2013) and the location of the flare ribbons (Bamba et al. 2013; Liu et al. 2013), as well as the high current density region (Janvier et al. 2014). Figures 1(g)–(i) show the evolution of the twist distribution map, with the magnetic twist of the field lines plotted at the footpoints of field lines according to a color scale. This shows that the high-twist (strongly right-handed twist corresponding to Tw > 0.5) areas are concentrated in only a limited part of the AR. The high-twist area grew and became even more twisted just before the X2.2 flare (Figure 1(i)). Most parts of the AR have twist values less than 0.25, but near the PIL the twist can reach more than 0.5, even up to about a full turn. This is consistent with the results of Sun et al. (2012) and Inoue et al. (2014a). A high-twist (strong negative/left-handed twist) area also developed in the eastern part of the AR, which did not exist initially on February 13. Both of these high-twist areas produced several flares. However, here we focus on the flares that resulted from the high-twist core region near the center of the AR, where the M6.6 and X2.2 flares occurred.


Outflows are ubiquitous in both luminous AGN and in local Seyfert galaxies, and occur on a wide range of physical scales, from highly ionised semi-relativistic winds and jets in the nuclear region at subparsec scales to galactic scale outflows seen in mildly ionised, molecular, and neutral gas (Morganti et al. 2016; Fiore et al. 2017; Fluetsch et al. 2019; Lutz et al. 2020; Veilleux et al. 2020, and references therein). In some cases molecular and ionised winds have similar velocities and are nearly co-spatial, suggesting a cooling sequence scenario where molecular gas forms from the cooling of the gas in the ionised wind (Richings & Faucher-Giguere 2017; Menci et al. 2019). Other AGN show ionised winds that are faster than the molecular winds, suggesting a different origin of the two phases (Veilleux et al. 2020, and references therein). The molecular phase is a crucial element of the feeding and feedback cycle of AGN because it constitutes the bulk of the total gas mass and it is the site of star formation activity. On galactic scales massive molecular winds are common in local Seyfert galaxies (e.g. Feruglio et al. 2010; Cicone et al. 2014; Dasyra et al. 2014; Morganti et al. 2015; García-Burillo et al. 2014, 2017, 2019); these winds likely suppress star formation (i.e. negative feedback) as they reduce the molecular gas reservoir by heating or expelling gas from the host-galaxy ISM. In late-type AGN-host galaxies, the gas kinematics appears complex at all scales, showing several components such as bars, rings, and (warped) discs, with high velocity dispersion regions (e.g. Shimizu et al. 2019; Feruglio et al. 2020; Fernández-Ontiveros et al. 2020; Alonso-Herrero et al. 2020; Aalto et al. 2020; Audibert et al. 2020). Accurate dynamical modelling of the molecular gas kinematics reveals kinematically decoupled nuclear structures, high velocity dispersion at nuclei, trailing spirals, and evidence of inflows and AGN-driven outflows. (e.g. Combes et al. 2019; Combes 2019, 2021). The outflow driving mechanism (wind shock, radiation pressure, or jet), their multiphase nature, and their relative weights and impact on the galaxy ISM are still open problems (Faucher-Giguère & Quataert 2012; Zubovas & King 2012; Richings & Faucher-Giguere 2017; Menci et al. 2019; Ishibashi et al. 2021). To date, far different outflow phases have been observed only for a handful of sources. Atomic, cold, and warm molecular outflows have been observed in radio galaxies (e.g. Morganti et al. 2007; Dasyra & Combes 2012; Dasyra et al. 2014; Tadhunter et al. 2014; Oosterloo et al. 2017). The nuclear semi-relativistic phase and the galaxy-scale molecular phase have been observed simultaneously in less than a dozen sources, with varied results: in some cases data suggest energy driven flows (Feruglio et al. 2015; Tombesi et al. 2015; Longinotti et al. 2018; Smith et al. 2019), in other cases data suggest momentum driven flows (e.g. García-Burillo et al. 2014; Feruglio et al. 2017; Fluetsch et al. 2019; Bischetti et al. 2019; Marasco et al. 2020). Fiore et al. (2017), using a compilation of local and high redshift winds, showed that there is a broad distribution of the momentum boost, suggesting that both energy- and momentum-conserving expansion may occur. Enlarging the sample of local AGN-host galaxies with outflows detected in different gas phases is important to understand the nature and driving mechanisms of galaxy-scale outflows.


However, this outward migration of the inner edge should stop at the corotation radius rco, where the Keplerian frequency of the disk equals the spin frequency of Jupiter. When rcav > rco, there will be two possibilities: the angular momentum will be transferred from Jupiter to the disk and then the gas accretion will stop, or otherwise the corotation radius and the disk edge will move outward together and then the accretion will continue (Takata & Stevenson 1996; Liu et al. 2017). Although the current corotation radius is rco ≈ 2.25 RJ, Jupiter at its time of formation was much larger than it is today (Burrows et al. 1997; Fortney et al. 2011), and this means that the corotation radius was also larger than the current one if the conservation of the angular momentum of Jupiter is assumed. Considering the transport of the angular momentum from Jupiter to the disk, the angular momentum should have been conserved since the disk disappeared. According to a formation model of Jupiter, the radius of the planet was ≈1.75 RJ after its rapid gas accretion and it decreased little by little (Lissauer et al. 2009). When the radius of Jupiter is 1.75 RJ, the corotation radius should be rco ≈ 4.7 RJ. We can then consider two scenarios of Io formation. In the first one, Io formed around r ≈ 4.7 RJ, slightly interior to the r = 5.89 RJ of our fiducial model, and then moved outward after the disk dissipated. The satellites, especially the inner ones, could move outward by the tidal force from Jupiter (Yoder & Peale 1981). The outer ones would be pushed by the inner ones and move outward with them because of the resonance. In this case, the position of the snow line should have been more inside than the fiducial case in this work, but this thermal condition could easily be reproduced by another parameter set. The second possibility is that Io was not the innermost satellite. If a body was present at r = 3.7 RJ, Io would have been situated at r = 5.7 RJ if they were trapped in a 2:1 resonance. This orbit is consistent with the corotation radius when the radius of Jupiter is ≈1.5 RJ, and this radius can be achieved during the contraction of Jupiter. The innermost body may have been broken by the tidal force of Jupiter when it has entered inside the Roche limit. Current Io, trapped in the Laplace resonance, actually moves inward little by little because of the tidal dissipation, and the innermost body may have also experienced such inward migration (Lainey et al. 2009).


Time domain structures (TDSs; electrostatic or electromagnetic electron holes, ion holes, solitary waves, double layers, nonlinear whistlers, etc.) are ∼1 ms pulses having significant electric fields parallel to the background magnetic field (Mozer et al. 2015). They are abundant through space, occurring along auroral zone magnetic field lines (Temerin et al. 1982; Mozer et al. 1997; Ergun et al. 1998), in the magnetospheric tail and plasma sheet (Cattell et al. 2005; Tong et al. 2018; Lotekar et al. 2020), at reconnection sites (Cattell et al. 2005; Steinvall et al. 2019; Lotekar et al. 2020), in the solar wind (Mangeney et al. 1999; Malaspina et al. 2013), in collisionless shocks (Wilson et al. 2010; Vasko et al. 2020; Wang et al. 2020), and in the magnetospheres of other planets (Pickett et al. 2015). TDSs are also expected along the Parker Solar Probe orbit (Mozer et al. 2020a). According to theoretical estimates and simulations (Cranmer & van Ballegooijen 2003; Valentini et al. 2011, 2014), these nonlinear structures can provide thermalization of electron and ion beams produced in the course of the turbulence cascade development at scales the order of the electron inertial length and down to the Debye length. This paper discusses such observations at a heliocentric distance of 35 solar radii. The electric field experiment on the Parker Solar Probe measures electric fields from DC to 20 MHz. A general description of the instrument and its electronics appears elsewhere (Bale et al. 2016). In this paper, the data from DC to 2 MHz are discussed. These measurements are obtained from the potentials of the four antennas, V1 through V4, that are located in the plane perpendicular to the Sun–satellite line. They produce E12 = (V1−V2)/3.5 and E34 = (V3−V4)/3.5, which are then rotated into the spacecraft coordinate system to produce EX and EY. The direction, X, is perpendicular to the Sun–spacecraft line, in the ecliptic plane, and pointing in the direction of solar rotation (against the ram direction), Y is perpendicular to the ecliptic plane, pointing southward, and Z points toward the Sun. The numerical factor, 3.5, is the effective antenna length (Mozer et al. 2020a). The uncertainties of the amplitudes of the waves and time domain structures reported in this paper are estimated to be about a factor of 2. These amplitudes are underestimated because the capacitive divider that couples the antennas to the electronics decreases the measured electric field relative to that on the antennas. They are often overestimated because short antennas produce overestimates of the electric field by factors of 2–4, as was observed during antenna deployment on the Cluster satellite and as is observed on the Parker Solar Probe from the ratio of the electric field to the magnetic field in whistlers.


In this paper, we are interested not only in the mathematical properties of the ambipolar diffusion as a nonlinear diffusion process, but also in the inclusion of ambipolar diffusion terms in MHD codes. In astrophysics, over the past few decades, multidimensional MHD computer codes have been developed that model a variety of physical processes including ambipolar diffusion. Representative examples of such codes and simulations outside solar physics can be found in Basu & Mouschovias (1994), Mac Low et al. (1995), Padoan et al. (2000), Basu & Ciolek (2004), Kudoh & Basu (2008), Choi et al. (2009), Gressel et al. (2015), Tomida et al. (2015), O’Sullivan & Downes (2007), Masson et al. (2012), Viganò et al. (2019), and Grassi et al. (2019). The consideration of ambipolar diffusion processes in solar physics started many decades ago (e.g. Parker 1963), but it has undergone a true explosion in terms of its use in large numerical models (e.g. Leake et al. 2005; Leake & Arber 2006; Arber et al. 2007; Cheung & Cameron 2012; Leake & Linton 2013; Martínez-Sykora et al. 2012, 2017a,b, 2020a,b; Ni et al. 2015, 2016, 2021; Khomenko et al. 2017, 2018, 2021; González-Morales et al. 2018, 2020; Nóbrega-Siverio et al. 2020a,b; Popescu Braileanu & Keppens 2021). Such numerical calculations often encounter a problem: given the comparatively high values of χa in different cosmic environments, the advance in time may grind to a halt in magnetised regions when a standard Courant-Friedrichs-Lewy condition is adopted for the timestep based on ηa. The recent papers by González-Morales et al. (2018) and Nóbrega-Siverio et al. (2020b) describe the construction of so-called super-time-stepping (STS) modules for the Mancha code and for the Bifrost code, respectively, designed with the aim to overcome that stiffness problem. In at least three of the papers cited above (Masson et al. 2012; Viganò et al. 2019; Nóbrega-Siverio et al. 2020b), the basic ZKBP solution in cylindrical coordinates was used to test the ambipolar diffusion module, given its simplicity and the analytical expression available for it. However, as already mentioned, the ambipolar diffusion problem tends to give rise to sharp current sheets and singularities. The ZKBP solution is comparatively smooth in that sense and it would be good to have some other canonical solutions on hand that include current sheets having higher degrees of singularity, which naturally occur in the ambipolar diffusion problem.