The most striking characteristic of this event is displayed by the AIA 304 Å movie in which a twisted coherent structure is gradually shown to have underwent a rolling motion during the fadeaway of the brightening (panels (d) and (e)). Interestingly, it is clearly evident from the Hα observations that the twisted structure is a filament, which consists of three sections with an approximate length of about 45 Mm (panel (k)). Taking the magnetic field polarity around the filament into account, it is obvious that the filament roughly separated oppositely polarized magnetic fields, with the western ends rooted in a negative-polarity region and the eastern ends rooted in a positive-polarity region (panel (l)). As a consequence, the axial field component of the filament can be determined as pointing to the right when viewed from its positive-polarity side, and the filament was identified as dextral, which is consistent with the preferential filament pattern in the northern hemisphere (Martin 1998). Careful inspection of the 304 Å observations also shows that the filament probably consists of two sets of mutually intertwined dark threadlike structures (panel (e)), which may naturally explain why it displays three sections in the Hα observations. One set of the dark threadlike structures may include its western and eastern parts (see the twin arrows). They first appeared above the brightening and then separated from each other and lifted up. Finally, they formed a coherent reverse s-shaped structure, with its dipped part blocked by the other sets of dark threadlike structures (panels (b) and (e)), which appeared to be co-spatial with the spread brightening and showed up immediately after the fade away of the brightening (panels (d) and (e)). The dynamic evolution of these dark threadlike structures is also displayed on the Hα images (panels (i)–(k)). The above observations suggested that the newly formed filament is a flux rope with twisted magnetic structures, and its formation is again attributed to reconnections between T1 and T2. Its apparent rolling motion might be thus understood in terms of a change in the orientation of the connecting T1 and T2. All these observations, including the two-sided spread brightenings, the newly formed EUV loop, and the dynamic formation of the flux rope seem to support the previous idea that the formation of the flux rope is the result of a tether-cutting type reconnection (Moore et al. 2001; Liu et al. 2010; Chen et al. 2014) between two sets of sheared arcade cool loops. However, our observation further reveals the formation of a filament by magnetic reconnection among T1 and T2.


Studies of the pulse characteristics of X-ray pulsars offer vital information about their nature and the geometry of the binary system. The shape of the pulse profile offers insight into the mode of accretion inflows, the pulsar luminosity, the geometry of the accretion column and the magnetic field configuration (Parmar et al. 1989a). Therefore, such studies offer an understanding of pulsar systems and the process of mass accretion in the presence of the strong magnetic field of a neutron star. Detailed studies of pulse characteristics were conducted during outburst activities of some of pulsars such as EXO 2030+375 (Parmar et al. 1989a), Cepheus X-4 (Koyama et al. 1991; Mihara et al. 1991; Mukerjee & Agrawal et al. 2000), XTE J1946+274 (Paul et al. 2001), etc., which offered valuable information and understanding of the physical processes responsible for the observed properties of these pulsars. Spectroscopic studies, however, reveal information about the environment surrounding a pulsar and the underlying mechanism responsible for energy generation in these systems. Detailed studies of cyclotron absorption features, if present in the pulsar spectrum, not only enable us to determine its surface magnetic field, but they also offer an insight into the line-producing region, its structure, and the geometry of the accretion column (Staubert et al. 2019). Therefore, detailed studies of cyclotron absorption features have been pursued by researchers since their discovery (Truemper et al. 1978), as they are an important diagnostic probe for pulsars. Cyclotron absorption features were detected in the spectrum of many Be binaries covering a wide range of energies, starting from a lower energy of ∼10 keV (Jun et al. 2012; DeCesar et al. 2013) to a higher energy at ∼100 keV (La Barbara et al. 2001). Detailed studies of cyclotron line sources and their properties were reported by Staubert et al. (2019) and Maitra (2017). The Be binaries, particularly because of their transient nature, offer us opportunities for detailed study of some of these interesting properties as a function of changes in source luminosity and in time. The studies of cyclotron line energy with respect to its pulse phase, source luminosity, and time, showed wide variations for some sources, such as Vela X-1, Cen X-3, and Her X-1 (Staubert et al. 2019). These interesting properties help us to systematically investigate and understand their underlying physical properties.


Since 2018 the Parker Solar Probe (PSP) mission is collecting solar wind plasma and magnetic field data through the inner heliosphere, reaching the closest distance to the Sun ever reached by any previous mission (Fox et al. 2016; Kasper et al. 2021). Thanks to the PSP journey around the Sun (it has completed 11 orbits) a different picture has been drawn for the near-Sun solar wind with respect to the near-Earth one (Bale et al. 2019; Kasper et al. 2019; Chhiber et al. 2020; Malaspina et al. 2020; Bandyopadhyay et al. 2022; Zank et al. 2022). Different near-Sun phenomena have been frequently encountered, with the emergence of magnetic field flips, i.e., the so-called switchbacks (Dudok de Wit et al. 2020; Zank et al. 2020), kinetic-scale current sheets (Lotekar et al. 2022), and a scale-invariant population of current sheets between ion and electron inertial scales (Chhiber et al. 2021). Going away from the Sun (from 0.17 to 0.8 au), evidence of radial evolution of different properties of solar wind turbulence (Chen et al. 2020) as the spectral slope of the inertial range (from −3/2 close to the Sun to −5/3, at distances larger than 0.4 au), an increase of the outer scale of turbulence, a decrease of the Alfvénic flux, and a decrease of the imbalance between outward (z
+) and inward (z
−) propagating components (Chen et al. 2020) has been provided. Although the near-Sun solar wind shares different properties with the near-Earth one (Allen et al. 2020; Cuesta et al. 2022), significant differences have been also found in the variance of magnetic fluctuations (about 2 orders of magnitude) and in the compressive component of inertial range turbulence. In a similar way, Alberti et al. (2020) first reported a breakdown of the scaling properties of the energy transfer rate, likely related to the breaking of the phase-coherence of inertial range fluctuations. These findings, also highlighted by Telloni et al. (2021) and Alberti et al. (2022) analyzing a radial alignment between PSP and Solar Orbiter, and PSP and BepiColombo, respectively, have been interpreted as an increase in the efficiency of the nonlinear energy cascade mechanism when moving away from the Sun. More recently, by investigating the helical content of turbulence Alberti et al. (2022) highlighted a damping of magnetic helicity over the inertial range between 0.17 and 0.6 au suggesting that the solar wind develops into turbulence by a concurrent effect of large-scale convection of helicity and creation/annihilation of helical wave structures. All these features shed new light onto the radial evolution of solar wind turbulence that urges to be considered in expanding models of the solar wind (Verdini et al. 2019; Grappin et al. 2021), and also to reproduce and investigate the role of proton heating and anisotropy of magnetic field fluctuations (Hellinger et al. 2015).


Several qLMXBs have been identified in GCs and in the Galactic field (for some examples, see table 4 in Guillot et al. 2009 and references therein). While LMXBs in the field were detected following the onset of a bright accretion outburst, most qLMXBs in GCs, including all those with the highest flux at Earth, have not shown accretion activity.3 Most of these sources have only been spectrally identified based on their similarities to field LMXBs, observed during quiescence (e.g. Cen X-4 or Aql X-1). Previous works have confirmed that H-atmosphere models accurately describe the spectra of qLMXBs, with radii in the range 10–15 km, as expected for NSs, either from single sources (e.g. Heinke et al. 2006a; Webb & Barret 2007; Guillot, Rutledge & Brown 2011; Heinke et al. 2014; Bogdanov et al. 2016), or from statistical analyses of multiple qLMXBs (e.g. Guillot et al. 2013; Guillot & Rutledge 2014; Lattimer & Steiner 2014; Guillot 2016; Steiner et al. 2018). However, in some cases the accreted material may not be hydrogen, but helium (e.g. Servillat et al. 2012; Catuneanu et al. 2013; Heinke et al. 2014). One way to circumvent this is to identify the nature of the donor star, i.e. to determine the nature of the material transferred on to the NS (e.g. with the detection of an H α emission line, presumably originating in a faint accretion disc, Haggard et al. 2004). The possibility of helium (or heavier element) atmospheres is well-founded on the existence of ultracompact X-ray binaries (UCXB), with white dwarfs or helium-dominated donors4 (e.g. Zurek et al. 2009; Altamirano et al. 2010; Sanna et al. 2017; Cadelano et al. 2019). In fact, around 1/3 of the LMXBs in GCs with constraints on the companion nature, possess a white dwarf donor (Bahramian et al. 2014). Since NS He-atmosphere models have harder spectra than H-atmosphere models, using the incorrect composition for the observed thermal emission can result in biases of the inferred radii (Servillat et al. 2012; Heinke et al. 2014).


We overplot the observed number of member galaxies and the host stellar mass in Figure 11(a) with colored symbols. Colors indicate the five groups of Δm
12. The circles and diamonds indicate the LV galaxy groups and SAGA survey sample, respectively. The LV sample, most of which is from the compilation by Carlsten et al. (2021), consists of 13 galaxy groups of which satellite membership is determined by measuring their distances using either the TRGB or SBF method: the MW (McConnachie 2012, for compiled data), M31 (McConnachie 2012; Martin et al. 2016; McConnachie et al. 2018, for compiled data), the Local Group (including the MW and M31 subgroups and quasi-isolated outlying members classified by McConnachie 2012), NGC 2403 (Carlin et al. 2021), NGC 4258 (Kim et al. 2011; Spencer et al. 2014; Carlsten et al. 2021), NGC 4631 (Tanaka et al. 2017; Carlsten et al. 2021), M51 (Carlsten et al. 2021), M101 (Bennet et al. 2017; Danieli et al. 2017; Carlsten et al. 2019b; Bennet et al. 2019), M94 (Smercina et al. 2018), NGC 1023 (Trentham & Tully 2009; Carlsten et al. 2021), M104 (Javanmardi et al. 2016; Carlsten et al. 2021), M81 (Chiboucas et al. 2009, 2013), and NGC 5128 (Crnojević et al. 2014; Müller et al. 2017; Crnojević et al. 2019; Müller et al. 2019). The other galaxy groups that are in the Carlsten et al. (2021) compilation but not this study are excluded because either the spatial coverage is too low (less than 20% of the projected virial area is covered) or the SBF S/N is too low to confirm satellites as faint as M

r
 > −12.3 mag. The SAGA survey sample (Mao et al. 2021) consists of galaxy groups with 36 MW-like host galaxies. The MW-like host galaxies are selected by their K-band magnitudes (−24.6  M

K
  −23 mag). The SAGA survey covered more than 80% of the projected R

h
 = 300 kpc area and confirmed satellite memberships from their redshifts. It is considered complete to satellites brighter than M

r
 = − 12.3 mag. Note that while the spatial coverage of the LV sample significantly differs from galaxy to galaxy, and most of them cover less than the virial area, the SAGA survey sample has a relatively consistent spatial coverage.


The most general third-order statistics is the three-point correlation function (hereafter referred to as 3PCF), which is defined in configurations space. Alternatively, one can study its Fourier space counterpart, the bispectrum. These two statistics contain, in principle, the same information. However, their analyses implicate different limitations and challenges, which can affect the physical interpretation of the results. A main advantage of the bispectrum is that an analysis in Fourier space allows for a clear exclusion of high-frequency modes in the density fluctuations, which are difficult to interpret theoretically due to their highly non-linear evolution. In configuration space, these high-frequency modes contribute to the 3PCF, in principle, at all scales. In practice, one therefore needs to restrict the analysis to large scales, where their contribution is negligible, lavishing a lot of valuable data. Another advantage of the bispectrum is that its covariance is diagonal for Gaussian density fluctuations. This approximation works well, even for evolved density fields, while deviations from Gaussianity can also be taken into account (Scoccimarro 2000; Sefusatti et al. 2006; Chan & Blot 2017). The covariance of the 3PCF, on the other hand, is not diagonal, even for Gaussian fluctuations, which makes the modelling more difficult (Srednicki 1993; Slepian & Eisenstein 2015; Byun et al. 2017; Gualdi et al. 2017). An additional difference in the analysis of the bispectrum and the 3PCF lies in the fact that the computation of the latter is more expensive. However, this aspect can be tackled by employing advanced algorithms and appropriate computational resources, as done in this work (see also, Barriga & Gaztañaga 2002; McBride et al. 2011a; Jarvis 2015; Slepian & Eisenstein 2015, and references therein). Besides its disadvantages, there are some arguments that speak for the 3PCF. One of them is the fact that the amplitude of the 3PCF (but not its errors) is not affected by shot-noise, whereas the latter affects the bispectrum amplitude at all scales and hence needs to be modelled for correcting the measurements. In addition, an analysis in configuration space has the advantage that complicated survey masks can be easily taken into account in the analysis of observational data, while in Fourier space such masks impose complicated effects on the measured bispectrum, which are difficult to model (e.g. Scoccimarro 2000). A more general consideration is that it is easier to interpret effects such as redshift space distortions or baryon acoustic oscillations (BAOs) on the statistics in configuration space, since that is where the physical processes that cause these effects happen. Studies of third-order correlations in the literature usually focus on either Fourier or configuration space (e.g. McBride et al. 2011b; Marín et al. 2013; Gil-Marín et al. 2015). However, it is worthwhile studying both statistics and cross-check the results, since their different advantages and disadvantages are quite complementary.


We used the code detail (Butler & Giddings 1985) based on the method of accelerated Λ iteration (Rybicki & Hummer 1991). The detail opacity package was updated by Przybilla et al. (2011) by including bound–free opacities of neutral and ionized species. The calculated departure coefficients, bi = nNLTE/

, were used by the code synthV_NLTE (Ryabchikova et al. 2016) to calculate the synthetic NLTE line profiles. Here, nNLTE and nLTE are the statistical equilibrium and thermal (Saha Boltzmann) number densities, respectively. The binmag code11

11

http://www.astro.uu.se/oleg/binmag.html

 (Kochukhov 2018) was used for automatic spectral line fitting and comparison with the observed spectrum. The typical uncertainties in the fitting procedure with the observed profile are less than 0.02 dex for weak lines and 0.03 dex for strong lines. For consistency with our NLTE studies of C i–C ii (Alexeeva et al. 2016), Ti i–Ti ii (Sitnova et al. 2016), and Ca i–Ca ii (Sitnova et al. 2018), here we use exactly the same model atmospheres for 21 Peg, HD 22136, π Cet, and ι Her, calculated with the code LLmodels (Shulyak et al. 2004), as in the earlier papers. For the remaining stars, the calculations were performed using plane-parallel (1D), chemically homogeneous model atmospheres from the Kurucz’s grid12

12

http://www.oact.inaf.it/castelli/castelli/grids.html

 (Castelli & Kurucz 2003). Table 1 lists the atomic data for the Ne i and Ne ii lines used in the present line-formation analysis. For Ne i lines belonging to the 2p53p–2p53s transition array, we adopted data of atomic oscillator strengths from the experimental measurements deduced using a neon-filled hollow cathode lamp in conjunction with two spectrographs (Piracha et al. 2015). For 2p53d–2p53p transitions at 8377 and 8495 Å, we also used experimental transition probabilities measured with the shock tube (Doherty 1962) and renormalized by the NIST group (Wiese et al. 1966). These values of transition probabilities are supported by the accurate theoretical calculations of Seaton (1998a). For the remaining Ne i lines and for the Ne ii lines, the oscillator strengths were taken from the NIST Handbook of Chemistry and Physics (Fuhr & Wiese 1998—Ne i) and from Kurucz’s website. Kurucz’s theoretical calculations agree very well with the theoretical calculations by Breit–Pauli R-matrix method used in the earlier papers on neon abundance analyses (see Section 3.4). Stark collisional data were adopted from the Kurucz’s website.


Almost all the efforts to reveal the geometry of GW170817 have been based on model fitting to the EM afterglow light curve3

3
Dhawan et al. (2020) suggested a method to estimate the viewing angle using the macronova/kilonova signal. However, while the afterglow light curve is based on rather clear physics the macronova/kilonova light curve involves uncertainties in all aspects, ranging from the composition of the ejecta to its three-dimensional distribution, unknown opacities of the relevant heavy elements and complicated radiation transfer calculations (see Nakar 2020 for a discussion of the various uncertainties). Thus, a concern arises that due to these numerous uncertainties it might be extremely difficult to control the systematics that may arise using this method.
 (Alexander et al. 2017, 2018; Haggard et al. 2017; Margutti et al. 2017; Troja et al. 2017, 2019; D’Avanzo et al. 2018; Dobie et al. 2018; Gill & Granot 2018; Granot et al. 2018b; Lazzati et al. 2018; Lyman et al. 2018; Margutti et al. 2018; Mooley et al. 2018a; Troja et al. 2018; Fong et al. 2019; Hajela et al. 2019; Lamb et al. 2019; Wu & MacFadyen 2019; Ryan et al. 2020; Takahashi & Ioka 2020). All recent studies agree that GW170817 have launched a relativistic jet that broke out of the ejecta successfully and then interacted with the circum-merger medium to produce the afterglow. They all find that the jet had an angular structure with a narrow highly energetic core, with a jet opening θj, which is observed from a viewing angle θobs ≫ θj. Each of these studies obtained a different estimate of θobs, and θj (see Section 5 and Figure 3). The viewing angles found by different studies are in the range of 14°–38° and the jet opening angle is in the range of 25–8°. The typical errors quoted in these studies are a few degrees on the viewing angle and a fraction of a degree on the jet opening angle. Thus, the various estimates are often highly inconsistent with each other. An exception is the work of Mooley et al. (2018b) who used the motion of the radio image as measured in VLBI observations (see also Ghirlanda et al. 2019; Hotokezaka et al. 2019) in addition to the light curve to constrain the system geometry.


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.


Already soon after the identification of the optical counterpart of Cyg X-1, X-ray light curves were found to show a strong orbital modulation of the X-ray absorption column, NH, due to absorption of X-rays from the black hole in the stellar wind (Li & Clark 1974; Remillard & Canizares 1984; Bałucińska-Church et al. 2000; Poutanen et al. 2008; Miškovičová et al. 2016; Grinberg et al. 2015). Together with observations of the orbital modulation of optical lines from HDE 226868 (Gies & Bolton 1986a,b; Gies et al. 2003), these phenomena led to the picture of the stellar wind of HDE 226868 as a line driven wind or CAK wind after Castor et al. (1975, see also Friend & Castor 1982 and Morton 1967) with an asymptotic velocity of v∞ ~ 2000 km s−1 (Muijres et al. 2012). This wind is disturbed by the gravitational potential of the black hole, which leads to a focusing of the wind toward the black hole; see Friend & Castor (1982) and Gies & Bolton (1986b) for early models and El Mellah et al. (2019) for a modern treatment ofthis process. In addition, the wind is also affected by the X-rays from the compact object: strong orbital modulation of NH is seen during the canonical hard state of the black hole, where the X-ray spectrum is dominated by a Comptonized power law (Parker et al. 2015; Nowak et al. 2011; Wilms et al. 2006, and references therein). The typical bolometric luminosity of Cyg X-1 in this state is around 2 × 1037 erg s−1 (e.g., Wilms et al. 2006; Nowak et al. 1999), albeit with a large uncertainty due to our lack of knowledge of the UV spectral shape. Only very little NH modulation is seen during the thermally dominated X-ray soft state (Wen et al. 1999; Boroson & Vrtilek 2010), in which the typical bolometric luminosity is at most a factor two higher than in the hard state (e.g., Tomsick et al. 2014; Zhang et al. 1997). Optical spectra show the stellar wind to be strongly photoionized during the latter state (Gies et al. 2003, 2008).


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.


As we all know, sunspots that can represent solar activity have a long history of research. There are many researches on sunspot variation and solar cycle prediction. The prediction of the sunspot cycle can be classified as following three types: The first is the time series method. In this method, the sunspot number is regarded as a function of time for statistical prediction, in which the observed value or smoothed value of the sunspot number is regarded as a non-stationary random time series (Solanki 2003). The traditional approach is to transform the non-stationary into stationary time series, such as the famous McNish–Lincoln method (McNish & Lincoln 1949) and Box–Jenkins method (Box & Jenkins 1990). These kinds of the method have not yet found an ideal way to accomplish the transformation. It can only get the general trend of solar activity with the help of the periodicity of the series itself but cannot get satisfying prediction accuracy. The neural network method developed in the last decade is also used in forecasting. For example, Chattopadhyay et al. (2011) found that the effect of the auto-regressive neural network (ARNN) model in forecasting the solar cycle is better than the traditional time series method. With the sunspot number from 1749 to 2019, Pala & Atici (2019) used a long-term memory algorithm and neural network auto-regressive (NNAR) algorithm to predict the solar activity in the 25th cycle, showing that sunspots will reach the peak between 2022 and 2023. Although the neural network method sometimes performs better than many classical time series methods, however usually it is just like a black box without physical meaning and the performance also needs further validated. Similar to the above method is the time curve fitting method, Wilson (1988,1992) proposed the concept of long and short sunspot cycles, by using three sinusoidal curves to fit the sunspot number curve and extrapolate the predicted value. Some people also used other curves or multiple line regression methods to predict the sunspot number (Nordemann 1992; Hathaway, Wilson & Reichmann 1994). In particular, Hathaway et al. (1994) proposed a simple function (HWR function) to approximate the solar cycle profile with a certain predictive function. This kind of method aims at the profile prediction of a solar cycle, which is suitable for the prediction of the solar activity in the declining phase of the cycle, but the prediction for the peak value of the cycle is poor and not robust.


It is expected that photons and/or cosmic rays coming from various sources could trigger the ejection of methanol from the icy dust grains into the gas phase and participate in the overall gas-to-ice balance of these cold regions. For the specific case of photons, this mechanism is known as photodesorption. Several experimental studies have been conducted to quantitatively constrain these processes in order to explain astrophysical observations, especially for methanol-containing ices. In one of these experiments, heavy ion 136Xe23+ irradiations were performed on methanol in pure ice and embedded in a water-ice matrix (Dartois et al. 2019). A sputtering yield of methanol close to that of the main water-ice matrix (Dartois et al. 2018), which is ~ 104 sputtered molecule per incident ion, was estimated for each studied ice. When it was embedded in a CO2 ice, Dartois et al. (2020) found that this sputtering yield is about six times higher. Experimental studies of UV photodesorption in the 7–10.5 eV range were first conducted for pure methanol ice at 20 K by Öberg et al. (2009). More recent experiments by Bertin et al. (2016) in the 7–14 eV range suggested an efficiency for methanol UV photodesorption from pure methanol ice of ~ 10−5 molecule/photon. This desorption was found to be below the detection threshold (10−6 molecule/photon) when methanol was mixed with CO ice for a wide range of dilution factors (from 1 in 4 to 1 in 50; Bertin et al. 2016). Accordingly, Cruz-Diaz et al. (2016) derived an upper limit of 3 × 10−5 molecule/photon for the UV photodesorption yield of methanol from pure methanol ice from 8 to 130 K (in the 6.88–10.9 eV range). In addition to these previous mechanisms, chemical desorption, which is the desorption induced by exothermic reactions, is a possible route for explaining the gas-phase enrichment in the ISM (Cazaux et al. 2016; Minissale et al. 2016b; Ligterink et al. 2018). However, chemical desorption of methanol by H addition onto CO, H2 CO, and CH3 OH ices was not detected (upper limit 5%; Minissale et al. 2016b), and more generally, chemical desorption of several other molecules appears to be very low when experiments are made on water substrates (Minissale et al. 2016a).


We model the NS structures using the EOSs summarized in Table 1. These have been chosen to span a representative range of maximum NS masses, but all with maximum gravitational masses

 given current observational limits (Demorest et al. 2010; Antoniadis et al. 2013). For each of these EOSs, we solve for the hydrostatic structure including general relativity and compute a grid of NS models spanning a wide range of masses. We calculate the structures for both a non-rotating NS and a maximally rotating NS for use in treating the merger remnant (further discussed in Section 3). For the latter case, we assume solid-body rotation because magnetic braking eliminates differential rotation on an Alfvén timescale of ∼10–100 ms (Baumgarte et al. 2000; Shapiro 2000). All models have been computed using the LORENE library and in particular its publicly available codes rotseq and nrotstar. The former can easily compute sequences of non-rotating NSs, while the latter has been used to compute equilibrium configurations at the mass-shedding limit (Stergioulas 2003). The different EOSs were imported in LORENE in a table format either produced by using a piecewise polytropic approximation (APR4, Endrizzi et al. 2016; H4, Kawamura et al. 2016; MS1, Ciolfi et al. 2017), provided by the EOS authors (SHT; Kastaun et al. 2016), or given by the Compose project (GM16

6

http://compose.obspm.fr/

; Glendenning & Moszkowski 1991; Douchin & Haensel 2001). This large grid of models gives us, for each mass and EOS, a relation between the gravitational mass
1

where e is the energy density and R is the NS radius, and the baryonic mass (Shapiro & Teukolsky 1983)
2

where m(r) is the enclosed mass at a given radius and ρ is the rest-mass density (both equations refer to non-rotating models, but similar ones can be derived for rotating models). The important point is that in general

 because of the gravitational redshift factor. In the fast rotating limit, we find that Mg is greater by ≈1.18–1.20, consistent with the calculations by Breu & Rezzolla (2016).


In the present era of “high precision” cosmology (see Riess et al. 2016), it is important to exploit the full potential of Cepheids as precise extragalactic distance indicators for determining the expansion rate of the universe and setting constraints on cosmology models. To achieve these goals, a deeper understanding and characterization of Cepheids is needed. Recent discoveries such as circumstellar environments (Nardetto et al. 2016), infrared excesses (Mérand et al. 2015), and ultraviolet emission line variability and possible more recent X-ray emissions (Engle et al. 2014) show that some important aspects of Cepheids may not be well understood. Cepheids have also been found to show additional complications that include cycle-to-cycle variations in their light and radial velocity curves (see Evans et al. 2015b; Anderson 2016; Anderson et al. 2016; Smolec & Śniegowska 2016; Derekas et al. 2017). These newly discovered properties and time-dependent phenomena of Cepheids, unless better understood and accounted for, could place impediments on achieving the challenging goal of determining the local Hubble constant (H0) with a precision of ∼1%, as suggested by Suyu et al. (2012). Great efforts are being undertaken to achieve this level of precision, and hopefully resolve the developing “Hubble Discrepancy” (see Riess et al. 2016), where theoretical values of the Hubble constant (H0) derived via the Lambda-cold dark matter (Λ-CDM) cosmology model (Λ = the cosmological constant), including cosmic microwave background data (e.g., Planck, WMAP (Wilkinson Microwave Anisotropy Probe)), show a small (albeit statistically significant) disagreement with the value of H0  will be derived via standard candles (e.g., Cepheids, SNe Ia (type Ia Supernovae)). As discussed by Suyu et al. (2012) and more recently by Riess et al. (2016), improved measurements of H0 provide critical independent constraints on dark energy and the validity of the present Λ-CDM model.


Several scenarios have been suggested to explain the presence of magnesium-enriched gas in between the galaxies of a group. Magnesium atoms are α elements released in the ISM and CGM by core collapse supernovae. One can therefore naturally imagine that the magnesium gas residing outside galaxies has been ejected through strong supernovae-driven outflows. The P Cygni shape of the Mg II doublet in the integrated spectrum of galaxy A (see Fig. 2 top) is in good agreement with this scenario. Indeed, according to radiative transfer (RT) models, this line profile is a signature of resonant scattering in an optically thick outflowing medium where the redshifted emission corresponds to back-scattered photons reflected by the receding medium (Haiman et al. 2000; Dijkstra et al. 2006; Verhamme et al. 2006; Kollmeier et al. 2010). The Mg II lines of galaxies D and E seem to be redshifted compared to their systemic redshifts (Fig. 2), however, the continuum is too faint to detect significant absorption lines and, thus, too faint to detect the P Cygni profiles, namely, the presence of outflows for those galaxies. We detected > 2σ Mg II emission aligned with the minor axis of galaxy E and near galaxy D (Fig. 3). These regions could have been enriched via outflows after supernovae feedback. However, the S/N of our data is too poor in these areas to carry out a resolved kinematics study. The resolved Mg II map (Fig. 6) shows that the two regions along the minor axis of galaxy A have different velocities with opposite signs (≈ + 120 and −80 km s−1 with respect to the systemic redshift of galaxy A), providing additional evidence of the presence of an outflow. Even if we do not eventually find clear evidence of an outflow in the four other galaxies, we cannot exclude the deposition of metals in the CGM by past feedback processes explaining the observed diffuse Mg II emission detected around each of the galaxy members. In that scenario, we could imagine that the low-surface-brightness gaseous bridge in-between the galaxy subgroups [A,B,C] and [D,E] could be due to galactic wind transfer between the group members as observed in the FIRE simulation (Anglés-Alcázar et al. 2017).


Pulsar timing experiments (Sazhin 1978; Detweiler 1979) allow us to explore the low-frequency (∼1–100 nHz) part of the gravitational-wave (GW) spectrum. By measuring deviations from the expected arrival times of radio pulses from an array of millisecond pulsars, we can search for a variety of GW signals and their sources. The most promising sources in the nanohertz part of the GW spectrum are supermassive binary black holes (SMBHBs) that form via the mergers of massive galaxies. Orbiting SMBHBs produce a stochastic GW background (GWB; Lommen & Backer 2001; Jaffe & Backer 2003; Volonteri et al. 2003; Wyithe & Loeb 2003; Enoki et al. 2004; Sesana et al. 2008; McWilliams et al. 2012; Sesana 2013; Ravi et al. 2015; Rosado et al. 2015; Kelley et al. 2016; Sesana et al. 2016; Dvorkin & Barausse 2017; Kelley et al. 2017; Bonetti et al. 2018; Ryu et al. 2018), individual periodic signals or continuous waves (CWs; Sesana et al. 2009; Sesana & Vecchio 2010; Mingarelli et al. 2012; Roedig & Sesana 2012; Ravi et al. 2012, 2015; Rosado et al. 2015; Schutz & Ma 2016; Mingarelli et al. 2017; Kelley et al. 2018), and transient GW bursts (van Haasteren & Levin 2010; Cordes & Jenet 2012; Ravi et al. 2015; Madison et al. 2017; Islo et al. 2019; Bécsy & Cornish 2021). We expect to detect the GWB first, followed by detection of individual SMBHBs (Siemens et al. 2013; Rosado et al. 2015; Taylor et al. 2016; Mingarelli et al. 2017) that stand out above the GWB. Detection of GWs from SMBHBs will yield insights into galaxy mergers and evolution not possible through any other means. Other potential sources in the nanohertz band include cosmic strings (Damour & Vilenkin 2000, 2001; Berezinsky et al. 2004; Damour & Vilenkin 2005; Siemens et al. 2006, 2007; Ölmez et al. 2010; Sanidas et al. 2013; Blanco-Pillado et al. 2018; Chang & Cui 2021; Ghayour et al. 2021; Gorghetto et al. 2021; Wu et al. 2021a; Blanco-Pillado et al. 2021; Lin 2021; Chiang & Lu 2021; Lazarides et al. 2021; Chakrabortty et al. 2021; Ellis & Lewicki 2021), phase transitions in the early universe (Witten 1984; Caprini et al. 2010; Addazi et al. 2021; Arzoumanian et al. 2021; Di Bari et al.2021; Borah et al. 2021; Nakai et al. 2021; Brandenburg et al.2021; Neronov et al. 2021), and relic GWs from inflation (Starobinskiǐ 1979; Allen 1988; Lazarides et al. 2021; Ashoorioon et al. 2021; Yi & Zhu 2021; Li et al. 2021; Poletti 2021; Vagnozzi 2021; Sharma 2021), all of which would provide unique insights into high-energy and early-universe physics.


Small-amplitude oscillations are observed without any clearly associated driver and can persist for several hours (Wang et al. 2012; Nisticò et al. 2013; Anfinogentov et al. 2015). Their amplitudes are of the order of 100 km and they show no observable damping. Even though it is clear they must be driven by some small-scale abundant process, the exact excitation mechanism of this oscillation regime is unclear. Several excitation mechanisms have been proposed to explain the persistent nature of these oscillations. These include mechanisms acting at coronal heights such as the onset of thermal instability in the corona (Kohutova & Verwichte 2017; Verwichte & Kohutova 2017), the presence of siphon flows in the coronal loop (Kohutova & Verwichte 2018), self-oscillation of coronal loops due to interaction with quasi-steady flows (Nakariakov et al. 2016; Karampelas & Van Doorsselaere 2020), and footpoint-concentrated drivers. A commonly assumed excitation mechanism is associated with turbulent vortex flows which are ubiquitous in the lower solar atmosphere (Carlsson et al. 2010; Shelyag et al. 2011; Liu et al. 2019) and result in random footpoint buffeting. This is typically modelled as a stochastic driver at the footpoints (e.g., Pagano & De Moortel 2019). Such a driver however does not reproduce the observational characteristics of this type of oscillation, in particular the stability of the oscillation phase and lack of any observable damping (Nakariakov et al. 2016). It has been proposed that a footpoint driver of the form of a broadband noise with a power-law fall-off can in principle lead to excitation of eigenmodes along coronal loops (Afanasyev et al. 2020), but this has not been tested through MHD simulations. Finally, excitation of transverse oscillations through solar p-mode coupling has also been proposed in several studies (Tomczyk & McIntosh 2009; Morton et al. 2016, 2019; Riedl et al. 2019). As p-modes correspond to acoustic waves generated by turbulent flows in the solar convection zone, they are subject to acoustic cut-off at the β = 1 equipartition layer. High magnetic field inclinations can however lead to p-mode leakage into chromosphere even for frequencies below the cut-off frequency (De Pontieu et al. 2004), and to subsequent coupling to different magnetoacoustic wave modes (Santamaria et al. 2015). However, three-dimensional (3D) MHD simulations of coronal fluxtubes with a gravity-acoustic wave driver at the footpoints did not reveal any evidence of the acoustic driving leading to significant transverse displacement of the fluxtubes at coronal heights (Riedl et al. 2019).


The expected pressure profile of the interstellar medium inside the Bondi sphere is p ∝ z−2 and, according to analytical and numerical models (Tchekhovskoy et al. 2008; Komissarov et al. 2009; Beskin et al. 2017), a jet propagating in a medium with such a pressure gradient develops the characteristic parabolic shape. Based on Eq. (3), estimating the Bondi radius requires the knowledge of the black hole mass and of the temperature of the accretion flow in the nuclear region. A detailed analysis of the X-ray emission in NGC 315 was carried out by Worrall et al. (2003, 2007) using sensitive Chandra data. The jet, which presents several X-ray-bright knots of synchrotron emission, is embedded in a hot gaseous atmosphere, as inferred from the presence of an X-ray thermal emission component in the spectrum. Such a feature is also detected within a circle of 1 arcsec radius centered around the nucleus, in addition to a dominant, mildly absorbed power-law component possibly associated to the jet. The nuclear hot atmosphere has a temperature

k
T
=
0
.

44

−
0.04

+
0.08

$ kT=0.44^{+0.08}_{-0.04} $

 keV. Assuming a black hole mass of 1.3 × 109 M⊙, we then estimate rB = 92 pc (dark blue vertical line in Fig. 3). Even if the black hole mass was smaller by a factor of several, this radius would still be much larger (two orders of magnitude) than the distance at which we observe the jet shape transition from parabolic to conical, zt = 0.58 ± 0.28 pc. This result would also not be affected by varying the gas temperature within the given small uncertainty. By assuming slightly different parameters, a similar value for the Bondi radius in NGC 315 was recently obtained by Inayoshi et al. (2020), who estimated an uncertainty of 50%3. Then, if the transition from parabolic to conical shape in NGC 315 is induced by a change in the external pressure gradient, this must occur not in the proximity of the black hole sphere of influence, but in the vicinity of the black hole, on sub-parsec scales. Based on the analysis of the VLA data in Fig. 3, right panel, we also note that no discontinuity is observed in the expansion profile after the jet crosses the Bondi radius: the jet shape is close to conical both inside and outside the Bondi sphere.


For variable star classification, both convolutional neural networks (CNNs; LeCun, Bengio & Hinton 2015) and recurrent neural networks (RNNs; Hochreiter & Schmidhuber 1997; Cho et al. 2014) have been shown to be competitive to the traditional RF-based methods. Naul et al. (2018) used an RNN autoencoder network to learn low-dimensional representations of period-folded light curves in an unsupervised fashion. This representation was then, in a supervised context, used as feature inputs to an RF classifier. They showed that the learned features are at least as good as, and often better than, two sets of state-of-the-art hand-crafted features (Richards et al. 2011; Kim & Bailer-Jones 2016), in terms of downstream classification accuracy. Becker et al. (2020) used an RNN for which instead of period-folding, each input light curve is grouped with a moving time-sample window of size 50 and stride 25. Although period-folding improves performance (Naul et al. 2018), Becker et al. (2020)’s time-space RNN does not require the period to be calculated, and is thus less computationally expensive in terms of preprocessing. Again, they found similar performance to an RF classifier with the Nun et al. (2015) features over three data sets, although lower accuracy was seen for many sub-classes with the OGLE data set (Table 2; see Section 3.3 for data description). More recently, Jamal & Bloom (2020) systematically benchmarked the performance of different configurations of RNN and CNN network architectures on variable star classification. Aside from other work (e.g. Aguirre, Pichara & Becker 2018; Tsang & Schultz 2019) evaluating neural network (NN) performance retrospectively on previously labelled data sets, Dékány & Grebel (2020) used an RNN classifier to identify a new sample of fundamental-mode RR Lyrae (RRab) stars. Similarly, Dékány et al. (2019) found Classical and Type II Cepheids with a CNN classifier, also using the VISTA Variables in the Via Lactea (VVV) survey (Minniti et al. 2010) and using period-folded light curves.


We determine the spectroscopic parameters by using a relatively high S/N (∼ 65 per pixel) spectrum taken without the iodine cell at TCES-TLS. As a first step, we applied the empirical software SpecMatch-Emp code (Hirano et al. 2018) that compares well-characterized FGKM stars observed with Keck/HIRES to the data, in our case, the TCES-TLS spectra with R = 67 000. We obtain a stellar effective temperature, Teff = 5804 ± 110 K, a stellar radius, R*  = 2.078 ± 0.180R⊙, and the abundance of the key species iron relative to hydrogen, [Fe/H] = 0.29 ± 0.09 (dex) as mentioned in Table 4. To perform a more detailed model, we used the spectral analysis package SME (Spectroscopy Made Easy; Valenti & Piskunov 1996; Piskunov & Valenti 2017) version 5.22. This code is based on grids of recalculated stellar atmospheric models that calculates a synthetic spectrum. The best-fitted stellar parameters are derived through a χ2 −minimization iteration that compares the synthetic and observed spectra for a given set of parameters. The spectra was synthesised based on the atomic and molecular line data from VALD (Ryabchikova et al. 2015) and the Atlas12 (Kurucz 2013) atmosphere grids. We refer to Fridlund et al. (2017) and Persson et al. (2018) for a more detailed description of the modelling. Briefly, we chose to model spectral features sensitive to different photospheric parameters: Teff from the Hα line wings, and the surface gravity, log g*, from the Ca i λλ6102, 6122, and 6162 triplet, and the λ6439 line. The abundances of iron and calcium, and the projected stellar rotational velocity, v sin i were fitted from narrow, unblended lines between 6100 and 6500 Å. We derive the vsin i as 7.0 ± 0.5 km s−1. We fixed the micro- and macro-turbulent velocities, Vmic and Vmac, to 1 and 3 km s−1 (Bruntt et al. 2010; Doyle et al. 2014), respectively. The results from SME are in good agreement within the uncertainties with SpecMatch-Emp (Table 4). The SME derived stellar parameters are supplied as priors in the global modelling. The finally adopted stellar parameters obtained through global modelling of the RV and transit data are indicated in the last row of Table 4 in bold font. For more details on the global modelling, see Section 3.3.2. One thing to note here is that we find the TOI-1789 is a late F-type star with our spectral analysis. Nevertheless, SIMBAD reported it as ‘K0’ spectral type.


The gravitational collapse of the G345.88-1.10 hub provides the means for rapid mass provision to the centre, along with non-steady accretion flows which might open the cavity on short timescales through an accretion burst. This can be the result of e.g. jet precession (Rosen & Krumholz 2020) and opening of the jet itself (Cesaroni et al. 2018). The modelling by Cesaroni et al. (2018) indicates that the jet opening angle can increase to values as high as 40–50°, but it should also be noted that this is model dependent. The simulations by Rosen & Krumholz (2020) indicate that a jet precession can be very rapid at the early stages of high-mass star formation with rapid angle changes that on average reach 40° kyr−1 with apparent peaks as high as 250° kyr−1. However, it should be noted that the opening of the cavities by an accretion burst also faces the issue that this is generally associated with a strong increase of the core brightness in the far-infrared (e.g. Stecklum et al. 2021; Hunter et al. 2021), which is not seen in G345.88-1.10. It could be that, after an accretion burst has occurred, there is a time delay between the dimming of the core and the dimming of the cavity. Such a time delay would be of the order of the jet’s crossing time of the cavity, i.e. ≲1000 yr. We could therefore be catching G345.88-1.10 right at that moment where the cavity is still bright but the core has dimmed. Although this would be a noteworthy coincidence, it can fit with the cooling timescale we estimate for the massive H1 fragment which should be lower than 20 yr and can be as low as a couple of days or months, see Appendix H. These timescales also seem to be in agreement with surveys of continuum variability, at least in low-mass star forming cores that typically find very rapid changes on the timescales of weeks to several years (e.g. Johnstone et al. 2013; Mairs et al. 2017; Lee et al. 2021). Because of these very short cooling timescales, it is even possible that multiple accretion bursts spread over few 10-100 yr are at the origin of the heated cavities. In Appendix H, we also estimated the cooling timescale in the cavities for which we find values between 1.7 × 103 and 2.7 × 104 yr which is significantly longer than for the core. Furthermore, the lower end of this estimated timescale is of the same order of magnitude as the crossing timescale for the jet in the cavities. This might explain why the full cavity is bright instead of only several subregions in the cavity.


Mid-infrared and millimeter polarimetric observation has so far been considered as the best method to probe the magnetic field. This is because if aspherical grains in disks become aligned with the magnetic field as is the case in the interstellar medium (ISM), the polarization vector arising from thermal emission of the aligned grains becomes perpendicular to the local magnetic field line (Cho & Lazarian 2007, henceforth CL07, Matsakos et al. 2016; Yang et al. 2016b; Bertrang et al. 2017). At mid-infrared wavelengths, Li et al. (2016) performed a polarimetric imaging observation of AB Aur using CanariCam. As a result, they detected a centrosymmetric polarization pattern, and the degree of polarization was as high as 1.5% at large radii. At millimeter wavelengths, polarimetric observations of disks have been performed (e.g., Hughes et al. 2009, 2013; Rao et al. 2014; Stephens et al. 2014; Cox et al. 2015; Kataoka et al. 2016b). Polarized emission from a circumstellar disk has been detected in the Class 0 phase (Rao et al. 2014; Cox et al. 2015). More evolved disks do not show a degree of linear polarization larger than 0.5% (Hughes et al. 2009, 2013). It should be mentioned that Stephens et al. (2014) detected polarized flux from HL Tau, which is classified as a Class I-II, with an average degree of linear polarization of 0.9%. More recently, Kataoka et al. (2016b) reported the first submillimeter polarization observation of a disk obtained with ALMA, and they clearly detected polarized flux from HD 142527. The polarization fraction at a peak position of polarized intensity was 3.26%, and the maximum polarization fraction was as high as 13.9%. The disk reveals radial polarization vectors; however, they flip by 90° in its northeast and northwest regions. In addition, the detected polarization fraction is much larger than the stringent limit set by Hughes et al. (2009, 2013), and further polarimetric observations by ALMA will reconcile this discrepancy.


The evolution of colour or the spectral index, α, (F(ν) ∝ ν−α where ν is the radiation frequency and F(ν) is the flux density provides an insight into the particle distribution giving rise to the observed flux density and its variability. In particular, at the synchrotron frequencies, within the simplest scenario of single-zone emission models with homogeneous magnetic field distributions, clear patterns between the spectral index and the total intensity are predicted, i.e. a ‘spectral hysteresis’, depending on the relative lengths of the radiative cooling time-scale and the escape time-scale of the accelerated particles from the emission zone (e.g. Kirk, Rieger & Mastichiadis 1998). A significant fraction of long-term multiband flux monitoring studies have revealed bluer-when-brighter trends for BL Lac objects but frequently redder-when-brighter trends for FSRQs (Gu et al. 2006; Osterman Meyer et al. 2009; Hao et al. 2010; Rani et al. 2010; Ikejiri et al. 2011; Bonning et al. 2012; Sandrinelli, Covino & Treves 2014; Li et al. 2018; Meng et al. 2018; Gupta et al. 2019) while ‘achromatic’ flux variability (no colour evolution, Stalin et al. 2006; Bonning et al. 2012; Gaur et al. 2019), and erratic patterns (Wierzcholska et al. 2015) have also been reported. It has been argued that particles accelerated to higher energies are injected at the emission zone before being cooled radiatively in BL Lac sources leading to their overall SEDs being bluer-when-brighter; however, the ‘redder’ and more variable jet-component can overwhelm the ‘bluer’ contribution from the accretion disc, leading to redder-when-brighter trends for FSRQ type sources (Gu et al. 2006). Achromatic variability is often ascribed to changes in the Doppler boosting factor (δ) as each frequency notes the same special relativistic multiplication of flux (Gaur et al. 2012). However, erratic colour trends together with the opposite behaviours, i.e. redder-when-brighter changes for BL Lacs (Gu & Ai 2011) and bluer-when-brighter trends for FSRQs (Wu et al. 2011), indicate that more complex scenarios, presumably involving the dominance of the relative contributions of the Doppler boosted jet emission component and the accretion disc component, respectively, are particularly relevant for blazars with peak synchrotron frequencies in the range of 1013–15 Hz (low-frequency peaked blazars; Isler et al. 2017; Gopal-Krishna, Britzen & Wiita 2019).


Finally, our models assume the absence of planetary magnetic fields. The early paradigm considering the evolution of terrestrial planets has implied that the planetary magnetic field is necessary to protect planetary atmospheres and reduce the atmospheric mass loss (see e.g. Dehant et al. 2007, and references therein). The later studies, however, show that this point of view is ambiguous. Thus, the effect of the magnetic field on the atmospheric escape can be considered as a result of the two concurring processes: reducing the escape by capturing the ionised atmospheric species within the closed magnetic field lines, and enhancing the escape of the atmospheric ions through the regions of the open magnetic lines (polar cusps, in the case of a dipole field) and the reconnection on the night-side (see, e.g. Khodachenko et al. 2015; Sakai et al. 2018; Carolan et al. 2021). Thus, for planets in the Solar System, it was shown both in the observations (Gunell et al. 2018; Ramstad & Barabash 2021) and by modelling (Sakai et al. 2018; Egan et al. 2019) that the presence of a weak magnetic field can intensify atmospheric escape. These results, however, should be taken with caution for young planets, and in particular those in the sub-Neptune range, because of the different atmospheric structures and the non-thermal mechanisms dominating the atmospheric mass loss in the Solar System, which are contrary to the planets considered in this study (see, e.g. Scherf & Lammer 2021, for the discussion). For hot Jupiters, Khodachenko et al. (2015) predict a significant suppression of escape for intrinsic magnetic fields larger than 0.3 G. The model with the closest setup to this study by Carolan et al. (2021) predicts, however, for the 0.7Mjup planet experiencing XUV (thermally) driven atmospheric escape, a small increase in the atmospheric mass-loss rate with increasing dipole field strength (about twice between 0 and 5 G). We therefore expect that the possible effect from the planetary intrinsic magnetic field depends largely on the strength and configuration of the planetary and stellar magnetic fields, but, according to the numbers reported in the literature, might not affect our results dramatically. The lack of studies for close-in sub-Neptune-like planets, however, holds us from making final conclusions.


The high-frequency break often found in interplanetary magnetic field power density spectra separates the fluid from the kinetic regime of fluctuations. This break is located around scales which are typical of protons kinetics like the proton inertial length λi = c/ωp and the proton Larmor radius λL = vth/Ωp, where ωp is the local plasma frequency while Ωp is the local gyro-frequency, with vth and c the thermal speed and the speed of light, respectively. Several authors tried to reproduce the location of the frequency break according to various models (Leamon et al. 1998; Perri, Carbone & Veltri 2010; Bourouaine et al. 2012) but Markovskii, Vasquez & Smith (2008) showed that none of the available model could predict a value for the frequency break in good agreement with the observations. Only recently, Bruno & Trenchi (2014), studying the radial behaviour of the frequency break location within the expanding high-speed wind, were able to conclude that the resonant condition for outward parallel propagating Alfv$\acute{\textrm{e}}$n/ion-cyclotron waves (ICWs) was the mechanism able to provide the best agreement with the observations. This result, although not expected on the basis of anisotropy predictions by any turbulent cascade (Chen et al. 2014), gave new relevance to the ion-cyclotron resonance mechanism in the frame of turbulence collisionless heating without cancelling the role of other possible mechanisms that might be at work as well. Leamon et al. (1999) proposed Landau damping of obliquely propagating kinetic Alfv$\acute{\textrm{e}}$n waves (KAWs) resulting in a frequency break corresponding to the scale of the Larmor radius λL; for Dmitruk, Matthaeus & Seenu (2004) 2D turbulence dissipation through turbulence reconnection process and generation of current sheets of the order of the ion inertial length λi enhances the role of this scale, which is the most relevant one also in the framework of incompressible Hall magnetohydrodynamics used by Galtier (2006) to explain the break.


Annealing is sometimes used to avoid effects of temperature fluctuations during the etching and/or to remove a background consisting of tracks of light ions. We did not anneal samples before etching. The reason is that nanometric structure transformations of olivine along the heavy projectile trajectory provide enhanced etching of this region. Figure 3 and simulations made in Gorbunov et al. (2015) demonstrate that the diameter of an emerging amorphized track core is up to about 10 nm in the trajectory sector where the Bragg peak of the electronic stopping of heavy ions is realized. The chemical activity of this track core may be reduced due to recrystallization during annealing. To stimulate such recrystallization within etching, the etching temperature must reach thresholds activating (a) fast diffusion of atoms/structure defects supplying structure modifications at times much shorter than the etching time, or (b) melting of the track core followed by its rapid solidification. Because of olivines’ high melting temperatures (1800°C–1850°C) the second scenario cannot be realized at the etching temperatures used (110°C) or during the hand-polishing of samples before etching. Such a temperature increase arising during treatments of samples cannot stimulate a fast diffusion of atoms, either, due to their high migration barriers (e.g., migration barriers of vacancies and interstitials in oxides with covalent binding exceeding 1–2 eV). This is well-illustrated in some experiments (Perelygin et al. 1985) when the procedure of track annealing is applied to study ancient tracks from GCR in olivine crystals from meteorites. Dissipation of “background” tracks of light iron group nuclei from GCR (initial density 1010–1011 cm−3) was detected in Perelygin & Stetsenko (1989) after annealing these crystals at higher temperatures (430 ± 1)°C for 32 hr before etching, and in a 6–8-fold decrease of track lengths for nuclei with Z ≥ 54. This correlates with the analysis (Perron et al. 1988), which demonstrated that the preliminary track annealing led to unpredictable changes in track lengths, resulting in a lower accuracy of nuclear charge determination. For example, path length variations of accelerated Kr and Xe nuclei (with energies of 12.5 and 10.0 MeV per nucleon, respectively), decelerated in olivine crystals from Marjalahti pallasite, depend on annealing time (Lal et al. 1969). The etched lengths of tracks of these nuclei are reduced by 2–3 times for the first 10–20 hr of annealing (382°C). A further increase of annealing time (up to 240 hr) is not followed by any significant decrease in track length, but these final lengths of tracks of Kr ions vary from 18 ± 3 μm to 11 ± 3 μm (40% difference), i.e., the dispersion of the measured lengths is too high. Annealing of tracks of U, Au, and Xe decelerated in olivine crystals from Marjalahti pallasite at temperatures of 430°C, 435°C, and 450°C resulted in a similar distribution of etched track lengths (Perron et al. 1988). Dispersion of L values measured in individual olivine crystals from Marjalahti pallasite sometimes reaches a 3–4-fold value. This effect has been observed, in particular, for tracks from U ions, annealed for 5 hr at a temperature of 450°C, when the L value measured in the same crystals varied within the range of Lmin = (217 ± 52) μm up to Lmax = (762 ± 77) μm. The annealing of tracks from U ions held for 5 hr at T = 435° gave the L values within the range of Lmin = (440 ± 100) μm to Lmax = (869 ± 53) μm (Perelygin & Stetsenko 1989). Similarly, almost twofold intervals of L variation were obtained for Xe and Au ion tracks. Taking into account these causes, the technique without preliminary annealing at a higher temperature is used in the presented work, i.e., we did not apply annealing of samples before their etching at a temperature of 110°C. The search for the heavy component in GCR within the framework of the OLIMPIYA project is based on the registration and measurement of the dynamic and geometric parameters of chemically etched tracks generated by nuclei with Z > 40 in combination with calibration experiments at heavy ion accelerator facilities. The detection method is an annealing-free technique based on layer-by-layer grinding and chemical etching. This technique provides for the geometrical parameters of tracks and the lengthwise track etching rate along the ion trace, as an additional parameter for identification of charges Z of the particle producing tracks.


Because of the high-energy extent of their emission, their large cosmological distances, and their fast variabilities, gamma-ray bursts (GRBs) have been deemed as the most promising sources for searching for LIV-induced vacuum dispersion (Amelino-Camelia et al. 1998; Jacob & Piran 2007; Amelino-Camelia & Smolin 2009; Amelino-Camelia 2013; Wei et al. 2016). To date, various limits on LIV have been obtained by studying the dispersion of light in observations of individual GRBs or a large sample of GRBs (Amelino-Camelia et al. 1998; Coleman & Glashow 1999; Schaefer 1999; Boggs et al. 2004; Pavlopoulos 2005; Kahniashvili et al. 2006; Jacob & Piran 2008; Abdo et al. 2009a, 2009b; Xiao & Ma 2009; Shao et al. 2010; Chang et al. 2012; Nemiroff et al. 2012; Kostelecký & Mewes 2013; Vasileiou et al. 2013; Zhang & Ma 2015; Xu & Ma 2016, see also Kostelecký & Russell 2011; Liberati 2013 and summary constraints for LIV therein). Although these limits on LIV have reached high precision, most were obtained by relying on the rough time lag of a single highest-energy photon. Performing a search for LIV using the true time lags of high-quality and high-energy light curves in different energy multi-photon bands is therefore crucial. Furthermore, the method of the arrival time difference used for testing LIV is tempered by our ignorance concerning the intrinsic time delay that depends on the unknown emission mechanism of GRBs. Most previous studies concentrated on the time delay induced by LIV, while neglecting the intrinsic time delay, which would impact the reliability of the resulting constraints on LIV. Most recently, however, Wei et al. (2017a, 2017b) provided some solutions to disentangle the intrinsic time delay problem. They first proposed that only GRB 160625B, which so far is the only burst with a well-defined transition from positive to negative spectral lags,3

3
The spectral lag is defined as the arrival time difference between high- and low-energy photons and is considered to be positive when high-energy photons precede low-energy photons.
 provides a good opportunity to distinguish the possible LIV effect from any source-intrinsic time delay in the emission of photons of different energy bands. By fitting the true multi-photon spectral lag data of GRB 160625B, they obtained both a reasonable formulation of the intrinsic energy-dependent time delay and robust limits on the QG energy scale and the Lorentz-violating coefficients of the Standard-Model Extension.


The opacity at the radiative–convective boundary controls the atmosphere’s cooling rate, L∝1/κ, and as such is key to understanding the evolution of super-Earth atmospheres. As discussed in Section 2, we use a constant value of the atmosphere’s opacity, κ = 0.1 cm2g−1, throughout this work. This choice is based on the typical order of magnitude value expected for H/He-dominated atmospheres (e.g. Freedman et al. 2008). In reality, the atmospheric opacity depends on many factors which are likely to vary over the course of super-Earth atmospheric evolution. More complex opacity models can include a power law increase in opacity with density (e.g. Gupta & Schlichting 2019), and power law increases with temperature and atmospheric metallicity in addition to density (e.g. Lee & Chiang 2015). We found that implementing an opacity dependence on density did not have a major effect on our final atmospheric masses. The strongest effect, on the critical radiative convective boundary to which a planet cools during spontaneous mass-loss, is only logarithmic (equation 18). However, if the overall composition of the atmosphere changes significantly as the super-Earths lose atmospheric mass, an increase in opacity with metallicity over time could affect our results. To test whether we expect the hydrodynamic outflow to significantly fractionate the atmosphere, thereby increasing the metallicity of the remnant atmosphere, we compute the cross-over mass, $\mu _\mathrm{c} = \mu + k_\mathrm{B} T_\mathrm{eq} \dot{M}/(4 \pi b \mu G M_\mathrm{c})$, where b is the binary diffusion coefficient between the two species. This is the molecular weight above which a species cannot be liberated from the planet by the hydrodynamic wind, as the drag forces cannot overcome gravity (Hunten, Pepin & Walker 1987). Using b ∼ 5 × 1017T0.75 cm−1s−1, a value typical of the binary diffusion coefficients of common secondary species in hydrogen gas (Zahnle & Kasting 1986), we find – given our mass-loss rates – the smallest value for the cross-over mass for the planets considered in this paper is about μc ∼ 103 amu. This is much larger than any potential heavy species in these atmospheres. We therefore conclude that secondary species are efficiently carried away by the outflow and that the atmosphere does not become significantly enhanced in heavy elements due to the wind itself for the planets considered in this paper.


If the variation in 10Be/9Be ratios of CAIs reflects those episodic accretion events, 10Be/9Be ratios of CH–CB CAIs observed in this study would give important constraints on the evolution of the solar protoplanetary disk. Astronomical observations suggest that FUori-type outbursts are confined to the first few hundreds of thousands of years, which correspond to the class I stage of the protoplanetary disk evolution (e.g., Schulz 2012). We propose that the high and variable 10Be/9Be ratios recorded in CH–CB CAIs reflect episodic cosmic-ray fluxes caused by FUori-type outbursts. On the other hand, relatively low and less variable 10Be/9Be ratios recorded in CV CAIs may reflect less intensive episodic accretion events, possibly the EXori-type outbursts, which are confined to the evolutional stage of a few million years after the formation of the protoplanetary disk (=class II). Note that CH–CB CAIs studied here show no (or very low) signs of 26Al-derived 26Mg excesses, while most CV CAIs show clear evidence for the past presence of 26Al. If 26Al was introduced into the solar system at the earliest stage of the disk evolution (e.g., Sahijpal & Goswami 1998), differences in Be–B and Al–Mg systematics between CH–CB and CV CAIs imply that the injection of 26Al have occurred between the evolutionary stages class I and class II of the solar protoplanetary disk. This scenario is in agreement with arguments by other authors that the 26Al-free CAIs formed prior to injection and homogenization of 26Al in the early solar system (Sahijpal & Goswami 1998; Sahijpal et al. 2000; Krot et al. 2008a see more discussion in Krot et al. 2012a). Importantly, as mentioned in the introduction, CH–CB chondrites may have accreted a significant amount of outer solar system materials (Murty et al. 2007; Ivanova et al. 2008; Briani et al. 2009; Bonal et al. 2010; Olsen et al. 2016; Van Kooten et al. 2016), suggesting that CH–CB chondrites formed at outer parts of the solar protoplanetary disk relative to CV chondrites. In this case, our new Be–B and Al–Mg data set implies that the earliest formed CAIs tend to be transported into the outer part of the solar protoplanetary disk, where the parent bodies of CH–CB chondrites likely accreted. Yang & Ciesla (2012) modeled the evolution of the protoplanetary disk and material transport in the protoplanetary disk. Interestingly, Yang & Ciesla (2012) showed that outward radial transport in class I would have been greater than that of later stages of YSO evolution, suggesting that the earliest formed CAIs could be preserved in primitive bodies that accreted in the outer part of the disk. This model is consistent with our interpretation for the Be–B and Al–Mg systematics on CH–CB CAIs. It should be noted, however, that it is possible that 26Al were heterogeneously distributed in the CAI-forming regions at the earliest stage of the solar system evolution (e.g., Krot et al. 2008a; Holst et al. 2013; Park et al. 2017 and reference therein). Because no Pb–Pb ages of CH–CB CAIs are available at present, we cannot discard that possibility. Very recently, Kööp et al. (2018) found helium and neon excesses in the 26Al-free hibonite-rich CAIs, which can be attributed to in situ irradiation by energetic particles. Because 26Al-rich CAIs in CV chondrites lack comparable noble gas irradiation records (Vogel et al. 2004), Kööp et al. (2018) concluded that 26Al-free hibonite-rich CAIs experienced intense energetic particle irradiation at the earliest stage of solar protoplanetary disk evolution. This conclusion seems to be consistent with our above scenario for 26Al-free CH–CB CAIs. Note, however, that 10Be/9Be ratios of 26Al-free hibonite-rich CAIs in CM chondrites tend to be in the range of those for 26Al-rich CV CAIs (Liu et al. 2009, 2010), which is inconsistent with the above scenario. Therefore, the relationship between 10Be and 26Al in the early solar system would be more complicated than we thought.


In principle, we could measure the multipole moments in a given simulation by directly populating dark matter haloes in the simulation with galaxies. However, this is computationally very expensive and comes with realization noise due to the random number and phase-space positions of galaxies. Instead, we use a tabulation method (Neistein & Khochfar 2012; Reid et al. 2014; Zheng & Guo 2016) to speed up the computation dramatically and eliminate any realization noise. We first take all haloes in a given simulation to serve as tracers of central galaxies. We furthermore assign to each halo of mass M a Poisson number of satellite tracers with expectation value $3 \times (M/10^{13} \, h^{-1}\rm M_\odot)$. This expectation value is chosen to be significantly larger than the number of satellites we typically expect in haloes of that mass (see e.g. Guo et al. 2015). We then bin all haloes and their central and satellite tracers by halo mass and whether the concentration is above or below the median. Next, we measure all cross- and autocorrelation multipole moments between all tracers in each bin. One can then show that an estimate for the galaxy number density and the multipole moments of any arbitrary galaxy–halo model are given by
(13)$$\begin{eqnarray*}
\hat{n}_{\rm gal} = \sum \limits _{i = {\rm c}, {\rm s}} \sum \limits _{k = 1}^{n_{\rm bins}} N_{{\rm h}, k} \langle N_i | M_k, c_k \rangle
\end{eqnarray*}$$and
(14)$$\begin{eqnarray*}
\hat{\xi }_\ell &=& \hat{n}_{\rm gal}^{-2} \sum \limits _{i = {\rm c}, {\rm s}} \sum \limits _{j = {\rm c}, {\rm s}} \sum \limits _{k = 1}^{n_{\rm bins}} \sum \limits _{l = 1}^{n_{\rm bins}} \Big [ N_{{\rm h}, k} N_{{\rm h}, l} \langle N_i | M_k, c_k \rangle \nonumber \\
&&\times \,\langle N_j | M_l, c_l \rangle \xi _{\ell , kl}^{ij} \Big ] \, ,
\end{eqnarray*}$$respectively. In the above expression, Nh, k denotes the number of haloes in bin k and, for example, $\xi _{\ell , kl}^{{\rm c}{\rm s}}$ denotes the multipole moments between centrals in bin k and satellites in bin l. The above estimate $\hat{\xi }_\ell$ approaches the expectation value of ξℓ for sufficiently small halo mass bins. We find that 100 logarithmic bins in halo mass is sufficient to adequately sample all haloes with mass $M \gt 3.52 \times 10^{13} (\Omega _{\rm m}/0.3) \, h^{-1}\, \rm M_\odot$ (corresponding to 100 particles). With such a bin width of ∼0.03 dex, any biases in ξ are less than $5{{\ \rm per\ cent}}$ of the observational uncertainty for a BOSS CMASS-like sample (see Guo et al. 2015). The above method only works for a fixed value of the satellite radial profile parameter η. In practice, it suffices to tabulate correlation function for bins in η of Δlog η = 0.1 and linearly interpolate between them.


HD 100546 is one of the closest very well studied Herbig Be stars (d = 110 ± 4 pc, Gaia Collaboration 2018). It shows clear evidence of a large flared disk, and based on images obtained with the Hubble Space Telescope (HST) and ground-based high-contrast images, an elliptical structure was detected that extends up to 350–380 au (Augereau et al. 2001). Furthermore, multiple-armed spiral patterns were identified as well (Grady et al. 2001; Ardila et al. 2007; Boccaletti et al. 2013; Avenhaus et al. 2014). The disk position angle measurements found in the literature range from ~ 130 to 160° (Grady et al. 2001; Pantin et al. 2000; Ardila et al. 2007; Panić et al. 2014; Augereau et al. 2001; Avenhaus et al. 2014), and the inclination of the disk is smaller than 50° (Avenhaus et al. 2014). An inner dust disk extending from ~0.2 to ~ 1−4 au was resolved using near-IR interferometry (Benisty et al. 2010; Tatulli et al. 2011; Mulders et al. 2013; Panić et al. 2014). The (pre-)transitional nature of HD 100546 was initially proposed by Bouwman et al. (2003) based on a spectral energy distribution (SED) analysis. The presence of a gap extending up to 10–15 au has been confirmed by mid-IR interferometry (Liu et al. 2003; Panić et al. 2014), spectroscopy in the UV and near-IR (Grady et al. 2005; Brittain et al. 2009; van der Plas et al. 2009), and high-resolution polarimetric imaging in the optical and near-IR (Avenhaus et al. 2014; Quanz et al. 2015; Garufi et al. 2016; Follette et al. 2017). Recent ALMA observations reveal an asymmetric ring between ~ 20−40 au with largely optically thin dust emission (Pineda et al. 2019). A central compact emission is also detected, which arises from the inner central disk, which given its mass and the accretion rate onto the star, must be replenished with material from the outer disk (Pineda et al. 2019). Miley et al. (2019) presented the first detection of C18 O in this disk, which spatially coincides with the spiral arms, and derived a lower-limit on the total gas mass (around 1% of the stellar mass) and a gas-to-dust mass ratio in the disk of ~ 20 assuming interstellar medium (ISM) abundances of C18O relative to H2. HD 100546 is also one of the few cases where protoplanet candidates have been suggested (e.g. Quanz et al. 2015; Currie et al. 2015), although this is still being debated (e.g. Follette et al. 2017; Rameau et al. 2017; Pérez et al. 2020). Recently, Pérez et al. (2020) detected a compact 1.3 mm continuum dust emission source that lies in the middle of the HD 100546 cavity (0.051′′ from the central star). This is compatible with circumplanetary disk emission.


In summary, our constraints on the elliptical galaxy structure in the context of previous observations and simulations are consistent with the following formation and evolution scenario for massive elliptical galaxies. The first stage of the formation of elliptical galaxies is through dissipational processes at z ≳ 2, when most of their present day stars are formed. The dissipation leads to contraction in the dark matter halo and the resultant total density profile observed in cosmological numerical simulations is steeper than the isothermal case (e.g. Gnedin et al. 2004; Naab et al. 2007; Duffy et al. 2010). After z ≈ 2, the growth of the elliptical galaxies is dominated by gas-poor dissipation-less mergers, explaining their growth in size without the addition of younger stellar populations (e.g. Newman et al. 2012; Nipoti et al. 2012). This growth mechanisms is consistent with the Reff–fdm correlation observed in our sample. Multiple dissipation-less mergers decrease the total density profile of the galaxies to bring it close to isothermal, and increase the half-mass radius and the central dark matter fraction with decreasing redshift (Tortora et al. 2014). Furthermore, AGN feedback expands back the contracted dark matter haloes (Martizzi, Teyssier & Moore 2013; Peirani et al. 2019), which is supported by the slope of our observed $\gamma ^{\rm LD}_{[0.4,\ 4]R_{\rm eff}}$–$f_{\rm dm}^{\rm 3D}$ distribution. Dynamical heating from accretion may also play a role in expanding the dark matter haloes in addition to the AGN feedback, however we do not find any indication either in favour or against the presence of dynamical heating in our sample. Gas-rich dissipational mergers can also happen at some point of the galaxies’ growth history. However, the small intrinsic scatter in the halo response parameter (σν ≲ 0.1) around the mean μν ∼ 0 in our sample, and the ages of the stellar populations (Thomas et al. 2005), indicate that such gas-rich mergers are relatively rare, even though their contribution cannot be ruled out or confirmed conclusively given the present precision of numerical simulations and observations (see, e.g. Sonnenfeld et al. 2014; Remus et al. 2017; Xu et al. 2017, for discussion).


A relation between the photon index and the Eddington ratio has been reported by several authors over the past two decades (e.g. Brandt, Mathur & Elvis 1997; Shemmer et al. 2006, 2008; Risaliti, Young & Elvis 2009; Brightman et al. 2013, 2016; Fanali et al. 2013; Kawamuro et al. 2016), which have shown that, for increasing λEdd, the X-ray continuum tend to be steeper. Most of these works have found that the correlation
(7)
\begin{equation*}
\Gamma =\psi \log \lambda _{\rm Edd}+ \omega
\end{equation*}
has a slope ψ ∼ 0.3 (e.g. Shemmer et al. 2008; Brightman et al. 2013), while a steeper slope (ψ ≃ 0.6) was reported by Risaliti et al. (2009), who studied SDSS quasars with archival XMM–Newton observations. More recently, Trakhtenbrot et al. (2017), using BASS, found instead a significantly weaker and flatter (ψ ≃ 0.15) correlation when using Γ obtained by considering complex spectral models (see Ricci et al. 2017a for details). Interestingly, when using Γ obtained by fitting the spectra of unobscured AGNs with a simple power law model in the 2–10 keV range, Trakhtenbrot et al. (2017) found a slope similar (ϕ = 0.30 ± 0.09) to that reported by previous studies. The existence of a relation between Γ and λEdd has been confirmed by repeated observations of individual sources, which have shown that the photon index increases with the flux (e.g. Perola et al. 1986; Matsuoka et al. 1990; Lamer et al. 2003; Sobolewska & Papadakis 2009). Interestingly, Sobolewska & Papadakis (2009) found that ψ differs from object to object, varying from ≃ 0.10 to ≃ 0.30, and that the slope for the average spectral slope versus the average Eddington ratio is ψ = 0.08 ± 0.02. This slope is consistent with that found for BASS by Trakhtenbrot et al. (2017), and with the value reported by Ricci et al. (2013; ψ = 0.12 ± 0.04) for a sample of 36 nearby AGNs, considering the average Γ and λEdd. The difference between the slopes found by the works reported above is likely related to the approach used for the spectral fitting (i.e. a simple power-law model or more complex models), to the energy band, and to the sample used.


CMEs are known for large-scale expulsion of magnetized plasma structures from closed magnetic field regions on the Sun. They were first detected in the coronagraphic images taken in 1971 by NASA’s OSO-7 spacecraft (Tousey 1973). However, some definite inferences for the solar wind (Eddington 1910; Birkeland 1916; Biermann 1951) as well as CMEs from the Sun (Chapman & Ferraro 1931; Eddy 1974) were made decades before their formal discovery. Following OSO-7, a series of spacecraft (Skylab, Helios, P78-1 Solwind, SOHO, Coriolis, and STEREO, etc.) have observed thousands of CMEs leading to a vast literature (Munro et al. 1979; Howard et al. 1985; Gosling 1993; Hundhausen 1999; Gopalswamy et al. 2000; Schwenn 2006; Vourlidas et al. 2010; Chen 2011; Wang et al. 2011; Webb & Howard 2012; Mishra & Srivastava 2013; Mishra et al. 2017; Harrison et al. 2018). CMEs have been observed to occur often having spatial and temporal relation with solar flares, eruptive prominences (Munro et al. 1979; Webb & Hundhausen 1987; Zhang et al. 2001; Gopalswamy et al. 2003) and with helmet streamer disruptions (Dryer 1996). Unlike CMEs from the Sun, to observe stellar CMEs are challenging because the close stellar environment cannot be spatially resolved. Although stellar CMEs have not yet been directly detected in Thomson-scattered optical light from other stars, it is believed that the extreme X-ray flares observed on stars may be in conjunction with extreme stellar CMEs (Houdebine, Foing & Rodono 1990; Wheatley 1998; Leitzinger et al. 2011; Aarnio, Matt & Stassun 2012; Osten & Wolk 2015; Vida et al. 2016). Indeed, the stellar X-ray flare, helmet streamers, and prominences observed on T Tauri Stars have shown similarities with those observed on the Sun (Haisch, Antunes & Schmitt 1995; Massi et al. 2008). The CMEs and flares themselves may not be causally related, they both seem to be involved with the reconfiguration of complex magnetic field lines within the corona caused by the same underlying physical processes, e.g. magnetic reconnection (Priest & Forbes 2002; Compagnino, Romano & Zuccarello 2017). But, even for the sun, it has been noted that not all flares are accompanied by CMEs and not all CMEs by flares (Munro et al. 1979; Harrison 1995; Yashiro et al. 2008b; Wang & Zhang 2008).


The 1D SDSS spectrum of SDSS J124754.95-033738.6 (Fig. 1) is dominated by A-type stars and shows strong Balmer absorption lines, which is a clear signature of post starburst E+A galaxies. We used the 1D SDSS spectrum to measure the equivalent width (EW) of the Hδ absorption line and found EW(Hδ) = 6.7 Å, which is above the typical 5  Å threshold used to select post-starburst E+A galaxies (e.g. Goto 2007; Alatalo et al. 2016). We then fitted a stellar population synthesis model using the python implementation of Penalized Pixel-Fitting stellar kinematics extraction code (pPXF; Cappellari 2012). pPXF is a public code for extraction of the stellar kinematics and stellar population from absorption line spectra of galaxies (Cappellari & Emsellem 2004). Its output includes the best-fitting stellar model, the relative contribution of stars with different ages, the stellar velocity dispersion, and the dust reddening towards the stars (assuming a Calzetti et al. 2000 extinction law). The code uses the MILES library, which contains single stellar population synthesis models that cover the entire optical wavelength range with an FWHM resolution of 2.3 Å  (Vazdekis et al. 2010). We used models produced with the Padova 2000 stellar isochrones assuming a Chabrier initial mass function (IMF; Chabrier 2003). The stellar ages range from 0.03 to 14 Gyr, thus allowing the analysis of systems with different star formation histories. The best-fitting stellar model is marked with red in Fig. 1. Its stellar age distribution consists of two star formation episodes, with a recent short episode that started 70 Myr ago and was quenched 30 Myr ago, and an older long episode that started 14 Gyr ago and ended 6 Gyr ago. The older episode is poorly constrained and we find similarly reasonable fits when forcing the code to use templates with different ages within the range 3–10 Gyr. According to the best-fitting model, the stellar velocity dispersion is 185 km sec−1 and the dust reddening towards the stars is EB–V = 0.188 mag. The total stellar mass is $\mathrm{M_{*}} = 10^{10.8}\, M_{\odot }$, which is consistent with other estimates (e.g. Chen et al. 2012). About ∼2 per cent of this mass was formed during the recent burst.


It is important to emphasize that any estimate of [Na/Fe] should be actually taken as an upper limit. Note that we can compute the theoretical response of stellar spectra to [Na/Fe] only for stars hotter than 3500 K (see Section 3.2). As discussed in Appendix A, a linear extrapolation of Na responses to cooler temperatures would likely lead to lower [Na/Fe] estimates, by about 0.1 dex. Moreover, as already noticed by CvD12b, atomic NaI transitions in the atmospheres of late-type stars are prone to substantial departures from LTE (Bruls, Rutten & Shchukina 1992; Gehren et al. 2006; Andrievsky al. 2007; Lind et al. 2011). In a Sun-like star, LTE calculations predict weaker lines (Allende Prieto et al. 2003) requiring corrections for the strongest lines, which can be as high as an effective change in the abundance of ∼0.5 dex. For a lower temperature star (with Teff ∼ 4000 K), more relevant for models having old ages (as those of our sample of ETGs), we may expect NLTE corrections in the range of 0.1–0.2 dex (based on fig. 4 of Lind et al. 2011). Hence, we may expect that NLTE models could enhance the predicted absorption in Na indices, resulting in lower inferred values of [Na/Fe]. However, note that our LTE-based methodology can match NaD, $\rm Na\,\small {I}8190$, $\rm Na\,\small {I}1.14$, and $\rm Na\,\small {I}2.21$, simultaneously, suggesting that NLTE corrections should be approximately the same for all four Na lines – an important aspect to test with future models. We emphasize that although we have introduced four free-fitting parameters to match the four Na lines (the $\alpha _{{\rm Na}_j}$ constants; see equation 1), in practice, the values of αNaD, $\rm \alpha _{{\rm Na}\,\small {I}1.14}$ and $\rm \alpha _{{\rm Na}\,\small {I}2.21}$ are fully consistent with those of α-MILES and CvD12a models. Effectively, we are able to fit the four Na-sensitive line strengths of the seven X-Shooter spectra – spanning a range of age, metallicity, and [α/Fe] – based on only one ‘extra’ free-fitting parameter (i.e. the $\rm \alpha _{{\rm Na}\,\small {I}8190}$).


The filtered MHD equations read
11

12

where we sum over repeated indices, and
13

14

15

16

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

 and

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

, and magnetic-field-line stretching, encoded in

. Usually, the magnetic subscale stress refers to the difference

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

18

where

 and

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

 are terms that convert kinetic to magnetic energy

 and vice versa

, and
19

20

21

22

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

 and

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

 and

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

 and

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


The ability both to rapidly quench and maintain low levels of star formation in red-sequence massive galaxies has often been attributed to the impact of active galactic nuclei (AGN). Radiatively-driven winds, mechanical energy, and/or thermal pressure release from the AGN are physical processes routinely incorporated into numerical simulations of galaxy evolution to solve the overcooling problem (e.g., Vogelsberger et al. 2014a; Schaye et al. 2015; Pillepich et al. 2018; Bassini et al. 2019; Wittor & Gaspari 2020), so that the characteristics of the observed galaxy population can be reproduced (e.g., Vogelsberger et al. 2014b; Nelson et al. 2018). Often two types of the AGN feedback mode are being distinguished, which are called the quasar mode or radiative mode (e.g., Di Matteo et al. 2005; Hopkins et al. 2008; Hopkins & Elvis 2010) and the radio mode also known as kinetic or maintenance mode (e.g., Bower et al. 2006; Croton et al. 2006; Fabian 2012; Gaspari et al. 2020). The quasar mode is thought to initially quench star formation through powerful radiatively driven winds that remove the gas from the galaxy (e.g., Nesvadba et al. 2008; Feruglio et al. 2010; Maiolino et al. 2012) and thereby suppress star formation. The radio mode is a heating mechanism affecting the gaseous halo that prevents continuous condensation of cold and warm gas, thereby quenching star formation over long timescales and maintaining a low level of star formation in red sequence galaxies (e.g., Brüggen & Kaiser 2002; McNamara et al. 2005; Gaspari et al. 2019; McDonald et al. 2021). Strong observational evidence for radio mode feedback has been collected from galaxy clusters hosting powerful radio galaxies (e.g., Fabian et al. 2006; McNamara & Nulsen 2007). The role of quasar mode feedback is much more controversial from an observational perspective. Various studies have reported negative (Ho 2005; Nandra et al. 2007; Schawinski et al. 2009; Farrah et al. 2012; Page et al. 2012; Mullaney et al. 2015; Shimizu et al. 2015; Wylezalek & Zakamska 2016; Kakkad et al. 2017; Catalán-Torrecilla et al. 2017; Bing et al. 2019; Bluck et al. 2020; Ramos Padilla et al. 2020; Brownson et al. 2020; Smith et al. 2020), positive (Kim et al. 2006; Cresci et al. 2015a,b; Bernhard et al. 2016; Santoro et al. 2016; Maiolino et al. 2017; Koss et al. 2021), or no effect from feedback (Elbaz et al. 2011; Bongiorno et al. 2012; Harrison et al. 2012; Husemann et al. 2014; Balmaverde et al. 2016; Leung et al. 2017; Woo et al. 2017; Shangguan et al. 2018; Scholtz et al. 2020) on the star formation rates of observed AGN host galaxies.


Unveiling the transport properties of charged particles in the presence of turbulent magnetic fields represents the key to understanding the propagation and acceleration of energetic particles in many space and astrophysical plasmas. Several parameters can influence the particle transport, like the turbulence level, the turbulence anisotropy, the spectral shape, and the particle energy, and many different regimes are considered in the literature (Zimbardo 2005; Pommois et al. 2007; Shalchi 2010, 2015; Zimbardo et al. 2012; Lazarian & Yan 2014; Litvinenko et al. 2017). Besides the ballistic and diffusive regimes, many observations suggest that intermediate, so-called superdiffusive regimes for which

 with α > 1, may exist. Here, r is the distance from the starting point, t is the time, and α is the anomalous diffusion exponent. These observations range from the analysis of nonrelativistic electrons accelerated in solar energetic events (Lin 1974), to the anomalously large parallel mean free paths inferred for solar energetic protons (Reames 1999) and for termination shock accelerated ions (Giacalone 2013). On a larger, astrophysical scale, Ragot & Kirk (1997) showed, by studying the spectral index evolution of diffuse radio emission from synchrotron emitting electrons in the Coma cluster of galaxies, that this can be interpreted in terms of superdiffusive transport. The transport properties can also be deduced by studying the energetic particle profiles upstream of shock waves, where particles are thought to be accelerated. In particular, the observations of power-law energetic particle profiles upstream of shock waves in the heliosphere (Perri & Zimbardo 2007, 2008, 2009, 2015; Sugiyama & Shiota 2011; Zimbardo et al. 2012) and in the supernova remnant shock precursors (Perri et al. 2016; Perri 2018) are an indication of superdiffusive transport. Further, superdiffusive transport also influences processes like diffusive shock acceleration (Kirk et al. 1996; Ragot & Kirk 1997; Perri & Zimbardo 2012a; Zimbardo & Perri 2013; Bykov et al. 2017) and stochastic Fermi acceleration (Sioulas et al. 2020), leading to modifications of the energy spectral index and of the acceleration time. As an application of superdiffusive shock acceleration (Perri & Zimbardo 2012a), we may mention that a discrepancy is found in the Mach numbers derived by X-rays and by radio observations of galaxy clusters’ merger shocks (Akamatsu et al. 2017; Colafrancesco et al. 2017; Van Weeren et al. 2017); this discrepancy could be explained by the modification of the energy spectral index implied by superdiffusive shock acceleration (Zimbardo & Perri 2017, 2018).