Parameter  is likely different for each AGN and may depend on the accretion rate. We have 0.3 for Mrk 110 (see Fig.1). The lines parallel to the best-fitting line to Mrk 110 cannot connect two points of Mrk 493 or IRAS 04416 even considering the corresponding errors. Mrk 110, Mrk 493 and IRAS 04416 have $\dot{\mathscr{M}}_{f=1}=$ 5.89, 75.9 and 426.6 or $\dot{\mathscr{M}}_{\rm {f}}=$ 0.49, 1.04 and 7.27, respectively. Mrk 493 and IRAS 04416 have larger accretion rates than Mrk 110 and it is possible that  depends on the accretion rate, but the present data do not allow us to test this hypothesis. There is a strong positive correlation between f and $\dot{\mathscr{M}}_{f=1}$, $f=6.8(\pm 1.6)\dot{\mathscr{M}}_{f=1}^{0.4\pm 0.1}$ (see Fig.3), which is consistent with f being dominated by the radiation pressure. This correlation supports the explanation of $f=5.4 r_{\rm {BLR}}^{0.3}$ in Mrk 110 arising due to the radiation pressure from the accretion disc. Thus, the relation $f=6.8\dot{\mathscr{M}}_{f=1}^{0.4}$ reflects the physical essence of relations like $f=5.4 r_{\rm {BLR}}^{0.3}$. The radiation pressure will produce more obvious effects on the BLR clouds as  increases. As the radiation pressure vanishes,  vanishes. The larger values of f  816 make MRM increase for Mrk 110. In like manner, larger f values may exist in quasars. Quasar J0100+2802 at z6.30, the most luminous quasar known at z6, has MRM(f1)1.21010M and Lbol1.621048ergs1 (Wu et al. 2015). It has LEdd  1.5  1038M/M  1.8  1048 erg s1 for solar composition gas and Lbol/LEdd0.9. $\dot{\mathscr{M}}_{f=1}= L_{\rm {bol}}/L_{\rm {Edd}}/\eta$ (Du etal.2014), where  is the efficiency of converting rest-mass energy to radiation (Thorne1974) and in general,  is of the order of 0.1. Thus $\dot{\mathscr{M}}_{f=1}\sim 9$ and f16 for J0100+2802. As f16, MRM1.91011M and Lbol/LEdd0.06. The larger black hole mass further gives rise to the most significant challenge to the Eddington limit growth of black holes in the early Universe (Willott etal.2010; Volonteri2012). A high f value is suggested for PG 1247+267 by the ultraviolet RM of carbon lines (Trevese etal.2014). PG 1247+267 has L(1350)3.91047ergs1 and ionization stratification like low-luminosity AGNs. The broad H has a redward shift of 0.008 with respect to [Oiii] 5007 (McIntosh etal.1999b), and has vFWHM7460kms1 (McIntosh etal.1999a). If zg0.008, f  13, consistent with the high f value suggested in Trevese etal. (2014). Thus, the new method is capable of estimating f in quasars. For the Eddington ratio Lbol/LEdd(f)Lbol/fLEdd(f1)1, we have $\dot{\mathscr{M}}_{f=1}=1133$, f113 and $\dot{\mathscr{M}}_{f}= 10$ for 0.1. Then, we have Lbol/LEdd113 when assuming f1. That we do not often see sources with such (apparent) Eddington ratios may suggest that the Thomson cross-section typically used in the radiation pressure calculation underestimates the coupling between the radiation and the BLR gas. On considering the line-driven radiation pressure (Castor, Abbott  Klein1975), the radiation pressure due to the gas opacity will be 103 times that due to the electron scattering opacity (Ferland etal.2009).


The results of this first exploratory work pave the way to a series of future investigations in which we will broaden the range of initial conditions and study their impact on the empirical parameters defined here. By changing the initial structural properties of the simulated clusters, we will compare the three parameters determined in stellar systems that, after one Hubble time of evolution, have reached different dynamical states. We will also include populations of primordial binaries, which are known to halt the core contraction earlier in the cluster evolution and at lower concentrations (see, e.g., Vesperini & Chernoff 1994; Trenti et al. 2007; Chatterjee et al. 2010). The main differences between the values of A
5, P
5, and S
2.5 in simulations with and without primordial binaries are expected during the advanced phases of the evolution, toward CC and post-CC, when the milder contraction of the clusters with primordial binaries might lead to a different and/or less extreme evolution of these parameters. The study presented here will also be further extended to explore the effects of different retention fractions of dark remnants (neutron stars and black holes; see, e.g., Alessandrini et al. 2016; Giersz et al. 2019; Kremer et al. 2020, 2021; Gieles et al. 2021, for some studies on the dynamical effects of dark remnants). Finally, a forthcoming paper will be dedicated to building nCRDs and determining the three parameters here defined in a sample of observed star clusters. This requires photometric observations (i) with a high enough angular resolution to resolve individual stars even in the innermost cluster regions, (ii) sampling each system at least out to 0.5 × r

h
, and (iii) deep enough to reach a few magnitudes below the MSTO. These requirements are achieved by most HST and adaptive-optics-assisted observations currently available for many GCs, thus making the determination of the three parameters from observations relatively straightforward, although particular care is needed to deal with typical observational difficulties such as photometric incompleteness, differential reddening, and Galactic field contamination. We will discuss the relation between these parameters and other dynamical indicators (in particular, the A
+ parameter measured from BSSs; see the Introduction), thus providing quantitative assessments of the operational ability of the three nCRD diagnostics to distinguish dynamically young GCs from systems in advanced states of dynamical evolution.


Furthermore, Duvall et al. (1993) noticed an inversion of the sense of asymmetry between spectrometric and photometric measurements, with line profiles in the velocity spectrum featuring more power in their low-frequency wing than in their high-frequency wing and vice-versa for line profiles in the intensity spectrum. Since intensity perturbations were expected to be proportional to velocity perturbations, one would have expected the asymmetries to be the same. Many hypotheses were posited to explain this puzzling result. Duvall et al. (1993) suggested that it was due to non-adiabatic effects lifting the proportionality relationship between the two kinds of perturbations (fluid displacement and temperature) but this hypothesis was later contradicted by Rast & Bogdan (1998). Non-adiabaticity was brought up again later on by Georgobiani et al. (2003) who suggested that the explanation resided in radiative transfer between the mode and the medium. Indeed, the observed radiation temperature corresponds to the gas temperature at local optical depth τ = 1. But optical depth depends on opacity, which non-linearly depends on temperature. Therefore, the temperature fluctuations due to the oscillating mode entails opacity fluctuations, which in turn impacts the “observed” radiation temperature. Given the non-linear nature of the κ − T relation, this modulation decreases the observed temperature fluctuations more significantly in the low-frequency wing of the mode than in its high-frequency wing. Since this radiative transfer does not impact the velocity measurements, this could explain the asymmetry reversal between velocity and intensity spectra. Using 3D simulations, Georgobiani et al. (2003) computed mode line profiles in both the velocity and the intensity power spectrum alternatively at mean unity optical depth and instantaneous unity optical depth. Their results indeed show that the modulation of the “observed” intensity fluctuations due to radiative transfer could be significant enough to reverse the sense of mode asymmetry. One of the hypothesis enjoying the most support for asymmetry reversal, however, is based on the effect of turbulent perturbations partially correlated with the mode, which thus impact its line profile (Nigam et al. 1998; Roxburgh & Vorontsov 1997; Rast & Bogdan 1998; Kumar & Basu 1999). Indeed, a part of these perturbations is coherent with the mode and, thus, leads to interference. This interference term may be constructive or destructive, depending on the phase difference between the mode and the coherent turbulent perturbations. For frequencies at which the interference is constructive, the power spectral density is slightly elevated, whereas it drops slightly for frequencies at which it is destructive. Typically, in the vicinity of a resonant mode, the dependence of the phase difference between mode and turbulent perturbation is such that the interference term is constructive for frequencies located in one wing of the mode and destructive in the other. Therefore, as a result of this interference behaviour, one of the wings falls off more slowly and the other more rapidly, leading to mode asymmetry. It has been suggested that the degree of correlation between the turbulent perturbations and the oscillation it excites is higher in intensity than in velocity, so that it changes the sign of mode asymmetry only in the intensity spectrum. While it is widely accepted that correlated turbulent perturbations must be taken into account to explain asymmetries in the intensity spectrum, the question of whether it has a significant impact on the velocity spectrum remains an open issue (see e.g. Jefferies et al. 2003).


Another way of obtaining information about the nucleosynthesis processes involved in producing carbon is to compare it with other elements that are characterised by a well-known source of production, as in the case of oxygen. In Fig. 5, we show the variation of [C/O] as a function of [Fe/H], which serves as a first-order approximation to the evolution with time. To calculate the [C/O] ratios, two oxygen abundance indicators are used independently. At subsolar metallicities, the abundance ratios with both oxygen indicators are mostly negative and show an increasing trend towards higher metallicity. This is explained by the fact that oxygen is entirely produced by SNe Type II from massive progenitors, which started to release theiryields at earlier ages in the Galaxy and, hence, at lower metallicities (e.g. Woosley & Weaver 1995). The massive stars producing carbon at low metallicities might be less massive than those producing oxygen (i.e. having a longer life), explaining a delayed contribution of carbon, hence, the negative [C/O] ratios. Alternatively, this could be explained by increasing O/C yields for more massive progenitors of SNeII. Once metallicity starts to increase, low- and intermediate-mass stars release carbon and massive stars start to eject more carbon than oxygen (Carigi et al. 2005). The [C/O] ratio seems to have a constant rise towards higher metallicities when using the forbidden oxygen line. However, in the case when the O I 6158 Å line is employed, we do observe that the maximum in [C/O] takes places close to solar metallicity to then become flat or decrease. This suggests that low-mass stars mostly contribute to carbon around solar metallicity, whereas at super-solar metallicities, massive stars produce carbon together with oxygen, thereby flattening or even decreasing the [C/O] ratio. This trend is in agreement with the metallicity dependent yields from Carigi et al. (2005), which provide higher carbon as [Fe/H] increases from massive stars (i.e. also increasing the O production) but lower carbon from low and intermediate mass stars as [Fe/H] increases (i.e. less production of C). The turning point of increased relative production of carbon from massive stars takes place at A(O) ~ 8.7 dex (see Fig. 2 of Carigi et al. 2005) which equals to [O/H] ~ 0.0 dex. This observed behaviour of [C/O] is in contrast to the steady increase of [C/O] up to [Fe/H] ~ 0.3 dex found, for example, by Franchini et al. (2021). Nevertheless, the general trend we find when using the [O I ] 6300 Å line is similar to the reported by Franchini et al. (2021), who use also that oxygen indicator. All thick-disk stars present negative [C/O] ratios and when using the oxygen line at 6158 Å thin-disk stars with [Fe/H] ≲ –0.2 have [C/O]  0 as well. Thick-disk stars and low-metallicity thin-disk stars at the same metallicity have similar [C/O] ratios, meaning that the balance between different production sites for oxygen and carbon is the same among both populations, despite [C/Fe] and [O/Fe] being systematically higher for thick-disk stars at a given metallicity.


In contrast, experimental studies based on irradiation of ices show that the second scenario is likely. Such studies show that glycolaldehyde, ethylene glycol, and methyl formate can be synthesized by irradiation of pure or mixed methanol (CH3OH) ices (Hudson & Moore 2000; Öberg et al. 2009). Interestingly, the (CH2OH)2/CH2OHCHO abundance ratio is found to be dependent on the initial ice composition as well as on the ice temperature during the UV irradiation. The CH3OH:CO ratio in the ices is a key parameter: for irradiated 20 K ices a composition of pure CH3OH leads to a (CH2OH)2/CH2OHCHO ratio higher than 10, while a CH3OH:CO 1:10 ice mixture produces a (CH2OH)2/CH2OHCHO ratio lower than 0.25 (Öberg et al. 2009). The difference found between IRAS 16293 and IRAS2A could then be related to a different grain mantle composition in the two sources. If the CH3OH:CO ratio in the grain mantles of IRAS2A was higher than in IRAS 16293, a higher (CH2OH)2/CH2OHCHO abundance ratio would be expected according to the laboratory results. In fact, the CH3OH gas-phase abundance in the inner envelope is found to be higher in IRAS2A (~4 × 10-7, Jørgensen et al. 2005b) than in IRAS 16293 (~1 × 10-7, Schöier et al. 2002), while the CO abundance is relatively similar (~(2–3) × 10-5, Jørgensen et al. 2002; Schöier et al. 2002). This could consequently be the result of the desorption of ices with a higher CH3OH:CO ratio in IRAS2A than IRAS 16293. The question then arises of how CH3OH can be more efficiently produced on grains in IRAS2A than in IRAS 16293. Several scenarios are possible: i) the initial conditions may play an important role in the CH3OH:CO ratio. In particular, experiments and simulations show that the efficiency of CH3OH formation through CO hydrogenation on the grains is dependent on temperature, ice composition (CO:H2O), and time (Watanabe et al. 2004; Fuchs et al. 2009); ii) the collapse timescale was longer in IRAS2A than in IRAS 16293, enabling the formation of more CH3OH; iii) the H2 density in the prestellar envelope of IRAS2A was lower than that of IRAS 16293. A less dense environment would lead to a higher atomic H density and consequently to a higher efficiency of CO hydrogenation. This was proposed by Maret et al. (2004) and Bottinelli et al. (2007) to explain the anticorrelation found between the inner abundances of H2CO and CH3OH and the ratios of submillimeter to bolometric luminosity (Lsmm/Lbol) of different low-mass protostars. The Lsmm/Lbol parameter is interpreted as an indication of different initial conditions, rather than an evolutionary parameter in this context (Maret et al. 2004). The Lsmm/Lbol ratios of IRAS2A (~0.005, Karska et al. 2013) and IRAS 16293 (~0.019, Froebrich 2005) are consistent with this hypothesis. The current H2 density profiles of these two sources also agree with this scenario if they keep the memory of the prestellar conditions. The density derived in the outer envelope of IRAS2A with a power-law model (Jørgensen et al. 2002) is lower than the density derived in IRAS 16293 by Crimier et al. (2010), whether it be for a Shu-like model or a power-law model, while the temperature profiles are relatively similar (see Fig. 5). Along the same lines, Hudson et al. (2005) showed with proton irradiation experiments that glycolaldehyde is more sensitive to radiation damage than ethylene glycol. Irradiation would be more important in less dense envelopes, which would also be consistent with a less dense prestellar envelope in IRAS2A. A recent experiment by Fedoseev et al. (2015) shows that these two species can also be synthesized by surface hydrogenations of CO molecules in dense molecular cloud conditions. They do not directly form from CH3OH, but the results of this experiment show that similarly to CH3OH, which results from successive hydrogenations of CO, ethylene glycol forms by two successive hydrogenations of glycolaldehyde. This consequently agrees with the proposed scenario.


From the best-fitting values of the normalization at a fixed energy, we can obtain the ratios of the hydrogen column densities for different dust layers, such as:

(16)

\begin{eqnarray}
\frac{N_{\rm H,12}}{N_{\rm H, 5}} \approx \frac{\mathcal {F}_{\rm X}^{(12)}(E)}{\mathcal {F}^{(5)}_{\rm X}(E)} \frac{\left(1-\langle x \rangle _{12} \right){\langle x \rangle _{12}}}{\left(1-x_5\right){x_5}},
\end{eqnarray}

where we assumed that the number of grains per hydrogen atom is the same in all clouds and dropped by the factor of Cd, i, since this is not sensitive to the grain composition (Mauche & Gorenstein 1986) (see also Section 2). In the above, NH, 12 represents the average column density of dust clouds 1 and 2. As already mentioned in Section 4.1 and later in Section 4.3, these are most probably one dust cloud of finite width, whose average column density we are probing. Having derived the ratios at four different energies, we calculated the weighted means, namely NH, 12/NH, 5 = 0.19 ± 0.03, NH, 12/NH, 34 = 0.059 ± 0.006, and NH, 34/NH, 5 = 3.5 ± 0.6. Thus, the intermediate dust clouds have the highest column density. This is 3.5 times higher than that of the fifth dust cloud, which may also explain the approximately equal intensities of rings 3–4 and 5, given their different distances from the observer. Interestingly, the column density of the clouds located closest to V404 Cyg is ∼6 per cent NH, 34. These findings are in rough qualitative agreement with the extinction histogram shown in Fig. 5, where the lowest extinction values are found at distances ≳2 kpc, i.e. where the dust layers 1 and 2 are located. Quantitatively, we find that the ratios NH, 34/NH, 5 and NH, 34/NH, 12 as derived from the extinction maps (Sale et al. 2014) are by a factor of ∼3 smaller than our estimates, while the NH, 12/NH, 5 ratio is the same (within uncertainty values). This implies that our analysis is overestimating the NH, 34 column density by a factor of ∼3. A simple explanation for this difference is that the dust-to-hydrogen ratio is not the same for all clouds as originally assumed in our calculations (the Ai/Aj term has dropped from the l.h.s. of equation 16). In any case, the ratio of the normalizations $\mathcal {F}_{\rm X}^{(i)}$ can be directly related to the ratio of dust column densities NH, iAi without resorting to any additional assumptions.


The diffuse hot gas X-ray luminosities in the 0.3–8 keV band are taken from the work of KF15. They have carefully removed the contribution from discrete sources such as low-mass X-ray binaries (Fabbiano 2006) to the total X-ray luminosity, leaving the diffuse gas contribution LX, Gas. A correction to bolometric would increase the X-ray luminosities by 0.08 dex on average. Most of the X-ray data come from Chandra observations. However, for some high-mass galaxies, the X-ray emission is particularly extended (e.g. NGC 4374, 4486, 4649, 5846) and in those cases ROSAT data from O‘Sullivan et al. (2001), corrected to the Chandra energy band, are used. Although the contribution from discrete sources in the ROSAT data cannot be subtracted as accurately as it can for Chandra data, their contribution is only about 1 per cent of the diffuse gas luminosity for these high-mass galaxies (see O'Sullivan et al. 2001). For further details, see KF15. Here we make a very small correction to the KF15 LX,Gas luminosities for the distances used in the SLUGGS survey (Brodie et al. 2014). The KF15 compilation did not include several galaxies that appear in the Alabi et al. (in preparation) study. Here we also include the X-ray luminosities for NGC 720, NGC 1316 and NGC 3115 from Boroson et al. (2011), and for NGC 5128 from KF13. Su et al. (2014) conducted a detailed XMM and Chandra study of NGC 1400. As well as the X-ray emission centred on NGC 1400, they detected an enhanced region of X-rays to the NE of the galaxy that they associated with stripped gas. Here we use the X-ray luminosity centred on NGC 1400 with a small adjustment to our X-ray band and distance, and assume an uncertainty of 20 per cent. We note that the X-ray luminosity would double if the enhanced region were also included. Two galaxies in Alabi et al. (in preparation) but not included here are NGC 2974 (not observed by Chandra) and NGC 4474 (the Chandra observation was only 5 ks).


Douchin & Haensel (2001; DH) formulated a unified EoS for NS on the basis of the SLy4 Skyrme nuclear effective force (Chabanat et al. 1998), where some parameters of the Skyrme interaction were adjusted to reproduce the Wiringa et al. calculation of neutron matter (Wiringa et al. 1988) above saturation density. Hence, the DH EoS contains certain microscopic input. In the DH model the inner crust was treated in the CLDM approach. More recently, unified EoSs for NS have been derived by the Brussels-Montreal group (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013). They are based on the BSk family of Skyrme nuclear effective forces (Goriely et al. 2010). Each force is fitted to the known masses of nuclei and adjusted among other constraints to reproduce a different microscopic EoS of neutron matter with different stiffness at high density. The inner crust is treated in the extended Thomas-Fermi approach with trial nucleon density profiles including perturbatively shell corrections for protons via the Strutinsky integral method. Analytical fits of these neutron-star EoSs have been constructed in order to facilitate their inclusion in astrophysical simulations (Potekhin et al. 2013). Quantal Hartree calculations for the NS crust have been systematically performed by (Shen et al. 2011b,a). This approach uses a virial expansion at low density and a RMF effective interaction at intermediate and high densities, and the EoS of the whole NS has been tabulated for different RMF parameter sets. Also recently, a complete EoS for supernova matter has been developed within the statistical model (Hempel & Schaffner-Bielich 2010). We shall adopt here the EoS of the BSk21 model (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013; Goriely et al. 2010) as a representative example of contemporary EoS for the complete NS structure, and a comparison with the other EoSs of the BSk family (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013) and the RMF family (Shen et al. 2011b,a) shall be left for future study.


In principle, Fig. 5, central panel G, shows that (469219) 2016 HO3 may have been locked in a Kozai–Lidov resonance with ω librating about 270° for nearly 100 kyr and probably more. Because of the Kozai–Lidov resonance, both e (central panel E) and i (central panel F) oscillate with the same frequency but out of phase (for a more detailed view, see Fig. 4, panels E and F); when the value of e reaches its maximum the value of i is the lowest and vice versa ($\sqrt{1 - e^2} \cos i \sim$ constant, see Fig. 4, panel B). During the simulated time and for the nominal orbit, 469219 reaches perihelion and aphelion the farthest possible from the ecliptic. Fig. 5, G-panels, show that for other incarnations of the orbit of 469219, different from the nominal one, ω may librate about 90° as well during the simulated time interval. However, is this a true Kozai–Lidov resonance? Namouni (1999) has shown that the secular evolution of co-orbital objects is viewed more naturally in the erωr-plane, where er and ωr are the relative eccentricity and argument of perihelion computed as defined in Namouni's work (see equations 3 in Namouni 1999); these are based on the vector eccentricity and the vector inclination. Fig. 6 shows the multi-planet erωr-portrait for the nominal orbit of this object. It clearly resembles figs 13 and 19 in Namouni (1999). Asteroid 469219 librates around $\omega _{\rm r}=-90{^\circ }$ for Venus, the Earth, and Jupiter. This behaviour corresponds to domain III in Namouni (1999), horseshoe-retrograde satellite orbit transitions and librations (around $\omega _{\rm r}=-90{^\circ }$ or 90°). For a given cycle, the lower part corresponds to the horseshoe phase and the upper part to the quasi-satellite or retrograde satellite phase. This is not the Kozai–Lidov resonance; in this case, the Kozai–Lidov domain (domain II in Namouni 1999) is characterized by libration around $\omega _{\rm r}=0{^\circ }$ (or 180°) which is only briefly observed at the end of the backwards integrations (see Fig. 6). The Kozai–Lidov resonance is however in action at some stage in the orbits displayed in Figs 5 and 8. Our calculations show that the orbital evolution followed by 469219 is the result of the dominant secular perturbation of Jupiter as the periodic switching between co-orbital states ceases after about 8 kyr if Jupiter is removed from the calculations. Fig. 7 shows that, without Jupiter, 469219 switches between the Kozai–Lidov domain and that of horseshoe-quasi-satellite orbit transitions and librations (including both −90°and 90°). Jupiter plays a stabilizing role in the dynamics of objects following orbits similar to that of 469219. It is not surprising that Jupiter instead of the Earth or Venus is acting as main secular perturber of 469219. Ito & Tanikawa (1999) have shown that the inner planets share the effect of the secular perturbation from Jupiter; in fact, Venus and our planet exchange angular momentum (Ito & Tanikawa 2002). In their work, these authors argue that the inner planets maintain their stability by sharing and weakening the secular perturbation from Jupiter. Tanikawa & Ito (2007) have extended this analysis to conclude that, regarding the secular perturbation from Jupiter, the terrestrial planets form a collection of loosely connected mutually dynamically dependent massive objects. The existence of such planetary grouping has direct implications on the dynamical situation studied here; if Jupiter is removed from the calculations, the overlapping secular resonances and the recurrent dynamics disappear as well.


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


We wanted to discuss the observed periods at sunspot. A period of nearly five minutes can be detected in Doppler velocities of CO 3-2 R14 and 7-6 R67 lines, which is consistent with previous findings in white light images or continuum spectrum (Beckers & Schultz 1972; Lites 1988; Nagashima et al. 2007; Yuan et al. 2014; Su et al. 2016), and might be considered the solar p-mode waves in the photosphere (Thomas 1985; Bogdan 2000; Solanki 2003). While a period of roughly three minutes is found in the Doppler velocities of the CO 3-2 R14 and Mg II k lines, which agrees closely with the previous observational results in UV–infrared lines or images at the sunspot umbra (e.g., Solanki et al. 1996; Bogdan 2000; Fludra 2001; Maltby et al. 2001; Centeno et al. 2008; Tian et al. 2014; Khomenko & Collados 2015; Yang et al. 2017). They are explained as the resonant modes of sunspot oscillations (Uexkuell et al. 1983; Thomas 1984; Gurman 1987; Khomenko & Collados 2015). On the other hand, the CO 3-2 R14 line is believed to provide the information in the upper photosphere or the temperature minimum region (Uitenbroek 2000; Ayres 2002; Ayres et al. 2006). Moreover, a time delay of about two minutes is measured between the CO 3-2 R14 and Mg II k lines, as shown in Fig. 9. So, the three-minute oscillation at the sunspot umbra could come from the upper photosphere or the temperature minimum region and then propagate to the chromosphere, supporting the interpretation that propagating waves above the sunspots originate from the lower solar atmosphere (De Moortel et al. 2002; O’Shea et al. 2002; Brynildsen et al. 2004; Khomenko & Collados 2015; Krishna Prasad et al. 2015). In other words, the three-minute oscillation can be regarded as the upwardly propagating slow magnetoacoustic waves (e.g., Su et al. 2016; Chae et al. 2019; Cho & Chae 2020; Feng et al. 2020b). Finally, Chae et al. (2017) found that the three-minute oscillation in the light bridge or umbral dots of a sunspot originates from the photosphere (see aslo Cho et al. 2019), which is consistent with our results and further suggests that the CYRA data is reliable.


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 $\rm \alpha _{{\rm Na}\,\small {I}8190}$).


We performed an analysis on simulated XMM maps of point sources, presented in Brunner et al. (2008) for similarly large XMM exposures in the Lockman Hole, detecting no extended emission in the simulated maps containing the detected by XMM point sources. The higher sensitivity of Chandra towards the detection of point sources allows us to make a statistical assessment of the effect of sub-threshold (for XMM) AGNs toward the detection of extended emission. Performance of XMM observations was accompanied by deepening the Chandra data within one year from each other, which makes Chandra maps suitable for XMM point source contamination analysis, limiting the effect of AGN long-term variability (Salvato et al. 2011; Paolillo et al. 2004). We have computed the variation of unresolved point source flux on the detection scales for XMM, using the Chandra image, masking out the sources detected in the XMM analysis. The constructed Chandra flux map has been further smoothed with a Gaussian of 16′′ width, approximating the effects of the XMM PSF. In the map, the uniform distribution of the faintest point sources results in nearly constant emission, which we subtract following the procedure for local cosmic background estimates for XMM, while bright sources and clustered sources make an enhancement. We find the contamination by point sources unresolved by XMM to the flux of identified extended sources is below the 5% level of the extended source’s flux. The highest peaks in the contamination map are associated with stand-alone sources near the (XMM) detection threshold, which by chance happened not to coincide with any of the detected groups and would contribute 30% to the faintest group flux. The importance of these sources is even higher in shallow surveys (Mirkazemi et al. 2015), to a degree requiring matched detection thresholds between point-like and extended sources, effectively removing faint extended sources from consideration. The importance of point source removal in XMM data is mentioned also in other cluster publications (Hilton et al. 2010; Pierre et al. 2012).


One remarkable feature present in the central region of Orion is an explosive event that occurred 550 ± 25 years ago (J. Bally, priv. comm.) and was revealed by the three runaway stars BN, n, and I (Gómez et al. 2005; Rodríguez et al. 2005, 2017), and by the CO and H2 fingers (e.g., Allen & Burton 1993; Zapata et al. 2009; Nissen et al. 2012; Youngblood et al. 2016; Bally et al. 2017). However, Luhman et al. (2017) showed that the object n is no longer a runaway member because its real proper motion is much lower than previously estimated; but conversely another object, named x, is moving away at high speed from the same explosion center. J. Bally (priv. comm.) confirms the fast proper motion of x and the absence of movement of n from ground-based H2 images 14 years apart. X is further out having passed our 20% beam coupling mark (see Fig. 1 of Paper I), and therefore does not appear in the figures presented in this Letter. Zapata et al. (2011) and Orozco-Aguilera et al. (2017) in their follow-up work with ALMA proposed that the hot core (HC) is externally heated despite its high temperature, and that the heating source could be the nearby explosion. Similarly, Blake et al. (1987), Wang et al. (2011), and Favre et al. (2011) advocated that the Compact Ridge is also externally heated, although the heating source should not be the same since we presented evidence in Paper I that the Compact Ridge has not yet been affected by the impact of the explosion. A possibility could be the outflow from source I hitting the Compact Ridge (Liu et al. 2002). In Paper I, we also presented evidence for an interaction between the explosive event and the main components of the Orion KL region including the HC, several infrared (IR) components (Rieke et al. 1973), and methyl formate (CH3OCHO; hereafter MF) peaks (Favre et al. 2011). We showed that the IRc6/MF5 and IRc20/MF4 sources, west of the explosion center, display emission lines of various species having only red wings, while sources on the east and south sides display emission lines having only blue wings. We also confirmed that excited emission lines are found preferentially surrounding the explosion center and that complex organic molecules (COMs) rich in oxygen (O-COMs) do not occupy the same volumes as CN rich COMs (CN-COMs). We identified the ethylene glycol peak (EGP) to be coincident with a hollow sphere of material, which we interpreted to have originated from the impact of a “bullet” launched from the explosion center (Favre et al. 2017; Wright & Plambeck 2017). We also proposed that the Compact Ridge (MF1) is sufficiently far away from the rest of the KL region to have not yet been perturbed by the explosion, the evidence being the absence of asymmetric emission line wings and the narrowness of the lines themselves (∼1 km s−1). In this Letter, we study further the interaction of the explosion blowout with the surrounding gas and dense sources.


Although it is a simple concept, obtaining galaxy sizes is not an easy task and is subject to a number of assumptions. The most common way to derive galaxy sizes is by performing light-profile fitting assuming a given shape of the surface brightness profile using a χ2 minimization (e.g. Simard et al. 1999; Peng et al. 2002; Ravindranath et al. 2004; Daddi et al. 2005; Ravindranath et al. 2006; Trujillo et al. 2006; Akiyama et al. 2008; Franx et al. 2008; Tasca et al. 2009; Cassata et al. 2010, 2013; Williams et al. 2010; Mosleh et al. 2011; Huang et al. 2013; Ono et al. 2013; Stott et al. 2013; Morishita et al. 2014; van der Wel et al. 2014; Straatman et al. 2015; Shibuya et al. 2015). Another method assumes circular or elliptical apertures around a predefined galactic center and computes the size enclosing a given percentage of the total galaxy flux (e.g. Ferguson et al. 2004; Bouwens et al. 2004; Hathi et al. 2008; Oesch et al. 2010; Ichikawa et al. 2012; Curtis-Lake et al. 2016). A third approach, involving counting the number of pixels belonging to the galaxy to derive its size, was also explored in Law et al. (2007). Studies of galaxy sizes at z> 2 became possible with the deep imaging obtained with HST. The first reports on size evolution found that galaxy sizes as observed in the UV rest-frame were becoming smaller at the highest redshifts (Bouwens et al. 2003, 2004; Ferguson et al. 2004). We have now access to the size evolution up to z ~ 10 from the deepest HST imaging data (e.g., Hathi et al. 2008; Jiang et al. 2013; Ono et al. 2013; Kawamata et al. 2015; Holwerda et al. 2015; Shibuya et al. 2015). With the multiwavelength and near-infrared coverage of CANDELS (Grogin et al. 2011; Koekemoer et al. 2011) optical rest-frame measurements are reported up to z ~ 3 for a large collection of galaxies in diverse populations (e.g. Bruce et al. 2012; van der Wel et al. 2014; Morishita et al. 2014). At z ~ 2 the size of star-forming galaxies (SFGs) is, to first order, independent of the observed rest-frame bands (Shibuya et al. 2015). It is generally accepted that galaxy sizes tend to decrease with increasing redshift (e.g. Bouwens et al. 2003, 2004; Ferguson et al. 2004; Mosleh et al. 2012) and that galaxy sizes depend on stellar mass (e.g. Franx et al. 2008; van der Wel et al. 2014; Morishita et al. 2014) and luminosity (e.g. Grazian et al. 2012; Huang et al. 2013). However, some results point to a scenario consistent with no size evolution as seen in UV rest-frame from HST data (Law et al. 2007; Curtis-Lake et al. 2016) and, at a fixed stellar mass, from optical rest-frame ground-based data (Ichikawa et al. 2012; Stott et al. 2013).


In recent years, the quest to observe embedded accreting planets as they form has come a long way as a result of combined observations that are covering the ultraviolet to the millimeter wavelength ranges. One instrument in particular has been playing a major role in this, due to its diffraction-limited and high-contrast observations: the Spectro-Polarimetric High contrast imager for Exoplanets REsearch (SPHERE; Beuzit et al. 2019), which covers the visible and near-infrared (VIS/NIR) wavelength ranges. Together with other instruments, it has revealed a large abundance of substructures that are now known to be commonly present in protoplanetary disks (PPDs) ranging from gaps and rings to spiral arms, cavities, and various asymmetric features (e.g., Garufi et al. 2016, 2018; Avenhaus et al. 2018; Andrews et al. 2018, DSHARP). These features are often interpreted as the result of embedded planets that interact with their natal circumstellar disk (CSD; e.g., Wolf & D’Angelo 2005; Fouchet et al. 2010; Ruge et al. 2013; Ober et al. 2015; Dong et al. 2016). However, other origins have been proposed as well (e.g., Flock et al. 2015; Zhang et al. 2015; Ruge et al. 2016; Gonzalez et al. 2017; Suriano et al. 2017, 2019; Dullemond & Penzlin 2018). Despite the ambiguity of their particular origins, the properties of the potential planets that may produce these features have been studied extensively, especially using hydrodynamics simulations (e.g., Bae et al. 2019; Toci et al. 2020; Calcino et al. 2020). Dong & Fung (2017), for instance, analyzed observed gap features in order to determine the masses of planets that may have caused them by using 2D and 3D hydrodynamics simulations with 3D radiative transfer simulations of five scattered light observations of CSDs around Herbig Ae/Be and T Tauri stars: HD 97048 (Ginski et al. 2016), TW Hya (van Boekel et al. 2017), HD 169142 (Momose et al. 2015), LkCa15 (Thalmann et al. 2016), and RX J1615 (de Boer et al. 2016). By assuming an α-viscosity model (Shakura & Sunyaev 1973) with αvisc = 10−3 and single gap-opening planets as origins, they deduced that the corresponding planetary masses are all of typical low-mass giant planets between about 0.1 and 1 MJ.


Both Greco etÂ al. (2009) and Servidio etÂ al. (2011) show that a remarkable similarity exists between the PDF of the field magnitude from 2D MHD simulations with a guide field and the PDF from ACE observations in the supersonic solar wind near Earth. This suggests that the common occurrence of strong magnetic field discontinuities in the solar wind (e.g., Li 2008) might be attributed to the ubiquitous presence of inertial-scale quasi-2D coherent magnetic field structures or flux ropes interspersed with current sheets and reconnection x-points. Additional arguments in support of this view come from theoretical considerations (e.g., Zank & Matthaeus 1992, 1993) and observations (Matthaeus etÂ al. 1990; Bieber etÂ al. 1996) that MHD turbulence in the supersonic solar wind can be thought of comprising to lowest order a dominant 2D component and a minor parallel propagating AlfvÃ©n wave component. Furthermore, recent observations in the supersonic solar wind suggest the common occurrence of magnetic islands with different sizes in the inertial range together with evidence for island merging near the heliospheric current sheet (Khabarova etÂ al. 2014). A statistical solar wind data analysis by Osman etÂ al. (2014) also supports the idea that strong magnetic field discontinuities have a larger likelihood of being associated with current sheets and x-point reconnection outflows and have a higher possibility that a connection exists between current sheets and such outflows. With today's higher resolution measurement capability, identification of x-point reconnection outflows in the solar wind has become quite common (e.g., Gosling 2010). Gosling (2010) found that most reconnection events are observed in the slow supersonic solar wind (â¼2â3 events per day near Earth), while in the fast supersonic solar wind much less are found (â¼0.6 events per day). Reconnection events are also regularly observed in association with coronal mass ejections (Gosling 2010) where inertial-scale flux-rope merging was reported at the current sheet behind a coronal mass ejection close to the Sun by Song etÂ al. (2012), and current sheet reconnection was observed at the turbulent leading edge of an interplanetary coronal mass ejection near Earth by Chain & Munoz (2011), for example.


Fig. 1 clearly shows that in increasing fluence the processes of dissociation are greater, and thus new molecular species come to light. We identify the new species by comparing the peak positions with similar works on acetone ices. New observed peaks were: a flat peak in around 3 μm that could be associated to amorphous water, but since several other alcohols have a similar peak and water is not a highly expected acetone radiation product (see Section 3), we could not make any strong assignment to this peak. Some new peaks in the range of 2000–3500 cm−1, which we assign to isopropanol, ketene, and carbon monoxide according to the work of Hudson (2018). Other two peaks in the region 2000–600 cm−1 we assign to CH4 and -CH=CH- bending (Hudson 2018; Matrajt et al. 2013). The most sharp and visible peak is the CO2 one. CO2 could be a contaminant, however the CO2 peak is not present in our control experiments, such as monitoring the ice sample before irradiation to confirm that without irradiation sample remains unaltered, or also irradiation of the bare substrate. Also, the CO2 peak increases with fluence showing this is a molecule being formed due to irradiation. Due the vacuum chamber pressure to be 10−9 mbar, some residual gas could contaminate the sample, but this is accounted for our error bars estimates. The H2CCO peak can be overlapped with a CO one since both are expected radiation products and have a peak near 2128 cm−1. However, as stated in Hudson (2018), the shift of this peak to higher wavenumbers with increasing fluence indicates this peak is most due to formation of ketene. In comparison with the work of Hudson (2018), he observed peaks for CH4, CO, H2CCO, and C3H8O. Here, we observed and confirm a peak for CO2 as well other similar peaks presented in the work of Hudson (2018) for isopropanol and ketene. Photo-irradiation of pure acetone ice with X-rays was also performed in Almeida et al. (2014), where authors employed a photo-stimulated desorption (PSID) and took the positive PSID spectra to analyse acetone fragmentation. They have thus detected lots of cations as fragments, such as HCO+, CO+, H+, C2CH$_3\, ^+$, CO$_2\, ^+$, H2CO+, etc. Tables 1 and 2 present a compilation of peak positions (in wavenumbers and wavelength), our corresponding assignments, band strengths and references used to determine molecular assignments. Question mark in Table 2 is a peak probably related to several different molecules being formed in the ice as explained before. Note that ketene band strength was taken from Berg & Ewing (1991) and it was also used as reference value in other recent works (Hudson & Loeffler 2013; Bergner, Öberg & Rajappan 2019). No reference band strength for C3H8O were found.


The beaming functions of the polar and fan beams are given by f sinmϕ and p coskϕ, respectively. Here ϕ is the angle between the magnetic field axis and the photon propagation and is thus a function of the angle between the magnetic and rotation axis (θ), the angle of the NS rotation axis, the observing angle (i), and the NS spin phase. The exponent values m and k can be as low as 1, but in the general case of the accretion column emission, they can have significantly higher values (Trümper et al. 2013). We constructed various pulse profiles for different combinations of fan- and polar-beam emission patterns with different relative intensities of the fan and polar beams (i.e., FPolar∕FFan ranging from ~0.01 to ~30). We note that these values exceed any realistic configuration between the fan beam and the reflected polar beam. More specifically, since the polar beam is a result of reflection of the fan beam, it is only for a very limited range of observing angles that its contribution will (seemingly) exceed that of the fan beam, and thus a value of FPolar∕FFan ≳ 2, is unlikely. On the other hand, the increasing height of the emitting region, which would result in a smaller fraction of the fan beam being reflected by the NS surface, is limited to ≲ 10 km (Mushtukov et al. 2015), thus limiting the FPolar∕FFan ratio to values greater than 0.1 (see, e.g., Fig. 2 of Poutanen et al. 2013). Despite these physical limitations, we have extended our estimates to these exaggerated values in order to better illustrate the contribution of each component (fan and polar) to the PF. Moreover, a value of FPolar∕FFan exceeding 10 qualitatively describes the pencil-beam regime, which is expected at lower accretion rates. We estimated the PF for a range of observer angles and for different combinations of angles between the magnetic and rotation axis. An indicative result for a 45° angle between the NS magnetic field and rotation axis and for an rG∕rNS = 0.25 is plotted inFig. 12.


Silicon monoxide (SiO) is predicted to be the most abundant Si-bearing molecule in the entire 1–10 R* range in the atmospheres of M stars. In S-type atmospheres, the calculated abundance of SiO decreases by two orders of magnitude in the 1–5 R* but retains a very high abundance beyond, and the same occurs in C-rich atmospheres, although in this case, the abundance drop in the 1–5 R* is even more pronounced (see Fig. 2; see also Agúndez & Cernicharo 2006). Observations indicate that the abundance of SiO does not differ significantly between envelopes around M-, S-, and C-type stars, although in all them the SiO abundance decreases with increasing mass-loss rate (González Delgado et al. 2003; Schöier et al. 2006; Ramstedt et al. 2009; Massalkhi et al. 2019, 2020). This decline in the SiO abundance with increasing envelope density is not a consequence of chemical equilibrium (Massalkhi et al. 2019), but has been interpreted as evidence that SiO disappears from the gas phase at high densities to be incorporated into dust grains (González Delgado et al. 2003; Schöier et al. 2006; Ramstedt et al. 2009; Massalkhi et al. 2019, 2020). It therefore appears that the gradual abundance decline calculated for SiO in the 1–5 R* region from stellar type in the sense M → S → C does not have a direct consequence in the SiO abundance that is injected into the expanding wind. However, this behavior predicted by chemical equilibrium probably explains why SiO masers are observed in M-type stars but not toward carbon stars (e.g., Pardo et al. 2004). Except for these details, chemical equilibrium and observations agree in the fact that SiO is one of the most abundant carriers of silicon in the atmospheres of M-, S-, and C-type stars. Calculations and observations also agree for SiS in that it is an abundant molecule regardless of the C/O. However, observations indicate a differentiation between C- and O-rich envelopes, with SiS being on average one order of magnitude more abundant in carbon-rich sources (Schöier et al. 2007; Danilovich et al. 2018; Massalkhi et al. 2019, 2020). Moreover, in some oxygen-rich envelopes, the fractional abundance of SiS relative to H2 is as low as ~10−8, which is well below the predictions of chemical equilibrium (Danilovich et al. 2019; Massalkhi et al. 2020).


For the clustering measurements, we use the sample of galaxies compiled in Data Release 11 (DR11) of the SDSS-III project. The SDSS-III is a spectroscopic investigation of galaxies and quasars selected from the imaging data obtained by the SDSS (York et al. 2000) I/II covering about 11,000 deg2 (Abazajian et al. 2009) using the dedicated 2.5 m SDSS Telescope (Gunn et al. 2006). The imaging employed a drift-scan mosaic CCD camera (Gunn et al. 1998) with five photometric bands (

 and z; Fukugita et al. 1996; Smith et al. 2002; Doi et al. 2010). The SDSS-III (Eisenstein et al. 2011) BOSS project (Ahn et al. 2012; Dawson et al. 2013) obtained additional imaging data of about 3000 deg2 (Aihara et al. 2011). The imaging data was processed by a series of pipelines (Lupton et al. 2001; Pier et al. 2003; Padmanabhan et al. 2008) and corrected for Galactic extinction (Schlegel et al. 1998) to obtain a reliable photometric catalog. This catalog was used as an input to select targets for spectroscopy (Dawson et al. 2013) for conducting the BOSS survey (Ahn et al. 2012) with the SDSS spectrographs (Smee et al. 2013). Targets are assigned to tiles of diameter 3° using an adaptive tiling algorithm designed to maximize the number of targets that can be successfully observed (Blanton et al. 2003). The resulting data were processed by an automated pipeline which performs spectral classification, redshift determination, and various parameter measurements, e.g., the stellar-mass measurements from a number of different stellar population synthesis codes which utilize the photometry and redshifts of the individual galaxies (Bolton et al. 2012). In addition to the galaxies targeted by the BOSS project, we also use galaxies that pass the target selection but have already been observed as part of the SDSS-I/II project (legacy galaxies). These legacy galaxies are subsampled in each sector so that they obey the same completeness as that of the CMASS sample (Anderson et al. 2014).


Since it is infeasible to observe the evolution of individual galaxies over time, theoretical approaches focusing on understanding the formation of ETGs have made use of numerical simulations to trace the evolution of individual galaxies. Through zoom-in and cosmological simulations, a consensus has emerged between these simulations that the formation of ETGs proceeds through two phases, where galaxies first go through dissipative gas-rich wet mergers followed by in situ star formation bursts at redshifts above z ≈ 2, and then evolve towards low redshift through non-dissipative gas-poor dry mergers (Naab et al. 2007; Guo & White 2008; Hopkins et al. 2009; Nipoti et al. 2009b; Nipoti, Treu & Bolton 2009a; Oser et al. 2010; Johansson, Naab & Ostriker 2012; Moster, Naab & White 2013; Remus et al. 2013; Furlong et al. 2015; Wellons et al. 2015, 2016; Rodriguez-Gomez et al. 2016). However, regarding the redshift evolution of ETGs’ total power-law density slopes, no consensus has been reached neither among different cosmological hydrodynamic simulations nor between simulations and observations, despite the many advances in cosmological simulations (Vogelsberger et al. 2019a). While the Magneticum pathfinder simulation (Remus et al. 2017) and the Illustris simulations (Xu et al. 2017) produce shallower total density profile with time, the Horizon-AGN simulations (Peirani et al. 2019) produce steeper total density profile with time, in better agreement with the redshift evolution trend found in observations. However, the latter simulation has smaller slope values compared to the former two, which are closer to the observed slope values due to different implementation of feedback models, etc. Apart from cosmological simulations, dedicated zoom-in simulations (Johansson, Naab & Burkert 2009; Johansson et al. 2012; Remus et al. 2013) have revealed that dry mergers that dominate the passive evolution of ETGs below z ≈ 2 could make the total density profile shallower than isothermal (Hilz et al. 2012; Hilz, Naab & Ostriker 2013; Remus et al. 2017). The inclusion of wet mergers is also crucial for reconciling the simulated redshift evolution trend of the slope with strong-lensing observations (Sonnenfeld, Nipoti & Treu 2014).


On the basis of its unusual morphology and steep spectrum, we suggest that R1 traces the synchrotron radiation from a wind launched from the accretion flow around the SMBH. Known as the ADAF wind, such an energetic outflow is a generic prediction by theories and numerical simulations of hot accretion flows in LLAGNs (Blandford & Begelman 1999; Yuan et al. 2012a, 2012b, 2015). Originating from the corona region of the hot accretion flow, the ADAF wind would have a wide opening angle compared to the highly collimated jet, thus more naturally matching the observed radio morphology. Relativistic electrons responsible for the synchrotron may be produced in the corona of ADAF, where frequent magnetic reconnection is expected to occur (Yuan et al. 2009). Alternatively, relativistic electrons may be produced via the outward propagating wind shocking the circumnuclear medium over a region of 10 pc, corresponding to ∼4 × 107Rs (here

 is the Schwarzschild radius of the putative SMBH). To our knowledge, there has been no dedicated theoretical effort to predict the observational signatures of an ADAF wind on relevant physical scales. Here we shall provide a simple estimate of the energetics related to the radio emission. First, we notice that the radiative efficiency of an ADAF (

) at highly sub-Eddington rates scales roughly with the net mass accretion rate (i.e., the mass inflow rate into the event horizon) as

 (Xie & Yuan 2012), where Lbol is the bolometric luminosity of the SMBH and

 is the Eddington accretion rate. Assuming that the 2–10 keV luminosity of X1 (

) is 10% of the bolometric luminosity, and adopting a canonical value of δ = 0.5, the fractional viscous heating of electrons in the ADAF,11

11
See Xie & Yuan (2012) for discussions about this parameter; adopting a smaller value of δ would result in a higher

.
 we may infer

. Numerical simulations show that the ADAF wind carries a kinetic energy of

 (Yuan et al. 2015), which is then

 according to the above estimate. This value is sufficient to account for the observed synchrotron radiation, given that typically 1% of the kinetic energy goes to shock-accelerating relativistic electrons (Nims et al. 2015). The ADAF wind may also have produced soft X-ray emission upon shock-heating the circumnuclear medium. We note that the observed 0.5–2 keV luminosity from X1 (

; Y15) is compatible with the estimated wind kinetic energy.


Even if non-accreting millisecond pulsars are unaffected by α-oscillations, some NSs in LMXBs (accreting millisecond pulsars), which are attached to sharper peaks centred at higher temperatures, still can be unstable with respect to α-oscillations and thus should exhibit them. To check this possibility, we need more X-ray observations with high temporal resolution that can be achieved by future missions such as LOFT (Feroci et al. 2012), NICER (Gendreau, Arzoumanian & Okajima 2012) and SRG (Merloni et al. 2012). Another opportunity to detect α-oscillations can be associated with the recently discovered transitional millisecond pulsars, which are switching between rotation- and accretion-powered states [currently, three of such objects are known: PSR J1023+0038 (ν ≈ 592.4 Hz, Archibald et al. 2009; Stappers et al. 2014), IGR J18245−2452 (ν ≈ 254.3 Hz, Papitto et al. 2013), and XSS J12270−4859 (ν ≈ 593.0 Hz, Roy et al. 2015)]. In a rotation-powered state these NSs are observed as radio pulsars, giving a chance to study their timing properties precisely. The accretion-powered state guarantees that these pulsars cannot be too cold, and thus likely to be affected by r-mode instability and α-oscillations. For example, the redshifted surface temperature of PSR J1023+0038 can be as large as 5 × 105 K (Homer et al. 2006; Bogdanov et al. 2011). It corresponds to the internal temperature T∞ = (1.5–3) × 107 K, implying that PSR J1023+0038 can be on the stability peak. Its timing behaviour was reported as ‘complex’ by Archibald et al. (2013) and can be influenced by α-oscillations. The reliable registration of α-oscillations would confirm the crucial role of the resonance interaction of oscillation modes in the evolution of NSs in LMXBs (Gusakov et al. 2014a,b). The measurements of α-oscillation parameters (such as the period of oscillations, $\widehat{P}$) would provide us with a new powerful tool to constrain the properties of superdense matter.


Despite significant advances, the solar wind remains challenging to model (and importantly forecast) due to the large range of scales that need to be incorporated. It is well known that energy is injected into the corona at all scales, from magnetohydrodynamic (MHD) waves (Nutto et al. 2012; Van Doorsselaere et al. 2020) to flares and coronal mass ejections with global extent (Aschwanden et al. 2017; Green et al. 2018; Wyper et al. 2018). In addition to the range of spatial scales, heating events take place on a variety of timescales (Hollweg 1973; Viall & Klimchuk 2017). Putting aside large-scale eruptions so as to focus on the quasi-steady input of energy into the corona, it is possible to distinguish three broad magnetic configurations of the solar atmosphere for modelling purposes. These are the quiet Sun (Danilovic et al. 2010; Rempel 2014), active or enhanced regions (Carlsson et al. 2016; Chen et al. 2021), and coronal holes (Wójcik et al. 2019). In each of these configurations, energy is channelled from the convection into the low corona. Coronal holes are the dominant source of the solar wind in the heliosphere (Cranmer et al. 2017; Stansby et al. 2021), typically producing the fast solar wind (McComas et al. 2008; Ebert et al. 2009; Macneil et al. 2020a; Wang 2020). The magnetic field configuration of a coronal hole is relatively simple, compared with the quiet Sun and active regions, given that the field is principally open to the solar wind (Lowder et al. 2017; Hofmeister et al. 2019). However, there are still a range of dynamic processes taking place, such as the braiding of magnetic field lines (Wedemeyer-Böhm et al. 2012; Wedemeyer et al. 2013; Huang et al. 2018) and the emergence of new magnetic flux (Murray et al. 2009). These can trigger the formation of jets (Shen et al. 2017; Yang et al. 2017) and other phenomena, which are then observed as spicules (Martínez-Sykora et al. 2017; Bose et al. 2021) or fibrils (Hansteen et al. 2006; Leenaarts et al. 2015).


We have rigorously developed the embedded gravitational lensing theory for point mass lenses in a series of recent papers (Chen et al. 2010, 2011, 2015; Kantowski et al. 2010, 2012, 2013) including the embedded lens equation, time delays, lensing magnifications, shears, etc. We successfully extended the lowest-order embedded point mass lens theory to arbitrary spherically symmetric distributed lenses in Kantowski et al. (2013). The gravitational correctness of the theory follows from its origin in Einstein’s gravity. The embedded lens theory is based on the Swiss cheese cosmologies (Einstein & Straus 1945; Schücking 1954; Kantowski 1969). The idea of embedding (or Swiss cheese) is to remove a co-moving sphere of homogeneous dust from the background Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology and replace it with the gravity field of a spherical inhomogeneity, maintaining the Einstein equations. In a Swiss cheese cosmology the total mass of the inhomogeneity (up to a small curvature factor) is the same as that of the removed homogeneous dust sphere. For a galaxy cluster, embedding requires the overdense cluster to be surrounded by large underdense regions often modeled as vacuum. For a cosmic void, embedding requires the underdense interior to be “compensated” by an overdense bounding ridge, i.e., a compensated void (Sato & Maeda 1983; Bertschinger 1985; Thompson & Vishniac 1987; Martínez-González et al. 1990; Amendola et al. 1999; Lavaux & Wandelt 2012). A low-density region without a compensating overdense boundary, or with an overdense boundary not containing enough mass to compensate the interior mass deficit, has a negative net mass (with respect to the homogeneous background) and is known as an “uncompensated” or “undercompensated” void (Fillmore & Goldreich 1984; Bertschinger 1985; Sheth & van de Weygaert 2004; Das & Spergel 2009).3

3
This dichotomy between compensated and uncompensated voids is slightly different from one based on the classification of the small initial perturbations from which voids are thought to be formed. The initial perturbation can be compensated or uncompensated, which leads to different void growth scenarios (Bertschinger 1985), but if the evolved void formed from either perturbation is surrounded by an overdense shell that “largely” compensates the underdense region (i.e., the majority of the void mass is swept into the boundary shell in the snowplowing fashion when the void is growing), we still call it compensated because the small mass deficit originating in the initial perturbation is unimportant for gravitational lensing.
 Similarly, an overcompensated void has positive net mass with respect to the homogeneous FLRW background. Numerical or theoretical models of over-or undercompensated voids do commonly exist (e.g., Sheth & van de Weygaert 2004; Cai et al. 2010, 2014; Ceccarelli et al. 2013; Hamaus et al. 2014). We focus on compensated void models in this paper, given that uncompensated void models do not satisfy Einstein’s equations. The critical difference between an embedded lens and a traditional lens lies in the fact that embedding effectively reduces the gravitational potential’s range, i.e., partially shields the lensing potential because the lens mass is made a contributor to the mean mass density of the universe and not simply superimposed upon it. At lowest order, this implies that the repulsive bending caused by the removed homogeneous dust sphere must be accounted for when computing the bending angle caused by the lens mass inhomogeneity and legitimizes the prior practice of treating negative density perturbations as repulsive and positive perturbations as attractive. In this paper we investigate the gravitational lensing of cosmic voids using the lowest-order embedded lens theory (Kantowski et al. 2013). We introduce the embedded lens theory in Section 2, build the simplest possible lens model for a void in Section 3, and study the lensing of the CMB by individual cosmic voids in Section 4. Steps we outline can be followed for many void models of current interest.


The TESS light curves present the best cadence of the datasets available for CR Cha. They cover 56 days. The 2019 TESS light curve (Fig. 1, middle panel), taken with a 30 min cadence, reveals both periodic and stochastic variations with a peak-to-peak amplitude of ∼0.04 mag. In order to find periodic signals in these photometric data, we computed the Lomb-Scargle periodogram (Lomb 1976; Scargle 1982), which is shown in the bottom panel of Fig. 1. The periodogram resulted in significant peaks at 2.314 ± 0.033 days and 1.156 ± 0.009 days. An analysis of the more recent TESS light curve taken with a 10 min cadence between 2021 April and June (Fig. 2), obtained with the same analysis technique as for the 2019 data (see Sect. 2.3), confirms the presence of these two peaks. The peak at 2.314 days is consistent with the stellar rotational period found in previous studies (P = 2.3 days; Bouvier et al. 1986), suggesting the presence of starspots on the stellar surface. The 1.156-day period is half the stellar rotational period. The TESS light curve also indicates a long-term oscillation with a timescale of ∼25 days, but the time coverage of our dataset is not long enough to probe these longer timescales. Robinson et al. (2021) modeled the effect of inclination on how periodic a light curve appears. They found that higher inclinations lead to more burst-dominated light curves. The moderate 31° inclination of CR Cha indicates that the light curve is expected to be not purely periodic. We were able to detect a rotational period in our analysis of the light curve, but at the same time, additional effects, such as accretion variation and flares also significantly contribute to the observed light curve. The TESS light curve shows a few flare-like events as well, indicated by the blue points in the middle panel of Fig. 1. During the 56-day-long TESS observing period in 2019, we found five flares with durations ranging from 3.8−7.2 h, which gives a flare rate of 0.09 days−1. However, these were events showing ∼0.02 mag brightening.


In the σ0–SFR plane, local (U)LIRGs and high-z galaxies tend to occupy the same region, regardless of their intrinsic difference in terms of morphology, gas fraction and starburstiness. In order to distinguish between normal MS and SB galaxies, we show in Fig. 7, bottom, the velocity dispersion σ0 normalised to σ0, MS (solid line in the top panel; Übler et al. 2019) as a function of the starburstiness δMS = sSFR/sSFR|MS for all targets already reported in the previous panels. The sSFR|MS is derived from the Speagle et al. (2014) relation, starting from the available stellar mass measurements from the literature for Johnson et al. (2016), Förster Schreiber et al. (2018), Molina et al. (2020), Cochrane et al. (2021), and KMOS3D individual targets; stellar masses of LIRGs and ULIRGs from this study, from Bellocchi et al. (2013), Pereira-Santaella et al. (2019) and Crespo et al. (2021), are instead derived from the dynamical mass estimates, assuming M* = (1 − fgas)×(1 − fDM)×Mdyn, where fgas and fDM are the gas and dark matter fractions4, respectively, and Mdyn is the dynamical mass within 2Re (see next section). For the gas fraction, we considered a conservative fgas = 0.1 (Isbell et al. 2018; higher fgas values would further increase their δMS). This gas fraction is consistent with the estimate we obtain considering the molecular gas mass inferred by ALMA data (Paper II; Lamperti et al., in prep.) and the M* measurements available for a few PUMA targets (see Table 2),

f

¯

gas

=
0.11
±
0.05

$ {\bar{f}}_{\mathrm{gas}} = 0.11 \pm 0.05 $

. For the dark matter fraction (within 2Re) we assumed fDM = 0.26, defined as 1 − Mbar/Mdyn, with Mbar = M* + Mgas = M*/(1 − fgas). The fDM estimate was derived for the PUMA and Johnson et al. (2016) SB galaxies for which stellar masses are available, and considering the dynamical masses within 2Re (see Sect. 3.7). Because of these assumptions, we considered a factor of 3 uncertainties for the stellar mass measurements of (U)LIRGs. These uncertainties, however, play a minor role in the derived δMS: at low z, the MS has a soft slope, and normal and massive MS galaxies have similar SFRs (e.g. at z ∼ 0.1, galaxies of 1010 and 1011 M⊙ have SFR|MS ∼ 1 and ∼3.5 M⊙ yr−1, respectively); on the other hand, local (U)LIRGs have much higher SFRs, from 10 s to 100 s M⊙ yr−1, and therefore δMS of the order of 10 − 100. Finally, for the Alaghband-Zadeh et al. (2012) and Harrison et al. (2012) high-z galaxies we assumed that M* = 1011 M⊙, following Harrison et al. (2012).


Regardless of the process or combination of processes responsible for generating the emission, the kinetic energy of the returning debris must eventually be dissipated in order to be observed. Even if some energy is deposited by circularization at large distances (Piran et al. 2015), the energy will be primarily dissipated by processes that operate closest to the black hole simply because the velocities there are the greatest. However, this would imply that most of the radiation would be emitted at very high energies (X-rays), and instead we observe many TDEs with significant (and sometimes dominant) optical/UV flux. A reprocessing layer, either static or outflowing (Miller 2015; Metzger & Stone 2016), can help explain the observed emission by reprocessing the luminosity generated by the various dissipation processes at play (Loeb & Ulmer 1997; Ulmer et al. 1998; Bogdanović et al. 2004; Guillochon et al. 2014; Jiang et al. 2016; Coughlin & Begelman 2014; Strubbe & Quataert 2009). The reprocessing of the radiation has also been used to successfully explain the line ratios observed in PS1-10jh (Gaskell & Rojas Lobos 2014; Roth et al. 2016). In this work we assume a simple blackbody photosphere for the reprocessing layer, so that the observed flux becomes
8

with an effective blackbody temperature
9

In the above equations, Fν is the specific flux, Rphot is the photospheric radius, D is the distance from the source, L is the bolometric luminosity from our fit, and Teff is the temperature of the photosphere. Most observations of TDEs have thermal temperatures that do not exhibit significant variation. For blackbody emission, the radius must increase as the luminosity (and

) increases and decrease as the luminosity decreases, in order for the temperature not to change significantly as the luminosity evolves. This simple behavior also explains the rise in temperatures at late times as the photospheric radius decreases and the bulk of the observed radiation shifts to higher energies. To model this dependence, we assume that the radius of the photosphere has a power-law dependence on the luminosity and fit for both the power-law exponent l and radius normalization Rph0,
10

Here ap is the semimajor axis of the accreting mass at peak

. This provides a reasonable typical scaling for the radius of the photosphere, with a minimum photosphere size set by Risco and a maximum photosphere size set by the semimajor axis of the accreting mass.


Feature VY may not be a dusty clump in the same sense as the other features since it has a significant flux contribution from the star. In our model, VY is modeled as dusty medium of a Gaussian density distribution centered on VY CMa and uniformly surrounding the star, as in an idealized spherical outflow. Alternatively, however, it could be a clump located in front of or behind the star and seen along the same line of sight. In our implementation, we clear the central space of dust within a radius of 90 AU (equivalent to a diameter of

0

.
″

15

$ 0{{\overset{\prime\prime}{.}}}15 $

) where solids would be too warm to exist heated by the cool but very luminous star. The peak surface brightness simulated with a beam of 152 mas are 34 and 140 mJy beam−1 in Bands 6 and 7, respectively. Of that, 13.0 and 30.1 mJy beam−1 comes from the blackbody radiation of the model star. O’Gorman et al. (2015) noted that stellar fluxes are underestimated in a blackbody model at millimeter and submillimeter wavelengths owing to the unaccounted presence of an extended radiophotosphere. We extrapolated fluxes expected from their radiophotosphere model getting 12 mJy in Band 6 and 44 mJy in Band 7. Given the small difference with our assumed blackbody fluxes and uncertainties in the radiophotosphere model of O’Gorman et al. (2015), we did not correct our model for this effect. We required 0.014 M⊙ of dust to explain the observed fluxes which is rather large compared to most other clumps (except C). The stellar contribution partially explains the very low spectral index of 1.7 toward VY because the stellar spectrum is expected to have α ≈ 2 (Lipscy et al. 2005). At the modeled parameters of VY, the medium must be very thick at visual light and obscure the stellar photosphere from a direct view for a terrestrial observer, as visual observations indeed seem to indicate. The stellar photosphere and its light variations are seen mainly through light scattered in the surrounding medium with a high degree of inhomogeneity (Humphreys et al. 2005).


Small grains, which contribute most to infrared emission, are removed by collisional fragmentation and blown out by radiation pressure. The removal timescale is much shorter than the ages of host stars. Disruptive collisions among underlying large bodies, which are called planetesimals, produce smaller bodies and collisional fragmentation among them results in even smaller bodies. This collisional cascade continues to supply small grains. The evolution of debris disks has been explained by the steady-state collisional cascade model (e.g., Wyatt 2008; Kobayashi & Tanaka 2010): the total mass of bodies decreases inversely proportional to time t. Therefore, the excess ratio (Fdisk/F∗) is given by (2)\begin{equation} \frac{F_{\rm disk}}{F_{*}} = \frac{t_0}{t},\label{cc} \end{equation}FdiskF∗=t0t,where t0 is the dissipation timescale that is determined by the collisional cascade. Under the assumption of the steady state of collisional cascade, the power-law size distribution of bodies is analytically obtained and the power-law index depends on the size dependence of the collisional strength of bodies (see Eq. (32) of  Kobayashi & Tanaka 2010). In the obtained size distribution, erosive collisions are more important than catastrophic collisions (see Fig. 10 of Kobayashi & Tanaka 2010). Taking into account the size distribution and erosive collisions, we derive t0 according to the collisional cascade (see Appendix E for derivation), (3)\begin{eqnarray} t_0&\sim& 1.3 \left( \frac{s_{\rm p}}{\rm 3000\,km} \right)^{0.96} \left( \frac{R}{\rm 2.5\,au} \right)^{4.18}\nonumber\\ &&\quad\times \left(\frac{\Delta R}{0.4 R}\right) \left( \frac{e}{\rm 0.1} \right)^{-1.4} {\rm Gyr},\label{eq:t0} \end{eqnarray}t0~1.3sp3000 km0.96R2.5 au4.18where sp is the size of planetesimals, R is the radius of the planetesimal belt, and e is the eccentricity of planetesimals. Interestingly, t0 is independent of the initial number density of planetesimals (Wyatt et al.  2007). Note that the perturbation from Moon-sized or larger bodies is needed to induce the collisional fragmentation of planetesimals (Kobayasi & Löhne 2014), which is implicitly assumed in this model.


Molecular clouds can be formed either directly from neutral medium or by assembling pre-existing, cold molecular clumps. The first scenario is commonly accepted (e.g., Hollenbach & McKee 1979). The second scenario is outlined by Pringle et al. (2001), who proposed that clouds formed out of pre-existing, CO-dark, molecular gas. Compared to the first scenario, the second scenario allows for fast cloud formation in a few Myr, which was suggested by observations (Beichman et al. 1986; Lee et al. 1999; Hartmann et al. 2001). The key problem for the second evolutionary scenario is how molecular gas can exist before it is collected together. Pringle et al. (2001) argued that the pre-existing molecular gas should be cold (10 K) and was shielded from photodissociation by patch dust with AV of ~0.5 mag (White et al. 1996; Berlind et al. 1997; González et al. 1998; Keel & White 2001). Under AV of ~0.5 mag, H2 should exist substantially while CO is in very low abundance. This is because the self-shielding threshold of AV = 0.02 and 0.5 mag (Wolfire et al. 2010) are widely considered as a condition for maintaining a stable population of abundant H2 and CO gas, respectively. Listz & Pety (2012) detected strong CO(1−0) emission (4−5 K) in regions with equivalent visual extinction less than 0.5 mag. Two obvious possibilities are 1) the CO gas is transient. Such gas may also have been seen in Goldsmith et al. (2008), who detected a 40% of the total CO mass in Taurus in regions with low to intermediate AV (mask 0 and 1 in their terminology). 2) Such CO gas lies in a highly clumpy medium with lower apparent averaged extinction when photons travel through lower density interclump medium. When small agglomerations of molecular gas are compressed and heated by shock, e.g., in a spiral arm, they become detectable. This scenario is supported by observations of GMC formation in spiral arms (Dobbs 2008) and simulations of molecular clouds formation (e.g., Clark et al. 2012).


UGC 4284 is classified as Scd(s) in the RC3 (de Vaucouleurs et al. 1991), and as SABc by Paturel et al. (2003). Kandalian & Kalloghlian (1998), Chapelon, Contini & Davoust (1999), and Cabrera-Lavers & Garzón (2004) found evidence of a central isophotal distortion that they explain postulating the existence of a bar with diameter of 38 arcsec. Other authors did not confirm the presence of a bar in UGC 4284, nevertheless they encountered non-circular and off-plane gas motion in the inner region of UGC 4284 that they discuss as originated by a warped gaseous disc (Coccato et al. 2004; Józsa 2007). Bearing in mind the purpose of the present study, it is important to determine which kind of baryonic components do actually exist for UGC 4284, and given the incongruity of the above-reported results we required to perform 2D isophotal analysis of the surface brightness of this galaxy, using galfit (Peng et al. 2002, 2010) and considering at least three principal components: disc, bulge, and bar. UGC 4284 has been observed with Hubble Space Telescope (HST) in the filters F555W (WFPC2 V), F814W (WFPC2 wide I), and F606W (WFPC2 wide V), none the less the filters F555W and F814W show only a small part of the periphery of the galaxy. In contrast the filter F606W exhibits a larger portion of the disc of UGC 4284, so we use that filter to decompose the disc of UGC 4284. The results of the 2D exponential disc fit are presented in Table 1. In the case of UGC 4284, we also examined the possibility of a bulge and a bar components given the inconsistency in the morphological classification of this galaxy. We use the Spitzer IRAC 4.5 μm image because UGC 4284 is indiscernible in the 2MASS J, H, K bands, and in all the SDSS filters are too faint to allow an obvious separation from the background. Neither the Sérsic component nor the Ferrers (Ferrers 1877) component produces acceptable fit parameters to reveal the presence of a bulge and a bar, and for this reason we conclude that UGC 4284 has only an exponential disc component in total agreement with the RC3 classification.


The idea of ionized material arising from solar flares and causing geomagnetic storms appears to date from around the 1930s (Hale 1931; Dellinger 1937; Newton 1939, 1943; Chapman 1950) and the idea persisted into the space age, where interplanetary shocks were attributed to being caused by flares (e.g., Sonnet et al. 1964; Gosling et al. 1968). By the 1970s, however, some workers had begun to express doubts that solar flares could be the source for interplanetary shocks, geomagnetic storms, and, after their discovery (Tousey 1973), CMEs observed by coronagraphs. Evidence against the flare being the source included: the absence of a 1:1 relationship between geomagnetic storms and flares (e.g., DeMastus et al. 1973; Gosling et al. 1974; MacQueen 1980; Joselyn & McIntosh 1981); the energy required to launch the mass ejection was much larger than that of the flare (e.g., MacQueen 1980; Webb et al. 1980); the location of the flare being at only one footpoint of the larger expanding structure (Harrison & Simnett 1984; Simnett & Harrison 1984, 1985); the lack of correlation between the time of the projected onset of the CME and that of the flare (Harrison et al. 1985, 1990; Harrison & Sime 1989); and a lack of lateral movement of the expanding bright front as its leading edge expanded outwards (Sime et al. 1984). These and other measurements were presented in a review paper by Kahler (1992) and another by Gosling (1993a), the latter now well known as the “solar flare myth” paper. In that paper, flares are described as being either connected to CMEs via a common primary physical process (labeled in his Figure 16 as “evolving solar magnetic fields”), or as being caused by the CME launch. By around 1996 Gosling’s “modern paradigm” was widely accepted as the correct general physical model for CMEs. This picture has changed little in the last two decades, apart from perhaps the general acceptance that a magnetic flux rope is the driving core of a CME, although this too is an idea dating from before the space age (e.g., Morrison 1954; Cocconi et al. 1958; Gold 1959).


Both for the hydrodynamical and the synthetic simulations, a blind analysis was performed on the simulated images. First, surface-brightness profiles were extracted by computing the azimuthal median in concentric annuli. The profiles were then deprojected using a non-parametric onion-peeling technique (Kriss, Cioffi & Canizares 1983; McLaughlin 1999) and converted into radial density profiles. For the synthetic simulations, we found a very good agreement between the true and the reconstructed density profiles, in all of the situations considered here. Even when adding as many as 103 randomly distributed clumps in the simulated image, our method is able to recover the underlying density profile with an accuracy of a few per cent at all radii. The addition of significant triaxiality to the halo did not affect our results (in agreement with the findings of Buote & Humphrey 2012), and similar conclusions were reached for the inclusion of a filamentary structure. In the case of the hydrodynamical simulations, we show in Fig. 1 the average surface-brightness profiles (in arbitrary units) obtained using our azimuthal median method and with the standard azimuthal mean. We can see that the azimuthal median results in a much more regular profile, showing the expected smooth radial decline. In Fig. 2 we show the comparison between the average true 3D density profile in the sample of Vazza et al. (2011b) and the average profile obtained with our method through deprojection. On the same figure, we also show the same comparison in the case of one particularly perturbed cluster, E2 (see Vazza et al. 2011b). As shown in the bottom panel, the deviations are typically at the level of 10 per cent or less, even in the case of the very perturbed system E2, and do not show any particular trend with radius. A similar result is found for the integrated gas mass. This demonstrates the ability of our method to recover the true density profiles from X-ray observations in the presence of inhomogeneities.


NGC 2110. NGC 2110 is another nearby (z = 0.00779, Gallimore et al. 1999), X-ray bright Seyfert galaxy. Diniz et al. (2015) report a black hole mass of

2
.

7

−
2.1

+
3.5

×

10
8

M
⊙

$ 2.7^{+ 3.5}_{- 2.1} \times 10^{8}\,{{M}_{\odot}} $

, from the relation with the stellar velocity dispersion. From BeppoSAX data, Malaguti et al. (1999) found the X-ray spectrum to be affected by complex absorption. This has been later confirmed by Evans et al. (2007), who find the Chandra+XMM–Newton data to be well fitted with a neutral, three-zone, partial-covering absorber. Rivers et al. (2014) find the Suzaku data to be well fitted with a stable full-covering absorber plus a variable partial-covering absorber. A soft excess below 1.5 keV is also present (Evans et al. 2007), and possibly due to extended circumnuclear emission seen with Chandra (Evans et al. 2006). No Compton reflection hump has been detected with Suzaku (Rivers et al. 2014) or NuSTAR (Marinucci et al. 2015), despite the presence of a complex Fe Kα line. According to the multi-epoch analysis of Marinucci et al. (2015), the Fe Kα line is likely the sum of a constant component (from distant, Compton-thick material) and a variable one (from Compton-thin material). Concerning the high-energy cut-off, ambiguous results have been reported in literature (see Table 1). Ricci et al. (2017) report a value of

448

−
55

+
63

$ 448^{+63}_{-55} $

 keV, while Lubiński et al. (2016) report a coronal temperature of

230

−
57

+
51

$ 230^{+51}_{-57} $

 keV and an optical depth of

0
.

52

−
0.13

+
0.14

$ 0.52^{+ 0.14}_{- 0.13} $

. From 2008–2009 INTEGRAL data, Beckmann & Do Cao (2010) report a cut-off of ∼80 keV with a hard photon index, but these results are not confirmed by NuSTAR (Marinucci et al. 2015). Indeed, only lower limits to the high-energy cut-off have been found with NuSTAR (210 keV: Marinucci et al. 2015), Suzaku (250 keV: Rivers et al. 2014) and BeppoSAX (143 keV: Risaliti 2002). No hard X-ray spectral variability has been detected by Caballero-Garcia et al. (2012) and Soldi et al. (2014) from BAT data, despite the significant flux variability.


Figure 4(a) shows a time–latitude diagram of the subsurface toroidal flux density calculated by integrating the toroidal field over the range of 0.7–1.0R
⊙. The toroidal field is antisymmetric because the dipolar parity always prevails in our model. The latitudinal migration pattern of the toroidal field is different from that of FTD models, which usually show concentrated flux at high latitudes due to the radial shear in the polar portion of the tachocline. For each cycle, a weak toroidal field starts from high latitudes along with another overlapped branch of the previous cycle near the equator. With the equatorward migration of the toroidal field, its flux density increases as the cycle evolutes. This scenario is consistent with that of the solar cycle and the extended solar cycle (Howard & Labonte 1980; Wilson et al. 1988; McIntosh et al. 2014). Below 40° latitude, the toroidal flux density is larger than 2.5 × 1023 Mx Radian−1. Considering the spatial scale of a typical active region to be a few degrees, these fluxes are comparable with that in active regions. According to Cameron & Jiang (2019), the toroidal field at lower latitudes corresponds to the expected amount of flux residing in active regions. The weaker toroidal field at higher latitudes corresponds to ephemeral regions, which are small bipolar magnetic regions that contain a maximum total flux of the order of 1020 Mx (Harvey & Martin 1973). In Figure 4, the vertical dashed line represents cycle minimum (t
min) when the toroidal flux of the last cycle disappears, and vertical dotted line represents cycle maximum (t
max) when the toroidal flux of the new cycle reaches a maximum. The interval between t
min and t
max is 4 yr, which is close to the average period of the rising phase for solar cycles (Hathaway 2015; Jiang et al. 2018). The solid and dashed curves of Figure 5 show the time evolution of unsigned toroidal flux,

∫5090°∫0.7R⊙R⊙r∣Bϕ∣drdθ

, of each hemisphere for odd and even cycles, respectively. The cycle period is 10.96 yr based on the interval between successive maxima of the toroidal flux. This period is consistent with the average period of observed solar activity (Hathaway 2015). If the cycle period is calculated as the interval between the start and end of the toroidal flux of a cycle, then it is 18.1 yr. This result is consistent with approximately the 18–22 yr period of the extended cycle (Wilson et al. 1988). The maximum toroidal flux produced in one hemisphere is about 2.6 × 1023 Mx, which matches the observed magnetic flux at the solar surface (Cameron & Schüssler 2015).


ZTF J092311.41+423634.16 (ZTF J0923+4236), the fifth-most variable white dwarf within 200 pc according to our Gaia-ZTF ranking parameter, demonstrates multiple transit-like phenomena of varying durations and depths. The highest-resolved of these features at MJD ≈ 58450 closely resembles a mirror image of the dips observed for ZTF J0139+5245 (Vanderbosch et al. 2020): this object displays a gradual ingress and sharp egress, also contrasting the transit shapes of WD 1145+017 (Figure 6) and the K dwarf KIC 12557548 (Rappaport et al. 2012; van Lieshout et al. 2016). Unlike those in ZTF J0139+5245, the observed transits in ZTF J0923+4236 appear more incongruous and complex, repeating on irregular intervals with varying shapes. The dip at MJD ≈  58450 appears to have a secondary feature before the onset of the larger dip. This more complicated structure, which appears to be transiting on the order of days, implies ZTF J0923+4236 may be at an evolutionary stage in between WD 1145+017 (roughly 4.5 hr orbital period) and ZTF J0139+5245 (roughly 107 day orbital period). We followed up ZTF J0923+4236 with high-speed photometry on MJD  =  59138 and 59139, using the McDonald 2.1 m telescope to assess short-term variability, observing small amplitude variations on timescales of ≈1 hr (Appendix C). These observations, however, were constrained to less than two hours in length, due to the observing conditions. McDonald 2.1 m observations on MJD  =  59168 spanning 3 hr in length do not show this same possible short-term variability to within the 4〈A〉 significance threshold (Appendix C). We observe broad Balmer lines in a relatively low-resolution follow-up spectrum from HET (see Figure 7), and classify ZTF J0923+4236 as a DA white dwarf. The lack of emission lines disfavors cataclysmic variable activity as the cause of photometric variability, leaving transiting planetary debris as a likely explanation. Future monitoring is suggested to place stronger constraints on the source of these transit-like features and any metal pollution or circumstellar gas around this white dwarf.


Mapping out the distribution of dark matter in our Galaxy rests as a paramount task with potentially far reaching implications for astroparticle physics and cosmology. This is important to understand galaxy formation and to feed searches aimed at unveiling the very nature of dark matter. In particular, direct and indirect dark matter searches rely heavily on the findings of numerical simulations. It is therefore essential to extract the Galactic dark matter distribution directly from observations. In the outer Milky Way (at Galactocentric radii greater than ∼20 kpc), where baryons contribute little to the total mass budget, the gravitational potential traces closely the dark matter component and the total mass enclosed can be constrained using convenient tracers (e.g., Sakamoto et al. 2003; Dehnen et al. 2006; Xue et al. 2008; Bhattacharjee et al. 2014; Kafle et al. 2014), although with important degeneracies in the tracer population modeling. By contrast, in the inner Galaxy (i.e., in the inner ∼20 kpc) the baryonic contribution is very significant and its morphology rather uncertain, which makes the evidence for dark matter difficult to establish and the extraction of its distribution a delicate undertaking (Iocco et al. 2015). This has been addressed by many authors with different methods (e.g., Dehnen & Binney 1998; Sofue et al. 2009; Catena & Ullio 2010; Weber & de Boer 2010; Iocco et al. 2011; Bovy & Rix 2013; Nesti & Salucci 2013; Loebman et al. 2014), all of which do, however, make explicit assumptions about the underlying dark matter profile: typically, a multi-parameter profile is fitted to the observations together with a given baryonic component. The class of “local” methods to measure the dark matter density in the solar neighborhood (e.g., Salucci et al. 2010; Garbari et al. 2012; Smith et al. 2012; Zhang et al. 2013; Read 2014) avoids this bias, yet such methods are not easily applicable elsewhere in the Galaxy. An approach free of profile assumptions has been developed and successfully tested in external galaxies (Persic et al. 1996; Salucci et al. 2007), but never applied to our own Galaxy given the sizeable uncertainties of both kinematic data and baryonic modeling.


We use the state-of-the-art open-source stellar-evolution code Modules for Experiments in Stellar Astrophysics (mesa, Paxton et al. 2011, 2013, 2015, 2018, 2019) in order to investigate a broader range of rotational velocities and metallicities. Moreover, since very massive stars have been observed in the Tarantula Nebula (e.g. Doran et al. 2013) in the Large Magellanic Cloud (LMC), we consider stellar models with initial masses up to nearly 160 M⊙ (a factor of 1.3 larger than in Starburst99). Finally, we account for the fact that the majority of stars are born in binary systems (Sana et al. 2012, 2013). The observational evidence for such large binary fraction led to a paradigm change in our understanding of stellar evolution. As one (or both) of the stars in a binary system fill their Roche lobes, a phase of mass transfer takes place. Material is exchanged between the companions through the first Lagrangian point or lost by the system. The outermost layers of the donor are stripped off and eventually accreted on to the secondary star. This significantly alters the masses and spectroscopic appearances of the stars and generates evolutionary sequences otherwise unattainable in a single-star scenario (e.g. De Marco & Izzard 2017), influencing the mass-loss and the rotation rates of stars. In some cases, the interaction and mass exchange can be unstable, leading to merger events. Although numerous uncertainties still exist regarding the modelling of binary systems, it is becoming increasingly clear that more realistic estimates of stellar feedback cannot ignore the impact of stellar multiplicity. This applies also to radiative feedback as interacting binaries enhance the production of hydrogen- and helium-ionizing photons (e.g. Eldridge et al. 2017; Götberg, de Mink & Groh 2017) and harden the spectra of a stellar population (Götberg et al. 2019). Of particular interest are stripped helium stars, i.e. massive helium stars produced by binary interaction which emit the majority of their light at wavelengths shorter than the Lyman limit (Stanway, Eldridge & Becker 2016; Götberg et al. 2019) on a time-scale beyond few Myr.


However, recent work by Brook & Di Cintio (2015a, 2015b) used results from simulations in which stellar feedback processes alter the DM content of dwarf galaxies to show that they can simultaneously match the densities and velocities of observed dwarfs. In this scenario, feedback from stars and supernovae creates bursty star formation histories in dwarf galaxies that fluctuate the gravitational potential well at the center of the dwarf (Pontzen & Governato 2012, 2014; Teyssier et al. 2013; Chan et al. 2015; Oñorbe et al. 2015; Dutton et al. 2016). DM core creation leads to a better match between theory and observed rotation curves (Katz et al. 2017; Santos-Santos et al. 2017). Feedback is particularly effective in dwarf galaxies with halo masses of a few 1010

 (Governato et al. 2012; Di Cintio et al. 2014b), where it can transform an initially steep inner DM density profile into a flatter “cored” profile. At lower halo masses, there is less star formation, leading to less energy injection and lower core formation efficiencies (Peñarrubia et al. 2012; Maxwell et al. 2015). At higher masses, the deeper potential wells of galaxies make core formation increasingly difficult (Di Cintio et al. 2014b; Pontzen & Governato 2014), at least if an additional source of feedback is neglected, such as active galactic nuceli (AGN) (Martizzi et al. 2013). In this model with baryonic feedback, it is possible to assign dwarf galaxies to relatively massive halos, despite the low rotational velocities measured from their spatially resolved stellar kinematics. This is because baryonic feedback can push DM out of the central regions, lowering the enclosed mass at the radii that stellar kinematics probe (but without affecting the total halo mass8

8
Modulo a slight reduction in halo mass caused by the loss of baryons or preventive feedback (Munshi et al. 2013; Sawala et al. 2013).
). Hence, the densities are lowered, and the apparent velocities of the galaxies, reconciling the observations with theory.