Observed high mass end power-law index of the galaxy-wide IMF resulting from the calculated IGIMF, \hbox{$\alpha_3^{\mathrm{gal}}$}α3gal (i.e., αgal in Eq. (15) for m> 1 M⊙), for a constant SFR over δt = 10 Myr in dependence of the galaxy-wide SFR. In Fig. 5, \hbox{$\alpha_3^{\mathrm{gal}}$}α3gal values diverge for different SFRs and also vary for different m at the high mass end. As at each m value there exists a different \hbox{$\alpha_3^{\mathrm{gal}}$}α3gal–SFR relation, we plot solid lines for log 10(m/M⊙) = 0.2, 0.4, ..., 2, i.e., 1.58, 2.51, ..., 100 M⊙ from black to gray (top to bottom) for the fiducial model and dotted lines for the corresponding SolarMetal model defined in Sect. 2.1. The blue squares are data from the GAMA galaxy survey (Gunawardhana et al. 2011). The red triangles and red dash-dotted line are data from Weidner et al. (2013b); the left triangle is for the MW field, the middle three triangles are galaxy studies, the right triangle is for the bulges of the MW and M 31, and the dash-dotted line is their IGIMF model assuming β = 2. A recent study has suggested that the 2 M⊙/yr SFR for MW is overestimated (Chomiuk & Povich 2011), but we leave this data point the same as in Weidner et al. (2013b). Gargiulo et al. (2015) report consistency between their IGIMF model assuming β = 2 (thick yellow dashed line) and the [α/Fe] abundance ratios of elliptical galaxies. The purple diamond is an individual analysis for the dwarf galaxy NGC 2915 (Bruzzese et al. 2015). Green stars are based on the Lee et al. (2009) 11HUGS observations of dwarf galaxies. The black circle is an observation for the solar neighborhood from Rybizki & Just (2015) with adopted MW SFR from Robitaille & Whitney (2010) as an upper limit of the solar neighborhood SFR because the Sun is located in an inter-arm region where the relevant SFR is significantly smaller (toward the direction indicated by the arrow; see Sect. 4.6 for further details). The thin horizontal dashed line represents the canonical IMF index α2 = α3 = 2.3.


To constrain the size of outflows that we could have missed, we performed simple simulations. We placed artificial, unipolar secondary sources next to a primary point source model representing Sgr A* and compared the closure phases obtained from the resulting artificial visibility data with the observations. We considered two geometries: a single-point source and a jet composed of ten equally spaced point sources (knots) with equal fluxes. We probed four orientations for the simulated outflows (see Fig. 2): along the major axis, along the minor axis of the beam, the jet direction claimed by Li et al. (2013), and the jet direction claimed by Yusef-Zadeh et al. (2012). We used total fluxes of 0.2 Jy and 0.55 Jy for the artificial sources; these values ensure that our simulated outflows are sufficiently faint to not violate the constraints given by the known recent brightness evolution of Sgr A* (0.2 Jy from the mean variability of ≈15% from June 2013 to February 2014 at 41 GHz, with 0.55 Jy corresponding to the strongest variation in the same period, Chandler & Sjouwerman 2014). For each simulation setup, we measured the average of absolute values of the closure phases for each triangle. We varied the distances of the model sources (for the jet model: the largest distance) from Sgr A* until we found a critical distance at which the absolute values of the simulated closure phases exceeded those of the observations by more than the 1σ error at all triangles. We summarize our results in Table 1. As expected, the critical distances are smaller for brighter outflows. Jet-like structures lead to larger critical distances than equally luminous single, compact sources. As a consequence of the very elongated beam, the critical distances for sources located along the major axis of the beam are larger by a factor of ≈7 than for those located along the minor axis. In a few cases (denoted “N/A” in Table 1), the absolute values of the simulated closure phases were similar to those of the observations for all distances of the model sources, meaning that we were unable to identify a critical distance. Overall, our observations limit the extension of asymmetric (in the observer frame) jet-like outflows from Sgr A* to projected distances of ≈2.5 mas along the major axis and ≈0.4 mas along the minor axis.


There is good observational and theoretical evidence that supermassive black holes (SMBHs) exist in nearly every galaxy in universe. Understanding the properties of these SMBHs will clarify their roles in galaxy formation and evolution across the cosmology history (e.g. Kormendy & Ho 2013). There are mainly two parameters for an SMBH, i.e. mass (MBH) and spin, which need to be determined. For a few very nearby (100 Mpc) quiescent galaxies, including our Galaxy, SMBH masses can be measured through the stellar or gaseous dynamics method (e.g. Tremaine et al. 2002; McConnell et al. 2011). It has been found that nearby quiescent galaxies follow a tight correlation between the central SMBH mass and the bulge or spheroid stellar velocity dispersion (σ*), which is called MBH–σ* relation (e.g. Kormendy & Ho 2013). Active galactic nuclei (AGNs) can be classified into type 1 or type 2 AGNs, depending on whether the broad-line regions (BLRs) can be viewed directly. For type 1 AGNs, the BLR can be used as a probe of the gravitational potential of the SMBHs. The SMBH mass can be weighed through the BLR clouds for type I AGNs across cosmos time. The SMBH masses in type I AGNs can be calculated as follows (e.g. Kaspi et al. 2000; Bian & Zhao 2002; Peterson et al. 2004; Collin et al. 2006; Du et al. 2016a; Yu et al. 2019):
(1)$$\begin{eqnarray*}
M_{\rm BH} =f_{\rm BLR}\frac{R_{\rm BLR}~(\Delta V)^2}{G},
\end{eqnarray*}$$where G is the gravitational constant. RBLR is the distance from black hole to the BLRs, and can be estimated from the reverberation mapping (RM) method (e.g. Blandford & McKee 1982; Peterson 1993). ΔV is the velocity of the BLR clouds, and usually traced by the full width at half-maximum (FWHM) or the line dispersion (σH β) of the broad H β emission line. fBLR is a virial factor to characterize the kinematics, geometry, and inclination of the BLR clouds. Using the MBH–σ* relation, we recently did the calibration of fBLR and found $f_{\rm BLR} \propto \rm FWHM^{-1.11}$ when FWHM(H β) is used as the tracer of ΔV in equation (1) (Mejia-Restrepo et al. 2018; Yu et al. 2019). It is consistent with the results by the BLR dynamical model to fit simultaneously the AGNs continuum/H β light curves and H β line profiles (e.g. Li et al. 2018; Pancoast et al. 2018; Williams et al. 2018).


Based on previous works (Kawamuro et al. 2013; Tazaki et al. 2013), we start with a base-line model,

in the XSPEC terminology. This model includes absorbed primary X-ray emission (i.e., a cut-off power law), a scattered component, and a reflection continuum from distant cold matter accompanied by a narrow iron-Kα line. Optically thin thermal emission from the host galaxy (apec in XSPEC) and other emission/absorption lines (zgauss) are also added if they are significantly required with a confidence level above 90% in terms of Δχ2. Because it is difficult to determine the cut-off energy from our data, we fix it at 300 keV, which is a typical value measured in nearby AGNs (Dadina 2008). The first constant factor, NXIS, is applied to the primary power-law component in the Suzaku spectra to absorb possible time variability between the Suzaku (one epoch) and Swift/BAT (averaged for 70 months) observations. The second constant term represents the scattered fraction, fscatt. As a reflection component from the torus, we employ the pexrav model, which calculates a reflected spectrum from an optically thick slab with a solid angle of Ω irradiated by a point source (Magdziarz & Zdziarski 1995). We set the reflection strength, R = Ω/2π, as a free parameter, and fix the inclination angle at 60°. It is confirmed that even if 30° is adopted, best-fit parameters do not significantly change. The shape of the incident spectrum is assumed to be the same as the power-law component. We basically assume that the reflection and scattered components did not vary between the Suzaku and Swift/BAT observations, considering that the size of the reflector most likely has a parsec scale. In the three low-mass LLAGNs (NGC 4395, NGC 5273, and NGC 5643), however, we assume that the reflection component varied in accordance with the primary emission because of a smaller size of the emitting regions. Thus, in these targets, R is defined with respect to the primary component in the Suzaku data. The zgauss component represents an iron-Kα fluorescence line. The line width is fixed at 20 eV, which corresponds to a typical velocity dispersion of ∼2000 km s−1 measured with Chandra/HETGS in local Seyfert galaxies (Shu et al. 2010). We always consider the Galactic absorption

, which is calculated with the nh command (Kalberla et al. 2005) in FTOOLS.


A substantial fraction of metal-poor stars that have recently evolved off the MS, e.g., giants and planetary nebulae (PNe), have been influenced by binary interactions. The IMF is significantly weighted toward low-mass stars (Bastian et al. 2010; Kroupa et al. 2013), and the MW star formation rate was ≈3 times larger ≈10 Gyr ago than it is now (Governato et al. 2007; De Lucia et al. 2014). Based on the measured IMF and modeled galactic star formation history, we estimate that ≈55% of MW giants and PNe have old, solar-type progenitors (τ* > 7 Gyr, M ≈ 0.8–1.2

). Such old, low-mass giants tend to be metal-poor (Ratnatunga & Yoss 1991; Carollo et al. 2010; Mackereth et al. 2017). The metallicity trend therefore dramatically affects the properties of low-mass evolved stars. For example, the enhanced close binary fraction of metal-poor solar-type stars substantially strengthens the conclusion that the shaping of PN morphologies is the result of binary interactions (Moe & De Marco 2006; De Marco 2009; Jones & Boffin 2017). Providing further corroboration, Badenes et al. (2015) measured the delay-time distribution of bright PNe in the LMC and discovered two distinct populations of PN progenitors: an old channel (τ* = 5–8 Gyr) deriving from solar-type stars (M ≈ 1.0–1.2

) and a young channel (35–800 Myr) evolving from late-B/early-A stars (≈2–8

). According to the measured age–metallicity relation of the LMC (Olszewski et al. 1991; Pagel & Tautvaisiene 1998; Cole et al. 2005; Carrera et al. 2011; Piatti & Geisler 2013), the old, solar-type progenitors are metal-poor ([Fe/H] ≲ −1.0) and hence have a large close binary fraction of Fclose = 40%–50%. The young progenitors have a higher metallicity of [Fe/H] ≈ −0.4 but are sufficiently massive so that they also have a large close binary fraction of Fclose = 40%–60%. Meanwhile, evolved stars with intermediate masses (M ≈ 1.2–2.0

) in the LMC have intermediate metallicities and therefore a smaller close binary fraction of Fclose ≈ 30%. If PNe derive from interactions in close binaries, then the variations in Fclose with respect to mass and metallicity can explain the observed bimodal mass/age distribution of PN progenitors in the LMC.


We suggest that the jet–facula collision does not cause a change in the field-line connectivity and only leads to the redistribution of jet material. There are two main reasons supporting this viewpoint. The first is the 3D magnetic configuration at the collision region. The penumbra and facula are both located at negative-polarity magnetic fields and the relative orientation of the two flux systems is nearly parallel (Fig. 5). When the magnetic field lines are parallel it is not easy to have reconnection (Feynman & Martin 1995; Galsgaard et al. 2007). As suggested by Gopalswamy et al. (2009), there are two possibilities during the CME–CH interaction. When the magnetic fields in the CME and the CH are parallel, deflection of the CME takes place. When the CME field lines are antiparallel to the CH field lines, magnetic reconnection is possible. In our event, the jet–facula collision is similar to the first situation of CME–CH interaction. The second reason is the absence of reconnection signatures. The jet–facula collision does not produce any impulsive brightenings in the collision region in the H α and EUV images. Although RFJ was heated after the collision, the heating of RFJ is less intense and concentrated than the reconnection heating, and is probably caused by collision-induced conversion of kinetic energy to thermal energy. Due to the interaction of the primary FJs with the facula structure, the material of primary FJs is redistributed, with partial material propagating along the QSL fan plane and forming the AFJs. It is the apparent material end that differentiates the primary FJs and AFJs observationally. In the aspect of magnetic fields, the primary FJs and AFJs are along the same magnetic field lines from the sunspot. Direct observations of the jet–facula collision process and apparent fan-shaped jets are very rare. Thus it is difficult to give an exact physical explanation based on the present observations. If more related cases could be observed in future, we expect to be able to interpret in depth the physical mechanism of collision-induced apparent jets.


Gamma-ray bursts (GRBs) are among the most powerful gamma-ray sources in the universe. They could be generated from the merger of binary compact objects (BCOs; Duncan & Thompson 1992; Usov 1992; Thompson 1994; Metzger et al. 2011) or the death of massive stars (Woosley 1993; Paczyński 1998; Woosley & Bloom 2006a). The merger of BCOs; a black hole (BH)–a neutron star (NS) or NS–NS, leading to kilonovae (KNe), is correlated with short-duration gamma-ray bursts (sGRBs; T
90

10

10

T
90 is defined as the time during which the cumulative number of collected counts above background rises from 5% to 95%. ≲ 2 s; Li & Paczyński 1998; Rosswog 2005; Metzger et al. 2010; Kasen et al. 2013; Metzger 2017). On the other hand, long-duration gamma-ray bursts (lGRBs; T
90 ≳ 2 s; Kouveliotou et al. 1993) are associated with the core collapse (CC) of dying massive stars (Woosley 1993; Galama et al. 1998) leading to supernovae (SNe; Bloom et al. 1999; Woosley & Bloom 2006b). It is believed that in both scenarios large quantities of materials with a wide range of velocities are ejected. In the framework of CC-SNe (depending on the type of SN association), several materials ejected with sub-relativistic velocities less than β ≲ 0.4
11

11
Hereafter, we adopt natural units c = ℏ = 1. have been reported (see, e.g., Kulkarni et al. 1998; Bloom et al. 1999; Woosley & Bloom 2006b; Valenti et al. 2008; Gal-Yam 2017; Izzo et al. 2019, 2020; Modjaz et al. 2020; Nicholl et al. 2020). Regarding the merger of two NSs, sub-relativistic materials such as the cocoon, the shock breakout, and the dynamical and wind ejecta are launched with velocities in the range 0.03 ≲ β ≲ 0.8
12

12
Some authors have considered the shock breakout material in the sub-, trans-, and ultra-relativistic regimes (see, e.g., Kyutoku et al. 2014; Metzger et al. 2015; Fraija et al. 2019c). (see, e.g., Dessart et al. 2009; Metzger & Fernández 2014; Fernández et al. 2015; Kyutoku et al. 2014; Metzger et al. 2015; Nagakura et al. 2014; Murguia-Berthier et al. 2014; Lazzati et al. 2017, 2018; Goriely et al. 2011; Hotokezaka et al. 2013; Bauswein et al. 2013; Wanajo et al. 2014). While the mass and velocity inferred for the first GRB/KN association
13

13
GRB 170817A/AT 2017gfo. were M
ej ≈ (10−4−10−2)M
⊙ and β ≈ (0.1−0.3), respectively (Coulter et al. 2017; Arcavi et al. 2017; Cowperthwaite et al. 2017; Nicholl et al. 2017; Metzger 2019), the mass and velocity inferred for the first GRB/SN association
14

14
GRB 980425/SN1998bw. was M
ej ≈ 10−5
M
⊙ and β ≈ (0.2–0.3), respectively (Kulkarni et al. 1998).


HD 97048 is yet another disk for which the dust emission at (sub-)mm wavelengths shows evidence of axisymmetric ring-like structures, here on spatial scales of around tens of au (Walsh et al. 2014; ALMA Partnership et al. 2015; Andrews et al. 2016; Nomura et al. 2016; Zhang et al. 2016). We predict that this substructure will be clearly evident in images of HD 97048 at higher spatial resolution (≈10–20 au, see Figure 13). There remains much debate in the literature on the origin of such axisymmetric substructure in protoplanetary disks including gaps and dust traps carved by forming planets (see, e.g., Dipierro et al. 2015; Pinilla et al. 2015; Rosotti et al. 2016), a change in dust opacity properties at the positions of snow lines (e.g., Banzatti et al. 2015; Zhang et al. 2015; Guidi et al. 2016; Okuzumi et al. 2016), and toroidal dust traps created by hydrodynamic or magnetohydrodynamic effects (see, e.g., Pinilla et al. 2012b; Lorén-Aguilar & Bate 2015; Ruge et al. 2016). To distinguish between each of the scenarios requires observations of dust emission at multiple and well-separated frequencies to determine the radial dust size and density distribution (and dust opacity index) along with emission from optically thin gas tracers to determine the gas surface density. Planets will create deep gaps in the gas surface density as well as influencing the dust (note that this is dependent on the planet mass, see e.g., Rosotti et al. 2016), toroidal instabilities will create much shallower features in the gas surface density, and opacity changes at snow lines will affect only the dust emission and will have no effect on the gas. We note that the ringed substructure seen here has very recently been confirmed in scattered light images of HD 97048 taken with VLT/SPHERE (Ginski et al. 2016). An initial (and shallow) comparison of the data sets shows remarkable coincidence between the positions of the (sub-)mm peaks and gaps and those seen in scattered light. That such structure is seen in both small (≈μm-sized) dust grains in the disk atmosphere and large (≈mm-sized) dust grains in the disk midplane points toward a (proto)planetary system origin; however, further data, particularly to better constrain the gas structure, are needed for confirmation. Since this paper has been accepted for publication, ALMA Cycle 2 data of HD 97048, for which longer baseline data were available and imaged with a uv clip (>160 kλ), resulted in a beam of 048 × 026 (18°) and resolved the inner dust cavity (40 – 46 au) and the bright dust ring at ≈150 au (van der Plas et al. 2016).


In our model, we compute the tidal response of the oceans and the solid-Earth to luni-solar semi-diurnal forcing, both combined with mimetic continental drift driven by plate tectonics. We focus on the dependence of dissipation on the Earth’s spin rate. We combine two analytical approaches that describe long-wavelength barotropic tidal flows over shallow spherical and hemispherical shells. The spherical shell describes a global ocean that we assume had existed in the earliest eons of the lifetime of the Earth (Motoyama et al. 2020). The existence of an early ocean is supported by evidence from the analysis of detrital zircon around 4.4 Ga (Wilde et al. 2001), from the interaction between the ocean and continental crust 4 billion years ago (Mojzsis et al. 1996), and from records of the oxygen isotope composition of seawater (Peck et al. 2001; Johnson & Wing 2020). The “globality” of this ocean is justified by the analysis of continental crust growth curves based on geochemical evidence in zircon crystallization ages (Dhuime et al. 2012; Hawkesworth et al. 2020). In compliance with these curves, we consider that a hemispherical oceanic shell has taken over in the most recent times. In our model, the center of this hemispheric continental cap follows the evolution of the paleogeographic center. In doing so, we emphasize on the role of “continentality” in the tidal response, while avoiding the under-sampling of geometric scenarios due to theoretical limitations (Hansen 1982; Tyler 2021) or due to uncertainties in plate tectonic models (Matthews et al. 2016; Daher et al. 2021). To compute this evolution, we adopt the recently developed paleogeographic reconstructions that cover the past billion years (Merdith et al. 2021). A postprocessing of these reconstructions allows us to produce the latitudinal evolution of the center of the continental cap captured in Fig. 1. The tidal frequencies at which oceanic resonances are excited and the amplitudes of these resonances vary with the surface position of the hemispherical ocean (Fig. B.1). Super-continental formations and breakups thus have their mark on the predicted lunar recession rate.


Quiescent prominences are objects formed by relatively cool plasma in the hot corona. Their cool material occurs mostly in the dipped magnetic field lines. In quiescent prominences, which can persist from several hours to several days, magnetic dips form quasi-vertical structures called threads. Quiescent prominences are often observed as part of magnetic structures composed of three coronal patterns: the prominence itself, surrounded by a low-density cavity and a dense helmet streamer overlying the cavity (Engvold 1989). The disruption of the helmet streamer often signifies the beginning of a coronal mass ejection (CME) that can reflect the three-part structure of the helmet streamer (when observed in the white light): the bright leading shell surrounding a dark cavity in which bright prominence material occurs (Crifo et al. 1983; Hundhausen 1999). As the masses of CMEs are most often inferred from the visible-light observations, the masses given in literature are usually only the masses of the leading shell. However, Burkepile et al. (2004) also saw highly structured material most probably originating from a prominence in 63% of CMEs associated with eruptive prominences at the limb observed in visible light using the broadband filter (λλ 5000−5350 Å). Although such observations are called as white light in literature, it would be better to consider them as observations in visible light, because naturally integral intensities in the visible spectral range are observed including both continuum and absorption lines, while white light is just a continuum caused by Thomson scattering on free electrons without the lines. Thus, the presence of absorption spectral lines in visible light complicates very much the estimation of prominence mass, but even if the influence of absorption lines was eliminated, continuum alone only allows us to estimate the mass of ionised material, thus mass of the prominence would be underestimated. Low (1996) stated that the contribution of an erupting prominence to the total mass of CME is usually one order of magnitude less than that of the shell, but in some cases these contributions can be comparable. Low et al. (2003) proposed theoretically an importance of the prominence mass for the deposit of magnetic energy for driving a CME. Thus, developing methods for the estimation of the total mass of prominences can help to explain the connection between prominences and CMEs and provide an important quantity for more accurate estimation of total mass ejected by a CME.


Another possible explanation for the peculiar solar composition is that some of the dust in the pre-solar nebula was radiatively cleansed by luminous hot stars in the solar neighbourhood before the formation of the Sun and its planets. This dust-cleansing scenario is supported by the finding that the open cluster M67 seems to have a chemical composition closer to the solar composition than most solar twins (Önehag et al. 2011, hereafter O11 and Önehag, Gustafsson & Korn 2014, hereafter O14). They suggested that the proto-solar nebula was dust-cleansed by massive stars, similar to what happened for the proto-cluster cloud of M67, while the majority of solar twins in the field would presumably have formed in less massive clusters where no nearby high-mass star (≥15 M⊙) was formed. M67 offers the possibility for studying the solar-type stars in a dense cluster environment. This cluster has about solar metallicity ([Fe/H] in the range −0.04 to +0.03, e.g. Hobbs & Thorburn 1991; Yong, Carney & Teixera de Almeida 2005; Randich et al. 2006; Pasquini et al. 2008). The age of M67 is also comparable with that of the Sun: 3.5–4.8 Gyr (Yadav et al. 2008). Pasquini et al. (2008) listed 10 solar-twin candidates in M67, including M67-1194 which hosts a hot Jupiter with a period of 6.9 d and a minimum mass of 0.34 MJup (Brucalassi et al. 2014). M67-1194 was studied by O11 and re-visited by O14. They found that unlike nearby solar twins, which were systematically analysed by Meléndez et al. (2009) and Ramírez, Meléndez & Asplund (2009), the chemical composition of M67-1194 is more solar-like and therefore suggested that the Sun may have been formed in a similar cluster environment, perhaps even in M67. While this scenario is plausible when considering chemical abundances and ages, the dynamics are problematic: the Sun has an orbit close to the Galactic plane, while M67 is presently some 450 pc above the plane. The probability that the Sun, if formed in M67 with an orbit similar to the present cluster orbit, was scattered or diffused out of the cluster into the present solar orbit, is found to be quite low, if the existence of the outer planetary system is taken into account (Pichardo et al. 2012). Gustafsson et al. (2016) suggested that the high-altitude metal-rich clusters (such as M67) were formed in orbits close to the Galactic plane and later scattered to higher orbits by interaction with giant molecular clouds and spiral arms. Thus, it is possible, though not very probable, that the Sun formed in such a cluster before scattering occurred. Currently, only one solar twin in M67 (M67-1194) was spectroscopically analysed with high precision (∼0.02 dex). It is thus crucial to analyse the chemical composition of additional solar-type stars in M67 of very high precision.


With only six free parameters, the standard Λ cold dark matter (ΛCDM) cosmological model fits no less than 2500 multipoles in the cosmic microwave background (CMB) angular power spectrum (Planck Collaboration XVI 2014), the Hubble diagram of Type Ia supernovae, the large-scale structure matter power spectrum, and even the detailed scale of baryonic acoustic oscillations. It thus provides the current basis for simulations of structure formation, and is extremely successful down to the scale of galaxy clusters and groups. Nevertheless, it still faces numerous challenges on galaxy scales. Among these, the most important ones are the too-big-to-fail problem (Boylan-Kolchin, Bullock & Kaplinghat 2011) and the satellite-plane problem (e.g. Pawlowski, Pflamm-Altenburg & Kroupa 2012; Ibata et al. 2014) for dwarf galaxies, the tightness of the baryonic Tully–Fisher relation (McGaugh 2012; Vogelsberger et al. 2014), or the unexpected diversity of rotation curve shapes at a given mass scale (Oman et al. 2015). The latter problem is actually a subset of a more general problem, i.e. that the shapes of rotation curves indeed do not depend on the Dark Matter (DM) halo mass, contrary to what would be expected in ΛCDM, but rather on the baryonic surface density, as has long been noted (e.g. Zwaan et al. 1995). This makes the problem even worse, since the rotation curve shapes are not only diverse at a given mass scale, but uniform at a given baryonic surface density scale, implying a completely ununderstood fine-tuning of putative feedback mechanisms. On the other hand, this behaviour of rotation curves is an a priori prediction of the formula proposed by Milgrom more than 30 yr ago (Milgrom 1983a,b), relating the total gravitational field to the Newtonian field generated by baryons alone, and which can be interpreted as a modification of Newtonian dynamics on galaxy scales below a characteristic acceleration (Modified Newtonian Dynamics (MOND), for a review see Famaey & McGaugh 2012; Milgrom 2014). With this simple formula, high surface brightness (HSB) galaxies are predicted to have rotation curves that rise steeply before becoming essentially flat, or even falling somewhat to the not-yet-reached asymptotic circular velocity, while low surface brightness (LSB) galaxies are predicted to have rotation curves that rise slowly to the asymptotic velocity. This is precisely what is observed, and was predicted by Milgrom long before LSB galaxies were even known to exist. The formula also predicts the tightness of the baryonic Tully–Fisher relation.


Figure 9 summarizes our constraints on the molecular gas mass fraction in the analyzed samples of galaxies. In order to convert CO luminosity to molecular gas mass, we consider two different assumptions for αCO. First, we assume a constant value of αCO = 3.6 M⊙ (K km s−1 pc2)−1 adopted by some previous studies (e.g., Daddi et al. 2010b; Decarli et al. 2014; Walter et al. 2016). We then also consider a metallicity-dependent conversion factor, evaluated by assuming a redshift and stellar mass–metallicity relation (Genzel et al. 2015). Previous studies investigating optically and FIR-selected galaxy samples have estimated the relationship between gas mass fraction, stellar mass, redshift, and SFR offset from the main sequence (e.g., Genzel et al. 2015; Scoville et al. 2017). While the PHIBSS project estimated molecular gas masses by measuring the CO(3–2) line emission (Tacconi et al. 2013; Genzel et al. 2015), Scoville et al. (2016, 2017) used the flux on the Rayleigh–Jeans tail of the dust continuum emission to estimate the total gas masses. We here assume that the samples of galaxies plotted, although not complete to any degree due to their preselection for having a spectroscopic redshift, may be somewhat representative of the star-forming main sequence (Figure 9). Their star formation rates are consistent with scatter around the main sequence and appear to include as many galaxies above and below the main sequence estimated by Speagle et al. (2014). Although our CO detections (both blind and with previous spectroscopic redshifts) are indicative of gas fractions compatible with or above (GN19) expectations for main-sequence galaxies, the individual CO nondetections and the stacked signal appear to be systematically lower than the predicted averages, suggesting lower gas mass fractions than might be expected (Figure 9). We can quantify the apparent deficit in stacked signal relative to expectations for the

 sample by calculating expected gas masses for the individual stacked galaxies predicted as a function of their redshift, stellar masses, and star formation rates. The expected sample average molecular gas mass is

 adopting the best-fit relation by Genzel et al. (2015) and

 according to the relation by Scoville et al. (2017). The constant CO luminosity conversion factor above would imply a ratio between expected and observed stacked CO luminosity of 4.8 ± 2.4 and 6.3 ± 3.1, according to the relations by Genzel et al. (2015) and Scoville et al. (2017), respectively. Applying instead the metallicity-dependent CO conversion factor suggested by Genzel et al. (2015) to individual galaxies would somewhat reduce the tension, implying ratios of 3.0 ± 1.7 and 3.8 ± 2.1, according to the relations by Genzel et al. (2015) and Scoville et al. (2017), respectively. While the constraints for low stellar mass galaxies may be compatible with an evolving CO conversion factor due to low metallicity, this is unlikely to resolve the apparent conflict at the high-mass end and may point to lower-than-expected gas masses.


One of the major endeavors of modern observational cosmology is to paint a coherent picture of the history of the universe. To this end, the final frontier remains the identification and characterization of the first sources that appeared in the universe, those which played a significant role in reionizing the intergalactic medium from a neutral state to a fully ionized one over the first billion years (corresponding to redshifts of 6 ≲ z ≲ 12). Extragalactic surveys (of deep fields as well as lensing clusters; Grogin et al. 2011; Koekemoer et al. 2011; Bradley et al. 2012; Ellis et al. 2013; Bradley et al. 2014; Schmidt et al. 2014; Treu et al. 2015; Lotz et al. 2017; Salmon et al. 2018; Coe et al. 2019) with the Hubble Space Telescope (HST) have yielded impressive gains in the number of galaxy candidates at redshifts z = 7–10, with samples reaching over 1000 objects, and revolutionized our understanding of galaxy evolution therein. Complementing these observations, the spectroscopic confirmation (e.g., Finkelstein et al. 2013; Oesch et al. 2015; Zitrin et al. 2015; Roberts-Borsani et al. 2016; Hoag et al. 2017; Stark et al. 2017; Hashimoto et al. 2018) and characterization (e.g., Laporte et al. 2017; Mainali et al. 2018; Endsley et al. 2021) of over a dozen sources has seen impressive advances with ground-based spectroscopy (e.g., probing the rest-frame UV and FIR with Keck/MOSFIRE, VLT/X-Shooter, and ALMA), particularly for the brightest and rarest objects. For the rest-frame optical, however, the Spitzer Space Telescope has, until now, afforded the only realistic means for statistical analyses. However, the Infrared Array Camera’s (IRAC) coarse spatial resolution and the limited depth probed by many surveys make robust and uncontaminated constraints on galaxy properties a challenging feat. Further advances with current facilities are challenging owing to the limited wavelength coverage of HST and the observed faintness of star-forming galaxies as one approaches redshifts of z > 10. The imminent arrival of the James Webb Space Telescope (JWST) has the potential to detect galaxies well beyond the current frontier of z ∼ 12 (e.g., Behroozi et al. 2020) thanks to the unprecedented resolution and sensitivity of its near-IR (NIR) imaging and spectroscopic capabilities, and revolutionize our current understanding of galaxy evolution.


Another important test for galaxy formation models, is whether they place the right amount of stellar mass into discs and bulges. Moffett et al. (2016) measured the SMF separating galaxies into different morphological types and also into discs/bulges. With this, they derived the fractional contribution from bulges/discs to the total stellar mass in bins of stellar mass. This is quite a difficult measurement to do in observations as light profile fitting is required, which can be robustly done in very disc- and bulge-dominated galaxies, but when both components contribute similarly, the measurement is less robust (Robotham et al. 2017). In Fig. 11, we compare Shark with these measurements for two measurements of bulge mass.9 The first one is considering all the mass in the central concentration (regardless of whether it was formed due to mergers or disc instabilities; solid line), and the second one assumes that the bulge mass formed through disc instabilities (either through the starburst triggered by the gas being fueled to the centre or the stars that are transferred from the disc to the bulge) is part of the disc (dashed line). The bulge mass formed via mergers include both the stars formed via merger-driven starbursts and stars that were accreted by the bulge as a result of a merger (but that were formed in the disc of the primary and/or in the secondary galaxies). The latter is done as pseudobulges in Moffett et al. (2016) were added up to the disc rather than the bulge, and those are thought to form through secular processes taking place in the discs of galaxies (Kormendy & Kennicutt 2004). The effect of assigning the bulge mass formed via disc instabilities to the disc has the effect of shifting the transition from disc- to bulge-dominated stellar budget to higher stellar masses, much closer to the Moffett et al. (2016) observations. In Shark, we find that the formation of elliptical galaxies (i.e. spheroid dominated, massive galaxies) is dominated by galaxy mergers rather than disc instabilities, as disc instabilities only increase the bulge contribution by ≈10 per cent at $10^{11}\, \rm M_{\odot }$. This is qualitatively similar to the finding in large cosmological hydrodynamical simulations that elliptical galaxies form primarily via galaxy mergers (Wellons et al. 2016; Clauwens et al. 2018; Lagos et al. 2018a).


Set II: we now focus on the observational constraints on the model parameters after the inclusion of the local measurement of H0 by Riess et al. (2018) with the previous data sets (CMB, Pantheon, and CC) in order to see how the parameters could be improved with the inclusion of this data point. Since for this present UM, the estimation of H0 from CMB alone is compatible with the local estimation of H0 by Riess et al. (2018), thus, we can safely add both the data sets to see whether we could have something interesting. Following this, we perform another couple of tests after the inclusion of R18. The observational results on the model parameters are summarized in Table 4. However, comparing the observational constraints reported in Table 3 (without R18 data) and Table 4 (with R18), one can see that the inclusion of R18 data (Riess et al. 2018) does not seem to improve the constraints on the model parameters. In fact, the estimation of the Hubble constant H0 remains almost similar to what we found in Table 3. In order to be more elaborate in this issue, we have compared the observational constraints on the model parameters before and after the inclusion of R18 to other data sets. In Figs 7 (CMB versus CMB+R18), 8 (CMB+CC versus CMB+CC+R18), 9 (CMB+Pantheon versus CMB+Pantheon+R18), and 10 (CMB+Pantheon+CC versus CMB+Pantheon+CC+R18), we have shown the comparisons which prove our claim. One can further point out that the strong correlation between the parameters μ and H0 as observed in Fig. 5 still remains after the inclusion of R18 [see specifically the (μ, H0) planes in Figs 7–10]. The physical nature of μ does not alter at all. That means the correlation between H0 and μ is still existing after the inclusion of R18 to the previous data sets, such as CMB, Pantheon, and CC. In addition to that since μ ≲ 0.9 according to all the observational data sets, thus, the transition from past decelerating era to current accelerating era occurs to be around z ≲ 0.6, similar to what we have found with previous data sets (Table 3).


In Figure 8, we also find small differences in the [Na, Al, O/Fe] abundance ratios between the stars in the bright and faint RC groups, although it is not as clear as in the case of [Na, Al, O/H] abundances. In particular, unlike Figure 7, stars in the bRC group are more enhanced in [Na/Fe] but appear to be more depleted in [Al/Fe] and [O/Fe] than those in the fRC group. The mean differences are 0.053 ± 0.021 dex, 0.032 ± 0.018 dex, and 0.071 ± 0.045 dex in [Na/Fe], [Al/Fe], and [O/Fe], respectively, which are marginally significant at p-values of 0.22, 0.18, and 0.23. When the relative fraction of RC stars is taken into account (27%; see Section 4), the difference in [Na/Fe] between the genuine RC stars would correspond to Δ[Na/Fe] ∼ 0.20 dex, which is comparable to that expected from our chemical evolution model for the bulge stars (Δ[Na/Fe] = 0.2 ∼ 0.3 dex; Kim & Lee 2018; Lee et al. 2019).10

10
The previous study by Lee et al. (2019) noted a clear separation of the two groups according to Na abundance among bright RGB stars in the outer bulge. The apparent lack of such a distinct difference between the two groups in this study may be due to a larger uncertainty on abundances of relatively faint sample stars.
 The overall chemical patterns, however, are not identical to those observed in typical GCs, where the later-generation stars are more enhanced in [Na, Al/Fe] and more depleted in [O, Mg/Fe] than the first-generation stars at a given metallicity, although the trend of [Na, Al O/Fe] between the two RCs is less clear. Figure 9 shows the comparison of stars in this study with stars in metal-rich GCs ([Fe/H] > −1.0) on the Na–O diagram. The stars used in this study have a different distribution from stars in GCs. Although the bRC group is slightly more enhanced in [Na/Fe] and more depleted in [O/Fe] than the fRC group, the [Na/Fe] variation of RC stars is smaller than that of GC stars. This discrepancy might imply the different chemical evolution between stars in the bulge and typical GCs. We note, however, that even though we employ only metal-rich GC stars for the comparison, the majority of stars are still far more metal-poor ([Fe/H]  −0.5) than stars in the bulge. Because the relatively small [Na/Fe] variation is expected from the chemical evolution model for metal-rich bulge stars and the O-depletion is indistinct in some metal-rich GCs, such as NGC 6121 and 47 Tuc (see Kim & Lee 2018; Lee et al. 2019), the direct comparison of bulge stars with similarly metal-rich GCs on the Na–O plane would require further spectroscopic observations for such GCs in the bulge.


Gaia DR2 contains unprecedented information about the Galaxy, which should allow us to infer its current structure, its equilibrium state, its evolution, modes of mass growth over time, dark matter distribution (and perhaps nature), to cite a few of the questions of modern Galactic astrophysics. As an example, it has been known for several decades that the Galactic disc contains large-scale non-axisymmetric features, including a central boxy/peanut-shaped bar (Okuda et al. 1977; Maihara et al. 1978; Weiland et al. 1994; Dwek et al. 1995; Binney et al. 1997; Babusiaux & Gilmore 2005; López-Corredoira et al. 2005; Rattenbury et al. 2007; Cao et al. 2013) and its possible in-plane extension (Hammersley et al. 2000; Benjamin et al. 2005; Cabrera-Lavers et al. 2007; Wegg et al. 2015), a warp (Burke 1957; Kerr 1957; Westerhout 1957; Weaver 1974; Djorgovski & Sosin 1989; Evans et al. 1998; Gyuk et al. 1999; Drimmel & Spergel 2001; López-Corredoira et al. 2002; Momany et al. 2006; Robin et al. 2008; Reylé et al. 2009; Amôres et al. 2017), and spiral arms (Georgelin & Georgelin 1976; Taylor & Cordes 1993; Drimmel 2000; Bissantz & Gerhard 2002; Churchwell et al. 2009; Vallée 2014; Reid et al. 2014; Hachisuka et al. 2015; Hou & Han 2015). However, full knowledge of these asymmetric structures, that is, of their spatial extent, pattern speeds, and number (in case of spiral arms) is still lacking. Since asymmetries constitute the driver of the secular evolution in galaxy discs (see e.g. Minchev et al. 2012; Fouvry et al. 2015; Halle et al. 2015; Aumer et al. 2017 and Kormendy 2013, for a review) by redistributing angular momentum between the inner and outer disc and between its baryonic and dark matter content (Debattista & Sellwood 2000; Bournaud & Combes 2002; Athanassoula 2003; Martinez-Valpuesta et al. 2006; Combes 2011), quantifying their characteristics is fundamental for understanding to what extent the Milky Way has “simply” evolved secularly in the last ~9 Gyr (Hammer et al. 2007; Martig et al. 2014), or whether some more complex evolutionary scenarios need to be invoked.


In order to understand the origin of the termination of the powerful jet in Mrk 231, consider the very low accretion rates in these FRI NLRGs, three to four orders of magnitude less than a quasar (Chiaberge et al. 1999, 2002; Hardcastle et al. 2009). However, there are the occasional FRI broad-line galaxies such as the Seyfert 1 galaxy, 3C 120, which has a very prominent FRI morphology on a 400 kpc scale (Walker et al. 1987). Thus, the low accretion rate of FRI NLRGs is not the full explanation of the discrepancy with Mrk 231, but is likely related. One difference between 3C 120 and Mrk 231 is that Mrk 231 has a low-ionization BAL wind (Lipari et al. 1994; Smith et al. 1995). In low radio states, it has also displayed evidence of a high-ionization X-ray-absorbing wind (Feruglio et al. 2015; Reynolds et al. 2017). There are also extreme amounts of intrinsic optical absorption in the galaxy itself from dusty gas (Lipari et al. 1994; Smith et al. 1995). All three circumstances point to a very dense nuclear environment through which the jet must propagate. Furthermore, in Reynolds et al. (2009), it was argued that the density of the free–free absorbing screen at K1 is consistent with the jet being stopped by the BAL wind at K1. By contrast, the extremely low, undetectable accretion of gas in FRI NLRGs is consistent with a very low-density nuclear environment. The launching of the jet in Mrk 231 does not seem to be stopped by the dense nuclear environment, but its propagation does seem to be thwarted. The case of 3C 120 does not seem to be accommodated by this discussion. It is noted that there is no evidence of either a BAL wind or a high-ionization X-ray-absorbing wind in 3C 120 (Oke & Zimmerman 1979; Ballentyne et al. 2004). Thus, it might be the case that there is not an extremely dense nuclear environment near the source of the jet in 3C 120; hence, jet propagation is not hindered. We cannot rule out the possibility that the BAL wind in Mrk 231 also diminishes the power of the jet-launching mechanism as well as providing a drag on its propagation.


When we now compare the photodesorption yields at 541 eV between fluences  5 × 1015 photon cm−2 and at 3 × 1017 photon cm−2 in Fig. 2, the CO2 photodesorption first increases from 2.6 × 10−2 molecule/photon to 7.3 × 10−2 molecule/photon. We also observed this phenomenon for CO photodesorption yield (the data are not shown for more clarity), which increased from 1.9 × 10−2 molecule/photon to 3.5 × 10−2 molecule/photon. Second, the estimated yield for the X-ray photodesorption of CH3OH from pure methanol ice decreased by almost one order of magnitude from 9.0 × 10−3 molecule/photon to 1.3 × 10−3 molecule/photon. This indi- cates that the photodesorption of CH3OH is higher for a lower fluence received by the ice when more intact methanol molecules are present in the ice. This aging process favors the photodesorption of simpler molecules such as CO2 or CO. Laffon et al. (2010) estimated with NEXAFS spectroscopy (at the C K-edge) that X-ray irradiation at 150 eV of pure methanol ice at 20 K leads to a survival rate of 50% for methanol after an absorbed dose of 1.1 MGy. In our fixed-energy experiments, we irradiated pure methanol ice with fluences between 5 × 1015 photon cm−2 and 2 × 1016 photon cm−2. Because we irradiated a volume of 0.1 cm2 × 100 ML, with a meanenergy of ~550 eV, and when we consider a volumic mass of condensed methanol of ~ 0.64 g cm−3 (at 20 K; Luna et al. 2018) and an X-ray absorption cross section of ~ 0.6 Mbarn (Ishii & Hitchcook 1988), the absorbed doses used in our fixed energy experiments change from ~ 2 to ~ 15 MGy, whichis quite similar to the absorbed doses in Laffon et al. (2010). This indicates that we could expect a methanol destruction rate of about 50% for our low-fluence experiments. In similar experiments, when irradiating a H2 O:CH4:NH3 (2:1:1) ice mixture covered by a layer of CO:CH3OH (3:1) with 250–1250 eV X-rays during 120 min with a flux of 7.6 × 1014 photon s−1, higher by almost two order of magnitudes than our experiments, Ciaravella et al. (2020) did not detect a desorption signal on the mass channel 31 (attributed to methanol desorption) and estimated that only ~ 20% of methanol molecules remained intact in the first minutes of the irradiation. The irradiation flux therefore appears to be critical for detecting methanol desorption in X-ray irradiation experiments of methanol-containing ices. A lower X-ray flux appears to favor methanol desorption because the methanol destruction rate is lower. This destruction of methanol molecules could also have a significant effect on the formation and desorption of more complex molecules.


Given that the CDM paradigm only begins to face significant problems at precisely such scales when complex baryonic physics begins to play an important role, it is natural to inquire whether it is the central culprit behind erroneous theoretical predictions. It was for example realized early on that energy from supernovae may be sufficient for driving gas out of the potential wells of dwarf galaxies, the associated mass deficit resulting in the expansion of the central halo region and the flattening of the density profile. More generally, many hydrodynamical simulations implementing stellar and active galactic nuclei (AGN) baryonic feedback processes in a cosmological context are able to reproduce cores (e.g. Governato et al. 2010, 2012; Macciò et al. 2012b; Martizzi et al. 2012; Di Cintio et al. 2014; Chan et al. 2015). However, the complexity of such simulations obscures the physical mechanisms through which these processes affect the dark matter distribution. These mechanisms normally invoke ‘heating’ of the cold central density cusp through an irreversible process, such as dynamical friction from infalling clumps (El-Zant, Shlosman & Hoffman 2001; El-Zant et al. 2004; Tonini, Lapi & Salucci 2006; Romano-Díaz et al. 2008; Goerdt et al. 2010; Cole, Dehnen & Wilkinson 2011; Del Popolo et al. 2014; Nipoti & Binney 2015). Alternatively, repeated gravitational potential fluctuations induced by stellar winds, supernova explosions and AGN could also dynamically heat the central halo (Read & Gilmore 2005; Mashchenko, Couchman & Wadsley 2006; Mashchenko, Wadsley & Couchman 2008; Peirani, Kay & Silk 2008; Governato et al. 2012; Pontzen & Governato 2012, 2014; Zolotov et al. 2012; Martizzi, Teyssier & Moore 2013; Teyssier et al. 2013; Madau, Shen & Governato 2014; Ogiya & Mori 2014). Although the last mechanism may seem most closely related to the supernovae driven wind outflows discussed above, it is in principle more closely connected to the dynamical friction proposal, in the sense that it involves irreversible stochastic dynamics: one may envisage the potential fluctuations leading to cusp-core transformation as originating from stochastic density variations; the relevant ‘clumps’ would be associated with fluctuation scales, as opposed to physically distinct objects dissipating orbital energy via dynamical friction; nevertheless, the basic physical mechanism through which the energy is transferred to the dark matter is similar. For, as is the case in general with processes involving fluctuation and dissipation, fluctuations in a gravitational system can be approximated as stochastic processes described by power spectra and correlation functions, and they can be accompanied by dissipation in the form of dynamical friction (Chandrasekhar 1943; Nelson & Tremaine 1999).


In Figures 1 and 2 we show that the X-ray (1.7 keV5

5
This value corresponds to the geometric mean of the XRT energy band, at which the error of the estimated flux can be reasonably suppressed.
), optical (R-band), and radio (6 GHz) fluxes varied with the time of observation applied to the proper corrections if observed at a distance of 200 Mpc, motivated by the fact that the averaged sensitive range of the Advanced LIGO/Virgo detectors in their full-sensitivity run is about 210 Mpc, for the current samples. Due to the faintness of the SGRB afterglow emission, there are gaps of the data between the previous more distant events and GW170817/GRB 170817A (please note that for the latter we only consider the quick decline phase as the early part is significantly influenced by the beam effect of the off-axis outflow). Therefore we extrapolate the very late (t > 200 day) X-ray and optical afterglow data of GRB 170817A to t ∼ 2 day after the burst and then compare them to other events. The radio to X-ray spectrum of the forward shock afterglow emission of GW170817/GRB 170817A is fν ∝ ν−0.6, which yields a p = 2.2 in the slow-cooling synchrotron radiation scenario (Lamb et al. 2018; Troja et al. 2018). In the jet model, such a p can also reasonably account for the very late flux decline of

 (Lamb et al. 2018). The extrapolation function of the forward shock emission of GRB 170817A to early times is thus taken as f ∝ t−2.2. Surprisingly, the forward shock afterglow emission of GW170817/GRB 170817A, the first neutron star merger event detected by Advanced LIGO/Virgo, are among the brightest ones for all SGRBs detected so far. Just a few events have X-ray afterglow emission brighter than that of GRB 170817A, as demonstrated in the right panels of Figure 1. The same conclusion holds for the optical and radio afterglow data, as shown in Figure 2, though these two samples are rather limited. We have also compared the distribution of the isotropic gamma-ray energy Eiso, calculated in the rest-frame energy band of 1–104 keV, for the SGRBs with well-measured spectra, and found no significant difference for the SGRBs with and without “long-lasting” afterglow emission (see Figure 3; where the number of events for the X-ray sample are smaller than that presented in Figure 1 because some bursts lack reliable spectral measurements). GRB170817A and GRB 150101B (Troja et al. 2018), two short events with the weakest detected prompt emission, have “bright” late-time afterglow emission because of their off-axis nature.


Oort Cloud. The conclusions that can be reached from this figure about the formation of the Oort Cloud are well known. For example, T93 showed that the parameter space in which an Oort Cloud forms is quite restricted, and that those Oort Clouds that do form have a narrow range of semimajor axes ∼10 000 au. While this parameter space is inhabited by Uranus and Neptune in the Solar system, which should thus readily supply objects to the Oort Cloud (even accounting for the possibility that these planets may have started closer to the Sun; Tsiganis et al. 2005), it could be that Oort Clouds are relatively rare. Many simulations have confirmed these predictions regarding the ability of planets to implant objects in the Oort Cloud (e.g. Dones et al. 2004) while also showing further subtleties such as the ability of Jupiter and Saturn to place a small fraction of the objects they scatter into the Oort Cloud even if ejection is the predominant outcome in such encounters (Brasser, Duncan & Levison 2008). The time-scale predicted for the scattering process to occur is also borne out in numerical simulations. For example, compare the prediction of Fig. 1 that it should take 0.1–1 Gyr for Uranus and Neptune to implant material in the Oort Cloud with fig. 13 of Dones et al. (2015). The radius at which the Oort Cloud forms in the simulations also agrees with that predicted of ∼10 000 au, with some studies includingthe differentiation between inner and outer Oort Clouds (e.g. Lewis, Quinn & Kaib 2013; Brasser & Schwamb 2015). Inspection of Fig. 1 shows that Oort Clouds could form at smaller orbital radii, but that such an outcome requires both low-mass planets and a large system age; for example, if Neptune and Uranus were each of Earth mass, then the Oort Cloud would be at ∼1000 au, but would take ∼20 Gyr to form. Another way to achieve a small Oort Cloud on a shorter time-scale is to place the planetary system in a dense stellar environment (as discussed in Section 3.2).


The first possible scenario is that all FRBs are generated from magnetars, the population of non-repeating FRBs are from magnetars born in the delay formation channels (Margalit et al. 2019) such as neutron star−neutron star mergers associated with short gamma-ray bursts (Rosswog et al. 2003; Price & Rosswog 2006; Giacomazzo & Perna 2013), neutron star−white dwarf mergers possibly associated with rapidly evolving supernovae (SNe) (Toonen et al. 2018; Zhong & Dai 2020), or white dwarf−white dwarf mergers (Yoon et al.2007; Schwab et al. 2016) possibly associated with SNe Ia, and accretion-induced collapse of white dwarfs (Nomoto & Kondo 1991; Tauris et al. 2013; Schwab et al. 2015); the population of repeating FRBs are from magnetars born in the prompt formation channels such as type I superluminous SNe, long gamma-ray bursts, or core-collapse SNe (Duncan & Thompson 1992; Kouveliotou et al. 1998; Kasen & Bildsten 2010). Nonetheless, it seems to be untrue based on recent observations in host galaxies and offsets of the repeaters FRBs 20180916B (Marcote et al. 2020; Tendulkar et al. 2021) and 20200120E (Bhardwaj et al. 2021a; Kirsten et al. 2021). So it may be that the observed non-repeating and repeating FRBs are respectively from less active and more active magnetars due to different magnetic field strengths. If this is the case, however, it is unclear whether the distribution discrepancies of properties between the one-off events and repeaters can arise from different magnetic field strengths. Moreover, if the one-off events and repeaters are produced by an identical mechanism like that generating FRB 20200428 and its associated X-ray burst, it is conceivable that the more active magnetars yielding repeaters could produce more frequent more violent outbreaks resulting in brighter bursts than the less active magnetars yielding one-off events. This appears to be inconsistent with the statistical results shown in Figure 3, though it is still a complicated issue.


As shown in Fig. 3, the differences in metallicity between different SN subclasses are not significant. This is in contradiction with what is expected from single-star evolution theory, where metallicity-driven winds are crucial: type Ic SNe, which are the most highly stripped, would show the highest metallicity, followed by type Ib, and finally the H-rich type II SNe. The observations, on the other hand, reveals that this is not the case. Some SNe Ic are even located in the low-metallicity part of the distribution in the current sample. This result strengthens the notion that metallicity may not play an important role in deciding theresulting SN type, in agreement with other works based on SN environments (Anderson et al. 2010, 2015; Leloudas et al. 2011; Galbany et al. 2016a). The environments of broad-lined SNe IcBL are found to be relatively metal poor compared to the normal CCSNe, in agreement with previous studies (Modjaz et al. 2011; Galbany et al. 2016a). However, we note that there are only two such SNe in the current sample. The explosion site of SN 1998bw (the first SN to be associated with a GRB: 980425; Galama et al. 1998; Krühler et al. 2017) in this study shows a lower metallicity of 12 + log(O/H) = 8.30 dex compared to the GRB-less SN 2009bb (Pignata et al. 2011), 12 + log(O/H) = 8.49 dex. Levesque et al. (2010a), using slit spectroscopy of the explosion site, concluded that the high metallicity of SN 2009bb site is consistent with typical GRB-less SNe IcBL and not with GRB hosts. Their metallicity value recalculated on the Marino et al. (2013) N2 scale is 12 + log(O/H) = 8.52 dex. These two different cases illustrate the importance of metallicity in deciding whether an SN IcBL progenitor would also produce GRB or not (Modjaz et al. 2008; Levesque et al. 2010b). Progenitors with higher metallicity are not able to spin fast enough and thus produce high angular momentum essential for GRB jet production, eventually producing a GRB-less SN IcBL (Woosley & Bloom 2006).


The CO photodesorption yield reaches its highest value when this ice is deposited at low temperatures (down to 7 K, the lowest temperature studied experimentally) and decreases gradually at higher deposition temperatures (Öberg et al. 2007; Öberg et al. 2009; Muñoz Caro et al. 2010, 2016; Sie et al. 2022). The explanation for this phenomenon motivated further research. It was found that the columnar structure of CO ice samples, grown at incidence angles larger than 45°, increases the effective ice surface exposed to UV photons and therefore the photodesorption efficiency (González Díaz et al. 2019), but ice surface effects cannot account for the large variations observed in the photodesorption of CO ice samples deposited at different temperatures (Muñoz Caro et al. 2016). Absorption band shifts of CO ice in the UV and IR ranges only occurred at deposition temperatures above 20 K (Lasne et al. 2015; Muñoz Caro et al. 2016), suggesting that CO ice grown at lower temperatures is amorphous below 20 K in our experiments, and therefore, the decreasing photodesorption yield is not related to a transition from amorphous to crystalline ice, instead it might be associated to a different degree of molecular disorder in CO ice samples, depending on their deposition temperature. Photon energy transfer via Wannier-Mott excitons between the first photoexcited molecule in the ice and a molecule on the ice surface capable to desorb was proposed (Chen et al. 2017; McCoustra & Thrower 2018). Molecular disorder seems to enhance this energy transfer between neighbour molecules. The colour temperature variations measured at different deposition temperatures could also be the result of molecular disorder (Carrascosa et al. 2021). Urso et al. (2016), Cazaux et al. (2017), and Carrascosa et al. (2021) did not find significant changes in the desorption behaviour or the colour temperature of pure CO ice during controlled warm-up, which points to a low value of the diffusion in the ice. Finally, Sie et al. (2022) investigated the CO photodesorption yield dependence on ice thickness.


It is important in our analysis to only keep sources for which the SFR and stellar mass estimates are reliable. To this end, we first excluded sources whose fit had reduced χ2,

χ

red
2

>5

$ \chi ^2_{\rm red}>5 $

. This criterion is based on visual inspection of the SED fits and has been adopted in previous studies (e.g., Masoura et al. 2018; Mountrichas et al. 2019; Buat et al. 2021). Increasing the limit to

χ

red
2

>6

$ \chi ^2_{\rm red}>6 $

 adds more sources to our sample, but most of them have bad fits and thus unreliable host galaxy measurements. Reducing the threshold to

χ

red
2

>4

$ \chi ^2_{\rm red}>4 $

 would exclude additional sources, the vast majority of which have reliable fits. This criterion eliminates 133 AGN (9% of the sample). For each parameter calculated by the SED fitting process, X-CIGALE estimates two values. One is evaluated from the best-fit model, and one weights all models allowed by the parametric grid, with the best-fit model having the heaviest weight (Boquien et al. 2019). This weight is based on the likelihood, exp (−χ2/2), associated with each model. A large difference between these two values for a specific parameter indicates that the fitting process did not result in a reliable estimation for this parameter (Mountrichas et al. 2021a,c; Buat et al. 2021). Thus, when we compared the stellar masses of type 1 and 2 AGN, we only included in our analysis sources with

1
5

≤

M

∗
,
best

M

∗
,
bayes

≤
5

$ \frac{1}{5}\leq \frac{M_{*,\rm best}}{M_{*, \rm bayes}} \leq 5 $

, where M∗,best and M∗,bayes are the best-fit and Bayesian-fit values of M*, respectively. This method to exclude unreliable estimations has been applied in recent studies (Mountrichas et al. 2021a,c; Buat et al. 2021). Using different values for the boundaries of the criterion (i.e. 0.1–0.33 for the lower limit and 3–10 for the upper limit) does not affect the results of our analysis. This criterion reduces the sample to 944 X-ray AGN (93% of the initial dataset). Of these systems, 729 are type 1 and 215 are type 2 (Table 2). Similarly, for the comparison of the SFR of the two AGN types, we require

1
5

≤

SFR
best

SFR
bayes

≤
5

$ \frac{1}{5}\leq \frac{\mathrm{SFR_{best}}}{\mathrm{SFR_{bayes}}} \leq 5 $

, where SFRbest and SFRbayes are the best and Bayesian values of the SFR, respectively, estimated by X-CIGALE. This reduces our sample to 860 X-ray AGN (85% of the initial dataset). Of these sources, 673 are type 1 and 187 are type 2. We note that throughout our analysis we used the Bayes calculations of X-CIGALE for the various parameters.


Also plotted in Fig. 2 is the pressure in the outer crust from some popular EoSs that model the complete structure of the NS. The figure is drawn up to nb = 3  ×  10-4 fm-3, thus comprising the change from the outer crust to the inner crust in order to allow comparison of the EoSs also in this region (notice, however, that inner crust results are not available for the FRDM). We show in Fig. 2 the EoS from the recent BSk21 Skyrme nuclear effective force (Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013; Goriely et al. 2010) tabulated in (Potekhin et al. 2013). The parameters of this force were fitted (Goriely et al. 2010) to reproduce with high accuracy almost all known nuclear masses, and to various physical conditions including the neutron matter EoS from microscopic calculations. We see in Fig. 2 that after the experimentally constrained region, the BSk21 pressure is similar to the BCPM and FRDM results, with just some displacement around the densities where the composition changes from a nucleus to the next one. In the seminal work of BPS (Baym et al. 1971b) the nuclear masses for the outer crust were provided by an early semi-empirical mass table. The corresponding EoS is seen to display a similar pattern with the BCPM, FRDM, and BSk21 results in Fig. 2. The EoS by Lattimer & Swesty (1991), taken here in its Ska version (Lattimer 2015; LS-Ska), and the EoS by (Shen et al. 1998b,a; Sumiyoshi 2015; Shen-TM1) were computed with, respectively, the Skyrme force Ska and the relativistic mean-field model TM1. In the two cases the calculations of masses are of semiclassical type and A and Z vary in a continuous way. Therefore, these EoSs do not present jumps at the densities associated with a change of nucleus in the crust. Beyond this feature, the influence of shell effects in the EoS is rather moderate because to the extent that the pressure at the densities of interest is largely determined by the electrons, small changes of the atomic number Z compared with its semiclassical estimate modify only marginally the electron density and, consequently, the pressure. The LS-Ska EoS shows good agreement with the previously discussed models, with some departure from them in the transition to the inner crust. The largest discrepancies in Fig. 2 are observed with the Shen-TM1 EoS that in this region predicts a softer crustal pressure with density than the other models.


We fitted the XMM-Newton spectra of ULX-1 and ULX-2 from observation 0794581201 with an absorbed power-law model, using two tbabs absorption components, one frozen to the Galactic value of NH = 1.84 × 1021 cm−2 and the other allowed to vary. In the case of ULX-1, a power-law model was not sufficient to produce a good fit, with χ2/dof = 131.9/90 and the fit showing significant soft residuals at ∼1 keV. These soft residuals are known to be a common feature in the spectra of ULXs and bright X-ray binaries (e.g., Bauer & Brandt 2004; Carpano et al. 2007; Middleton et al. 2015b), and found in other ULXs to be a combination of emission and absorption features related to powerful outflowing winds (including in NGC 6946 ULX-3; Pinto et al. 2016). We used an additional Gaussian component to empirically fit these soft residuals, which resulted in a very large statistical improvement and provided an acceptable fit (χ2/dof = 84.5/87). Using the best-fitting model for each source, we calculated the absorbed 0.3–10 keV flux of both objects. We do not correct for absorption since extending steep power laws, which are empirical rather than physical models, to low energies is likely to overestimate the true flux of the object beneath the absorption—unabsorbed fluxes using such models can be a factor of 2 or 3 higher than those for more physically motivated models, and the amount of absorption is itself model-dependent, so we make fewer assumptions by just considering the observed, absorbed flux. For comparison, we also fitted both spectra with an absorbed multicolor disk model. Although this was able to produce a statistically acceptable fit, the Gaussian representing the soft residuals in ULX-1 contributes to a physically unreasonable portion of the spectrum, broadening to fit the majority of the soft emission, and the residuals for ULX-2 are even less well characterized than for a power-law fit. Therefore, a steep power law seems to be the best empirical model for both spectra. We present the spectral fit results for these two sources in Table 3 and the best-fitting model plots in Figure 2.


The observations of the characteristic double-horned line profiles (Stewart et al. 2014) are all restricted to very low redshifts (z  0.5). Our understanding of the kinematics of H i at high redshifts (z > 0.5) majorly depends on the study of the QSO absorption spectra where the absorption features are mainly dominated by the Lyman−α systems (Zafar et al. 2013). The systems with the largest column densities, the DLAs, are proposed to be the progenitors of the present-day spiral galaxies (Wolfe et al. 2005). Modelling of DLAs observations suggests that DLAs resemble rotating disc galaxies with circular velocities typically of the order of $100\!-\!200\, {\rm km\, s}^{-1}$ (Wolfe et al. 1986; Kauffmann & Charlot 1994; Klypin et al. 1995; Lanzetta, Wolfe & Turnshek 1995; Wolfe 1995; Jedamzik & Prochaska 1998). A number of theoretical studies indicate that the DLAs can have circular velocities as low as ${\sim } 50 \, {\rm km\, s}^{-1}$ (e.g. Kauffmann 1996) which is supported by a number of numerical simulations (Pontzen et al. 2008; Cen 2012; Bird et al. 2014, 2015). QSO absorption spectra also suggest that the gas inside the DLAs has a velocity dispersion of $\sigma _v \approx 5\!-\!10\, {\rm km\, s}^{-1}$ (Wolfe et al. 2005) which is comparable with the nearby galaxies. Other observations also reveal that the high-redshift galaxies show rotational motion (e.g. see Pettini 2009 and references therein). Based on these considerations we have assumed that across the entire range z ≤ 6 the H i resides in rotating disc galaxies which exhibit a double-horned line profile similar to those seen for local galaxies. The value of the parameters α, hf, σv are found to vary from galaxy to galaxy in the local Universe. The statistics of these parameters and their redshift evolution are largely unknown. In our analysis each simulation corresponds to fixed values of these parameters which are held constant over the entire z range. We have carried out simulations covering the entire range of parameter values in order to estimate how this variation affects the RSD. Considering vcirc which determines the overall width of the line profile, it may be noted that the values are determined by the halo mass distribution which evolves with z.


The linear relationship that we observe between breakpoint energy and core temperature is in line with previous measurements (e.g. McComas et al. 1992; Štverák et al. 2009), for both the halo and strahl. According to Scudder & Olbert (1979), a linear trend in the halo relation also follows under the assumption that binary Coulomb collisions dominate electron dynamics in the solar wind. However, in order to align with available experimental data, Scudder & Olbert (1979) set a scaling factor of Ebp/kBTc = 7, which differs from our scaling factor of Ebp/kBTc = 5.5 ± 0.1. With a scaling factor of Ebp/kBTc = 7, Scudder & Olbert (1979) predict that a transformation of thermal electrons into the suprathermal population occurs as the solar wind flows out from the Sun. Findings by Štverák et al. (2009), on the other hand, show that the (nh + ns)/nc ratio remains roughly constant with heliocentric distance in the slow wind, suggesting a lack of interchange between the thermal and suprathermal populations. However Štverák et al. (2009) observes some variability in the (nh + ns)/nc ratio in the fast wind, which they attribute to either statistical effects due to a lack of samples or a possible “interplay” between thermal and suprathermal electrons. Scudder & Olbert (1979) also predict that the halo Ebp/kBTc ratio remains constant with heliocentric distance, whereas Štverák et al. (2009) find that the halo Ebp/kBTc ratio decreases with heliocentric distance. These findings by Štverák et al. (2009), along with the discrepancy between our calculated ratio of Ebp/kBTc = 5.5 ± 0.1 and the prediction of Ebp/kBTc = 7, suggest that the model of Scudder & Olbert (1979) requires a minor update to either the theory or to the input parameters. The discrepancy, however, may also be indicative of other processes, such as wave-particle scattering (e.g. Gary et al. 1994), that possibly modifies the ratio between breakpoint energy and core temperature while preserving its linear relationship.


In order to investigate the gas kinematics at an early evolutionary stage and the formation of Keplerian disks, we conduct ALMA observations toward three candidate young protostars, Lupus 3 MMS, IRAS 15398−3559, and IRAS 16253−2429. They are selected from our SMA sample (Yen et al. 2015a). These three protostars all have relatively low protostellar masses (0.1 M⊙), inferred from the infalling motions in their protostellar envelopes, and they do not show clear signs of a spin-up rotation on a 1000 au scale; i.e., no signatures of Keplerian disks are seen in our SMA observations (Yen et al. 2015a). Lupus 3 MMS is a Class 0 protostar with a bolometric luminosity (Lbol) of 0.41 L⊙ and a bolometric temperature (Tbol) of 39 K in the Lupus 3 cloud at a distance of 200 pc (Tachihara et al. 2007; Comerón 2008; Dunham et al. 2013). Our SMA results suggest that the protostellar mass in Lupus 3 MMS can be as low as 0.1 M⊙ (Yen et al. 2015a). IRAS 15398−3559 is a Class 0/I protostar with an Lbol of 1.2 L⊙ and a Tbol of 61 K in the Lupus 1 cloud at a distance of 150 pc (Froebrich 2005; Comerón 2008). Early single-dish observations of its CO outflow suggest that IRAS 15398−3559 is close to face on (van Kempen et al. 2009). Recent SMA and ALMA observations show that it is actually closer to edge on (Oya et al. 2014; Bjerkeli et al. 2016). With this new estimated inclination angle (∼70°), our SMA data suggest a low protostellar mass (0.1 M⊙) and a low specific angular momentum in the protostellar envelope (∼1 × 10−4 km s−1 pc; Yen et al. 2015a). IRAS 16253−2429 is a Class 0 protostar with an Lbol of 0.24 L⊙ and a Tbol of 36 K in the ρ Ophiuchus star-forming region at a distance of 125 pc (Dunham et al. 2013). Both CARMA and our SMA results suggest that its protostellar mass is 0.1 M⊙ (Tobin et al. 2012a; Yen et al. 2015a). These three protostars are all embedded in dense cores with masses ≳0.5 M⊙ (Froebrich 2005; Tachihara et al. 2007; Enoch et al. 2009). Therefore, they are excellent targets by which to study the gas motions on a 100 au scale at an early evolutionary stage.


Various strategies have been devised to identify modes. One can, for instance, search for frequency patterns appropriate for rapid rotation. The background for this search is the discovery of asymptotically uniform frequency spacings in the numerically computed spectra of uniformly rotating polytropic models (Lignières et al. 2006; Reese et al. 2008) and differentially rotating realistic self-consistent field (SCF) models (Reese et al. 2009a). These uniform spacings have also been modelled through asymptotic semi-analytical formulas (Pasek et al. 2012). In observed spectra, recurrent frequency spacings that may correspond to the large separation or half its value have been found in some stars (García Hernández et al. 2009; García Hernández et al. 2013; Paparó et al. 2016). Moreover, García Hernández et al. (2015) show that mean density estimates based on this type of spacings (obtained via a scaling relation similar to the one in Reese et al. 2008, but based on SCF models) are compatible with independent mass and radii measurements obtained for δ Scuti stars in binary systems. Nonetheless, it is expected that various effects may contribute to hide these regular frequency patterns. First, as mentioned before, the full spectrum is a superposition of sub-spectra corresponding to different classes of modes and some of the uniform spacings only concern one class. This complicates their detection in the full spectrum. Also, owing to their asymptotic nature, these spacings might not be relevant to analyse the low to moderate (up to radial order n ~ 10) frequency domain, typical of most rapidly rotating pulsators. A third effect that may come into play is the presence of mixed modes in evolved stars and/or sharp sound speed gradients since they can potentially modify the regular spacings. Finally, mode selection effects that are due to the non-linearly determined intrinsic mode amplitudes could affect the detectability of the regular patterns. As a first attempt, Reese et al. (2009b) developed a strategy to find these frequency spacings but ran into difficulties when including chaotic modes, which come from another class of modes. Lignières et al. (2010) addressed the same question with encouraging results but their analysis was restricted to the asymptotic regime and relied on simplifying assumptions regarding the spectrum of chaotic modes and the mode visibilities. In this paper, our first goal is to search for regular frequency spacings in the most realistic synthetic spectra available, using relevant frequency ranges and accurate visibility calculations. While they can provide guidance to a similar search in real data, we already know that these results must be taken with caution since the intrinsic mode amplitudes used in this paper are not realistic, but based on ad-hoc prescriptions.


The lack of data on inelastic processes due to collisions with neutral hydrogen atoms has been a major limitation on modelling of F-, G- and K-star spectra in statistical equilibrium, and thus to reliably proceeding beyond the assumption of local thermodynamic equilibrium (LTE) in analysis of stellar spectra and the determination of elemental abundances. This problem has been well documented, e.g. see Lambert (1993); Barklem (2016a) and references therein. Significant progress has been made in recent times through detailed full-quantum scattering calculations, based on quantum chemical data, for the cases of simple atoms such as Li, Na, Mg and Ca (Belyaev & Barklem 2003; Barklem, Belyaev & Asplund 2003; Belyaev et al. 2010; Barklem et al. 2010; Belyaev et al. 2012; Barklem et al. 2012; Mitrushchenkov et al. 2017). These calculations have demonstrated the importance of the ionic-covalent curve crossing mechanism leading naturally to charge transfer processes (mutual neutralization and ion-pair production), in addition to excitation and de-excitation processes. The importance of this mechanism has allowed various simplified model approaches to be developed, which may be used in cases where suitable quantum chemistry data are not been available. In particular a semi-empirical model has been employed for Al, Si, Be and Ca (Belyaev 2013a,b; Belyaev, Yakovleva & Barklem 2014b; Yakovleva, Voronov & Belyaev 2016; Belyaev et al. 2016), and a theoretical model based on a two-electron asymptotic linear combinations of atomic orbitals (LCAO) approach, has also been employed for Ca (Barklem 2016b, 2017). Comparisons of the two methods show quite good agreement and reasonable agreement with the full quantum calculations is found, particularly for the most important processes with the largest rates (Barklem 2016b, 2017; Mashonkina, Sitnova & Belyaev 2017; Mitrushchenkov et al. 2017). Thus, the model approaches provide a useful route for obtaining estimates of the rates for these processes for many elements of astrophysical interest.


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


Spectral energy distributions in accordance with the physical parameters of the best-fit spectra were generated with FASTWIND, to provide the flux density per surface unit through our studied bands. The composite flux measured at Earth from a binary at a distance d, at a wavelength λ, reddened to extinction A(λ), is given by \begin{eqnarray*} f_{\lambda}=\dfrac{1}{d^2}\left(R_{1}^{2}F_{1,\lambda}+R_{2}^{2}F_{2,\lambda}\right) \times 10^{-0.4A(\lambda)} \end{eqnarray*}fλ=1d2(R12F1,λ+R22F2,λ)×10−0.4A(λ)where R1,2 and F1,2 are the radii and the surface fluxes of the components, respectively. The composite SED was reddened according to the new family of optical and near-infrared extinction laws for O-type stars provided by Maíz Apellániz et al. (2014), which constitute an improvement of the widely used extinction laws by Cardelli et al. (1989). We ran a fitting algorithm over a wide range of distances with a step of 0.05 kpc, setting free the monochromatic parameters R5495 and E(4405 − 5495) for the type and amount of extinction, respectively, and the best-fit values were considered to be those that minimized the weighted-χ2. To estimate the uncertainty of our measurements, we used a Monte Carlo approach. In particular, we ran the fitting procedure 1000 times using sets of randomly selected parameters (photometry and radii) within their uncertainties assuming a Gaussian distribution is used. The corresponding values of distance are shown in Table 6 for every set of radii and temperatures determined from the four different fit models. Our adopted radii measured with ELC yielded d = 3.52 ± 0.08 kpc, E(4405 − 5495) = 3.66 ± 0.06 mag, R5495 = 3.26 ± 0.04 and A5495 = 11.9 ± 0.1 mag, based on a photometric Teff2 ~ 36 kK. Assuming a spectroscopic Teff2 = 37 kK, the distance changed slightly to d = 3.55 ± 0.08 kpc. Having three degrees of freedom, the reduced-χ2 of our resulting fits was measured to be \hbox{$\chi^2_\textrm{red}\sim11$}χred2~11.


Radio astronomy is recognized as one of the most effective techniques to search for interstellar molecules. By comparing the spectra of candidate molecules in the laboratory with the spectra observed in astronomical surveys, we can determine whether these molecules exist in interstellar space. Therefore, it is necessary to provide rotational spectra of candidates for astronomical detection. Radio astronomy has helped to detect several sulfur-containing molecules in the ISM in recent years: in particular, thiols, the sulfur analogs of alcohols. Methanethiol (or methyl mercaptan, CH3SH) was detected in the Sagittarius B2 (Sgr B2) region of the center of our Galaxy (Linke et al. 1979; Gibb et al. 2000; Müller et al. 2016; Rodríguez-Almeida et al. 2021) and in the protostar IRAS 16293-2422 (Majumdar et al. 2016). Two groups reported to have detected several signs of ethanethiol (C2H5SH) in Sgr B2 (Müller et al. 2016) and Orion (Kolesniková et al. 2014). Most recently, Rodriguez-Almeida reported the first unambiguous detection of ethanethiol in the ISM, toward the G+0.603-0.027 molecular cloud (Rodríguez-Almeida et al. 2021). Moreover, several sulfur-containing species have been observed in comets (Altwegg et al. 2017). Some recent efforts, both from spectroscopy and astronomical searches, to detect S-stitutes of other classes of compounds have also been reported. For instance, thioformic acid (HC(O)SH) was very recently detected in G+0.693–0.027. Its trans-isomer has an abundance of ~1 × 10–10 (Rodríguez-Almeida et al. 2021). Conversely, thioformamide (NH2CHS), the counterpart of for-mamide (NH2CHO), was characterized in the laboratory up to 660 GHz, and its transitions were searched for toward the hot cores Sgr B2(N1S) and Sgr B2(N2), but it was not detected (Motiyenko et al. 2020). The rotational spectrum of thioac-etamide was recently analyzed in the 59.6–110.0 GHz frequency region (5.03–2.72 mm). Its emission was searched for in regions associated with star formation using the IRAM 30 m ASAI observations toward the prestellar core L1544 and the outflow shock L1157–B1. The molecule was not detected, but the study allowed placing constraints on the thioacetamide abundances (Maris et al. 2019; Remijan et al. 2022).


Owing to their dusty circumstellar environments, a large mid-infrared (mid-IR) excess is a characteristic feature of post-AGB stars and a detection of cold circumstellar material using mid-IR photometry can be used to identify these objects. The first extensive search for these objects was initiated in the mid-80's using results from the Infrared Astronomical Satellite (Neugebauer et al. 1984) which enabled the identification of post-AGB stars in our Galaxy (Kwok 1993). The Toru$\acute{\rm n}$ catalogue (Szczerba et al. 2007) for Galactic post-AGB stars lists around 391 very likely post-AGB objects. The Galactic sample of post-AGB stars have been found to be a very diverse group of objects (Van Winckel 2003). Studies showed that the majority of the optically visible Galactic post-AGB stars could be classified based on their spectral energy distributions (SEDs) into two groups: shell-sources and disc-sources (Van Winckel 2003). The shell-sources show a double-peaked SED with the hot central star peaking at shorter wavelengths while the cold, detached, expanding dust shell peaks at longer wavelengths. This type of SED is considered to be characteristic of objects that follow the single-star evolution scenario mentioned above. The disc-sources do not show two distinct flux peaks in the mid-IR but they do display a clear near-infrared (near-IR) excess indicating that circumstellar dust must be close to the central star, near sublimation temperature. It is now well established that this feature in the SED indicates the presence of a stable compact circumbinary disc, and therefore these sources are referred to as disc-sources (de Ruyter et al. 2006; Deroo et al. 2007; Gielen et al. 2011a; Hillen et al. 2013). The rotation of the disc was resolved with the ALMA array (Bujarrabal et al. 2013a) in one object and using single dish observations Bujarrabal et al. (2013b) confirmed that disc rotation is indeed widespread. Moreover, these disc-sources are confirmed to be binaries and show orbital periods between 100 and 2000 d (Van Winckel et al. 2009; Gorlova et al. 2014). In contrast, for the Galactic shell-sources long-term radial velocity monitoring efforts have not yet resulted in any clear detected binary orbit (Hrivnak et al. 2011), which either confirms the single-star nature of these objects or introduces a possibility that these systems can have companions on very wide orbits.


NASA’s Kepler mission has unveiled a wealth of new planetary systems (e.g. Borucki et al. 2010). These systems offer new insights into the process of planet formation and evolution. One of Kepler’s key findings is that the most common planets in our Galaxy, observed to date, are between 1 and 4 R⊕, i.e. larger than Earth but smaller than Neptune (Fressin et al. 2013; Petigura, Marcy & Howard 2013). Further observations revealed a transition in average densities at planet sizes ∼1.5 R⊕ (Marcy et al. 2014; Rogers 2015), with smaller planets having densities consistent with rocky compositions while larger planets having lower densities indicating significant H/He envelopes. In addition, Owen & Wu (2013) noticed a bimodal distribution of observed planet radii. Since then, refined measurements have provided strong observational evidence for the sparseness of short-period planets in the size range of ∼1.5–2.0 R⊕ relative to the smaller and larger planets, yielding a valley in the small exoplanet radius distribution (e.g. Fulton et al. 2017; Fulton & Petigura 2018). For example, the California-Kepler Survey reported measurements from a large sample of 2025 planets, detecting a factor of ∼2 deficit in the relative occurrence of planets with sizes ∼1.5–2.0 R⊕ (Fulton et al. 2017). Studies suggest that this valley likely marks the transition from the smaller rocky planets: ‘super-Earths’, to planets with significant H/He envelopes typically containing a few per cent of the planet’s total mass: ‘sub-Neptunes’ (e.g. Lopez & Fortney 2013, 2014; Owen & Wu 2013; Rogers 2015; Ginzburg, Schlichting & Sari 2016). Furthermore, the location of this valley is observed to decrease to smaller planet radii, Rp, with increasing orbital period, P. In a recent study involving asteroseismology-based high precision stellar parameter measurements for a sample of 117 planets, a slope $\text{d log} R_\mathrm{ p}/ \text{d log} P = -0.09^{+0.02}_{-0.04}$ was reported for the radius valley by Van Eylen et al. (2018). A similar value for the slope of $-0.11^{+0.03}_{-0.03}$ was reported by Martinez et al. (2019).


Following the original BGK kinetic-theoretical scheme (Bernstein et al. 1957), we transform the above equations to the energy frame, defined as
5

w=12v2+ϕ.

In the energy frame, the ion distribution transforms into
6

fi(w)=Γ(κi)πκi−3/2Γ(κi−1/2)1+2wκi−3/2−κi,

where
7

f(x,v)dv=f(w)dw/2w−ϕ.

Here, the total energy (w) is normalized with

mvth,i2

, i.e., 2k

B

T

i
. As the ions encounter a negative potential well (a pulse), depending on their respective velocities, some of them will become trapped and some of them will pass through. Hence two types of population exist: a trapped population, and a passing population. We assume the passing populations to follow the initial distribution function - a kappa distribution function. In addition, we also assume the form of the potential in which particles are trapped to be prescribed. Spacecraft observations show that wave potential structures of Gaussian form are common in space and astrophysical plasmas (Matsumoto et al. 1994; Williams et al. 2006). A negative wave potential well acts as a perturbation capable of trapping ions in it. We assume this potential well to have Gaussian form, given by
8

ϕ(x)=−ψexp−x22δ2,

where ψ (>0) denotes the amplitude, and δ is the width of the perturbation, respectively. More precisely, δ is actually the distance where the potential decreases to 0.6065 times the maximum amplitude of ψ. The FWHM of the perturbation is actually given by Δ = 2.35δ. The net charge density can thus be expressed as
9

d2ϕdx2=1−Hne−ni,p−ni,tr+H,

where n

i,p
 is the passing ion density, and

ni,tr

 is the trapped ion density. Particles with suitable velocities falling in the potential range

−−ϕ,+−ϕ

 will become trapped, and the rest will pass through. Thus, the range of integration for both passing and trapped ion distributions is given by
10

ni,p=∫−∞−−ϕfp(x,v)dv+∫+−ϕ∞fp(x,v)dv.

As the passing ions follow the kappa distribution, we obtain the passing ion density as
11

ni,p=1−2AB−ϕ2F1[κi,1/2,3/2;ϕ/B],

where 2
F
1 is the hypergeometric function of the first kind. Now that we have obtained the passing ion density, we move on to the derivation of the trapped ion density. In terms of distribution function, the trapped ion density is given by
12

ni,tr=∫−−ϕ+−ϕftr(x,v)dv.

We may now derive the trapped ion density by rearranging Equation (9) as
13

ni,tr=1−Hne−ni,p−d2ϕdx2+H.

Substituting from Equation (11) and differentiating the potential in Equation (8) twice, in Equation (13), we obtain the trapped electron density as
14

ni,tr=1−H1−Trϕ(κe−3/2)0.5−κe+2ϕlog−ϕψδ2+ϕδ2−1+2AB−ϕ2F1[κi,1/2,3/2;+ϕ/B]+H.

For convenience, we make a transformation − ϕ = ∣ϕ∣ → ρ, (>0), and we obtain the trapped ion density as
15

ni,tr=1−HρTrκe−32+10.5−κe−2ρlogρψδ2−ρδ2−1+2ABρ2F1[κi,1/2,3/2;−ρ/B]+H.


Recent theoretical work has suggested that the presence, or lack thereof, of long-period giant planets could affect the formation of such systems. Batygin & Laughlin (2015) argued that the migration of Jupiter within our own solar system might have disrupted a massive primordial inner protoplanetary disk that could have formed multiple short-period super-Earths; they predicted that systems like the Kepler short-period multiple systems should typically lack long-period giant planets. A related question is, how common are planetary systems broadly similar in architecture to our solar system, with small close-in planets and more distant giant planets? We can begin to answer these questions in the near future through the combination of searches for short-period super-Earths and data from the long-term RV programs that have been monitoring many bright FGK stars for well over a decade. Super-Earths can be found with either high-precision RV observations or space-based transit searches. Such high-precision RV surveys include those being undertaken currently with HARPS (e.g., Díaz et al. 2016), HARPS-N (M15), APF (Vogt et al. 2014), and CHIRON (Tokovinin et al. 2013), and in the near future with MINERVA (Swift et al. 2015), CARMENES (Quirrenbach et al. 2014), ESPRESSO (Mégevand et al. 2014), and SPIRou (Artigau et al. 2014). The major upcoming space-based transit survey is that of TESS (Ricker et al. 2015). Long-term RV programs include the McDonald Observatory Planet Search (e.g., Endl et al. 2016), the Anglo-Australian Planet Search (e.g., Jones et al. 2010), the Lick-Carnegie Exoplanet Survey (e.g., Rowan et al. 2016), the CORALIE planet search (Marmier et al. 2013), and the planet search at ESO (e.g., Zechmeister et al. 2013). Long-period giant planets will also be found by Gaia, which will produce a huge sample of astrometrically detected planets (Perryman et al. 2014). While most of the Kepler sample is too faint to have been observed previously by long-term RV surveys (e.g., Coughlin et al. 2015), Gaia will be able to astrometrically detect long-period planets around many of these stars. Our own McDonald Observatory Planet Search program now has a baseline of 12–15 years for ∼200 FGKM stars, and a handful of stars also have lower precision observations dating back more than 25 years. HD 219134 is one of these stars, and here we present an analysis of our RV observations of this star, as well as our data on the stellar activity.


Quasi-periodic pulsations (QPPs) often refer to the quasi-periodic intensity variations during solar/stellar flares (see Zimovets et al. 2021, for a recent review). In many observations, the flare QPPs were found to show a nonstationary property in the time series integrated over the whole Sun/star or over the oscillation region, for instance, each pulsation has an anharmonic and symmetric triangular profile shape (e.g., Kolotkov et al. 2015; Nakariakov et al. 2019). The signature of flare QPPs can be detected in flare light curves across a broad band of the electromagnetic spectrum, i.e., radio/microwave emissions (Ning et al. 2005; Reznikova & Shibasaki 2011; Nakariakov et al. 2018; Yu & Chen 2019), UV/EUV wavelengths (Shen et al. 2018; Hayes et al. 2019; Reeves et al. 2020; Miao et al. 2021), SXR/HXR and γ-ray channels (Nakariakov et al. 2010; Ning 2017; Hayes et al. 2020; Li et al. 2020c), and the Hα (Srivastava et al. 2008; Kashapova et al. 2020; Li et al. 2020b) or Lyα (Van Doorsselaere et al. 2011; Milligan et al. 2017; Li 2021) emissions. The quasi-periods of these QPPs were reported from subseconds to tens of minutes (e.g., Tan et al. 2010; Shen et al. 2013, 2019; Kolotkov et al. 2018; Karlický & Rybák 2020; Clarke et al. 2021). It should be stated that the observed periods are generally related to the specific channels or flare phases (Tian et al. 2016; Dennis et al. 2017; Pugh et al. 2019), suggesting that the various classes of QPPs could be produced by different generation mechanisms (e.g., Kupriyanova et al. 2020). In the literature, the flare-related QPPs were most often explained by magnetohydrodynamic (MHD) waves, more specifically sausage waves, kink waves, and slow waves (Li et al. 2020a; Nakariakov & Kolotkov 2020; Wang et al. 2021), or by a repetitive regime of magnetic reconnection that could be spontaneous (i.e., self-oscillatory process) or triggered owing to external MHD oscillations (Thurgood et al. 2017; Yuan et al. 2019; Clarke et al. 2021). They can also be interpreted in terms of the LRC-circuit oscillation in current-carrying loops (Tan et al. 2016; Li et al. 2020b) or caused by the interaction between supra-arcade downflows and flare loops (Xue et al. 2020; Samanta et al. 2021).