Recently, quasars observed with multiple measurements, another potential cosmological probe with a higher redshift range that reaches to z ∼ 5, is becoming popular to constrain cosmological models in the largely unexplored portion of redshift range from z ∼ 2 to z ∼ 5. A sample that contains 120 angular size measurements in intermediate-luminosity quasars from the very long baseline interferometry (VLBI) observations (Cao et al. 2017a,b) has become an effective standard ruler, which have been extensively applied to test cosmological models (Li et al. 2017; Melia et al. 2017; Qi et al. 2017; Zheng et al. 2017; Xu et al. 2018; Ryan, Chen & Ratra 2019), measuring the speed of light (Cao et al. 2017a, 2020a), exploring cosmic curvature at different redshifts (Cao et al. 2019; Qi et al. 2019), and the validity of cosmic distance duality relation (Zheng et al. 2020). Then, Risaliti & Lusso (2019) put forward a new compilation of quasars containing 1598 quasi-stellar object (QSO) X-ray and ultraviolet (UV) flux measurements in the redshift range of 0.036 ≤ z ≤ 5.1003, which have been used to constrain cosmological models (Khadka & Ratra 2020b) and cosmic curvature at high redshifts (Liu et al. 2020a,c), as well as test the cosmic opacity (Geng et al. 2020; Liu et al. 2020b). Making use of this data to explore cosmological researches mainly depends on the empirical relationship between the X-ray and UV luminosity of these high-redshift quasars proposed by Avni & Tananbaum (1986), which leads to the Hubble diagram constructed by quasars (Risaliti & Lusso 2015, 2017; Lusso & Risaliti 2016; Bisogni, Risaliti & Lusso 2017). In general, the advantage of these two QSO measurements over other traditional cosmological probes is that QSO has a larger redshift range, which may be rewarding in exploring the behaviour of the non-standard cosmological models at high redshifts, providing an important supplement to other astrophysical observations and also demonstrating the ability of QSO as an additional cosmological probe (Zheng et al. 2021).


At scales comparable with dp, a variety of observations in the solar wind have suggested that fluctuations may consist primarily of kinetic Alfvén waves (KAWs; Bale et al. 2005; Sahraoui et al. 2009). In the linear fluctuation terminology, KAWs are waves belonging to the Alfvén branch, at wavevectors k almost perpendicular to the ambient magnetic field B0, with \hbox{$k \sim d_{\rm p}^{-1}$}k~dp-1. A detailed discussion of the properties of KAWs can be found in Hollweg (1999; see also references therein for a more complete view of the subject), for example. In the last decades, KAWs have received considerable attention due to their possible role in a normal mode description of turbulence. Indeed, theoretical studies (e.g., Shebalin et al. 1983; Carbone & Veltri 1990; Oughton et al. 1994) have shown that the turbulent cascade in magnetized plasma tends to develop mainly in directions perpendicular to B0. Anisotropic spectra have been commonly observed in space plasmas, showing the presence of a significant population of quasi-perpendicular wavevectors (Matthaeus et al. 1986, 1990). The above considerations suggest that fluctuations with characteristics similar to KAWs are naturally generated by a turbulent cascade at scales close to dp. Many solar wind observational studies (Bale et al. 2005; Sahraoui et al. 2009; Podesta & TenBarge 2012; Salem et al. 2012; Chen et al. 2013; Kiyani et al. 2013), theoretical works (Howes et al. 2008a; Schekochihin et al. 2009; Sahraoui et al. 2012) as well as numerical simulations (Gary & Nishimura 2004; Howes et al. 2008b; TenBarge & Howes 2012) have suggested that fluctuations near the end of the magnetohydrodynamics inertial cascade range may consist primarily of KAWs, and that such fluctuations can play an important role in the dissipation of turbulent energy. Due to a non-vanishing parallel component of the electric field associated with KAWs, these waves have also been considered in the problem of particle acceleration (Voitenko & Goossens 2004; Décamp & Malara 2006). Particle acceleration in Alfvén waves in a dispersive regime has been studied both in 2D (Tsiklauri et al. 2005; Tsiklauri 2011) and 3D (Tsiklauri 2012) configurations. Recently, Vasconez et al. (2014) have studied collisionless Landau damping and wave-particle resonant interactions in KAWs.


There is growing observational and numerical evidence that star-forming regions may be in a state of global gravitational contraction; see Vázquez-Semadeni et al. (2019). The supersonic collisions of flows of warm diffuse atomic gas simulated with both self-gravity and cooling exhibit the hierarchical collapse of the turbulent medium, as was shown by Vázquez-Semadeni et al. (2007) and Naranjo-Romero, Vázquez-Semadeni & Loughnane (2015) for example. This implies that gravitational instability (GI hereafter) manifests itself in a wide range of sufficiently large scales during the evolution of molecular clouds. Theoretical work has revealed that flattened dense structures form as a result of large collisions of diffuse matter. Later on, they give birth to filaments, which then fragment into multiple cores. This scenario is provided by the dynamical instability of self-gravitating layers, cylinders, and spheres, respectively. The linear stability analysis of these idealized configurations (e.g. Ledoux 1951; Chandrasekhar & Fermi 1953; Bonnor 1956; Elmegreen & Elmegreen 1978; Nagasawa 1987; Fiege & Pudritz 2000) as well as the corresponding non-linear solutions (e.g. Larson 1969; Penston 1969; Miyama, Narita & Hayashi 1987; Inutsuka & Miyama 1997; Masunaga & Inutsuka 2000, and many others) confirms this view. At the same time, as was noted by Larson (1985), the specific geometry of self-gravitating objects is not crucial for the instability condition, which does not differ much from the basic one derived for the unbounded uniform medium. In the latter case, the study of GI goes back to Jeans (1902), who established that plane-wave perturbations on such a background having finite pressure are heavy sound waves propagating at the subsonic velocity, which vanishes as the wavelength approaches the value now referred to as the Jeans length. Perturbations with scale larger than the Jeans length are the growing and damping static waves. Thus, the critical scales for GI of realistic configurations mentioned above are always similar to the Jeans scale, which includes typical speed of sound and density chosen appropriately for the corresponding configuration. However, the most unstable scale for realistic configurations has a finite value in contrast to the Jeans result, when the largest growth rate (corresponding to the inverse free-fall time) manifests at the infinitely large scale. The largest growth rates for GI of realistic configurations are commonly the fractions of the inverse free-fall time.


We find a similar dichotomy of bars in previous studies (Elmegreen & Elmegreen 1985, 1989; Baumgart & Peterson 1986; Elmegreen et al. 1996; Regan & Elmegreen 1997; Kim et al. 2015). They investigated two types of bars: flat and exponential profiles in surface brightness. Flat bars have nearly constant light distributions along the bar, whereas those of exponential bars decrease exponentially. They also differ in their structures and the intensity contrast between the bar and the disk: flat bars are longer, wider, and stronger than exponential bars and have a higher contrast than exponential bars. Besides, Athanassoula (1992) explained that flat bars could have roughly rectangular orbits around the end of the bar through the stellar orbit calculation. These properties can also be explained by the locations of resonances (Lynden-Bell 1979; Contopoulos & Papayannopoulos 1980; Sellwood 1981; Contopoulos et al. 1989; Athanassoula 1992; Skokos et al. 2002). A flat density profile develops in crowding stellar orbits between the inner 4:1 resonance and corotation radius (Combes & Elmegreen 1993; Elmegreen & Elmegreen 1985; Elmegreen et al. 1996). Exponential bars end near the inner Lindblad resonance and do not have such crowding orbits (Lynden-Bell 1979; Elmegreen & Elmegreen 1985; Elmegreen et al. 1996). Therefore, flat bars and exponential bars may be expected to have different pattern speeds based on the value of

, where Rcr and Rbar are the radius of the corotation resonance and the bar, respectively (Debattista & Sellwood 2000; Valenzuela & Klypin 2003). Although some studies reported the observational lack of slow bars (Debattista & Sellwood 2000; Aguerri et al. 2015), others showed that the pattern speed of bars roughly depends on the Hubble type: fast bars in early-type spirals and slow bars in late-type spirals (Aguerri et al. 1998; Rautiainen et al. 2008). More observational data will help us understand the relation between the density profile and the pattern speed of bars.


In Sects. 4.3 and 4.4 we showed that our image simulations match the actual data very well and that the re-weighting factors are close to unity for subsets of galaxies split by size and S/N, with fluctuations of the order of 10−4 or less. Consequently, the estimates of the shear biases presented in Table 2 should be accurate. Nonetheless it is worthwhile to explore the robustness of our results and attempt to quantify the potential systematic uncertainties that may still be present. For instance, we simplified the galaxy morphologies by representing them with Sérsic profiles. Our input catalogue is incomplete at the faintest magnitudes, but the missing galaxies may still affect the estimate of the multiplicative bias. Varying star densities can affect the results (e.g. Hoekstra et al. 2015, 2017). In this section we therefore explore the sensitivity of the shear measurement bias to various assumptions and simplifications made in the simulations. These results help to assess the robustness of the calibration presented in the previous section. In the language described in Sect. 2.2, these tests correspond to various evaluations of the Δ terms from different simulations. As these tests can become computationally expensive very quickly, we use only 5 of the 13 PSF sets. This results in only minor changes in the mean residual bias values ( 0.005; see lower right panel of Fig. 13), and hence they remain a good representation of the data. The smaller volume of simulations naturally results in a larger statistical uncertainty, but we note that we are interested in determining the change in the mean values of the multiplicative biases of the different tomographic samples when we vary the inputs. The errors are tightly correlated among the different simulations within a tomographic bin, as there is a significant overlap among the input samples of galaxies in the different simulations and because the noise realisations in the images are identical in many of these simulations, unless explicitly mentioned otherwise. Hence, the shifts are not driven by noise. Our main objective is to ensure that uncertainties in the input quantities do not change the bias by more than 0.02. The results in this section indicate that they are indeed controlled under 0.02, but it appears that we cannot impose a tighter limit on the overall uncertainty at this time.


Most DSFGs are discovered in wide-area observations using single-dish far-IR (FIR)/millimeter instruments such as the Submillimeter Common-User Bolometer Array (SCUBA/SCUBA-2) on the James Clerk Maxwell Telescope (JCMT; e.g., Smail et al. 1997; Hughes et al. 1998; Chapman et al. 2005; Koprowski et al. 2017; Simpson et al. 2019), the Herschel Space Observatory
10

10
Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. (Pilbratt et al. 2010; Eales et al. 2010; Oliver et al. 2012), and the AzTEC instrument (Scott et al. 2008; Aretxaga et al. 2011). Multi-wavelength follow-up of hundreds of survey-identified DSFGs reveals that most sit between 1  z  3 (Casey et al. 2012a; Magnelli et al. 2011, 2013; Gruppioni et al. 2013; Le Floc’h et al. 2005). While there exists a handful of individually studied DSFGs at redshifts as high as z ∼ 5–7 (e.g., Cooray et al. 2014; Strandet et al. 2017; Marrone et al. 2018; Zavala et al. 2018b; Casey et al. 2019; Reuter et al. 2020), such high-z systems have proven difficult to both identify and spectroscopically confirm. This is because (i) DSFGs at z > 4 are outnumbered by the dominant DSFG population at z ≈ 1–3 and (ii) there are serious physical and evolutionary degeneracies that make DSFG photometric redshifts highly uncertain (with precision often σ
Δz/1+z
 ≳ 1; Casey 2020). This latter point is often seen as a benefit: their strongly negative k-correction means that the flux density of DSFGs at z > 1 remains constant with increasing z for λ
obs ≳ 850 μm, meaning a DSFG at z ∼ 10 can be observed as readily as a DSFG at z ∼ 1 (Blain et al. 2002). However, when searching for high-z DSFGs, this negative k-correction is also a hindrance as it becomes difficult to identify redshifts for galaxies with only long-wavelength emission. This effect is further exacerbated by the (sub)millimeter color degeneracy between dust temperature and redshift. Thus, barring clear identification at other wavelengths, it is easy to confuse z ∼ 2 and z ∼ 6 DSFGs with solely submillimeter observations.


As in G18, we compiled existing constraints on the molecular gas fraction fgas of quiescent and pSB galaxies from recent literature, namely: local QGs consisting of the ATLAS3D (Young et al. 2011; Cappellari et al. 2013; Davis et al. 2014) and HRS (Boselli et al. 2014; Lianou et al. 2016) ETG samples as well as the samples of pSB galaxies (hereafter, the “low-z pSB” sample) of French et al. (2015) and Alatalo et al. (2016); at low and intermediate redshift, the ETG sample of Spilker et al. (2018) and the pSB sample of Suess et al. (2017); at intermediate and high redshift, constraints from Hayashi et al. (2018) on gas in z ∼ 1.46 cluster ETGs, as well as on individual galaxies from Sargent et al. (2015), Bezanson et al. (2019), and Rudnick et al. (2017). Given its size, we divided the ATLAS3D sample into high- and low-mass subsamples, choosing 5 × 1010 M⊙ as the cut-off mass. In addition, we also included fgas estimates derived from the (median) stacked FIR spectral energy distributions of ETGs at z ∼ 1.8 (G18; 977 galaxies), z ∼ 1.2, z ∼ 0.8, and z ∼ 0.5 (1394, 1536, and 563 galaxies, respectively; Magdis et al. 2020, hereafter M20). Finally, at higher redshift (z ∼ 3), we converted star formation rates (SFR) estimated from spectroscopy (Schreiber et al. 2018a; D’Eugenio et al. 2020) into gas masses assuming the star formation efficiency found by G18. As a consequence of our zmax = 3.5, we did not include higher-redshift quiescent galaxies (Glazebrook et al. 2017; Schreiber et al. 2018b; Tanaka et al. 2019; Valentino et al. 2020) in the analysis and considered z ∼ 3 galaxies as pSB. The dust-based estimates of G18 and M20 (and, by extension, the z ∼ 3 semi-constraints) assume a gas-to-dust ratio (G/D). It is dependent on metallicity, which is presumed to be solar or higher owing to both the relatively high gas-phase metallicity of MS galaxies at z ≲ 1 (e.g., Mannucci et al. 2010) and the already high stellar metallicities of QGs at z >  1 (Onodera et al. 2015; Estrada-Carpenter et al. 2019). Here we adopted an intermediate value between the solar and supersolar G/Ds used in M20, and we increased the error bars of these points to include both the solar and supersolar confidence estimates. These various samples, which are summarized with their selection criteria in Table B.1, combine into a nonhomogeneous dataset: some were specifically selected as ETGs, and others were based on varying degrees of quiescence. In particular, pSB galaxies are not necessarily truly quiescent and could, in principle, resume normal star formation. However, as a possible precursor of QGs, they provide useful, though not constraining (see Sect. 4), comparison samples for the model. Here we refer to all equally as either QGs or pSB galaxies, and we make the assumption that, on average, these different samples are not otherwise significantly biased with regard to their gas content compared to the full population, given each mass limit and type.


High-redshift z ≳ 2 galaxies with prominent Lyman-α emission (Partridge & Peebles 1967), referred to as Lyman-α emitters (LAEs), have become the subject of intense research over the last two decades. Since LAEs are believed to be powered at least partially by ongoing star formation, they are expected to belong to a relatively low-mass and young class of actively star-forming galaxies. This suggests that the number density of LAEs is large enough to map out the large-scale structure of the high-redshift universe. Increasing numbers of LAEs are being observed by surveys including narrow-band imaging (e.g., Nakajima et al. 2012) and integral field unit spectroscopy such as MUSE (e.g., Bacon et al. 2006), amounting to about 104 emitters known to date since the first detections (e.g., Cowie & Hu 1998; Hu & McMahon 1996). These observations enable us to study galaxy clustering at somewhat small scales (e.g., Diener et al. 2017; Ouchi et al. 2010, 2018) as well as evolution of the Lyman-α luminosity function (e.g., Konno et al. 2016, 2018; Ouchi et al. 2008). A remarkable example for such surveys is the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX; Adams et al. 2011; Hill et al. 2008). HETDEX will map out the three-dimensional distribution of nearly one million LAEs (Leung et al. 2017) at 1.9  z  3.5 over 400 deg2. This allows us to precisely measure the large-scale (≳10 Mpc) clustering of LAEs (Agrawal et al. 2017; Chiang et al. 2013) and of the Lyman-α intensity map (Saito et al., in prep.) with the primary scientific goal being to determine the cosmic expansion history via baryon acoustic oscillations (BAOs) and the growth of structure via redshift-space distortions (RSD). We refer the reader to Alam et al. (2017) and references therein for recent efforts of BAO and RSD measurements. In addition, these surveys offer exciting opportunities to study the connection between LAEs and their environment, including the cross-correlation between LAEs and the Lyman-α forest or other galaxy populations.


Several mechanisms have been suggested to explain the formation of moving groups. A common explanation is that these velocity structures are the remnants of open clusters, or formed by interactions with a bar (Eggen 1965; Dehnen 2000). One problem with the cluster formation idea is that stars in moving groups can have a variety of different ages and compositions, so it is unlikely that they all came from the same cluster (Eggen 1965; Kushniruk et al. 2020). Analysis of GALAH data (Quillen et al. 2018) indicates that some moving groups, such as the Hercules moving group, may be due to a resonant bar. It has also been suggested that moving groups could have been formed from perturbations due to the Magellanic Clouds via gravitational interactions (Dehnen 1998). Recent work also finds that transient spiral structure (Hunt et al. 2018) may lead to the formation of moving groups, as well as perturbations due to spiral arms in the MW (Michtchenko et al. 2018). Moving groups in Gaia data have also been identified and analysed in action space. In the (JR, Jz) plane there are at least seven overdensities that follow lines of constant slope in this plane, which correspond to known moving groups in the solar neighbourhood (Trick, Coronado & Rix 2019). It is likely that there may be multiple causal mechanisms at play in the formation of moving groups in the Milky Way. The analysis of Gaia DR2 data has revealed many facets of a Galaxy that are clearly out of equilibrium, including the so-called phase-space spiral (Antoja et al. 2018), and the Enceladus merger (Helmi et al. 2018), that have been interpreted as arising from interactions with dwarf galaxies. Analysis of Gaia DR2 data also led to the discovery of a new dwarf galaxy (Torrealba et al. 2019) that likely interacted with the Milky Way (Chakrabarti et al. 2019). However, the formation of moving groups due to dwarf galaxy interactions has not yet been studied with full N-body simulations. Motivated by these earlier works that indicate that the MW may has been perturbed by dwarf galaxies, we focus our study here in trying to understand if some of the moving groups in the Galaxy may have arisen from dwarf galaxy interactions.


The question of the evolution of exoplanet systems after the main sequence of their host is generally addressed by studying exoplanets around subgiants, RGB stars, and normal HB (RC) stars (hereafter the ’classical’ evolved stars). These classical evolved stars are typically very large stars, with radii ranging from ~ 5− 10 R⊙ to more than 1000 R⊙. This is much larger than hot subdwarfs, which have radii in the range ~ 0.1−0.3 R⊙ (Heber 2016). Their mass is typically higher than ~ 1.5 M⊙, compared to~0.47 M⊙ for hot subdwarfs. The transit and radial velocity (RV) methods are both challenging for these classical evolved stars because the transit depth is diluted and there are additional noise sources (Van Eylen et al. 2016). Another difficulty forthe question of the fate of exoplanet systems after the RGB phase itself is the difficulty of distinguishing RGB and RC stars based on their spectroscopic parameters alone, which is sometimes hard even with help of asteroseismology (Campante et al. 2019). As a consequence, only large or massive planets are detected around the classical evolved stars (Jones et al. 2021, and references therein). A dearth of close-in giant planets is observed around these evolved stars compared to solar-type main-sequence stars (Sato et al. 2008; Döllinger et al. 2009). This may be caused by planet engulfment by the host star, but current technologies do not allow us to determine whether smaller planets and remnants (such as the dense cores of former giant planets) are present. The lack of close-in giant planets may also be explained by the intrinsically different planetary formation for these intermediate-mass stars (see the discussion in Jones et al. 2021). Ultimately, the very existence of planet remnants may be linked to the ejection of most of the envelope on the RGB that occurs for hot subdwarfs, while for classical evolved stars, nothing stops the in-spiraling planet inside the host star, and in all cases, the planet finally merges with the star, is fully tidally disrupted, or is totally ablated by heating or by the strong stellar wind. In other words, the ejection of the envelope not only enables the detection of small objects as remnants, but most importantly, it may even be the reason for the existence of these remnants by stopping the spiraling-in in the host star.


The atmosphere above the Canary Islands, and especially the western islands Tenerife and La Palma, has been extensively characterized over the past 50 yr (Kiepenheuer 1972; McInnes & Walker 1974; Brandt & Righini 1985; Murdin 1985; Stickland et al. 1987; Whittet, Bode & Murdin 1987; Menéndez-Valdés & Blanco 1992; Jímenez, González Jorge & Rabello-Soares 1998; Mahoney, Muñoz-Tuñón & Varela 1998; Maring et al. 2000; Torres et al. 2002; Rodríguez et al. 2004; Alonso-Pérez et al. 2007; Basart et al. 2009; Lombardi, Zitelli & Ortolani 2009; Delgado et al. 2010; Vernin et al. 2011; Cuevas et al. 2013; Rodriguez-Franco & Cuevas 2013; Varela et al. 2014; Laken et al. 2016; Vogiatzis et al. 2018; Hidalgo et al. 2021). Due to the combination of large-scale atmospheric circulation on the descending branch of the Hadley cell (see e.g. Palmén & Newton 1969; Rodríguez et al. 2004), and the ‘Trade’ or ‘Alisios’ winds coming from the Azores high area, a stable and strong temperature inversion layer (TIL) appears (Font 1956; Huetz-de-Lemps 1969), whose top is typically found at heights around 1200 m a.s.l. in summer and 1800 m a.s.l. in winter (Torres et al. 2002; Carrillo et al. 2016). Whenever the temperature inversion is able to separate two well-defined regimes, the moist marine boundary layer (MBL) and above it, the dry free troposphere (FT), the phenomenon is called an ‘Alisio’ inversion. This happens about 80 per cent of the time (Torres et al. 2002). Under these conditions, the FT can be characterized as ‘ultraclean’, i. e., the concentration of accumulation mode particulate matter is lower than 50 cm−3 (Pennypacker, Diamond & Wood 2020). The clean atmospheric conditions are one of the reasons why the Canarian observatories ‘Observatorio del Teide (OT)’, located at ∼2400 m a.s.l., and ‘Observatorio del Roque de los Muchachos (ORM)’, located between ∼2100 and ∼2400 m a.s.l., are known to belong to the best astronomical sites worldwide.


Very small asteroids (VSAs) are objects with diameters D  150 m. They often rotate with periods shorter than 2 h enabling us to study their internal structure by comparing the centrifugal force with the material forces holding them together (Holsapple 2007). Because of their small sizes, VSAs are sensitive to the YORP effect (Rubincam 2000), which is a torque induced on the rotating body by the thermal radiation emitted by its surface complemented by a torque produced by scattered sunlight. YORP can either spin up or slow down the asteroid rotation as well as change the obliquity of its spin axis ϵ, which is an angle between the normal to the asteroid orbital plane and its rotation axis. While the fast rotation has been observed for many VSAs, their spin axes were not determined except for one object1, (54 509) YORP (whose name is the same as the name of the effect itself). (54 509) was the first asteroid for which the effect of YORP has been observed (Lowry et al. 2007; Taylor et al. 2007). The obliquity of the (54 509) spin axis is ϵ = 173°, which means it is nearly perpendicular to the asteroid orbital plane. Such an orientation of the spin axis was found as an end state of the YORP evolution in the simulations performed by Čapek & Vokrouhlický (2004) for objects with finite surface thermal conductivity. If their prediction is true, then for the VSAs that experienced a strong YORP effect for a long time (and the fastest rotating VSAs are such objects), we should observe spin axis obliquities close to 0° or 180°. Recently Golubov et al. (2021) have shown that for very small objects of a highly irregular shape, the transverse heat conduction (TYORP) can add new asymptotic states for the obliquity. For this reason it would be interesting to verify those predictions with observationsof VSAs. To do that, we should observe their lightcurves at many different positions on the sky to be able to determine their spin axes. For near-Earth objects (NEAs) this condition is met either by the Earth co-orbital asteroids – and (54 509) is an example of such objects – or by objects for which their close encounter with the Earth can be observed along a long arc on the sky.


An alternative possibility to reduce the fraction of X-ray sources in the WISE R75 wedge is to allow a large fraction of heavily obscured AGN. This can be achieved for example, by increasing the fraction of Compton-thick AGN in the X-ray luminosity function above the current assumption of 34 per cent, or by increasing the scatter in the relation that links X-ray obscuration to optical extinction beyond the adopted value of 0.5 dex. Relaxing the above model assumptions would allow heavily obscured and hence, X-ray faint, sources to be selected by the WISE R75 criteria. There is indeed evidence for a potentially large population of heavily obscured, possibly Compton-thick AGN, among the WISE population (e.g. Assef et al. 2015; Mountrichas et al. 2017; Yan et al. 2019). The SDSS spectroscopic follow-up programme presented by LaMassa et al. (2019) also revealed a non-negligible number of WISE R75 sources that are optically faint ($r\gtrsim 22$ mag), lie at redshifts $z\lesssim 1$ and are spectroscopically identified by their prominent [O ii] 3727 emission lines. These sources are prime candidates for heavily obscured AGN. Our baseline model predicts that the most heavily obscured, Compton-thick, WISE AGN are at low redshift, $z\lesssim 0.6$ (see Fig. 19) and relatively optically bright. The top panel of Fig. 22 demonstrates the latter point by plotting the r-band distribution of the Compton-thick AGN population predicted by the model. Observationally, the identification of such AGN needs to account for the relatively high level of contamination of the WISE R75 AGN selection by star-forming galaxies at redshifts $z\lesssim 0.6$ (s1ee Fig. 14). One approach to achieve this is via diagnostic optical emission-line ratios (e.g. Kewley et al. 2001) to separate star-forming galaxies from Seyfert-2s. Observations at hard X-rays can also provide useful information on the nuclear activity of a galaxy and the level of line-of-sight obscuration. The bottom panel of Fig. 22 shows the expected 2–10 keV X-ray flux distribution of the Compton-thick AGN predicted by the model. The expected fluxes have already been reached in deep X-ray survey fields, for example, COSMOS-Legacy (Civano et al. 2016). Study of the X-ray spectral properties of WISE-selected AGN in such fields can test the baseline model predictions for the demographics of Compton-thick AGN in the WISE R75 wedge.


Similarly to long bursts, short GRBs are thought to be produced by a relativistic jet with a typical half-opening angle θjet ~ 5–15 deg (Fong et al. 2016). However, whether or not BNS mergers can always efficiently produce a relativistic jet is still debated (Paschalidis et al. 2015; Ruiz et al. 2016; Kawamura et al. 2016). Given the small probability that our line of sight was within the jet half-opening angle, 1 − cos(θjet), it is unlikelythat the first short GRB associated to a GW event had a jet pointing towards the Earth. The extremely low γ-ray luminosity of GRB 170817A has been interpreted as being due to (i) the debeamed radiation of a jet observed off-beam (i.e. viewing angle θview > θjet), provided that the jet bulk Lorentz factor is significantly smaller than usually assumed (see, e.g. Pian et al. 2017). Alternatively, the jet could be (ii) structured, with a fast and energetic inner core surrounded by a slower, less energetic layer/sheath/cocoon (first proposed for long GRBs – Lipunov et al. 2001; Rossi et al. 2002; Salafia et al. 2015 – and only recently extended to short GRBs – Kathirgamaraju et al. 2018; Lazzati et al. 2017a; Gottlieb et al. 2017; Lazzati et al. 2017b; Lyman et al. 2018; Margutti et al. 2018; Troja et al. 2018a). In this scenario the faint, off-beam emission is due to the slower component, which originates from the interaction of the jet with the merger dynamical ejecta or the post-merger winds. Recently, Mooley et al. (2018) suggested the possibility that (iii) the jet was not successful in excavating its way through the ambient medium and that GRB 170817A was due to its vestige, a quasi-isotropic cocoon with a velocity profile. Last but not least, (iv) a jet-less interpretation of GRB 17017A could still be viable: an isotropic fireball, expanding ahead of the kilonova ejecta, which could account for both the low luminosity of the γ-ray event and the properties of the EM component in the radio and X-ray bands (Salafia et al. 2017). In this case, all BNS mergers should have this kind of faint, hard X-ray counterpart. All of the above scenarios have relatively clear predictions for the temporal and spectral evolution of the electromagnetic emission from X-rays to the radioband. A comprehensive discussion of the possible physical scenarios leading to the observed broad-band emission of GW 170817/GRB 170817A can be found in Nakar & Piran (2018). Recent radio and X-ray observations(Mooley et al. 2018; Margutti et al. 2018; Ruan et al. 2018; Troja et al. 2018a), carried out until ~ 110−115 d after the event, indicate that the source flux is steadily rising and that the spectral energy distribution (SED) over these bands is consistent with a single power-law component. These results disfavour interpretation (i) reported above (an off-beam homogeneous jet).


The period candidates of other three ULXs may range from ∼100 to ∼600 d. Apart from noise and artefacts, all the candidate periods are only significant in a specific epoch. This suggests that they are not associated with any stable mechanism such as orbital motion. Instead, such long-term (> 100 d) X-ray quasi-periodic variations are likely related to superorbital periods that are thought to be due to radiation-driven warping of accretion discs (Ogilvie & Dubus 2001) or tidal interaction-induced disc precession (Whitehurst & King 1991). Alternatively, mass transfer rate-related events such as X-ray state changes and disc instability can also cause long-term modulations (Kotze & Charles 2012). In particular, there are two intermittent quasi-periodicities for both NGC 5408 X-1 and M81 X-6, suggesting that the quasi-periods are changing or evolving. They resemble some Galactic X-ray binaries that show similar behaviour (e.g. Cyg X–2 and SMC X–1; Kotze & Charles 2012) and it has been suggested that a warped disc could lead to an unstable steadily precessing disc, causing quasi-periodic behaviour (Ogilvie & Dubus 2001). We note that there are many uncertainties on the physical parameters of ULXs. To determine the origin of superorbital periods of ULXs, one has to know at least the mass ratio between the companion and the compact star (q = MC/MX) and the binary separation. Unfortunately, it is very difficult to get these parameters for ULXs. For the three ULXs discussed here (i.e. excluding ESO 243-49 HLX-1), only M81 X-6 has better constraints on the black hole mass and the nature of the companion. The masses of the black hole and companion star are estimated (MX = 18 M⊙, MC = 23 M⊙) such that q can be derived. In this case, we can rule out a tidal interaction-induced disc precession scenario that requires q  0.25–0.33 (Whitehurst & King 1991). For a warped disc, the binary separation and the mass ratio suggest that M81 X-6 lies in the intermediate instability zone for radiation-driven warping in X-ray binaries (see fig. 1 of Kotze & Charles 2012). The quasi-periodic variability may represent the switching time-scale between a warped disc and a flat disc.


The year 2020 marks the 350 yr anniversary of the discovery of the eruption of Nova 1670 (or CK Vul) made by European astronomers (Shara et al. 1985). Their observations, predominantly performed with a naked eye, traced the object’s evolution on the sky in 1670−1672. From the archive records, we know that the eruption was rather unusual, in particular it was very much unlike classical novae. The light curve of CK Vul displayed three peaks and the star was described as reddish in the later stages of the eruption (Hevelius 1671; Shara et al. 1985). These characteristics resemble closest the behavior often observed in (luminous) red novae (Kato 2003; Tylenda et al. 2013), a modern category of eruptive stars known from our and other galaxies (e.g. Pastorello et al. 2019). Red novae are recognized as manifestations of on-going mergers of non-compact stars such as main-sequence dwarfs, sub-giants, or red giants (Soker & Tylenda 2003; Tylenda & Soker 2006; Tylenda et al. 2011; Pastorello et al. 2019). While the number of known red novae, mainly extragalactic ones, is quickly rising (e.g., Stritzinger et al. 2020), we know only a few red-nova remnants that are decades old (Kamiński et al. 2018a). The remnant of the 1670 eruption of CK Vul, as a candidate post-merger site, could be the oldest (counting from the onset of the eruption) known object of this type and as such offers the opportunity to investigate a merger aftermath centuries after the stellar coalescence. The nature of the progenitor system of CK Vul has been debated. Eyres et al. (2018) proposed that the seventeenth-century merger took place between a white dwarf and a brown dwarf, but there is little quantitative evidence to support this. Based on the analysis of the source’s chemical and isotopic composition, including the unique presence of the radioactive isotope of 26Al, Kamiński et al. (2018b) found that the progenitor system of CK Vul included at least one red-giant-branch (RGB) star with a fully developed helium core.


Dust distribution:We employed the standard flared disk model with well-mixed gas and dust, which has been successfully used to explain the observed SEDs of a large sample of young stellar objects and BDs (e.g., Wolf et al. 2003; Sauter et al. 2009; Harvey et al. 2012a; Joergens et al. 2013; Liu et al. 2015). The structure of the dust density is assumed with a Gaussian vertical profile (1)\begin{equation} \rho_{\rm{dust}}=\rho_{0}\left(\frac{R_{*}}{\varpi}\right)^{\alpha}\exp\left[-\frac{1}{2}\left(\frac{z}{h(\varpi)}\right)^2\right], \label{dust_density} \end{equation}ρdust=ρ0R∗ϖαexp−12zh(ϖ)2,and the surface density is described as a power-law function (2)\begin{equation} \Sigma(\varpi)=\Sigma_{0}\left(\frac{R_{*}}{\varpi}\right)^p, \end{equation}Σ(ϖ)=Σ0R∗ϖp,where ϖ is the radial distance from the central star measured in the disk midplane, and h(ϖ) is the scale height of the disk. The disk extends from an inner radius Rin to an outer radius Rout. To the best of our knowledge, among our sample, there are five objects that have been identified as binary systems so far. They are 2M1207 (a~55 AU, Chauvin et al. 2004), J04221332+1934392 (a~7 AU, Todorov et al. 2014), J04414489+2301513 (a~15 AU, Todorov et al. 2014), USD161833 (a~134 AU, Bouy et al. 2006), and USD161939 (a ~ 26 AU, Bouy et al. 2006), where a refers to the separation within the system. The disks around individual components in binary systems are expected to have truncation radii of the order of (0.3 − 0.5)a (Papaloizou & Pringle 1977). We adopted 0.5 a as the disk outer radii for 2M1207, USD161833, and USD161939. For the close pairs (a ≲ 15 AU, J04221332+1934392 and J04414489+2301513), dynamical simulations of star-disk interactions suggest that individual disks are unlikely to survive (e.g., Artymowicz & Lubow 1994). Disk modeling is complicated in those close multiple systems. For simplicity, we assume that the emission is associated with circumbinary disks of 100 AU in size. For other objects, we fix Rout = 100 AU in the modeling because the choice of this parameter value makes essentially no difference to the synthetic SEDs in the simulated wavelength range (Harvey et al. 2012a). The scale height follows the power-law distribution(3)\begin{equation} h(\varpi) = H_{100}\left(\frac{\varpi}{100\,\rm{AU}}\right)^\beta,\\ \end{equation}h(ϖ)=H100ϖ100 AUβ,with the exponent β characterizing the degree of flaring and H100 representing the scale height at a distance of 100 AU from the central star. The indices α, p, and β are codependent through p = α − β. We fix p = 1, which is the typical value found for T Tauri disks in the sub-millimeter (e.g., Isella et al. 2009; Guilloteau et al. 2011), since only spatially resolved data can place constraints on this parameter (e.g., Ricci et al. 2013, 2014).               Dust properties:We assume the dust grains to be a homogeneous mixture of 75% amorphous silicate and 25% carbon with a mean density of ρgrain = 2.5 g cm-3 and the complex refractive indices given by Jäger et al. (1994, 1998), and Dorschner et al. (1995). Porous grains are not considered because the fluxes at wavelengths beyond ~ 2 μm are almost independent of the degree of grain porosity in low-mass disks, as shown by Kirchschlager & Wolf (2014). The grain size distribution is given by the standard power law dn(a) ∝ a-3.5da with minimum and maximum grain sizes amin = 0.1 μm and amax = 100 μm, respectively. The choice of the minimum value for the grain size, amin, ensures that its exact value has a negligible impact on the synthetic SEDs. Since there is no information about the maximum grain sizes of our target disks, as provided, e.g., by the (sub)millimeter spectral index, we adopt amax = 100 μm. The Herschel/PACS far-IR observations are sensitive to dust grains with this assumed sizes. Strong grain growth up to millimeter sizes as detected in some BD disks (e.g., Ricci et al. 2012, 2013, 2014; Broekhoven-Fiene et al. 2014) would remain undetected in our data and could affect the disk mass. Our prescription for the dust properties is identical to those used in Liu et al. (2015).


The leading edges of the transients normally leave bright traces in the images of visible light, inspiring many methods that were developed to derive their locations and velocities, such as the icecream cone model (Fisher & Munro 1984), the graduated cylindrical shell (GCS) model (Thernisien 2011), geometric triangulation methods (Liu et al. 2010), mask-fitting methods (Feng et al. 2012), and trace-fitting methods including the point-p, fixed-Φ, harmonic mean, and self-similar expansion fitting methods (e.g., Sheeley et al. 1999; Howard et al. 2006; Davies et al. 2012; Möstl & Davies 2013). To derive the velocity distribution inside one transient rather than only at its leading edge, some other techniques have been proposed. Colaninno & Vourlidas (2006) applied an optical flow tool to extract the velocity vector of a coronal mass ejection (CME) in digital images. Feng et al. (2015) derived the radial velocity profiles of the whole CME from the spatial distribution of its density given by the mass continuum equation. A cross-correlation method was applied to derive continuous 2D speed maps of a CME from coronagraphic images by Bemporad et al. (2018). In their work, the radial shift pixel by pixel is determined by maximizing the cross correlation between the signal in a radial window at one frame and the signal in a radial shifted window at the previous frame, and the radial speed just equals the radial shift over the time interval between the two frames. Ying et al. (2019) improved this cross-correlation method by analyzing data in three steps: forward step (FS), backward step (BS), and average step (AS). In the FS (BS), the 2D velocity map between the current and the previous (next) frame is constructed with almost the same method as Bemporad et al. (2018). In the AS the average, velocity is obtained from the FS and BS. The velocities derived by all these methods are the component of the flow velocity vector projected onto the POS. This may underestimate the velocity especially for transients that do not propagate in the POS. Methods such as the polarizaition ratio technique (Moran & Davila 2004; DeForest et al. 2017) or the local correlation tracking (LCT) method (Mierla et al. 2009) can derive the 3D geometric information of the whole transients, but not the velocity distribution. Bemporad et al. (2018) chose the propagating direction averaged over the whole CME derived by the polarization ratio technique to correct the radial speed in the 2D maps, but the key information along the LOS is still lacking.


In Figure 6, we plot the histogram distributions of the calculated number of Galactic BH–He XRBs as a function of the companion mass, BH mass, orbital period, and orbital eccentricity for Models A–D. Since the progenitor systems containing a BH and an OB star possess similar distributions of the OB star masses and the orbital periods in all models, the BH–He XRBs also have similar distributions of helium masses and orbital periods under the assumptions of different models. The masses of the helium stars are mainly distributed in the range of

, and the orbital periods are distributed in a wide range (∼0.1–1000 days) with a peak at ∼30–100 days. Some recent investigations showed that the mass-transfer process in the lobe-filling BH binaries is more stable than previously expected (e.g., Pavlovskii et al. 2017; Shao & Li 2018); the maximal mass ratio of the donor star to the BH for stable mass transfer can reach as high as ∼6. Hence only a few BH–He XRBs with orbital periods of ≲1 day are produced in our calculations. Remarkably, such wind-fed XRBs in close orbits may be bright enough to be detected. In nearby galaxies, there also exist a couple such close XRBs (Esposito et al. 2015, and references therein). During the evolution of the progenitor binaries, mass accretion of the BH can increase its mass. We see that the BH masses in the BH–He XRBs are distributed in a broad range of

. Model A predicts that BHs are more likely to possess masses of

 since more binaries survive from BH formation via direct collapse without natal kicks, while Models B–D tend to produce light BHs with mass distributions that peak at

 due to the IMF. Differently from the BH systems with an OB star, almost all BH–He XRBs have relatively low eccentricities of ≲0.4, whose distribution has two distinct peaks at ≲0.1 and ∼0.3. Tides and mass transfer between binary components tend to circularize the orbits during the progenitor system evolution. Our obtained low eccentricities can coincide with the observations of Galactic W-R−O binaries (van der Hucht 2001) that are also post-mass-transfer systems; although, we do not include a detailed treatment for the orbital evolution of mass-transferring eccentric binaries (e.g., Sepinsky et al. 2009; Dosopoulou & Kalogera 2016).


The opacity file used for the PAH/VSG population (draine_opac_new.dat) was computed by Bruce Draine (Draine & Li 2007) and is available at https://github.com/hyperion-rt/hyperion-pah/tree/master/PAH-Legacy/input. It was computed taking two lognormal size distributions, one with grain radii below 20 Å and another for grains with radii from 20 to 200 Å. PAHs constitute a mass fraction of 4.5 per cent of this grain population and they have the size-dependent fractional ionization of the diffuse ISM (Wood et al. 2008). The presence of the 8.6-μm feature in the Spitzer IRS spectrum of MPI13 implies the existence of ionized PAHs. The PAH/VSG grain population is not in thermal equilibrium with the radiation field. However, their emissivities can be computed based on specific energy absorbed in each grid cell and assuming that the emissivity is the function of the mean intensity of the radiation field, which approximates the spectral shape to the first order (Robitaille et al. 2012; Whitney et al. 2013). The code uses the pre-computed emissivity tables of Draine & Li (2007) for different specific energy. As a Monte Carlo energy pocket is absorbed by a PAH/VSG, the pocket is reprocessed, sampling a new frequency from pre-computed emissivity tables. A detailed discussion on this can be found in Wood et al. (2008). The updated version of Hochunk3D is hence quite useful in modelling the circumstellar shells around evolved stars, which have thermally fluctuating dust. The code uses the method of Lucy (1999) to calculate the dust temperature very efficiently by summing up photon path-lengths. The temperature of the grid cell is updated when an iteration of simulation is completed, and the temperature converges in three to five iterations; this efficiency is due to the fact that flux is conserved exactly across all surfaces (Lucy 1999). By constructing Monte Carlo radiation fields that are rigorously divergence-free, rapid convergence is achieved with the temperature correction procedure in this method. We have performed the Lucy temperature correction of dust with five iterations.


Our group is addressing this problem by combining a variety of complementary perspectives: (i) by constructing a new generation of high-quality star density profiles derived from star counts instead of surface brightness (see Lanzoni et al. 2007a, 2010, 2019; Miocchi et al. 2013; Pallanca et al. 2021); (ii) by investigating the population of stellar exotica (Ferraro et al. 2001, 2003, 2015, 2016; Pallanca et al. 2010, 2013,2014, 2017; Cadelano et al. 2017, 2018, 2020) and their connection with the dynamical evolution of the parent cluster (see Ferraro et al. 2009, 2012, 2018a, 2019; Lanzoni et al. 2016); (iii) by characterizing the three-dimensional (3D) global velocity space through the analysis of the velocity dispersion profile and rotation curve from resolved star spectroscopy (Lanzoni et al. 2013, 2018a, 2018b; Ferraro et al. 2018b) and proper motions (PMs; see Raso et al. 2020). The determination of GGC internal kinematics from resolved star velocities is particularly relevant and challenging. In this context we promoted the ESO-VLT Multi-Instrument Kinematic Survey (hereafter the MIKiS survey; Ferraro et al. 2018b, 2018c), a project specifically designed to characterize the kinematical properties of a sample of GGCs in different dynamical evolutionary stages from the radial velocities (RVs) of hundreds of individual stars distributed over the entire radial range of each stellar system. To this end, the survey fully exploits the spectroscopic capabilities of different instruments currently available at the ESO Very Large Telescope (VLT): originally designed to use the adaptive optics (AO) assisted integral-field spectrograph SINFONI, the multiobject integral-field spectrograph KMOS, and the multiobject fiber-fed spectrograph FLAMES/GIRAFFE, it has been recently complemented with individual projects and an ongoing large program (PI: Ferraro) fully exploiting the remarkable performances of the AO-assisted integral-field spectrograph MUSE.


Molecular line ratio diagnostics are often used to investigate the physics and chemistry of the ISM in all of these environments. For example, as the gas chemistry located in the central, nuclear regions of galaxies is believed to be dominated by X-rays produced by the AGN, in so-called X-ray dominated regions (XDRs), the molecular content of the ISM surrounding such nuclei will greatly differ from that in starburst regions (Usero et al. 2004; García-Burillo et al. 2010). Hence, line ratios of specific molecules have been proposed as indicators of certain energetic or physical processes, for example HCN/HCO+ as a tracer of AGNs (Loenen et al. 2007), HCN/HNC as a mechanical heating tracer (Hacar et al. 2020), and HCN/CO as a density tracer (Leroy et al. 2017). In particular, the “submillimeter-HCN diagram”, first proposed in Izumi et al. (2013) and later expanded upon in Izumi et al. (2016), is a very notable example of the use of molecular line ratios as a probe of AGN-galaxies; this diagram makes use of two line ratios, HCN(4−3)/HCO+(4−3) and HCN(4−3)/CS(7−6), where all of the molecules involved are considered tracers of dense gas. Izumi et al. (2016) observed a clear trend that AGNs, including the Seyfert composite galaxy NGC 1068, tend to show higher HCN/HCO+ and/or HCN/CS than in SB galaxies as long as the observations were at high enough spatial resolutions to separate energetically discrete regions. Izumi et al. (2016) propose a scenario where it is the high temperature that is responsible for the HCN enhancement, whereby neutral-neutral reactions with high reaction barriers are enhanced (Harada et al. 2010), thus leading to the possible enhancement of HCN and the depletion of HCO+ via newly available formation and destruction paths, respectively. However, while of course higher gas temperatures are expected in AGN-dominated regions, these are not unique to these environments, as starburst regions and/or regions where outflows dominate can also harbour high enough temperatures for such enhancement to occur. Additionally, the higher temperatures could increase HCN excitation, relative to HCO+ and CS, without necessarily changing their relative abundances (Imanishi et al. 2018a). Finally, infrared radiative pumping is also a possible explanation of the HCN intensity enhancement relative to HCO+ and CS. Infrared pumping is a result of the emission of 14 μm infrared photons due to the presence of hot dust around AGN. These photons vibrationally excite HCN to the ν2 = 1 state. Upon de-exciting from this state back to the vibrational ground state, ν = 0, the HCN line intensities are thus pumped to higher fluxes (Imanishi et al. 2018a). However, we note that it is also not unlikely that the 12 μm infrared photons can similarly vibrationally excite HCO+, thus nullifying the extent of this effect (Imanishi et al. 2016).


Owing to their brightness at rest-frame FIR wavelengths, the ionized and neutral species of Carbon, Nitrogen, and Oxygen are powerful diagnostic lines for tracing the ISM of nearby and distant galaxies. When combined with photodissociation region (PDR) models (Tielens & Hollenbach 1985), measurement of the emission from different lines provide a means to constrain quantities such as the ionization rate and metallicity of the ISM of galaxies. Multilevel FIR transition lines have now been widely surveyed in local galaxies, originally by ISO (e.g. Luhman et al. 1998; Malhotra et al. 2001) and more recently using the PACS spectrometer (Poglitsch et al. 2010) on the ESA Herschel Space Observatory (Pilbratt et al. 2010). The [C ii]158 μm line is typically the brightest in star-forming galaxies, arising from ionized, and even neutral gas where it is the main coolant (Wolfire et al. 2003). Another commonly observed FIR line tracer of the ionized ISM is [N ii]122 μm. It has the advantage that it can be found associated with lower excitation gas, close to that observed in our own Galaxy (e.g. Goldsmith et al. 2015; Herrera-Camus et al. 2016). Another major coolant of the ISM is [O i]63 μm (Wolfire et al. 2003). Owing to its high excitation temperature and critical density, it can dominate the cooling in regions of starburst activity (Kaufman et al. 1999; Kaufman, Wolfire & Hollenbach 2006; Brauher, Dale & Helou 2008; Croxall et al. 2012; Narayanan & Krumholz 2017). When combined with measurements of the [C ii]158 μm line intensity and FIR luminosity, the [O i]63 μm line intensity can constrain the FUV field, G, and the gas density using PDR models. The luminosity in these FIR lines generally exhibits a deficit in the most FIR luminous galaxies compared to the trend expected from lower luminosity galaxies (e.g. Malhotra et al. 2001; Graciá-Carpio et al. 2011; Díaz-Santos et al. 2017). This has made the emission from lines like [O i]63 μm more challenging to detect at high-redshifts.


It is also possible that these clusters have a smaller extent and can just be missed by our extent selection as our detection algorithm sets the extent to zero if it is smaller than 6 (Brunner et al. 2022). Following the method presented in Ghirardini et al. (2021a), we estimated several dynamical properties of the clusters in the point source sample and compared them with the extent-selected sample presented in Ghirardini et al. (2021a). In Fig. 5 we compare the distributions of the core radii (Rcore) constrained by the V06 model and the concentration parameter (cSB) between these two samples. The concentration parameter is defined as the ratio of the surface brightness within 0.1 R500 to the surface brightness within R500 (Ghirardini et al. 2021a; Santos et al. 2008; Maughan et al. 2012). Intuitively, the expectation is that the smaller the core radius, the more compact the cluster. The left panel of Fig. 5 clearly shows that the clusters in the point source sample have relatively smaller core radii, hence the emission is more concentrated in a smaller area. Consistently, the concentration of the point source sample shows a clear excess in higher values than the extent-selected sample, indicating that a significantly larger fraction of cool-core clusters and clusters host a central AGN. We performed the same experiment by applying cuts in flux 1.5 × 10−14 ergs s−1 cm−2 and in detection likelihood to test whether the clusters are missed by the extent selection because they are fainter and/or more compact than the extent-selected clusters. The distribution of number density, core radius, and concentration parameter remains the same, indicating that the population of clusters in the point source catalog is more compact than the extent-selected sample. The extent-selected sample does not show a clear bias toward cool-core clusters or clusters with a central AGN, but contains the fraction of cool-cores is similar to that of SZ surveys (Ghirardini et al. 2021a). In this sample, we observe the opposite trend.


We searched the literature carefully and selected all published GRB-DLAs and QSO-DLAs sightlines conforming to our requirements which are as follows. The object must have spectral energy distributions (SEDs) and optical spectroscopic data available with measurements of AV, column densities of Zn ii and Fe ii, or of S ii and Si ii. The GRBs are selected only if they had their optical extinction derived from simultaneous SED fitting to X-ray-to-optical/NIR data using either a single or broken power law (see Greiner et al. 2011; Zafar et al. 2011; Schady et al. 2012; Covino et al. 2013; Bolmer et al. 2018; Zafar et al. 2018a for discussion on AV determination). This is a reliable method to determine extinctions at higher redshifts where the intrinsic slopes are constrained by the X-ray data. Note that there is some degeneracy between broken power-law break frequency (see De Cia et al. 2011) and extinction, which could lead to inference of grey dust for some instances (Watson et al. 2006; Perley et al. 2008; Friis et al. 2015). However, overall a fixed spectral break change (Δβ = 0.5) between the optical and X-ray slopes is preferred for GRBs (Greiner et al. 2011; Zafar et al. 2011; Japelj et al. 2015). For QSO-DLAs, reddening must be determined either from QSO colours or extinctions through template fitting to the QSO SED. Those methods are less robust than the X-ray-supported GRB fits, but are widely adapted. We refer the reader to Zafar et al. (2015) and Krogager et al. (2015, 2016) for more discussions on AV determination for QSO. The requirement for the pairs of elements (Zn ii and Fe ii, or of S ii and Si ii) are in order to be able to derive depletions. Here, Zn and S are volatile elements and Fe and Si are refractory elements (e.g. Ledoux, Bergeron & Petitjean 2002; Draine 2003; Vladilo et al. 2011; De Cia et al. 2016). Defined this way our initial sample consists of 28 GRBs and 32 QSO-DLAs with the required measurements available. To this we add sources where only part of the required measurements are complete but where limits have been determined for the rest. The vast majority of the elemental abundances have been determined via detailed spectral line fitting, for eight GRBs elemental abundances (or limits) were derived from rest-frame equivalent widths of non-saturated lines provided by Fynbo et al. (2009) as described in Laskar, Berger & Chary (2011) and Zafar & Watson (2013, see references to Table 1).


In Fig. 4, 29 observations of 15B-type asteroids are presented. As shown by Gil-Hutton & Cañada-Assandri (2012) and Gil-Hutton et al. (2014), in any plot of the observations of B-type objects a dispersion always appears in the whole phase angle range and it seems that these objects do not follow a single phase-polarization curve. The reason is probably that the asteroids classified by Bus & Binzel (2002) as members of this taxonomic class include objects that belong to the old F-class, originally proposed by Gradie & Tedesco (1982) and included in the Tholen taxonomy, due to its flat spectrum and low albedo; but several F-class objects have phase-polarization curves that are characterized by a comparatively low value of the inversion angle (Belskaya et al. 2005). Therefore, we also include in Fig. 4 nine observations of five asteroids classified as F-class by Tholen (1989) but included in other taxonomic types by Lazzaro et al.: (426) Hippo (X-type), (530) Turandot (C-type), (762) Pulcova (Cb-type), (778) Theobalda (C-type), and (877) Walkure (without a Bus taxonomy classification). The group of objects formed by (142) Polana, (213) Lilaea, (877) Walkure, and (1021) Flammario, all of them belonging to the old F-class, have observations indicating a low value of inversion angle, and the single observation of (314) Rosalia also indicates a similar polarimetric behavior even though it was not classified using the taxonomy of Tholen. On the other hand, the asteroids (62) Erato, (372) Palma, (635) Vundtia, and (981) Martina have measurements well below the theoretical phase-polarization curve for this taxonomic class, so it would seem to have a polarimetric behavior that corresponds more to a C-type than to a B-type. The apparent discrepancies might be indicative of some heterogeneity in the polarimetric properties within this particular taxonomic type, or alternatively, there might be some misclassification of the objects as could be the case for (635) Vundtia and (981) Martina, which were classified as C- and CFU-type by Tholen (1984).


However, if the magnetic curvature contraction term (last term in Equation (15)) is dominated by the compression term (second-to-last term in Equation (15)) so that

, the contraction or merging is strongly compressible (∇ ·  VE  0), resulting in an increase in flux-rope magnetic energy instead. In this case the plasma environment is doing positive mechanical work on the flux-rope structure, pushing magnetic field lines together to enhance flux-rope magnetic energy. Although it appears that small-scale flux ropes tend to contract or merge predominantly incompressibly in discussions of particle simulations (e.g., Drake et al. 2006; Dahlin et al. 2016), and it is also thought of as intrinsically incompressible in its manifestation as the quasi-2D turbulence component in N i MHD theory of solar wind turbulence (Zank et al. 2017), there is observational evidence to the contrary. For example, when primary current sheets associated with interplanetary coronal mass ejections (ICMEs) interact with the heliospheric current sheet, these structures are disturbed and several small-scale flux-rope structures may be formed when turbulent magnetic reconnection occurs in these structures. The flux ropes, being trapped between the converging heliospheric current sheet and the primary current sheets of ICMEs, experience compression, which may lead to efficient particle acceleration (e.g., Khabarova et al. 2015). However, it is possible that the particles are bounded in space because they cannot escape easily the region filled with small-scale flux ropes, which implies more efficient acceleration. Furthermore, in N i MHD theory of quasi-2D magnetic island turbulence, incompressible flux ropes can be compressed by large-scale density and flow velocity gradients in the nonuniform solar wind (Zank et al. 2017; see also discussion of Equation (69) in Section 8.2). Closer to the Sun, Guidoni et al. (2016) discuss the possibility of strong plasma compression during magnetic island contraction for islands propagating sunward during a solar flare event.


One of the most astonishing characteristics of Liller 1 is the extremely large value of the collision rate parameter. Verbunt & Hut (1987) showed that Liller 1 has the second-highest value of stellar encounter rate (after Terzan 5; see also Lanzoni et al. 2010) among all star clusters in the Galaxy, thus suggesting that it represents an ideal environment where exotic objects, generated by collisions, can form. In fact, it is commonly believed that dynamical interactions in GCs facilitate the formation of close binary systems and exotic objects such as cataclysmic variables (CVs), low-mass X-ray binaries (LMXBs), millisecond pulsars (MSPs), and blue straggler stars (BSSs) (e.g., Bailyn 1992; Paresce et al. 1992; Ferraro et al. 2001, 2009a, 2012; Ransom et al. 2005; Pooley & Hut 2006). Moreover, Hui et al. (2010) found that clusters with large collisional parameters and high metallicity (see also Bellazzini et al. 1995) usually host more MSPs. Indeed, Terzan 5 hosts the largest population of MSPs among all Galactic GCs (Ransom et al. 2005).
6

6

Note that Terzan 5 is suspected to not be a genuine GC, because it harbors at least three stellar populations with different iron abundances (Ferraro et al. 2009a; Origlia et al. 2011, 2013; Massari et al. 2014).
 A strong γ-ray emission has been recently detected in the direction of Liller 1 by the Large Area Telescope (LAT) on board Fermi (Tam et al. 2011). This is the most intense emission detected so far from a Galactic GC, again suggesting the presence of a large number of MSPs. However, no direct radio detection of these objects has been obtained so far in this system (Ransom et al. 2005). The only exotic object identified in the cluster is the rapid burster MXB 1730-335, an LMXB observed to emit radio waves and type I and type II X-ray bursts (Hoffman et al. 1978). It seems to be located in the central region of Liller 1, but no optical/IR counterpart of this object has been found so far (Homer et al. 2001).


The gamma-ray emission from the solar disk due to CR cascades in the solar atmosphere is denoted as a disk component. This secondary gamma-ray produced by the hadronic interaction of cosmic ray with the solar surface was first proposed by Dolan & Fazio (1965). While only upper limits were obtained by early measurements over the range 20 keV–10 MeV (Peterson et al. 1966). A detailed theoretical model for gamma-rays from the collision of cosmic ray with the solar atmosphere was presented by Seckel et al. (1991). The predicted gamma-ray flux at energies from 10 MeV to 10 GeV has a large uncertainty, being sensitive to the assumptions about the cosmic-ray transport in the magnetic field near the Sun. Gamma rays from the Sun were first detected by the Energetic Gamma-ray Experiment Telescope (Orlando & Strong 2008). The measured flux from 100 MeV to 2 GeV was within the range of the theoretical predictions. The Fermi collaboration (Abdo et al. 2011) reported the detection of high energy gamma-rays at 0.1–10 GeV from the quiescent Sun using the first 1.5 yr data. However, the measured solar disk emission flux was about a factor of seven higher than that predicted about this disk component by a “nominal” model (Seckel et al. 1991). This mismatch motivated Ng et al. (2016) to analyze 6 yr of public Fermi-LAT data. The obtained gamma-ray spectrum follows a simple power-law shape (α = −2.3) in 1–100 GeV without any evident high energy cutoff. For the flux in 1–10 GeV, a significant time variation of the solar disk gamma-ray flux that anticorrelates with solar activity was discovered, suggesting that the solar magnetic field would play an important role. An updated analysis with 9 yr of Fermi-LAT data, from 2008 August 7 to 2017 July 27, was performed, and Tang et al. (2018) confirmed these results and extended the gamma-ray spectrum up to >200 GeV. Notably, the bright gamma-ray flux above 100 GeV is dominant only during solar minimum at the end of Cycle 23 (Linden et al. 2018). The HAWC measurements in periods of high solar activity may support these findings (Albert et al. 2018a). Data collected from 2014 November to 2017 December, the second half of solar cycle 24, have been used to set strong upper limits on the flux of 1–100 TeV gamma-rays from the solar disk, about 10% of the maximum gamma-ray flux estimated by Linden et al. (2018). The HAWC 95% upper limit at 1 TeV is about 13% of the flux extrapolated from the solar minimum Fermi-LAT gamma-ray spectrum.


Generally, solar eruptions release their prestored magnetic energy via three phases, namely the precursor, impulsive, and gradual phases (Zhang et al. 2001; Zhou et al. 2016). Thereinto, the latter two, jointly termed as the main phase, correspond to the impulsive acceleration of the erupting CME flux rope, while the less-studied precursor phase includes key information on the eruptive structure and its trigger process. In the past, the limited observations showed that precursor activities of solar eruptions can come in various forms, in which preceding flux emergence (e.g., Palacios et al. 2015; Yan et al. 2017; Yang & Chen 2019) or cancellation (e.g., Green et al. 2011; Yang et al. 2016; Chen et al. 2018) in magnetograms, pre-eruption brightenings in Hα/EUV images (e.g., Bi et al. 2012; Dudík et al. 2016; Wang et al. 2017; Awasthi et al. 2018; Chen et al. 2018), as well as nonthermal processes in microwave or hard X-ray wavelength (Joshi et al. 2011; Altyntsev et al. 2012; Chen et al. 2017) are most common ones. In recent years, in the precursor phase of many CME/flare eruptive events, a type of new progenitor of CME flux ropes, namely hot channels (HCs, Cheng et al. 2011, 2013; Zhang et al. 2012), have been detected in the AIA high-temperature passbands (e.g., 131 and 94 Å). These newfound features commonly exist in the low corona with obvious helical/twisted fine fields or distinct writhed elbows (Cheng et al. 2013; Zhang et al. 2015), and they are found to be directly related to the occurrence of CMEs (Li & Zhang 2013; Patsourakos et al. 2013) and major eruptive flares (Nindos et al. 2015). To date, HCs have been evidenced as MFRs by some joint remote-sensing and in situ observations (e.g., Song et al. 2015), but for many HC eruption events, two problems are still elusive: (1) whether a corresponding MFR already exists before the HC eruption or is newly/partially built up during the eruption; and (2) whether its loss-of-equilibrium is initially facilitated by the preflare reconnection beneath/above the HC (Antiochos et al. 1999; Moore et al. 2001) or directly triggered the ideal magnetohydrodynamic (MHD) instabilities (Török et al. 2004; Kliem & Török 2006).


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.


Planet formation occurs in disks around young stellar objects. Interactions between planets and disks are very complex. Young planets are expected to cause rings, cavities, spirals, and disturbances in the velocity field and other features in the disk, which in turn may be used to infer the presence of these young planets. In the past few years, much evidence about this phase of planet formation has been accumulated because high-resolution images in the millimeter and sub-millimeter wavelength ranges have been provided by the Very Large Array (VLA) and the Atacama Large Millimeter Array (ALMA; see e.g. the case of HL Tau; ALMA Partnership 2015), and by high-contrast imagers such as the Gemini Planet Imager (GPI, Macintosh et al. 2014) and SPHERE (Spectro- Polarimetic High contrast imager for Exoplanets REsearch, Beuzit et al. 2008; see, e.g., Avenhaus et al. 2018). The literature on indirect evidence of the presence of planets is now becoming very rich, and nearby young stars surrounded by gas-rich disks are intensively studied for this purpose. In most cases, available data cannot fully eliminate alternative hypotheses, or the data have ambiguous interpretations (see, e.g., Bae et al. 2018 and Dong et al. 2018), although strong indirect evidence of the presence of planets from local disturbances of the velocity field have recently been considered for the case of HD 163296 (Pinte et al. 2018; Teague et al. 2018). In general, small grains are thought to be more strongly coupled with gas and are thus less sensitive to radial drift and concentration that can strongly affect large grains (see the discussion in Dipierro et al. 2018). For this reason, observations at short wavelengths provide an important complementary view of what can be seen with ALMA. On the other hand, a direct detection of still-forming planets embedded within primordial gas-rich disks, which is expected to be possible with high-contrast imaging in the near infrared (NIR), is still scarce; remarkable cases are LkCa-15 (Kraus & Ireland 2012; Sallum et al. 2015) and PDS-70 (Keppler et al. 2018; Müller et al. 2018; Wagner et al. 2018). In particular, in this second case, a clear detection of an accreting planet in the cavity between the inner and outer ring was obtained, making it an archetype for planet formation and planet-disk interactions. However, many cases remain ambiguous; a classical example is HD 100546 (see, e.g., Quanz et al. 2013a, 2015; Currie et al. 2014, 2015; Rameau et al. 2017; Sissa et al. 2018).


Figure 10 (see also Figs. A.4 and A.5) compare the spatial distributions of the Hα and 857 GHz emission in the Taurus–California–Perseus region (e.g., Taurus, Auriga, California, and Perseus). The 857 GHz dust emission traces each molecular cloud and exhibits a hole-like structure. This hole-like structure can also be seen in HI emission, as shown in Figs. A.4 and A.5. The Hα emission fills the hole-like structure seen in the 857 GHz dust emission near the center of the field. The Taurus, California, and Perseus molecular complexes traced by the 857 GHz dust emission are distributed at the edge of the hole-likestructure. Lim et al. (2013) also found evidence of a shell-like structure using dust extinction and 12 CO (1–0) maps. The hole-like structure may result from the expansion of a large-scale supershell produced by a supernova in the Per OB2 association that compresses the Taurus cloud from the far side (Olano & Poeppel 1987; Bally et al. 2008). An Hα absorption feature is detected toward the Taurus cloud (see Figs. 10 and A.6), suggesting that the Taurus cloud lies at the front surface of the large-scale supershell produced by the Per OB2 association. The distance to the Per OB2 association is estimated to be 340 pc from the Sun (Cernis 1993), while the distance to the Taurus cloud is ~140 pc (Elias 1978). These distances are consistent with the Taurus cloud lying in front of the Per OB2 association. The B211/B213 filament also appears to be in front of the HI shell (see Fig. 10 in Chapman et al. 2011). This morphology suggests that the B211/B213 filament may have formed as a result of an expanding supershell. This may provide another reason for the different initial gas velocities for the northeastern and southwestern sheet components in addition to large-scale acceleration by the gravitational potential of the B211/B213 cloud (see Sect. 4.2.3). The Local Bubble surrounding the Sun might also compress the Taurus cloud from the opposite direction. The Local Bubble surrounding the Sun was produced by supernovae (Snowden et al. 1998; Sfeir et al. 1999), and the wall of the Local Bubble is located close to the Taurus cloud (Könyves et al. 2007; Lallement et al. 2014).


Assuming that the force-field approach to the solution of the Parker (1965) cosmic-ray transport equation is valid, the connection between historic cosmic-ray intensities and the solar properties they encountered lies in the effective diffusion coefficient that is assumed in this approximation. Establishing such a connection, however, is no simple task. Many theories have been proposed to describe the scattering of cosmic rays in the heliosphere. The most likely candidates for this task, given their reasonable agreement with observations and numerical simulations of cosmic-ray diffusion coefficients, are the quasilinear theory (QLT) of Jokipii (1966), the weakly nonlinear theory (WNLT) of Shalchi et al. (2004b), and the nonlinear guiding center theory (NLGC; or one of its variants; see, e.g., Matthaeus et al. 2003; Shalchi 2006, 2009, 2010; Ruffolo et al. 2012). Shalchi (2009) provides in depth theoretical treatments of most the abovementioned theories. These scattering theories all require as a key input an expression for the power spectrum of the turbulent fluctuations of the HMF. These spectra depend upon basic turbulence quantities, such as the magnetic variance, and various correlation scales. Turbulence power spectra are discussed in detail by, e.g., Batchelor (1970) and Matthaeus et al. (2007), whereas more background on the abovementioned turbulence quantities can be found in, e.g., Matthaeus & Goldstein (1982), Petrosyan et al. (2010), Matthaeus & Velli (2011), and Bruno & Carbone (2013). These basic turbulence quantities have been observed to show a marked dependence on the solar cycle at Earth (see, e.g., Smith et al. 2006b; Burger et al. 2014; Zhao et al. 2018). It follows then that mean free paths derived from these scattering theories would be expected to depend on the solar cycle as well, and several studies have reported such a dependence. Chen & Bieber (1993) find from an analysis of cosmic-ray anisotropies and gradients as observed by means of NMs, that larger mean free paths are associated with solar minima, and smaller mean free paths with solar maxima. The authors also report a mean free path dependence on solar magnetic polarity. Nel (2016) and Zhao et al. (2018) both extensively analyze spacecraft observations, using the turbulence quantities so calculated as inputs for expressions for diffusion coefficients derived from the QLT and NLGC theories. Both authors report that the resulting mean free paths display solar cycle dependences.


The first investigations of the rotational spectra of ethyl isocyanide were carried out in 1966 by Bolton et al. (1966). The spectra of the first vibrational and torsional excited states were measured in the centimeter wave domain (Anderson & Gwinn 1968). In this initial study, the dipole moment was determined to be μa = 3.79 D and μb = 1.31 D; this value is usually large for a molecule that includes a CN group. This causes dense and intense rotational spectra in the millimeter wave range and also in the submillimeter wave range up to 900 GHz (bQ lines). Anderson & Gwinn (1968) also observed some A–E splittings due to the internal rotation motion of the methyl group. The most recent spectroscopic study is from Krüger & Dreizler (1992) who reinvestigated the internal rotation measurements and also determined hyperfine coupling parameters due to the nitrogen quadrupole. As in our previous studies of ethyl cyanide isotopologs, it was not possible to observe internal rotation and hyperfine splittings due to our Doppler limited resolution. Our analysis was rather easy, starting from a prediction based on Krüger & Dreizler (1992) parameters. First, we analyzed and fit the most intense transitions, the aRh transitions, up to 330 GHz. These transitions were shifted only a few MHz from the initial predictions. Then bR and bQ lines were searched and included in the fit up to 330 GHz. Next, all the spectra were analyzed up to 990 GHz without difficulty. For the fitting, we employed ASFIT (Kisiel 2001) and predictions were made with SPCAT (Pickett 1991). The global fits included 6 transitions from Anderson & Gwinn (1968), 29 lines from Krüger & Dreizler (1992), and 2906 from this work. The maximal quantum numbers are J = 103 and Ka = 30. Both reductions A and S were tested. A reduction permits us to check theagreement of our new parameters set with those from Krüger & Dreizler (1992) (Table 1). Using S reduction slightly decreases root mean square from 30.3 to28.7 kHz. The condition numbers are nearly the same: 295 and 310 for the A and S reductions, respectively.The A reduction requires 23 parameters, but 5 additional parameters are required for the S reduction (Table 2). For this reason we used the A reduction even if this molecule is close to the prolate limit with kappa = −0.9521. Part of the new measurements are in Table 3. Owing to its large size, the complete version of the global fit Table S1 is supplied at the CDS. The fitting files .lin (S2), .par (S3), and the prediction .cat (S4) are also available at CDS.


J0815+4729 is a main-sequence star (T

eff

=
6215
±
82

 K,

log
g

 = 4.7±0.5) with a metallicity of [Fe/H] ≤ −5.8 dex. Finding unevolved stars at this extremely low metallicity is very important since their stellar surface composition is not expected to be significantly modified by any internal mixing processes as in giant stars (Spite et al. 2005). J0815+4729 is similar to HE 1327–2326 in regard to its carbon enhancement, effective temperature, and metallicity. HE 1327–2326 is considered a turn-off/subgiant star, while J0815+4729 appears to be a dwarf. The ISIS spectrum of HE 1327–2326 indicates a metallicity of [Fe/H] ∼ −4.9 since the stellar Ca line is blended in that spectrum with the ISM features (Aguado et al. 2017b). However, the authors proposed a simple analysis taking into account the ISM absorption based on the UVES spectrum of HE 1327–2326. For J0815+4729, we require a high-resolution spectrum to clearly isolate the stellar Ca feature from possible additional ISM lines, and thus together with the detection of Fe lines, to establish the metallicity of this star. There are two other confirmed dwarf stars in this metallicity regime: one without any detectable carbon, J1029+1729 (Caffau et al. 2011), and another carbon-enhanced unevolved star, J1035+0641 (Bonifacio et al. 2015). The majority of extremely metal-poor stars shows overabundances of carbon, [C/Fe] > 0.7, and it appears that carbon-enhanced metal-poor (CEMP) stars split into two groups, with dramatically different carbon abundances (see, e.g., Beers & Christlieb 2005; Allende Prieto et al. 2015; Bonifacio et al. 2015 and references therein). The two carbon bands (high and low) studied have different origins. On the one hand, CEMP stars in the high-carbon band (A(C) ∼ 8.2) are probably produced by mass transfer from a binary companion, most likely an AGB star (Starkenburg et al. 2014). On the other hand, objects lying in the low-carbon band (A(C) ∼ 6.8) are thought to show the original carbon abundance inherited by the star from the ISM (Stancliffe 2009; Bonifacio et al. 2015; Abate et al. 2016). J0815+4729 has an abundance ratio of

[

C

/

Fe

]

≥
+
5.0

 dex  corresponding to A(C) ∼ 7.7 dex (adopting [Fe/H] ≤ −5.8). In Figure 4 (bottom panel), we show the carbon abundance ratio [C/Fe] for all stars at [Fe/H]  −4.5. All stars in this metallicity regime are considered to belong to the low-carbon band (Bonifacio et al. 2015), except for J0815+4729, which appears to be in between the low- and high-carbon bands. Both metallicity and carbon abundance are considered upper and lower limits, respectively. High-resolution spectra would be very useful to measure other elemental abundances and investigate the properties of the first supernovae. In particular, the barium abundance, or that of any other s-element, is not measurable from ISIS or OSIRIS spectra, and this is required to determine whether J0815+4729 is a CEMP-s, CEMP-r, or i-process star (Hampel et al. 2016). If we establish the abundance pattern, we will learn about the progenitor properties. Finally, the radial velocity accuracy from medium-resolution data is not enough to discard variations among different exposures, which would be indicative of binarity.


Regarding non-restricted hierarchical three-body systems, Krymolowski & Mazeh (1999) and Ford, Kozinsky & Rasio (2000) presented secular equations of motion (or Hamiltonian) up to the octupole order in semimajor axial ratio by using Hamiltonian perturbation techniques. Lee & Peale (2003) adopted both the octupole-level perturbation theory and direct numerical integrations to investigate the dynamical evolution for coplanar hierarchical planetary systems. In particular, the dynamics of apsidal resonance with critical argument of σ = ϖ1 − ϖ2 (ϖ1, 2 are the longitudes of pericentre) is studied and applied to some representative exoplanetary systems (Lee & Peale 2003). In a hierarchical planetary system with two comparable-mass planets orbiting a central star, Naoz et al. (2011) showed that orbits of the inner planet could flip from prograde to retrograde and back again due to the secular planet–planet interaction. Based on this behaviour, it becomes possible to form hot Jupiters on retrograde orbits by combining the eccentric ZLK effect and tidal friction (Naoz et al. 2011; Naoz, Farr & Rasio 2012; Teyssandier et al. 2013; Petrovich 2015; Petrovich & Tremaine 2016; Dawson & Johnson 2018). Naoz et al. (2013) re-derived the secular evolution equations for hierarchical three-body systems at the octupole-level approximation and found that orbital flips of inner planet are possible even at the quadrupole-level approximation. They pointed out that the relation h1 − h2 = π can be used to simplify the expression of Hamiltonian but the evolutions of H1 and H2 should be derived from the conservation of the total angular momentum rather than from the Hamiltonian canonical relations. Tan et al. (2020) explored the secular resonances with critical arguments arising in the Hamiltonian under the resonant Hamiltonian model, which is obtained by directly removing those terms involving short-period angles from the octupole-level Hamiltonian (i.e. only the secular and resonant terms are retained). It is of no problem when dealing with the quadrupole-order resonance (the ZLK resonance) because in this case the omitting terms are of octupole order. However, it may be inadequate to formulate the resonant model by directly removing those quadrupole-order periodic terms from the Hamiltonian when studying the octupole-order resonances. Hamers (2021) performed a semianalytic study about the properties of the ZLK oscillations at the quadrupole-level approximation, including the maximum eccentricities, time-scales of eccentricity/inclination oscillation and orbit flips. Naoz (2016) and Shevchenko (2016) reviewed various applications of the eccentric ZLK effect to a broad range of astrophysical systems, such as planetary and exoplanetary systems, stellar systems, and galaxies.


The hot emission line of Fe xxi 1354.09 Å and the cool emission line of Si iv 1402.77 Å have been used in many spectroscopic studies to investigate chromospheric evaporation (e.g., Tian et al. 2014, 2015; Li et al. 2015b, 2017a, 2017b; Brosius et al. 2016; Zhang et al. 2016a, 2016b). It is widely accepted that the forbidden line of Fe xxi 1354.09 Å is a hot (log T ∼ 7.05) and broad emission line during solar flares (Doschek et al. 1975; Cheng et al. 1979; Mason et al. 1986; Innes et al. 2003a, 2003b). Meanwhile, IRIS spectroscopic observations show that Fe xxi 1354.09 Å is always blended with a number of cool and narrow emission lines, which are from neutral or singly ionized species. Those blended emission lines can be easily detected at the position of the flare ribbon, including known and unknown emission lines, such as the C i line at 1354.29 Å, the Fe ii lines at 1353.02 Å, 1354.01 Å, and 1354.75 Å, the Si ii lines at 1352.64 Å and 1353.72 Å, and the unidentified lines at 1353.32 Å and 1353.39 Å (e.g., Li et al. 2015a, 2016a; Polito et al. 2015, 2016; Tian et al. 2015, 2016; Young et al. 2015; Tian 2017). In order to extract the hot line of Fe xxi 1354.09 Å and the cool line of C i 1354.29 Å (log T ∼ 4.0; Huang et al. 2014), we apply a multi-Gaussian function superimposed on a linear background to fit the IRIS spectrum at the “O i” window (e.g., Li et al. 2015a, 2016a), which has been pre-processed (i.e., IRIS spectral image deformation, bad pixel despiking and wavelength calibration) with the standard routines in Solar Soft Ware (SSW; Freeland et al. 2000). In short, the line positions and widths of these blended emission lines are fixed or constrained, and their peak intensities are tied to isolated emission lines from similar species. More details can be found in our previous papers (Li et al. 2015a, 2016a). On the other hand, the cool line of Si iv 1402.77 Å (log T ∼ 4.8) at the “Si iv” window is relatively isolated, and it can be well fitted with a single-Gaussian function superimposed on a linear background (Li et al. 2014, 2017a). Using the relatively strong neutral lines (i.e., “O i” 1355.60 Å and “S i” 1401.51 Å), we also perform an absolute wavelength calibration for the spectra at the “O i” and “Si iv” windows, respectively (Tian et al. 2015; Tian 2017). Finally, the Doppler velocities of Fe xxi 1354.09 Å, C i 1354.29 Å, and Si iv 1402.77 Å are determined by fitting line centers removed from their rest wavelengths (Cheng & Ding 2016b; Guo et al. 2017; Li et al. 2017a). As the hot Fe xxi line is absent in the non-flaring spectrum, the rest wavelength for the Fe xxi line (i.e., 1354.09 Å) is determined by averaging the line centers of the Fe XXI profiles which were used in the previous IRIS observations (Brosius & Daw 2015; Polito et al. 2015, 2016; Sadykov et al. 2015; Tian et al. 2015; Young et al. 2015; Brosius et al. 2016; Lee et al. 2017), while the rest wavelengths for the C i and Si iv lines, i.e., 1354.29 Å and 1402.77 Å, respectively, are determined from their quiet-Sun spectra (Li et al. 2014, 2015a).


We noticed that the fast wind stream had He++ beams moving ahead of the protons, low number densities, and low heavy-ion charge state ratios, which are characteristic of coronal-hole-originated solar wind. It should be noted that although the solar wind stream originates from the same coronal hole, the speed and the stream arrival time to 1 au varied from one Carrington rotation to another as was seen in Figure 2. The timing of the coronal-hole-originated solar wind observation aligned well with the PSP orbit. PSP started passing through the leading edge of the high-speed stream, continued as the high-speed stream corotates over the spacecraft, and ended passing the trailing edge of the stream as seen in Figure 3, standing as a perfect classic CIR/SIR event (Cohen et al. 2020). The decrease in crossing width and steepening of the increasing velocity profile at L1 versus at PSP is unlikely to be a product of the evolution of the coronal hole and is most likely a product of the faster wind stream overtaking the slower plasma at the interface during propagation (Burlaga 1974). Analyzing the SIR observed at ACE on 2018 November 4 to the corresponding SIR observed at PSP around 2018 November 15 indicated the enhancement of low-energy (keV) suprathermal ions (Figure 6) at the stream interface as the keV range ions are enhanced by local acceleration. The keV ions were enhanced again after the interface region, but for a short period of time compared to the PSP observation (Figure 8), while high-energy (MeV) suprathermal ions propagate along field lines to the inner heliosphere (Filwett et al. 2019) and are enhanced after the interface region in which articles accelerated at distant shocks dominated (see Desai et al. 2020; Joyce et al. 2021) and lasted longer in time in PSP. Minor enhancements in MeV particles were inconsistently observed over various Carrington rotations at ACE (not shown), but these were often at or just above the instrument noise floor. We cannot make any conclusive inferences as to the evolution of higher-energy ions in the coronal wind from these observations. In the future, as we approach solar maximum, it is likely that there will be more equatorial coronal holes observed during upcoming PSP orbits, which will allow us to compare more in depth the evolution of the solar wind structure at 1 au with PSP.


The solutions in Sect. 3 show that it is possible for a high X-ray flux in galactic nuclei to alter the carbon ionization balance and reduce the C+ abundance and correspondingly the [C ii] luminosity. In the presence of a high flux of soft X-rays above 1 keV, a condition encountered in many AGNs (Stacey et al. 2010; Ebrero et al. 2009), the abundance of singly ionized carbon is reduced and converted into higher ionization states. This reduction occurs primarily in the hot highly ionized gas that fills most of the galactic central zone, to some degree in the dense ionized skins surrounding molecular clouds, less so in diffuse atomic hydrogen clouds, and very little, if at all, in the dense PDRs at the edge of the CO molecular cores. Furthermore, in galactic nuclei with a high X-ray flux we would expect to see an increase in the dust temperature and infrared luminosity (Voit 1991). Therefore in galactic nuclei, and in particular in AGNs, we expect a reduction in [C ii] emission relative to FIR/IR emission depending on the relative contribution of different ISM components to the [C ii] luminosity. Unfortunately the next most abundant ion, C2+, does not have fine structure FIR emission lines as its 2s2 ground state has spin zero, and C3+, although it has spin angular momentum due to its unpaired electron in the 2S level, does not have a nuclear spin or orbital angular momentum to break the degeneracy of the two electron spin states. Instead to test the effect of X-ray ionization on the carbon balance we would need studies of their UV emission. For example the [C iv] UV resonance lines are detected in extragalactic sources and have been used to trace the formation rate of massive stars (Leitherer & Lamers 1991; Robert et al. 1993). [C iv] UV absorption lines have also been used to study the properties of the Galactic Halo (Savage et al. 2000) where carbon is presumed to be collisionally ionized in hot coronal gas (Gnat & Sternberg 2007).


We note that Pavesi et al. (2019) derived a lower κs parameter log(κs) ≈ −1 for HZ10, by observing the CO(2-1) line, which implies a low star formation efficiency for this source. The conflict between the two results can be explained by the fact that Pavesi et al. (2019) estimated the gas mass by adopting a large CO-to-Mgas conversion factor αCO = 4.5 M⊙ (K km s−1 pc2)−1, a value that is close to the Galactic conversion factor αCO = 4.36 M⊙ (K km s−1 pc2)−1 (Bolatto et al. 2013). Although the Galactic conversion factor is a derived value for Milky Way and normal, star-forming galaxies in the local Universe, it may not be applicable for more extreme environments of starburst galaxies at high-z (see Carilli & Walter 2013 for a review). The conversion factor depends on the physical conditions of the gas in the ISM (temperature, surface density, dynamics, and metallicity), as well as the star formation and associated feedback (Narayanan et al. 2011, 2012; Genzel et al. 2012; Feldmann et al. 2012; Renaud et al. 2019; see, e.g., Bolatto et al. 2013 for a review). It is typically in the range between 0.8 and 4.36 M⊙ (K km s−1 pc2)−1 (see, e.g., Bolatto et al. 2013; Carilli & Walter 2013, and Combes 2018 for reviews). Low metallicities (Z = 0.6 Z⊙ for HZ10) will drive αCO towards values higher than the Galactic value (Narayanan et al. 2012; Genzel et al. 2012; Popping et al. 2014), although αCO spans a broad range of values of αCO ∼ 0.4 − 11 M⊙ (K km s−1 pc2)−1, due to large uncertainties (see, e.g., Fig. 9 of Bolatto et al. 2013). On the other hand, high values of temperature, surface density, and velocity dispersion in a turbulent ISM of starbursts and merging systems will shift αCO towards lower values (Narayanan et al. 2011, 2012; Vallini et al. 2018). HZ10 has an extremely high value of the burstiness parameter log(κs) ∼ 1.4 and high total density of the [C II] emitting gas log(n) ∼ 3.35 cm−3, and it is also a multi-component system (Jones et al. 2017, Carniani et al. 2018a). Thus, for this source we assumed αCO = 0.8 M⊙ (K km s−1 pc2)−1, usually adopted for starburst galaxies (e.g., Downes & Solomon 1998; Bolatto et al. 2013). We obtained log(κs) = 0.53 ± 0.34, which is within the 2σ uncertainties of the

log

(

κ
s

)

=
1
.

43

−
0.53

+
0.38

$ \log{(\kappa_s)} = 1.43_{-0.53}^{+0.38} $

, estimated exploiting the C III] emission and the Vallini et al. (2020) model.