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).


The KN coincident with GW170817 showed a rapidly fading EM transient in the optical and infrared bands. The term kilonova was historically coined from the perception of its brightness being a thousand times larger than a nova (Li & Paczyński 1998; Rosswog 2005; Metzger et al. 2010). We discuss in this work that, even if far from such a standardized luminosity, clear dependencies on physical BNS quantities can be extracted. For AT 2017gfo, the observed spectral evolution is suggested to arise from a mixed composition of r-process elements in the ejected material (Gillanders et al. 2022); while early-time spectra are consistent with light r-process elements (nuclear masses A ∼ 90 − 140), later spectra require intermediate composition, producing even heavier elements such as lanthanides. An alternative scenario, such as dust formation in the KN that could also explain such a blue-red evolution, has been ruled out (Gall et al. 2017). In addition, a broad feature observed at ∼0.7 − 1 μm has been interpreted as due to Sr II (Watson et al. 2019; Domoto et al. 2021; Gillanders et al. 2022). Since then, no other KN has been firmly detected (see e.g., Coughlin 2020 and references therein for a summary of the follow-up efforts during LIGO and Virgo’s third observing campaign). Another merger candidate is linked to GW190814, located farther away at ∼240 Mpc, whose origin remains uncertain. However, it lacks of any EM counterpart and could likely be caused by a binary black hole merger (Essick & Landry 2020; Tews et al. 2021). GW190425 was the first BNS candidate in O3. The LALInference localization pipeline (Veitch et al. 2015) provided a 90% credible region of 7461 deg2, estimated luminosity distance of 156 ± 41 Mpc, much larger than that for GW170817, which complicated the search campaign resulting in no EM counterpart identified. The inferred merger parameters from the GW analysis published in Abbott et al. (2020a) for chirp mass

1
.

44

−
0.02

+
0.02

M
⊙

$ 1.44^{+0.02}_{-0.02}\,M_{\odot} $

 are the following. Total mass

M
1

+

M
2

≃
3
.

4

−
0.1

+
0.3

M
⊙

$ M_{1}+M_{2} \simeq 3.4_{-0.1}^{+0.3}\,M_{\odot} $

, with M1 ∈ (1.62, 1.88) M⊙, M2 ∈ (1.45, 1.69) M⊙, and

Λ
∼

≤
600

$ \tilde{\Lambda} \leq 600 $

 for low spin prior, or M1 ∈ (1.61, 2.52) M⊙, M2 ∈ (1.12, 1.68) M⊙, and

Λ
∼

≤
1100

$ \tilde{\Lambda} \leq 1100 $

 for high-spin prior. Note that for the other confirmed BNS event, GW170817, the inferred total mass is

M
1

+

M
2

≃
2
.

73

−
0.01

+
0.04

M
⊙

$ M_{1}+M_{2} \simeq 2.73_{-0.01}^{+0.04}\,M_{\odot} $

 with M1 ∈ (1.36, 1.60) M⊙, M2 ∈ (1.16, 1.36) M⊙, and

Λ
∼

=

300

−
230

+
420

$ \tilde{\Lambda} = 300_{-230}^{+420} $

 for low-spin prior (Abbott et al. 2019).


Stellar population evolution studies beyond z ≈ 1 have primarily focused on ages through studies of luminosity changes. Beifiori et al. (2017) used new data for 19 galaxies in z = 1.3–1.6 clusters obtained with the Very Large Telescope/KMOS to extend the redshift coverage of the results regarding the evolution of the mass-to-light (M/L) ratios of bulge-dominated passive galaxies. The authors used their new results together with the available literature results covering up to z = 1.3 (van Dokkum & Franx 1996; Jørgensen et al. 1999, 2006, 2014; Kelson et al. 2000; Wuyts et al. 2004; Holden et al. 2005, 2010; Barr et al. 2006; van Dokkum & van der Marel 2007; Saglia et al. 2010; Jørgensen & Chiboucas 2013) and low-redshift reference data for the Coma cluster (Jørgensen 1999; Jørgensen et al. 2006) to further solidify the evidence supporting passive evolution and a formation redshift zform ≈ 2. The formation redshift should be understood as the epoch of the last major star formation episode. At z ≈ 1 the massive (Mass > 1011 M) bulge-dominated galaxies in clusters appear to be in place and mostly passively evolving. Lower mass galaxies may still be added to the red sequence and from then on passively evolve (e.g., Sánchez-Blázquez et al. 2009; Choi et al. 2014), but see also Cerulo et al. (2016) for results supporting that the red sequence well below L⋆ is fully populated in rich clusters already at

. Ultimately, the properties of galaxies mapped over a large fraction of the age of the universe, may constrain the models for building the galaxies. It is difficult to understand within the prevailing hierarchical model favored by the ΛCDM (cold dark matter) cosmology, the existence of such massive passive galaxies with relatively old stellar populations at z ≈ 1, while less massive galaxies appear to harbor younger stellar populations, e.g., Jørgensen et al. (2017, and references therein), see Kauffmann et al. (2003) for a discussion of this tension between the observational results and the hierarchical models of galaxy formation. However, more recent cosmological simulations like Illustris (Genel et al. 2014; Vogelsberger et al. 2014; Wellons et al. 2015) and UniverseMachine (Behroozi et al. 2019) find that massive quiescent galaxies can be in place by z ≳ 2.


The LoTSS survey, homogeneously covering the whole northern sky complete down to the sub mJy limit will overcome statistical limitations due to shot noise. The large galaxy number density and large sky coverage will substantially reduce cosmic variance in cosmological analysis. The radio galaxies, tracing the background dark matter, will constrain the shape of power spectrum, i.e., the early universe physics, dark matter, baryon, density of neutrinos, the inflation power spectrum, and the degree of non-Gaussianity in density fluctuations. The upcoming LoTSS catalogs, covering a large sky area, will help us to explore further regarding large-scale anomalies (de Oliveira-Costa et al. 2004; Ralston & Jain 2004; Schwarz et al. 2004; Tiwari & Aluri 2019) and the current puzzling dipole signal observed with radio catalogs (Blake & Wall 2002; Singal 2011; Gibelyou & Huterer 2012; Rubart & Schwarz 2013; Tiwari & Jain 2015; Tiwari et al. 2015; Tiwari & Nusser 2016; Colin et al. 2017; Siewert et al. 2021). Furthermore, LoTSS will significantly improve on present low-frequency radio catalogs, e.g., TIFR GMRT Sky Survey (TGSS; Intema et al. 2017) and GaLactic and Extragalactic All-sky MWA (GLEAM; Hurley-Walker et al. 2017), and analyses based on these surveys (Dolfi et al. 2019; Rana & Bagla 2019; Tiwari 2019; Tiwari et al. 2019; Choudhuri et al. 2020). Unfortunately, the link between the galaxy and total matter power spectra depends on some unknowns from astrophysics, such as the galaxy bias factor, which depends on galaxy type and is quite different for radio AGNs and star-forming galaxies. The LoTSS population is a mixture of AGNs and star-forming galaxies, and therefore understanding galaxy bias, relative number densities, and luminosity evolution is nontrivial. The purpose of this work is to present a detailed cosmological analysis of LoTSS galaxies and study the effect of survey footprint, shot noise, and other systematics. We have produced galaxy mocks for the survey and have customized and calibrated the data pipeline for galaxy clustering statistics recovery.


A new result brought by our work is the role of incident polarization on the reflected spectral outcome. Although some X-ray polarization of the primary radiation is expected to be due to Comptonization of thermal radiation inside the corona, general estimates for the polarization degree of the primary source are rather low ($\lesssim 10\,{\rm {per \, cent}}$) according to the recent analysis in Beheshtipour et al. (2017), Tamborra et al. (2018), and Beheshtipour (2018). If some polarization was present, then, for symmetric reasons, vertically or horizontally polarized light should be dominant in case of extended coronal models (Dabrowski & Lasenby 2001; Niedzwiecki & Zycki 2008; Schnittman & Krolik 2010) at low heights. In case of lamp-post models (Matt, Perola & Piro 1991; Martocchia & Matt 1996; Henri & Petrucci 1997; Martocchia, Karas & Matt 2000; Dovčiak, Karas & Yaqoob 2004a; Miniutti & Fabian 2004) general-relativistic effects will rotate the polarization position angle along null geodesics from the corona towards the disc (Connors et al. 1980) and the situation becomes more general for incident disc irradiation, i.e. any incident state of polarization is possible. Our computations, apart from the unpolarized case, assumed two extreme cases of initial $p = 100\,{\rm {per \, cent}}$ polarization in order to estimate its possible effects in comparison with the completely unpolarized light and in order to test that the code adheres to the stated orientation conventions. Having appended these two initially polarized cases to our tables, it also allows for interpolation of reflection results for any input polarization state from this basis of the three computed independent polarization states, which will be necessary in future construction of global spectropolarimetric models. We aim to address any impact of light bending and other relativistic effects for a distant observer in our future works that will introduce the stokes local tables integrated over the accretion disc with some adopted global geometry.


While spatially extended optical jets and bipolar CO molecular outflows have been observed in numerous Class 0/I protostars (e.g. Reipurth & Bally 2001; Bally 2016, and references therein), near-infrared high-resolution spectroscopy and spectroimaging observations in the past two decades have made it possible to study the kinematics of the outflowing gas and physical properties at the base of the jet within a few hundred au of the driving source in Class 0/I protostars (e.g. Davis et al. 2001, 2003, 2011; Nisini et al. 2005, 2016; Caratti o Garatti et al. 2006; Takami et al. 2006; Antoniucci et al. 2008, 2011, 2017; Garcia Lopez et al. 2008, 2013). These microjets are bright in [Fe ii] forbidden and H2 rovibrational emission lines, hence showing the presence of forbidden emission-line (FEL) regions and molecular hydrogen emission-line (MHEL) regions in low-mass Class 0/I protostars. While multiple low- and high-velocity components are observed in both MHELs and FELs, the higher velocity gas is slightly further offset from the driving source than the slower gas, and the kinematics of the H2 emission differs from [Fe ii] emission, revealing complicated kinematic structures. Evidence of H2 emission from cavity walls is also seen in some protostars, suggesting the presence of a wide-angled wind. Strong emission in the well-known accretion diagnostics of Paschen and Brackett hydrogen recombination lines is observed in protostars, with the ratio of the accretion luminosity to bolometric luminosity spanning from ∼0.1 to ∼1. The mass accretion and loss rates for Class 0/I low-mass protostars span the range of 10−6–10−8 M⊙ yr−1, and the derived jet efficiencies (ratio between mass ejection and accretion rates) range between ∼1 per cent and 10 per cent (e.g. Davis et al. 2001, 2003, 2011; Nisini et al. 2005, 2016; Caratti o Garatti et al. 2006; Takami et al. 2006; Antoniucci et al. 2008, 2011, 2017; Garcia Lopez et al. 2008, 2013). These measurements are within the range predicted by the magnetohydrodynamic jet launching models (e.g. Frank et al. 2014).


It was found that the complex dielectric function from Pecharromán et al. (1999) for the sample obtained by heating bayerite at 1273 K, assuming a spheroid with depolarization parameters of (0.35, 0.003), produced an opacity with 11, 20, 28, and 32 μm features, so this component was included in the models. However, with only this component, the observed 20 μm features in the residual spectra were found to be wider than those in the models. By adding the opacity of the sample obtained by heating boehmite at 1173 K, the width of the 20 μm feature could be matched. This was done using the complex dielectric function for the sample obtained by heating boehmite at 1173 K from Pecharromán et al. (1999), assuming a spheroid with depolarization parameters of (0.35, 0.035). The complex dielectric functions of the samples obtained by heating bayerite and boehmite to various temperatures (Pecharromán et al. 1999) were derived by modeling the reflectance spectra of pellets obtained by pressing powders of these materials under great pressure. This method required Pecharromán et al. (1999) to assume an effective medium theory, such that a pellet is a mixture of one of their samples with a matrix of air. Pecharromán et al. (1999) noted that heating bayerite at 500°C eliminates the XRD pattern of bayerite, and they note that at 700°C, the infrared reflectance spectrum of the boehmite sample no longer shows OH− stretching bands. This must mean that the samples obtained from heating bayerite at 1273 K and from heating boehmite at 1173 K are no longer bayerite or boehmite, respectively. XRD performed by Pecharromán et al. (1999) of the sample of bayerite prepared at 1273 K suggests only θ-alumina was present, and their infrared and NMR spectroscopy confirms this. XRD of their sample obtained from heating boehmite to 1173 K (Pecharromán et al. 1999) suggests δ-alumina to be present, though some amounts of θ-alumina and α-alumina are present, as they deduce from XRD and infrared and NMR spectroscopy.


On larger scales, the clusters in which BCGs reside can generally be divided into two categories: cool core clusters, which exhibit very peaked surface brightness distributions at X-ray wavelengths, and non cool core clusters, with similar overall X-ray luminosities but with smoother, less peaked X-ray surface brightness distributions. Some authors (e.g. Hudson et al. 2010; Santos et al. 2010) define an intermediate category called moderate or weak cool core clusters. Since cool core clusters have short radiative cooling time-scales on the order of 108 yr in their centres (e.g. Voigt & Fabian 2004; McNamara & Nulsen 2007, 2012; Hlavacek-Larrondo et al. 2012), starbursts are expected to be common at the centre of such clusters. Indeed, the central cool gas in these clusters should condense onto the BCG, forming stars at rates of hundreds of solar masses per year (e.g. Fabian 1994). However, most BCGs are relatively quiescent and those that do show evidence of star formation generally tend to have star formation rates 1 order of magnitude smaller, on the order of $1-150 \, \mathrm{M_{\odot }\, {yr}^{-1}}$ (e.g. Donahue et al. 2007; Bildfell et al. 2008; O’Dea et al. 2008, 2010; Rawle et al. 2012). This mismatch between expected and observed star-forming rates, known as the cooling flow problem, is thought to be caused by active galactic nuclei (AGNs) feedback processes from the BCG. AGNs can release copious amounts of energy into the intracluster medium (ICM) through many ways, including: jetted outflows that inflate cavities, weak shocks, sound waves, or turbulence in the ICM (e.g. Markevitch & Vikhlinin 2007; McNamara & Nulsen 2007, 2012; Zhuravleva et al. 2014; Fabian et al. 2017). Alone, the energy released by jetted outflows appears to be on the same order as the energy needed to offset cooling (e.g. Rafferty et al. 2006; McNamara & Nulsen 2007; Hlavacek-Larrondo et al. 2012), therefore suggesting that AGN feedback is a good candidate for solving the cooling flow problem.


The discovery of a correlation between the mass of supermassive black holes (SMBHs) and several properties of their host galaxies (e.g. Magorrian et al. 1998; Ferrarese & Merritt 2000; Gebhardt et al. 2000; Kormendy & Ho 2013) has suggested that the growth of SMBHs and their host galaxies are tightly connected. Mergers of galaxies are thought to be one of the most important mechanisms with which galaxies build up their stellar masses (White & Rees 1978). Both observational (e.g. Lonsdale, Persson & Matthews 1984; Joseph & Wright 1985; Armus, Heckman & Miley 1987; Clements et al. 1996; Alonso-Herrero et al. 2000; Ellison et al. 2008) and theoretical (e.g. Mihos & Hernquist 1996; Di Matteo et al. 2007) studies have shown that galaxy mergers enhance star formation (SF). Simulations have also shown that the interaction between two or more galaxies can reduce the angular momentum of the circumnuclear material (e.g. Barnes & Hernquist 1991; Blumenthal & Barnes 2018), thus providing an effective mechanism to trigger accretion on to SMBHs (e.g. Di Matteo, Springel & Hernquist 2005). Observationally, several works have confirmed this scenario. Koss et al. (2010) and Silverman et al. (2011) found a higher AGN fraction in pairs than in isolated galaxies with similar stellar masses. It has been shown that the fraction of AGN in mergers tends to increase as the separation between the two galaxies decreases (Ellison et al. 2011), and peaks after coalescence (Ellison et al. 2013). Koss et al. (2012) have shown that the average luminosity of dual AGN also increases with decreasing separation (see also Hou, Li & Liu 2020), and it is higher for the primary (i.e. more massive) component of the system (see also De Rosa et al. 2019, for a recent review). While AGNs with moderate X-ray luminosities are typically found in non-interacting disc galaxies (e.g. Koss et al. 2011; Kocevski et al. 2012; Schawinski et al. 2012), more luminous objects are commonly found in merging systems (e.g. Treister et al. 2012; Glikman et al. 2015; Hong et al. 2015). Treister et al. (2012) showed that, while for 2–10 keV AGN luminosities of $L_{2-10}\sim 10^{41}\rm \, erg\, s^{-1}$ only a small fraction (${\lt}1{{\ \rm per\ cent}}$) of AGNs are in mergers, at $L_{2-10}\sim 10^{46}\rm \, erg\, s^{-1}$ ∼ 70–80 per cent of the sources are found in interacting systems (see also Glikman et al. 2015). Recent evidence has suggested that hot dust obscured galaxies (Hot DOGs; Wu et al. 2012; Assef et al. 2015), which are some of the most luminous galaxies observed so far ($L_{\rm \, IR} \gt 10^{13} \mathrm{ L}_{\odot }$), are also found in mergers (e.g. Fan et al. 2016). These observations suggest that, while at low luminosities SMBH accretion is triggered by secular processes, at high luminosities mergers can play a dominant role. This is in agreement with the evolutionary scenario proposed by Sanders et al. (1988) for ultra-luminous [$L_{\rm \, IR}(8\!-\!1000\, \mu \rm m)\ge 10^{12}\,L_{\odot }$] infrared galaxies (ULIRGs; e.g. Sanders & Mirabel 1996; Pérez-Torres et al. 2021). In this scheme, two gas-rich disc galaxies collide, triggering SF and accretion on to the SMBH. The strong accretion on to the SMBH would lead the source to evolve first in a luminous red quasar (e.g. Urrutia, Lacy & Becker 2008; Glikman et al. 2015; LaMassa et al. 2016) and then in an unobscured blue quasar.


Now we turn to the question of whether there are any general trends or strong correlations between the degree of HSP compliance, the average Fidx, and the average Φ derived from the AR samples contained in the defined HRs. As shown in the scatter plot of the average Fidx versus the HSP (Figure 5(a)), we find a weak tendency that HRs with lower degrees of HSP compliance show larger values of the average Fidx, with the linear Pearson correlation coefficient (PCC) of −0.55. In the scatter plot, the anti-HSP region with the largest average Fidx can be considered as an extreme case, which lies far away from both the vertical and horizontal dashes lines used to separate data points of the five lowest HSP and the five largest average Fidx, respectively. On the other hand, a positive correlation exists between the average Φ and the average Fidx with the linear PCC = 0.65 (refer to Figure 5(b)). Such correlation of Φ with flaring activity in individual ARs has been reported in many previous studies (e.g., Leka & Barnes 2003, 2007; Park et al. 2010; Liu et al. 2017; Lee et al. 2018), but it is reported here for the first time on this larger spatial scale of the HRs over a much longer period of solar cycle 24. As shown in Figure 5(c), a negative, although weak, correlation appears between the HSP and the average Φ with the linear PCC = −0.36. In contrast, a weak trend was reported in Paper I that ARs with larger values of Φ show a higher HSP. These two contrasting trends of the HSP with the average Φ are mainly due to the different ways of dividing the same AR samples into smaller subsets. The AR subsets in this study were selected based on heliographic locations of the AR samples in the defined Carrington longitude–latitude plane, while those in Paper I as a function of Φ values. The two highest flare-productive HRs with the average Fidx ≥15 have the average Φ values ranked in the top two as well as lower degrees of HSP compliance (i.e., one with the lowest HSP and the other with the HSP in the bottom 20%). Meanwhile, the two highly flare-productive regions can be considered as obvious outliers, compared to the positive trend of the HSP with respect to the average Φ in Paper I. This may indicate that the HSP for those regions is obscured by vigorous turbulent convective flows interacting with rising flux tubes therein. As mentioned earlier, the two X-class flaring ARs, NOAA 12673 and NOAA 12192, are located at the two HRs, respectively. Even excluding these two influential ARs, however, all of the trends as described in Figure 5 remain the same, although the correlations become less strong (i.e., the linear PCCs of −0.25, 0.51, and −0.27 for the cases in Figures 5(a), (b), and (c)).


It is well known that a per cent level understanding of the anisotropy of the redshift-space galaxy clustering is needed to accurately recover cosmological information from the RSD signal in order to shed light on the issue of dark energy versus modified gravity. From a statistical point of view, the source of the anisotropy is the galaxy line-of-sight pairwise velocity distribution. It is therefore important to adopt a realistic functional form for this velocity PDF when fitting models to the data. To this purpose, in Paper I we introduced the GG prescription for the velocity PDF. In this work, we have continued the development of this model by making explicit the dependence of the GG distribution on quantities predictable by theory, namely its first three moments, and extending it to the more general concept of GQG. To keep the model as simple as possible, we have proposed an ansatz with two free dimensionless parameters that describe how infall velocity and velocity dispersion vary when moving from one place to another in our Universe. Since their interpretation is clear, these parameters can be theoretically predicted or, assuming a more pragmatic approach, tuned to simulations or used as nuisance parameters. State-of-the-art PT has proven successful in predicting the large-scale behaviour of the velocity PDF and the correspondent monopole and quadrupole of the redshift-space correlation function (e.g. Reid & White 2011; Wang, Reid & White 2014), at least for massive haloes, M ∼ 1013 M⊙. Unfortunately, by definition, any PT breaks down for small separations. Consequently, alternative approaches have been suggested in the literature, spanning from purely theoretical (e.g. Sheth 1996) to hybrid techniques in which N-body simulations plus an HOD are employed to deal with the issue of non-linearities (e.g. Tinker 2007; Reid et al. 2014). One of the main results from our work is to provide a framework in which perturbation and small-scale theories are smoothly joined, so that all available RSD information can be coherently extracted from redshift surveys. A fundamental requirement for a redshift-space model is that it must be precise on all scales interest, and it should inform the user of the scales on which the model can be trusted. We have compared to N-body simulations the well-known GSM (Reid & White 2011), the more recent ESM (Uhlemann et al. 2015) and the GQG prescription over a broad range of separations, from 0 to 80 h−1 Mpc. Different redshifts, from z = 0 to 1, and different tracers, namely DM particles and two mass-selected catalogues of DM haloes, have been considered. We have concluded that, among the three, QGQ is the only model capable of providing a precise redshift-space correlation function on scales down to ∼5 h−1 Mpc over the range of redshifts covered by future surveys. Keeping in mind that the range of validity of the models depends on tracer, redshift and order of the Legendre multipoles we are interested in, for finiteness, we can say that all the models converge to the expected amplitude on scales ≳30 h−1 Mpc, at least for multipole and quadrupole. Since these scales roughly coincide with the range of validity of state-of-the-art PTs, if we rely only on PT and if we are not interested in higher order multipoles, the most natural choice is the simplest model among the three, i.e. the GSM. As for the ESM, we have found it to be unbiased down to smaller scales and for higher order multipoles than the GSM, thus confirming the results by Uhlemann et al. (2015), but, on the other hand, it seems to behave even worse than the GSM on the smallest scales. We can therefore think of it as a natural extension of the GSM in the perspective of further PT developments. In particular, a better prediction of the third moment of the velocity PDF is required before the ESM can be applied to data on smaller scales. Formally, the same argument holds for the GQG model, none the less, since this latter is meant to include non-linear scales, it could be possible to obtain a prediction for the third moment by interpolating between (very) small and (very) large scales. More precisely, as shown in the lower-right panel of Fig. A1, the functions $c^{(3)}_t$ and $c^{(3)}_r$, which fully characterize the third moment, are peaked at r ≲ 10 h−1 Mpc. By adopting a model for the small-scale limit that includes those separation, most likely using simulations in a similar way to that proposed in Reid et al. (2014), we would then be able to interpolate between these peaks and their large-scale limit, which is trivially 0.


The number of BHs, their mass distribution, and the number density are poorly known in NSCs. Theoretically, a single-mass distribution of objects forms a power-law density cusp around a massive object with n(r) ∝ r−1.75 (Bahcall & Wolf 1976), where n(r) is the number density, and r is the distance from the MBH. For multi-mass distributions, lighter and heavier objects develop shallower (∝r−1.5) and steeper cusps (typically ∝r−2 to r−2.2, and r−3 in extreme cases), respectively (Bahcall & Wolf 1977; Freitag et al. 2006; Hopman & Alexander 2006b; Keshet et al. 2009; Aharon & Perets 2016). Recent observations of the stellar distribution in the Milky Way NSC identify a cusp with n(r) ∝ r−1.25 (Gallego-Cano et al. 2018; Schödel et al. 2018), which is consistent with the profile after a Hubble time (Baumgardt et al. 2018). As BHs are heavier than typical stars, they are expected to relax into the steeper cusps. The relaxation time of BH populations is much shorter: 0.1–1 Gyr (O’Leary et al. 2009), although it can become much longer than that in the case of a shallow stellar density profile (Dosopoulou & Antonini 2017). In this work, we assume that the BH number density follows a cusp with either n(r) ∝ r−2 or r−3 in our two sets of calculations.The BH mass in the two cases is set arbitrarily to 107 and 4 × 106 M⊙, respectively, and we refer to the two models as Bahcall–Wolf–like (BW) and GC examples. Note that here GC refers to the assumed MBH mass (Ghez et al. 2008) and the observed stellar distribution (see below). In reality, the cusp distribution varies with the BH mass. Thus, we have also generated initial conditions for the BW case so that β in the number density distribution, n(r) ∝ r−(3/2+β), is calculated by β(m) = m/4M0, where m is the binary mass, and M0 is the weight average mass (e.g., Alexander & Hopman 2009; Keshet et al. 2009; Aharon & Perets 2016). We found that, due to the stability conditions, the initial condition distribution does not change significantly. For the GC case, the initial conditions’ distribution will change more significantly if we allow β to vary with the mass. However, we keep β = 3 to investigate the effects of a steep number density distribution on the rates. As we will show later in this work, the choice of the number density distribution will have a very limited effect on the merger rate.


Among the suggestedmechanisms responsible for the strong damping of the coronal loop oscillations (e.g., Ruderman & Roberts 2002; Ofman 2005, 2009; Morton & Erdélyi 2009) resonant absorption of the MHD waves, which was established first by Ionson (1978), is a strong candidate. Several works developed this theory (e.g., Davila 1987; Sakurai et al. 1991a, 1991b; Goossens et al. 1995; Goossens & Ruderman 1995; Erdélyi 1997; Cally & Andries 2010). The necessary condition for the resonant absorption is a continuum of Alfvén or slow frequency across the loop (Ionson 1978; Hollweg 1984, 1987; Davila 1987; Sakurai et al. 1991a). Resonant absorption occurs when the frequency of the global MHD mode matches at least with one of the frequencies of the background Alfvén or slow continuum at a location called he resonance point. As a result, the energy of the global MHD mode transfers to the local Alfvén modes in a layer around the resonance point, named the resonance layer (Lee & Roberts 1986; see also Goossens et al. 2013; Soler & Terradas 2015). In the absence of dissipation mechanisms, the amplitude of the oscillations diverges at the resonance point. Dissipation is important in the resonance layer, where the oscillations make large gradients. The background Alfvén or slow continuum can be due to the variation of the plasma density (e.g., Davila 1987; Ofman et al. 1994; Ruderman & Roberts 2002; Terradas et al. 2006; Soler & Terradas 2015), twisted magnetic field (Ebrahimi & Karami 2016), or both of them together (Karami & Bahari 2010; Giagkiozis et al. 2016). There are a variety of theoretical works related to the damping of the coronal loop oscillations based on the theory of resonant absorption of MHD waves (e.g., Goossens et al. 2002, 2009; Ruderman & Roberts 2002; Van Doorsselaere et al. 2004; Andries et al. 2005; Terradas et al. 2006; Karami et al. 2009; Karami & Bahari 2010; Soler et al. 2013; Soler & Terradas 2015; Ebrahimi & Karami 2016; Giagkiozis et al. 2016; Jung Yu & Van Doorsselaere 2016). For a good review about the theory of resonant absorption, see also Goossens et al. (2011).


Aided by the tight localization constraints of the three-detector network and the proximity of the GW source, multiple independent surveys across the EM spectrum were launched in search of a counterpart beyond the sGRB (Abbott et al. 2017c). Such a counterpart, SSS17a (later IAU-designated AT 2017gfo), was first discovered in the optical less than 11 hours after merger, associated with the galaxy NGC 4993 (Coulter et al. 2017a, 2017b), a nearby early-type E/S0 galaxy (Lauberts 1982). Five other teams made independent detections of the same optical transient and host galaxy all within about one hour and reported their results within about five hours of one another (Allam et al. 2017; Arcavi et al. 2017a, 2017b; Lipunov 2017b; Tanvir & Levan 2017; Yang et al. 2017; Soares-Santos et al. 2017; Lipunov et al. 2017a). The same source was followed up and consistently localized at other wavelengths (e.g., Corsi et al. 2017; Deller et al. 2017a, 2017b, 2017c; Goldstein et al. 2017; Haggard et al. 2017a, 2017b; Mooley et al. 2017; Savchenko et al. 2017; Alexander et al. 2017; Haggard et al. 2017c; Goldstein et al. 2017; Savchenko et al. 2017). The source was reported to be offset from the center of the galaxy by a projected distance of about 10″ (e.g., Coulter et al. 2017a, 2017b; Haggard et al. 2017a, 2017b; Kasliwal et al. 2017; Yang et al. 2017; Yu et al. 2017). NGC 4993 has a Tully–Fisher distance of ∼40 Mpc (Freedman et al. 2001; NASA/IPAC Extragalactic Database164

164
The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
), which is consistent with the luminosity distance measurement from gravitational waves (

 Mpc). Using the Tully–Fisher distance, the ∼10″ offset corresponds to a physical offset of ≃2.0 kpc. This value is consistent with offset measurements of sGRBs in other galaxies, though below the median value of ∼3–4 kpc (Fong et al. 2010; Fong & Berger 2013; Berger 2014).


Depending on the specific driver, the characteristics of turbulence will then be imprinted within the ISM mainly as three-dimensional density and velocity fluctuations, and these fluctuations have been traditionally studied via correlation functions such as the spatial power spectrum (SPS) (e.g., Crovisier & Dickey 1983), Δ-variance (e.g., Stutzki et al. 1998), and structure function (e.g., Padoan et al. 2002; Burkhart et al. 2015b). In particular, the SPS approach has been applied to observations of various Galactic and extragalactic environments (e.g., Plume et al. 2000; Dickey et al. 2001; Elmegreen et al. 2001; Burkhart et al. 2010; Combes et al. 2012; Zhang et al. 2012; Pingel et al. 2013), showing power spectral slopes β roughly ranging from −2.7 to −3.7 depending on the tracers used (e.g., H i, carbon monoxide (CO), and dust). These slopes essentially provide information on the relative amount of structure as a function of spatial scale and can be compared with theoretical models of turbulence (mainly numerical simulations) to characterize turbulence cascade (e.g., Burkhart et al. 2010), to determine the influence of shocks (e.g., Beresnyak et al. 2005), to reveal the injection and dissipation scales of turbulent energy (e.g., Kowal & Lazarian 2007; Federrath & Klessen 2013; Chen et al. 2015), and to trace the evolution of MCs (e.g., Burkhart et al. 2015a). The proximity and abundance of multi-wavelength observations make MCs in the solar neighborhood an ideal laboratory for probing the impact of turbulence on their formation and evolution. In this paper, we focus on the Perseus MC, which is a nearby (∼300 pc; e.g., Herbig & Jones 1983; Černis 1990), low-mass (∼2 × 104 M⊙; e.g., Sancisi et al. 1974; Lada et al. 2010) cloud. Its star formation activities, as well as atomic and molecular gas content, have been extensively examined over the past decade (e.g., Ridge et al. 2006; Jørgensen et al. 2007; Pineda et al. 2008; Lee et al. 2012, 2014, 2015; Mercimek et al. 2017), revealing that the cloud consists of several individual dark and star-forming regions (e.g., B5, B1, B1E, IC 348, and NGC 1333) and is actively forming low- to intermediate-mass stars (see Bally et al. 2008 for a review).


Since the launch of Swift (Gehrels et al. 2004) in 2004, the nature of jet breaks in gamma-ray burst (GRB) afterglows has become increasingly puzzling. There is strong evidence that the ejecta from the GRB central engine must be jet-like (Zhang & Mészáros 2004). Thus a collimation correction factor,

, where

 is the jet opening angle with typical values of 5°–10°, can be applied to relieve the energy budget problem, so that a typical GRB energy is

 erg, where

 is the isotropic equivalent energy release in gamma-rays. Such collimated ejecta expand outward relativistically with Lorentz factors Γ of several hundred initially. Internally, the ejecta release their energy through internal shocks (Rees & Meszaros 1994; Kobayashi et al. 1997; Daigne & Mochkovitch 1998), or magnetic dissipation processes (e.g., the ICMART model; Zhang & Yan 2011) or photospheric dissipation (e.g., Guiriec et al. 2010, 2011, 2015; Lazzati & Begelman 2010; Ryde et al. 2010, 2011; Pe’er & Ryde 2011) and produce the prompt gamma-ray emission of GRBs. Externally, the ejecta are further decelerated by an ambient medium (e.g., a constant density interstellar medium (ISM); or a stellar-wind environment with density inversely proportional to distance squared) and produce long-term broadband afterglows through external shocks (see e.g., Gao et al. 2013, for a review). Due to relativistic beaming, only a portion of the radiation from the ejecta front surface, which is within a cone of half-opening angle

, can be observed (Rhoads 1997, for reviews see Piran 2004; Granot 2007; van Eerten 2013). An unavoidable consequence of this general picture is that when the ejecta are decelerated to

, the light curve should steepen because (1) the maximum observable portion of the ejecta (the cone of the whole jet with opening angle

) is now smaller than that which is expected (a cone with half-opening angle

 and (2) the onset of lateral spreading of the ejecta, predicted to become noticeable in the observer frame around the same time (Rhoads 1999), causes the blast wave to decelerate further. Such a “jet break” in a GRB light curve is expected to behave achromatically because it only reflects the ejecta geometry, under the assumption that the afterglow emission regions and mechanisms do not change in different spectral regimes (Rhoads 1999; Sari 1999; Huang et al. 2000; Granot et al. 2002; see also reviews by Mészáros 2002; Piran 2004; Zhang & Mészáros 2004). The achromaticity was apparently confirmed in the optical and near-IR band in a few cases of pre-Swift GRBs (Kulkarni et al. 1999; Harrison et al. 2001; Klose et al. 2004).


Figure 9 shows the components required for such a time-domain survey, with the PC beamformer as specified above. The required components are shown in four different colors. Visibilities computed in the uGMRT backend (GWB; marked in blue) at 1 ms time resolution are transferred to the the PC beamformer nodes (marked in orange) with an aggregate data rate of ∼3 GB s−1. We aim to implement in-field phasing (Kudale & Chengalur 2017) using a sky model derived from the time-averaged visibilities in order to improve the coherence in phasing up to a baseline length of several kilometers. This optimizes the GMRT PA sensitivity beyond a central compact core (most current PA observations use only the antennas in the central square). In addition to deriving the phasing model, a baseline-based flag masking the bad baselines will also be generated in real time from these time-averaged visibilities. Coherent additions of these visibilities will result in 128 such visibility beams. The multi-DM search for single pulses (colored in yellow) on each of these visibility beams would need to be executed on a separate FRB cluster, followed by coincidence filtering to remove spurious events (Bhat et al. 2013). We also propose recording these 128 beams with a 1 ms time resolution, giving a total data rate of 200 MB s−1 into a disk for a quasi-real-time search for pulsars using the same cluster. We note that the proposed 1 ms time resolution is sufficient to detect double neutron star systems, young pulsars, and normal pulsars, as well as objects like radio magnetars. Visibility buffers corresponding to candidate single-pulse events will be recorded at a 1 ms time resolution covering the full DM sweep time-range. For an event at a DM of 2000 pc cm−3, the total DM sweep time over 200 MHz band in uGMRT 300–500 MHz band is ∼50 s, which results in a 40 GB buffer size on each of the PC beam nodes. This means one can easily hold few buffers for accommodating the pipeline delay and flush them into storage based on the real-time triggers. These visibilities will be processed through the processing blocks (marked in green) for millisecond imaging localization at quasi-real-time. This block includes removal of dispersion delay, followed by a flagging and calibration pipeline and snapshot imaging. We note that part of this imaging pipeline for localizing time-domain events has already been demonstrated for the GHRSS Phase1 survey (Bhattacharyya et al. 2016).


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


It is interesting that the sources with suspected or confirmed Lyman continuum radiation at high redshifts are peculiar and rare, bright SFGs with rather hard ionizing spectra marked by high-ionization emission lines (e.g., N v, C iv, He ii, O iii, C iii). Their presence at high redshift can be hardly explained by pure SFGs, even requiring uncommon assumptions (e.g., large stellar rotation, binary stellar population, top-heavy initial mass function, extremely low metallicity) as discussed by a number of recent works (see Bowler et al. 2014; Bradley et al. 2014; Kehrig et al. 2015; Stark et al. 2015; Jaskot & Ravindranath 2016; Stark 2016; Senchyna et al. 2017, 2019, 2020; Berg et al. 2018; Nakajima et al. 2018; Chisholm et al. 2019; Jaskot et al. 2019; Le Fevre et al. 2019b; Nanayakkara et al. 2019; Schaerer et al. 2019; Stanway & Eldridge 2019). The majority of galaxies showing Lyman continuum emission (both at low z and at z ∼ 3–4) populate the upper end of the Baldwin, Phillips, and Terlevich (BPT) diagram (Baldwin et al. 1981) or occupy a region of high-ionization line ratio in between SFGs and AGNs, or mainly populated by AGNs (see, e.g., Figures 11 and 14 by Nakajima et al. 2018). Indeed, Le Fevre et al. (2019b) find a marginal 2σ detection in the X-ray stacking of strong C iii emitters at 2  z  4, consistent with the presence of low-luminosity AGNs. Interestingly, evidence recently emerged that local confirmed Lyman continuum emitters or low-z Green Peas, blue compact galaxies, Lyman break analogs, which are usually associated with reliable Lyman continuum candidates, are characterized by significant X-ray emission, not compatible with star formation activity but more plausibly powered by low-luminosity AGN activity or by a large population of high-mass X-ray binaries (Kaaret et al. 2017; Bao et al. 2019; Bluem et al. 2019; Latimer et al. 2019; Plat et al. 2019; Prescott & Sanderson 2019; Senchyna et al. 2019, 2020; Svoboda et al. 2019; Wu et al. 2019; Baldassare et al. 2020; Birchall et al. 2020; Dittenber et al. 2020). It is thus possible that pure stellar radiation from SFGs is a negligible source of H i ionizing radiation, and the bulk of Lyman continuum photons escaping at low and high z are produced instead by accretion onto supermassive black holes (SMBHs).


When the characteristic time of variability of the mass flux along the accretion disk is longer than the relaxation time of the local disk equilibrium, it is possible to use the approximation of local equilibrium Shakura (1972), see also Bisnovatyi-Kogan (2011), to calculate the transient disk structure. The equilibrium along a radius of the accretion disk around a star with a mass M is determined by the Keplerian rotational velocity ΩK(1)\begin{equation} \Omega=\Omega_{\rm K}=\left(\frac{GM}{r^3}\right)^{1/2}\cdot \label{omega} \end{equation}Ω=ΩK=GMr31/2·Writing the equation of the vertical equilibrium in approximate algebraic form, we obtain (2)\begin{equation} h=\sqrt 2 \frac{v_{\rm s}}{\Omega}, \label{h} \end{equation}h=2vsΩ,where \hbox{$v_{\rm s}=\sqrt{P/\rho}$}vs=P/ρ is the speed proportional to the sound velocity, P and ρ are the (gas + radiation) pressure and density at the symmetry plane of the accretion disk, and h is the semi-thickness of the accretion disk. The specific angular momentum l of the matter in the accretion disk is connected to the rotation velocity as(3)\begin{equation} l=r\,v_\phi=r^2\Omega. \label{l} \end{equation}l=r vφ=r2Ω.The mass flux through the disk at radius r is connected to the radial velocity vr as (4)\begin{equation} \dot M=-4\pi h\rho r v_r, \quad \dot M>0,\quad v_r<0. \label{mflux} \end{equation}Ṁ=−4πhρrvr, Ṁ>0, vr0.We use an α approximation for the turbulent viscosity (Shakura 1972) when the (rφ) component of the stress tensor trφ is written as (5)\begin{equation} t_{r\phi}=\alpha\, P, \label{trphi} \end{equation}trφ=α P,where the phenomenological non-dimensional parameter α ≤ 1. The condition of stationarity of the angular momentum, in which the outward viscous radial flux of the angular momentum is balanced by the angular momentum of the inward flux of the mass, is written as (see, e.g., Bisnovatyi-Kogan 2011) (6)\begin{equation} r^2 h \alpha P=\frac{\dot M}{4\pi}(l-l_{\rm in}). \label{angmom} \end{equation}r2hαP=Ṁ4π(l−lin).The main input into the time lag comes from the outer regions of the disk with l ≫ lin. Then we have from Eqs. (4) and (6) the expression for the radial velocity in the form (7)\begin{equation} v_r=-\alpha\frac{v_{\rm s}^2}{v_\phi}\cdot \label{vr} \end{equation}vr=−αvs2vφ·We also define the surface density Σ, and write Eq. (6) in light of Eq. (3), using condition l ≫ lin, in the form (8)\begin{equation} \Sigma=2\rho h,\quad \dot M \Omega=4\pi \alpha P h. \label{sigma} \end{equation}Σ=2ρh, ṀΩ=4παPh.The equation of the local thermal balance in the accretion disk, when the heat produced by viscosity Q+ is entirely emitted through the sites of the optically thick accretion disk with a total flux Q−, at l ≫ lin is written as (see, e.g., Bisnovatyi-Kogan 2011)(9)\begin{equation} \frac{3}{2}\dot M \Omega^2=\frac{16\pi ac T^4}{3\varkappa \Sigma}\cdot \label{theq} \end{equation}32ṀΩ2=16πacT43ϰΣ·Here T is the temperature in the symmetry plane of the accretion disk, a is the constant of the radiation energy density, c is the speed of light, and ϰ is the Thompson (scattering) opacity of the matter.


Observationally, it is a big challenge to conclude whether AGN’s feedback could regulate star formation or not, and how it regulates star formation. On one hand, if strong outflows emerge, they could clear out the star-forming gas to suppress star formation (Alexander & Hickox 2012; García-Burillo et al. 2014; Alatalo et al. 2015; Hopkins et al. 2016; Wylezalek & Zakamska 2016). The heating by jets propagating through the galaxies could prevent gas from cooling and cut-off the gas supply for further star formation (Karouzos et al. 2014; Choi et al. 2015). On the other hand, the outflows and jets interact with the gas in host galaxies and compress it to trigger new star formation (Silk 2013; Zubovas et al. 2013; Zubovas & Bourne 2017). In fact observations show either no or positive relationships between star formation rates and SMBH accretion rates but no negative trends are seen (Shi et al. 2007, 2009; Baum et al. 2010; Xu et al. 2015; Zhang et al. 2016; Mallmann et al. 2018). Whether AGN’s feedback plays the role may also depends on the spatial scale that observations could resolve and time-scale that the observed tracers could probe (Harrison et al. 2012; Cresci et al. 2015; Feruglio et al. 2015). For example, radiation from AGNs nearly instantaneously impact the surrounding ISM while the attenuation from ISM probably limits their impact to the nuclear regions (Roos et al. 2015). Outflows or jets travel slowly and may be decelerated after interactions with ambient gas, which delays their effects on star formation at large distances from the nuclei (Harrison 2017; Harrison et al. 2018). Feedback by jets or outflows on ISM also depends on their orientation relative to the dusty torus, making their effects on star formation to be anisotropic. The short duty cycle of AGNs could also make feedback by radiation from AGNs temporally variable in strength. Case studies of individual AGNs find evidence of coexistence of positive and negative feedback on star formation (Zinn et al. 2013), suggesting the complicated nature of AGN feedback.


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


Multiple solar missions, such as the Solar Dynamics Observatory (SDO) and the Interface Region Imaging Spectrograph (IRIS), have shown that a diversity of waves occur in the solar atmosphere (Jess et al. 2009; McIntosh et al. 2011; Okamoto & De Pontieu 2011). The various wave types that occur include Alfvén waves (Alfvén 1942). These waves are transverse magnetohydrodynamic (MHD) waves that travel along the magnetic field lines. Alfvén waves were reported to be present in both the photosphere and chromosphere (Srivastava et al. 2017; Baker et al. 2021). As they pass by, they modify the transverse magnetic field and velocity components but, do not alter the gas pressure or the mass density (Nakariakov & Verwichte 2005), at least in the linear limit and in a homogeneous background plasma. A thorough understanding of Alfvén waves is essential because they could be a part of the solution to the major problems of heliophysics, such as the solar coronal heating and wind acceleration (Uchida & Kaburaki 1974; Ofman 2010). Recent theoretical research revealed that Alfvén waves can carry enough energy to heat the solar corona (Yang & Xiang 2016). However, the details of the mechanism(s) of the thermal energy release related to their dissipation remain unknown. One potential candidate for that may be associated with ion–neutral collisions (Soler et al. 2017). Piddington (1956), Osterbrock (1961), and Haerendel (1992) were the first to study ion–neutral collisions, but they did not find that this interaction affects the chromospheric temperature. Ballester et al. (2018) showed that ambipolar diffusion leads to substantial chromospheric heating, and Zaqarashvili et al. (2013) derived a dispersion relation for two-fluid Alfvén waves and confirmed that the damping of Alfvén waves resulting from the ion–neutral collisions is quite significant. Khomenko (2017), based on a two-fluid model, stated that the presence of neutrals affects the solar atmosphere. The effect of ion–neutral interactions is expected to influence the energy balance of the chromosphere. Zaqarashvili et al. (2013) also confirmed that low- and high-frequency photospheric Alfvén waves might not reach the solar corona because ion–neutral collisions damp them very efficiently in the upper chromosphere. According to Song & Vasyliūnas (2011), the rate of Alfvén wave damping varies with magnetic field strength and wave frequency. For a strong magnetic field, wave damping is low. Low-frequency waves are also weakly damped, and so there is a chance to detect low-frequency Alfvén waves in the solar corona under the condition of a strong magnetic field.


The standard cosmological model stands on the shoulders of a fundamental assumption: that the universe is statistically homogeneous and isotropic on the largest scales. This assumption has been thoroughly tested over the last years both with cosmic microwave background (CMB) and Large-scale structure data. In particular, the analysis of CMB data, most notably from the Wilkinson Microwave Anisotropy Probe (WMAP; Bennett et al. 2013) and Planck (Planck Collaboration I 2020) experiments, has not yet provided conclusive evidence for the hypothesis of Cosmological Isotropy (Eriksen et al. 2004, 2007; Hajian, Souradeep & Cornish 2005; Land & Magueijo 2007; Hansen et al. 2009; Samal et al. 2009; see also Planck Collaboration VII 2020 and references therein). Moreover, Galactic foreground contamination or known systematic effects in the data alone can not explain the observed CMB ‘anomalies’, i.e. large-scale deviations from the concordance Lambda cold dark matter (ΛCDM) model (see e.g. Rassat et al. 2014; see Planck Collaboration VII 2020 for a recent overview). Power asymmetry from CMB data has also been a matter of intense debate and scrutiny (Gaztañaga, Fosalba & Elizalde 1998; Eriksen et al. 2007; Lew 2008; Hoftuft et al. 2009; Paci et al. 2010; Axelsson et al. 2013; Shaikh et al. 2019, see also Dai et al. 2013 for a comprehensive discussion and references therein), and evidence has been reported that this could source deviations from isotropy on cosmological scales (Hansen et al. 2009). However, a more recent analysis based on Planck data finds no evidence for such power asymmetry when all scales are taken into account (Quartin & Notari 2015). This is in qualitative agreement with the latest results from the Planck Collaboration analysis (Planck Collaboration VII 2020) where they conclude that the observed power asymmetry is not robust to foreground contamination or systematic residuals. It is important to note that previous analysis have concentrated on quantifying potential deviations from statistical isotropy using a statistical prior. First analyses using WMAPdata looked for the direction of maximal asymmetry in the sky, thus quantifying anisotropy for a given preferred direction (Hansen et al. 2009). In turn, this led to proposing a particular angular distribution of power in the sky to simply capture the observed anisotropy, such as the so-called ‘dipole anisotropy’ modulation (Prunet et al. 2005; Gordon 2007). This same model has been further constrained with Planck data (Planck Collaboration XXIII 2014; Planck Collaboration XVI 2016; Planck Collaboration VII 2020; Aiola et al. 2015; Mukherjee et al. 2016). Alternatively, a recent analysis (Ho & Chiang 2018) focuses on quantifying possible CMB peak shifts across the sky, finding significant variations, but they attribute this behaviour to possible systematic effects or the solar dipole. Complementary evidence for cosmological anisotropy has been investigated using probes of the low-redshift universe (see Colin et al. 2011; Secrest et al. 2021 and references therein).


Recent observations of transit spectra of hot Jupiter atmospheres show limited spectral modulation due to H2O that has been largely interpreted as the indicator of the presence of aerosols (Barstow et al. 2016; Iyer et al. 2016; Sing et al. 2016; Pinhas et al. 2019). Whether these aerosols are condensate clouds of photochemical organic aerosols or other refractory materials remains unknown. Although thermochemical equilibrium models predict the formation of condensate clouds with various composition in these hot atmospheres (Lecavelier Des Etangs et al. 2008; Lee et al. 2015; Parmentier et al. 2016), recent laboratory works highlighted that photochemistry could strongly affect the composition of exoplanet atmospheres and lead to the formation of aerosols in a variety of conditions, including the ones encountered in hot Jupiters (Hörst et al. 2018; Fleury et al. 2019; He et al. 2019, 2018a, 2018b). These photochemical aerosols could represent another source of opacity to explain some of the observed transit spectra of hot Jupiter atmospheres, e.g., of HD 189733 b (Lavvas & Koskinen 2017). On the other hand, the bulk elemental ratio can also drastically affect the molecular composition of these atmospheres. In the external layers (region with pressure 1 bar) of atmospheres with temperatures higher than 1000 K, carbon preferentially bonds with oxygen to form CO, and the excess of oxygen bonds with hydrogen to form H2O when the C/O ratio is 1. At a higher CO ratio ≥ 1, CO remains an abundant species but the water mixing ratio decreases (Lodders & Fegley 2002; Moses et al. 2013; Venot et al. 2015; Heng & Lyons 2016; Tsai et al. 2017; Goyal et al. 2018; Drummond et al. 2019). For this reason, another explanation for the low spectral modulation due to water observed in some hot Jupiter atmospheres is that these atmospheres have low H2O abundances presumably reflecting high C/O ratios (Madhusudhan et al. 2011; Madhusudhan 2012). However, the existence of such “carbon-rich” exoplanets continues to be debated. The first analysis of the hot Jupiter WASP-12b observations suggested a C/O ratio > 1 (Madhusudhan et al. 2011), but another study found a C/O ratio  1 using another approach (Kreidberg et al. 2015), leaving the question of the C/O ratio in WASP-12b’s atmosphere open. In addition, a recent survey suggests that the carbon enrichment of hot Jupiter atmospheres compared to their host stars may be common, but uncertainties on C/O measurements in exoplanet atmospheres are large and prevent a firm conclusion from being reached (Brewer et al. 2017).


The gas velocity is unknown since no exact analytic solution for turbulence in a disc – and turbulence in general – are known. However, statistical properties of turbulence can be inferred from laboratory, numerical experiment or theory, and turbulent fluctuations can be modelled using stochastic processes, independently from the origin of the turbulence itself. In a seminal study, Thomson (1987) proved that the only expression of vg that is consistent with Kolmogorov turbulence and the hydrodynamical equations is
(16)$$\begin{eqnarray*}
\frac{\mathrm{d}v_{\rm g}}{\mathrm{d}t} = -\frac{v_{\rm g}}{t_{\rm e}} + \frac{\sqrt{D}}{t_{\rm e}}\dot{w} ,
\end{eqnarray*}$$where te denotes the Lagrangian time-scale of the turbulence, D is the turbulent diffusivity (in units m2s−1). w is a Wiener process, such that its derivative is a white noise such that
(17)$$\begin{eqnarray*}
\left\langle \dot{w} (t) \right\rangle = 0,
\end{eqnarray*}$$(18)$$\begin{eqnarray*}
\left\langle \dot{w} (t) \, \dot{w} (t^{\prime }) \right\rangle = \delta (t - t^{\prime }) ,
\end{eqnarray*}$$where δ denotes the Dirac distribution and the notation · > is the expectation operator (see also Sawford 1984; Wilson & Sawford 1996). Equation (16) describes turbulent fluctuations from a Lagrangian point of view (Taylor 1922). From equation (16), the gas velocity can be rewritten
(19)$$\begin{eqnarray*}
v_{\rm g} = \zeta \left(t,t_{\rm e},D \right) ,
\end{eqnarray*}$$where ζ is a stationary Ornstein–Uhlenbeck process defined by
(20)$$\begin{eqnarray*}
\left\langle \zeta (t,t_{\rm e},D) \right\rangle = 0,
\end{eqnarray*}$$(21)$$\begin{eqnarray*}
\left\langle \zeta (t,t_{\rm e},D) \, \zeta (t^{\prime },t_{\rm e},D) \right\rangle = \frac{D}{2 t_{\rm e}} \rm {e}^{-\frac{\vert t - t^{\prime } \vert }{t_{\rm e}}} .
\end{eqnarray*}$$Equation (16) defines a model of turbulence with two parameters, D and te. In discs, te is typically of order one orbital period, since turbulent vortices are stretched out by differential rotation in a few orbits (e.g. Beckwith, Armitage & Simon 2011). From equation (21), D is related to the autocorrelation of the turbulent noise according to
(22)$$\begin{eqnarray*}
D = 2 \int _{0}^{+\infty } \left\langle v_{\rm g}\left(0 \right) v_{\rm g}\left(t \right)\right\rangle \mathrm{d}t .
\end{eqnarray*}$$Equation (22) can alternatively be seen as a definition of the turbulent diffusivity, useful in practice to measure D in numerical simulations. The Wiener–Khinchin theorem ensures that the power spectrum of the turbulent velocity field S(ω) is the Fourier transform of this autocorrelation function, i.e.
(23)$$\begin{eqnarray*}
S \left(\omega \right) = \frac{1}{2 \pi } \int _{-\infty }^{+\infty } \mathrm{e}^{- i \omega t} \left\langle v_{\rm g}\left(0 \right) v_{\rm g}\left(t \right)\right\rangle \mathrm{d}t = \frac{D}{2\pi \left(1 + \omega ^2 t_{\rm e}^2 \right)} .
\end{eqnarray*}$$Thus, in the inertial subrange ($\omega ^2 t_{\rm e}^2 \gg 1$), we have S(ω) ∝ ω−2, whose equivalent in the wavelength space is $\tilde{S}(k)\propto k^{-5/3}$ (Batchelor 1950). From equation (23), the standard deviation of the velocity fluctuation σ is
(24)$$\begin{eqnarray*}
\sigma ^{2} \equiv \int _{-\infty }^{+\infty } S\left(\omega \right) \mathrm{d} \omega = \frac{D}{2t_{\rm e}} .
\end{eqnarray*}$$Physically, equation (24) is a turbulent fluctuation–dissipation theorem.


On the basis of the 1.3 mm continuum image made from the SMA archival data, Nakamura et al. (2012) found conspicuous substructures inside a prestellar core in the Oph B2 region, which had been previously identified as a single core (B2-N5) in single-dish molecular line (N2H+ (J = 1−0)) observations (Friesen et al. 2010). The substructures consist of several small condensations, and their typical mass and size are around 0.05 M⊙ and 500 au, respectively. The mass is comparable to or larger than the local Jeans mass of 0.04 M⊙, and thus the self-gravity of the condensations appears to play an important role in their dynamics. Similarly, Kamazaki et al. (2001) found small condensations of 1000 au scale inside the SM1 core in the Oph A region based on 3 mm dust continuum observations with the Nobeyama Millimeter Array (see also Nakamura et al. 2012; Friesen et al. 2014). The masses of the condensations are around 0.01−0.1 M⊙, comparable to or larger than the local Jeans mass. Recently, Kirk et al. (2017) carried out comprehensive survey observations with ALMA Band 3 toward 60 dense cores that were identified in Oph with SCUBA at the James Clerk Maxwell telescope (JCMT). They found 38 compact emission structures of ∼100 au size within the dense cores. On the other hand, on the basis of 3 mm continuum observations with CARMA, Schnee et al. (2010) found no significant substructures inside prestellar cores in Perseus (see also Dunham et al. 2016), although their target cores are in relatively isolated environments. These observations suggest that internal structures of prestellar cores and their physical properties may strongly depend on cloud environment. It still remains unclear, however, whether or not they are really different between clustered environments and isolated environments. As a step toward a more comprehensive understanding of the star formation process, it is important to characterize better the substructures inside dense cores in cluster-forming regions. In the present paper, we further investigate the internal structures of the Oph B2 region using Cycle 2 ALMA data at a spatial resolution of ∼3″, corresponding to ∼410 au at Oph distance.


GX 301-2 is an HMXB consisting of a highly magnetized (B ∼ 4 × 1012 G, or even larger Doroshenko et al. 2010) pulsar and a B-type hyper-giant star Wray 977 (Vidal 1973; Kaper et al. 1995; Staubert et al. 2019). According to modelling of high-resolution optical spectra, Wray 977 has a mass of 43 ± 10 $\, \mathrm{M}_{\odot }$, a radius of 62 R⊙, and looses mass through powerful stellar winds at a rate of $\sim \! 10^{-5}\, \mathrm{M}_\odot \, {\rm yr}^{-1}$ with terminal velocity of 300 $\rm km\, s^{-1}$ (Kaper, van der Meer & Najarro 2006). The system is highly eccentric (e ∼ 0.46), with an orbital period of ∼41.5 d, and exhibits strong variation of the X-ray flux with orbital phase (Koh et al. 1997; Doroshenko et al. 2010). In particular, periodic outbursts at the orbital phase ∼1.4 d before the periastron passage (Sato et al. 1986), and a fainter one near the apastron passage are observed (Pravdo et al. 1995). The broad-band X-ray spectrum is orbital phase-dependent and can be approximately described as a power law with a high-energy cutoff and a cyclotron resonant scattering feature around 40 keV (Kreykenbohm et al. 2004; Mukherjee & Paul 2004; La Barbera et al. 2005; Doroshenko et al. 2010; Suchy et al. 2012; Islam & Paul 2014; Fürst et al. 2018; Nabizadeh et al. 2019). During the periastron flares, the source exhibits strong variability with an amplitude of up to a factor of 25, reaching a few hundreds mCrab in the energy band of 2–10 keV (e.g. Rothschild & Soong 1987; Pravdo et al. 1995). The flares are accompanied by the variability of the equivalent hydrogen column density ($\rm \mathit{ N}_{\rm H}$) and of the fluorescent iron lines, which is believed to be associated with clumpiness of the stellar wind, launched from the donor star (Mukherjee & Paul 2004). We note the clumpiness in this paper refers to any inhomogeneities in the stellar wind/stream, which are higher density regions, regardless of its specific formation mechanisms. On the other hand, Fürst et al. (2011) reported a long XMM–Newton observation in GX 301-2 around its periastron, which also exhibits systematic variations of the flux and $\rm \mathit{ N}_{H}$ at a time-scale of a few kiloseconds. Several wind accretion models, consisting of stellar winds and a gas stream, were proposed to explain the observed flares (e.g. Haberl 1991; Leahy 1991; Leahy & Kostka 2008; Mönkkönen et al. 2020).


Admittedly, although the prediction success rate of SPM3 is greatly improved compared with the previous SPM2 model, its improvements in the shock TT prediction are limited. Many factors could potentially cause this. On one hand, the sample events used in this study are CMEs from Solar Cycle 23 when SOHO was the only spacecraft tracking their movements in the sky-plane. The CME speed derived in this way is the projected speed, which does not represent the propagation speed of the CME along the Sun–Earth direction. Large uncertainties in VCME restrict further improvements to the TT prediction of the shock. Possible solutions to this restriction could include adopting the CME’s radial speed, which is derived from models (such as cone models) based on single spacecraft observations (Jang et al. 2014). Another solution involves estimating the initial geometry and three-dimensional (3D) speeds of CMEs based on observations from multiple spacecraft (STEREO, SOHO; Kilpua et al. 2012; Gopalswamy et al. 2013; Lee et al. 2013). On the other hand, the input parameters used in this study were obtained when the disturbances propagated near the Sun. Therefore, the lead time of SPM3's prediction is very long, nearly the whole TT of the disturbance from the Sun to Earth, as the model is analytic and thus requires no running time. Models based on heliospheric image data (STEREO HIs and SMEI) can provide more accurate predictions for arrival times but with shorter lead times (Colaninno et al. 2013; Mishra & Srivastava 2013; Möstl et al. 2014). For example, Webb (2013) applied the Tapping–Howard model (Tapping & Howard 2009) to predict the arrival time at Earth of the 2011 February 15 CME event based on HI and/or SMEI observations, and the corresponding prediction accuracy could be within an hour. However, the prediction’s lead time was only several hours. Kilometric Type II radio burst emission can also be used to track shock dynamics in the inner heliosphere and provide shock arrive time predictions (Corona-Romero et al. 2013; Xie et al. 2013). Further prediction models considering these factors should be developed based on the events of Solar Cycle 24. This is the next goal of our research.


A growing body of work suggests that planet formation is strongly dependent on the birth environment of the host star. Stars preferentially form in groups (Lada & Lada 2003), and in sufficiently dense environments the evolution of a PPD can be significantly influenced by neighbours (de Juan Ovelar et al. 2012). Close star–disc encounters are one such environmental influence on PPDs that can result in enhanced accretion and hasten disc depletion (Clarke & Pringle 1993; Ostriker 1994; Pfalzner et al. 2005; Olczak, Pfalzner & Spurzem 2006; Bate 2018; Winter et al. 2018a; Cuello et al. 2019). However, the stellar number densities required for tidal truncation are high, and in practice few observed regions satisfy this condition (Winter et al. 2018b, 2019a). The influence of tidal truncation is therefore limited to stellar multiples, either in bound systems (Dai et al. 2015; Kurtovic et al. 2018) or during the decay of higher order multiplicity (Winter, Booth & Clarke 2018c). Since stellar multiplicity does not appear to be strongly dependent on environment (see Duchêne & Kraus 2013, for a review), this suggests that encounters are not an environmental influence, but may set disc initial conditions during the early phases of cluster evolution (Bate 2018). Discs can also be externally depleted via thermal winds driven by far-ultraviolet (FUV) and extreme ultraviolet (EUV) photons from neighbouring massive stars (Johnstone, Fabian & Taylor 1998; Störzer & Hollenbach 1999; Adams et al. 2004; Facchini, Clarke & Bisbas 2016; Haworth et al. 2018; Haworth & Clarke 2019). This process of external photoevaporation dominates over dynamical encounters in observed environments, and can deplete PPDs rapidly for many stars that are born in massive and dense clustered environments (Scally & Clarke 2001; Winter et al. 2018b). Many stars in the solar neighbourhood are born in regions where UV fields are sufficient to significantly shorten disc lifetimes (Fatuzzo & Adams 2008; Winter et al. 2018b), and the fraction of stars born in such environments may be much greater outside of this region, dependent on galactic environment (Winter et al. 2019a). From an observational perspective, Guarcello et al. (2016) report disc survival fractions that decrease with increasing FUV flux in Cygnus OB2 (see also Winter, Clarke & Rosotti 2019b), and Ansdell et al. 2017 find a correlation between the dust mass in PPDs and separation from σ Ori. However, Richert et al. (2015) find no correlation of disc fraction with distance from OB stars. Reconciling these contradictory findings may require appealing to the inefficiency of external photoevaporation at small radii within the disc, dynamical and projection effects, or the stellar age gradient apparent in many star forming regions (Getman et al. 2018).


Many stars in the solar neighbourhood are born in regions where UV fields are sufficient to significantly shorten disc lifetimes


The existence of winds is shown by blueshifted absorption lines from highly ionized ions. These are only seen in soft state but not in hard state (Ponti et al. 2012), anticorrelated with the radio jet which is seen in the hard state but not in the soft. This was thought to be evidence that the wind was magnetically driven by the same field as was responsible for the jet, but in a different geometric configuration (Miller et al. 2012). However, in Tomaru et al. (2019, hereafter Paper I) we show instead that thermally driven winds can explain this switch (see also Done, Tomaru & Takahashi 2018; Shidatsu & Done 2019). Thermal driving produces a wind by irradiation from the central source heating the surface of accretion disc up to the Compton temperature ($T_\text{IC} \sim 10^7 \!-\!10^8\, \text{K}$), which is hot enough for its thermal energy to overcome the gravity at large radii. The characteristic radius at which the wind can be launched is called the Compton radius, defined by RIC = μmpGM/kTIC ∼ 105 − 106Rg (Begelman, McKee & Shields 1983). Paper I show the first modern radiation hydrodynamic simulations of thermal (and thermal-radiative) winds designed to investigate the switch in wind properties between the hard and soft states changing illumination spectra. These simulations were tailored to the BHB system H1743−332, where there is Chandra high-resolution data in both states giving detailed spectral information on the wind or its absence (Miller et al. 2012; Shidatsu & Done 2019). They incorporate radiation force on the electrons, both bound and free, as they show that this is important factor driving the escape of the thermal wind in the fairly high Eddington fraction (L/LEdd ∼ 0.2–0.3), fairly low Compton temperature (TIC ∼ 0.1 × 108 K) characteristics of the soft state. The only other modern hydrodynamic simulation of thermal winds (e.g. Luketic et al. 2010; Higginbottom & Proga 2015; Higginbot et al. 2016) has not included radiation pressure, which is important in setting the velocity structure for L ≥ 0.3LEdd as required here (Paper I).


If we consider for the bulk density the value 4500 kg m−3, which is one of the highest measured in the asteroid population out of those asteroids with good quality of data (see Carry 2012), it will strengthen the hypothesis that Psyche could be an exposed metal core of a differentiated asteroid (Elkins-Tanton et al. 2017). According to the models of asteroid differentiation, the process that led to the formation of Psyche happened very early. Considering Psyche's current diameter, Deff = 226 km (Shepard et al. 2017), the Psyche parent body (PPB) was supposed to be ∼500 km in diameter and have suffered severe ‘hit-and-run’ impact events capable of removing all crust and mantle, exposing the core (Elkins-Tanton et al. 2016). In addition, Psyche should have ∼40 per cent macroporosity, if we assume that it is made of blocks of iron/nickel with a density around 7500 kg m−3. In that case, the core itself was possibly destroyed and re-accumulated, implying a severe collisional history. When an asteroid is disrupted catastrophically, with a remaining mass ≤50 per cent of the initial one, after a collision with another body, an asteroid family is formed. If the collision happened in the Main Belt, a family of asteroid fragments should be in the region of Psyche; however, no family related to Psyche has been found yet (Davis, Farinella & Marzari 1999). One possibility to solve this issue is that the potential Psyche asteroid family was created at an early time, e.g. within the first 500 Myr of Solar system history (Davis et al. 1999). This would allow the family fragments to be ground down by collisional evolution and be unobservable today. The same models show that, even in this case, today there should be several surviving fragments having diameters around 20 km and above the detection limit. There is a lack of primordial asteroid families in the Main Belt (Brož et al. 2013; Spoto, Milani & Knežević 2015), very likely due to the classical methods that are used to identify them. The hierarchical clustering method (HCM) is not sensitive enough to find old and dispersed families, as it searches for asteroids forming compact groups in orbital element space (semi-major axis, eccentricity and inclination). A new approach has been proposed and implemented with success (Walsh et al. 2013; Delbo’ et al. 2017), as it is able to distinguish very old families, having eccentricities and inclinations dispersed in space. Therefore the possibility of the absence of a Psyche family could be due to searching biases. However, this may be an unlikely hypothesis, because A-type asteroids that could represent mantle material (almost pure olivine) from differentiated bodies do not exist extensively in the orbital space related to Psyche, but instead are distributed randomly in the Main Belt (Davis et al. 1999; DeMeo et al. 2015). In order to study this puzzling small body further, NASA is sending a new Discovery Mission to Psyche. The main goal is to get insight into whether it is a core of a parent body and understand the procedures of differentiation, making all the above questions more valid than ever. The alternative theory is that Psyche is a planetesimal that bears primitive unmelted material (Elkins-Tanton et al. 2016).


Line driven winds are not expected to be smooth flows, but show strong density perturbations or “clumps” (Owocki et al. 1988; Feldmeier et al. 1997; Puls et al. 2006, 2008; Oskinova et al. 2012; Sundqvist & Owocki 2013). In X-ray binaries, thedensity contrast could even be further enhanced by the interaction between the wind and the strong X-rays from the compact object (Blondin 1994; Blondin & Woo 1995; Manousakis & Walter 2011, 2015, and references therein). For Vela X-1 and Cyg X-1 it has been estimated that more than 90% of the wind mass is contained in less than 10% of the wind volume (Sako et al. 1999; Rahoui et al. 2011). When the line of sight to the compact object passes through one of these clumps, X-rays are absorbed by the moderately ionized material in the clump, leading to a so-called dipping event. This is also observed for other sources (Hemphill et al. 2014; Grinberg et al. 2017). During the hard state of Cyg X-1, such short-term dipping events are observed predominantly during the upper conjunction of the black hole, i.e., when the line of sight passes through the densest region of the stellar wind and is most likely to pass through a clump (Li & Clark 1974; Mason et al. 1974; Parsignault et al. 1976; Pravdo et al. 1980; Remillard & Canizares 1984; Kitamoto et al. 1984; Bałucińska-Church et al. 2000; Feng & Cui 2002; Poutanen et al. 2008; Hanke et al. 2009; Miškovičová et al. 2016; Grinberg et al. 2015). The precise structure of the clumps, i.e., their density and ionization structure, is unknown. Most recent 2D simulations of such a stellar wind show a very complex evolution of velocity and density structures with the formation of characteristic small-scale clumps of various shapes embedded in areas with lower density (Sundqvist et al. 2018). Sundqvist et al. (2018) have found a typical clump mass of 1017 g and an average clump size of 1% of the stellar radius at a distance of two stellar radii. These results qualitatively confirm earlier theoretical models (e.g., Oskinova et al. 2012; Sundqvist & Owocki 2013) and observations (e.g., Grinberg et al. 2015). See also the review paper by Martínez-Núñez et al. (2017).


Ricci et al. (2017c, hereafter R17c) recently reported on a study of the relationship between obscuration and accretion rate in a large, relatively unbiased, and complete sample of local AGNs. Specifically, they investigated 836 AGNs with a median redshift of 〈z〉 = 0.037 selected by the hard X-ray (14–195 keV) Swift Burst Alert Telescope (BAT; Gehrels et al. 2004; Barthelmy et al. 2005; Krimm et al. 2013) all-sky survey (Baumgartner et al. 2013; Koss et al. 2017; Oh et al. 2018), which is sensitive to sources with column densities up to NH ≈ 1024 cm−2.  Approximately one-half of the sources had robust measurements of column densities, intrinsic X-ray luminosities, and black hole masses, from which R17c was able to show that while unobscured AGNs are seen with Eddington fractions up to the Eddington limit, very few local, obscured AGNs are found with Eddington fractions above approximately 10%. This strengthened earlier results based on smaller samples (e.g., Fabian et al. 2009) and was interpreted as evidence for radiation-pressure-driven AGN feedback (e.g., King 2003; Murray et al. 2005) clearing the immediate BH environment of dusty gas (e.g., Fabian et al. 2006, 2008). For dusty gas (neutral or partially ionized), the effective cross section between matter and radiation (σdust) becomes larger than that between electrons and radiation for ionized gas (σT, for Thompson scattering), due to absorption of radiation by dust. This is given by the Eddington ratio for ionized gas,
1

where Lbol is the bolometric luminosity, LEdd is the Eddington luminosity with MBH the BH mass, and mp is the proton mass. For dusty gas, we use σdust instead of σT in Equation (1), where fEdd is redefined as the effective Eddington ratio (fEdd,dust = fEddσdust/σT). AGNs are strong ionizing sources, but they are fully ionized close to their accretion disks (e.g., Osterbrock 1979; Ballantyne et al. 2001), though the greater than parsec-scale environment starts to be composed of dusty gas (e.g., Kishimoto et al. 2011; Minezaki et al. 2019).


Observations have shown that the shape of the Lyα line is diverse. It includes broad damped absorption profiles, P-Cygni profiles, double-peak profiles, pure symmetric emission profiles, and combinations thereof (Kunth et al. 1998; Mas-Hesse et al. 2003; Shapley et al. 2003; Møller et al. 2004; Noll et al. 2004; Tapken et al. 2004; Venemans et al. 2005; Wilman et al. 2005). This variety can be understood through a detailed radiative transfer calculation, which is analytically solvable only for simple cases (e.g., a static, plane-parallel slab by Harrington 1973 and Neufeld 1990, and a static uniform sphere by Dijkstra et al. 2006). Later, numerical algorithms based on Monte Carlo techniques were developed to solve radiative transfer for more general cases. Now theoretical studies mostly rely on them (e.g., Spaans 1996; Loeb & Rybicki 1999; Ahn et al. 2000, 2002; Zheng & Miralda-Escudé 2002; Richling 2003; Cantalupo et al. 2005; Dijkstra et al. 2006; Hansen & Oh 2006; Tasitsiomi 2006; Verhamme et al. 2006, 2015; Laursen et al. 2013; Behrens et al. 2014; Duval et al. 2014; Gronke et al. 2015; Smith et al. 2019; Lao & Smith 2020; Michel-Dansac et al. 2020). Meanwhile, a galaxy model needs to be constructed to perform such a radiative transfer calculation. One can adopt a realistic galaxy model from hydrodynamical simulations. Galaxies from such simulations can be useful for performing a statistical study of Lyα properties, but they cannot be directly used to model individual galaxies in observations. Therefore it would be better to adopt a simple but manageable toy model for the purpose of reproducing observations. One example for such models is a shell model, in which a central Lyα source is surrounded by a constantly expanding, homogeneous, spherical shell of H i medium with dust. Although this shell model has surprisingly well reproduced many observed Lyα line profiles (e.g., Ahn 2004; Schaerer & Verhamme 2008; Verhamme et al. 2008; Schaerer et al. 2011; Gronke et al. 2015; Yang et al. 2016; Gronke 2017; Karman et al. 2017), because of its extreme simplicity and contrivance, there is still room for improvement (e.g., see Section 7.2 in Yang et al. 2016; Orlitová et al. 2018).


In this context, it must also be noted here that these conclusions are specific to the geometry of the GCS model, which is an idealized geometrical figure that has its limitations and constraints (see Thernisien et al. 2009). Regarding the evolution of the legs, the identification of the two separate legs of the CMEs requires observation at the absolute lower heights. Thus the legs can be identified in the K-Cor FOV, while they are not seen in the COR-1 FOV at the same time, as shown in Figure 1; but it should also be noted that despite the promising FOV of K-Cor, the poor image quality due to the challenges faced from it being a ground-based coronagraph makes it difficult to fit (refer to the discussion in Section 2.2). In this regard, the upcoming ADITYA-L1 mission (Seetha & Megala 2017), with the Visible Emission Line Coronagraph (VELC; FOV: 1.05–3 R
⊙; Banerjee et al. 2017; Prasad et al. 2017) on board, and PROBA-3 (FOV : 1.02–3 R
⊙; Renotte et al. 2014), with the giant Association de Satellites pour l’Imagerie et l’Interferométrie de la Couronne Solaire (ASPIICS; Lamy et al. 2017), will provide much better data and hence will help in arriving at much stronger conclusions on the evolution of CME legs. Having said that, it must also be noted that a true estimation of the volume of CME legs will require the CME to be seen FO, as an FO view will help in identifying the inner edges of the CME and hence the volume of its legs. The studied CMEs in this work are all seen FO in the K-Cor FOV (please see Figure 1). Thus, in future, for a larger statistical study, the appearance of the CME (whether FO or EO) should also be considered in the estimation of the volume of the CME legs. Apart from that, around one-third of CMEs have been reported as having a flux-rope morphology (see Vourlidas et al. 2013), which happens to be the bedrock of the GCS model, thus a study of the three separate sections of the flux-rope model of the CME will help us to have a much better understanding of the validity of self-similar expansion, and thus provide more precise constraints to models that study flux-rope initiation and evolution.


The data presented here comprise quasi-simultaneous observations during secondary eclipse of WASP-33 b around the V and Y bands. The predicted planet-star flux ratio in the V-band is 0.2 ppt, four times lower than the accuracy of our measurements. Therefore, we can neglect the planet imprint and use this band to measure the stellar pulsations, and most specifically to tune their current phases (see phase shifts in von Essen et al. 2014). Particularly, our model for the light contribution of the stellar pulsations consists of eight sinusoidal pulsation frequencies with corresponding amplitudes and phases. Hence, to reduce the number of 24 free parameters and the values they can take, we use prior knowledge about the pulsation spectrum of the star that was acquired during von Essen et al. (2014). As the frequency resolution is 1/ΔT (Kurtz 1983), 3.5 h of data are not sufficient to determine the pulsations frequencies. Therefore, during our fitting procedure we use the frequencies determined in von Essen et al. (2014) as starting values plus their derived errors as Gaussian priors. As pointed out in von Essen et al. (2014), we found clear evidences of pulsation phase variability with a maximum change of 2 × 10-3 c/d. In other words, as an example after one year time a phase-constant model would appear to have the correct shape with respect to the pulsation pattern of the star, but shifted several minutes in time. To account for this, the eight phases were considered as fitting parameters. The von Essen et al. (2014) photometric follow-up started in August, 2010, and ended in October, 2012, coinciding with these LBT data. We then used the phases determined in von Essen et al. (2014) during our last observing season as starting values, and we restricted them to the limiting cases derived in Sect. 3.5 of von Essen et al. (2014), rather than allowing them to take arbitrary values. The pulsation amplitudes in δ Scuti stars are expected to be wavelength-dependent (see e.g. Daszyńska-Daszkiewicz 2008). Our follow-up campaign and these data were acquired in the blue wavelength range. Therefore the amplitudes estimated in von Essen et al. (2014), listed in Table 1, are used in this work as fixed values. This approach would be incorrect if the pulsation amplitudes would be significantly variable (see e.g., Breger et al. 2005). Nonetheless, the short time span of LBT data, and the achieved photometric precision compared to the intrinsically low values of WASP-33’s amplitudes, make the detection of any amplitude variability impossible.


In Sifón et al. (2013), we used the σ–M200 scaling relation of Evrard et al. (2008) to estimate dynamical masses. As discussed in Section 1, the scaling relation of Evrard et al. (2008) was calibrated from a suite of N-body simulations using DM particles to estimate velocity dispersions. However, the galaxies, from which velocity measurements are made in reality do not sample the same velocity distribution as the DM particles. They feel dynamical friction and some are tidally disrupted, which distorts their velocity distribution and biases their dispersion (e.g. Carlberg 1994; Colín et al. 2000). Recent high-resolution hydrodynamical simulations of ‘zoomed’ cosmological haloes have shown that there is a significant difference between the velocity distributions of DM particles and galaxies themselves; whether galaxies (i.e. overdensities of stars in hydrodynamical simulations) or DM subhaloes are used makes comparatively little difference (Munari et al. 2013). Results from state-of-the art numerical simulations depend on the exact definition of a galaxy and the member selection applied, but the current consensus is that galaxies are biased high (i.e. at a given mass the velocity dispersion of galaxies or subhaloes is larger than that of DM particles) by 5–10 per cent with respect to DM particles (Lau et al. 2010; Munari et al. 2013; Wu et al. 2013), translating into a positive 15–20 per cent bias in dynamical masses when using DM particles. This is illustrated in Fig. 5: DM particles are not significantly impacted by either dynamical friction or baryonic physics; therefore, the scaling relations for DM particles are essentially the same for all simulations. In contrast, DM subhaloes are affected by baryons in such a way that including baryonic feedback (most importantly feedback from active galactic nuclei – AGN, but also from cooling and star formation) makes their velocity dispersions much more similar to those of simulated galaxies. This means we can rely on our analysis of the previous section, based on DM subhaloes, to correct the velocity dispersions measured for ACT clusters, and then estimate dynamical masses using predictions obtained either from galaxies or subhaloes. The difference between the Saro et al. (2013) and Munari et al. (2013) galaxy scaling relations depends on the details of the semi-analytic and hydrodynamical implementations used in Saro et al. (2013) and Munari et al. (2013), respectively. The different cosmologies used in the Millenium simulation (in particular, σ8 = 0.9; Springel et al. 2005) by Saro et al. (2013) and the simulations by (Munari et al. 2013, σ8 = 0.8) may also play a role.


Cosmic rays (CRs) represent a crucial ingredient in the dynamical and chemical evolution of interstellar clouds. Interaction of CRs with molecular clouds is accompanied by various processes generating observable radiation signatures, such as ionization of molecular hydrogen (see, e.g., Oka et al. 2005; Dalgarno 2006; Indriolo & McCall 2012) and iron (e.g., Dogiel et al. 1998, 2011; Tatischeff et al. 2012; Yusef-Zadeh et al. 2013; Nobukawa et al. 2015; Krivonos et al. 2017), as well as production of neutral pions whose decay generates gamma-rays in the GeV (e.g., Yang et al. 2014, 2015; Tibaldo et al. 2015) and TeV (e.g., Aharonian et al. 2006; Abramowski et al. 2016; Abdalla et al. 2017) energy ranges. Being a unique source of ionization in dark clouds, where the interstellar radiation cannot penetrate, CRs provide a partial coupling of the gas to magnetic field lines, which could slow down or prevent further contraction of the cloud (e.g., Shu et al. 1987). CRs are fundamental to the beginning of astrochemistry because they promote the formation of

 ions, which can easily donate a proton to elements such as C and O, and thus eventually form molecules containing elements heavier than H (e.g., Yamamoto 2017). Through the ionization of H2 molecules and the consequent production of secondary electrons, CRs are an important heating source of dark regions (e.g., Goldsmith 2001). Their interaction with H2 can also result in molecular excitation, followed by fluorescence producing a tenuous UV field within dark clouds and dense cores (Cecchi-Pestellini & Aiello 1992; Shen et al. 2004; Ivlev et al. 2015a); this UV field can photodesorb molecules from the icy dust mantles and help to maintain a non-negligible amount of heavy molecules (such as water) in the gas phase (e.g., Caselli et al. 2012). Furthermore, CRs can directly impinge on dust grains and heat up the icy mantles, causing catastrophic explosions of these mantles (Léger et al. 1985; Ivlev et al. 2015b) and activating the chemistry in solids (Shingledecker et al. 2017). Finally, CRs play a fundamental role in the charging of dust grains and the consequent coagulation of dust (Okuzumi 2009; Ivlev et al. 2015a, 2016), which is particularly important for the formation of circumstellar disks (e.g., Zhao et al. 2016) and of planets in more evolved protoplanetary disks (e.g., Testi et al. 2014).


Gomez’s Hamburger (IRAS 18059-3211; hereafter GoHam) is an A star surrounded by a dusty disk. When first studied by Ruiz et al. (1987), it was classified as an evolved object (post-AGB star) on the basis of its spectral type and the presence of dust. However, all recent studies (Bujarrabal et al. 2008, 2009; Wood et al. 2008; De Beck et al. 2010) clearly indicate that it is a young A star surrounded by a protoplanetary disk. The distance to GoHam is not known precisely, but a value d = 250 ± 50 pc is required to satisfy all the existing observational constraints (Wood et al. 2008; Berné et al. 2009; Bujarrabal et al. 2009). We here adopt this value with the uncertainty. GoHam presents intense CO emission; SMA maps of 12CO and 13CO J = 2 − 1 lines very clearly show the Keplerian dynamics of the disk (Bujarrabal et al. 2008, 2009). The lower limit for the disk mass derived from these CO observations is of about 10-2M⊙, while the mass upper limit is estimated to be ~0.3 M⊙  based on dust emission (Bujarrabal et al. 2008; Wood et al. 2008) and assuming an interstellar dust-to-gas mass ratio of 0.01. Overall, GoHam appears to be similar to isolated Herbig stars (Meeus et al. 2001) such as HD 100546 and HD 169142, in a more massive version, but still smaller than the recently discovered disk around CAHA J23056+6016 (Quanz et al. 2010). GoHam is seen almost perfectly edge on, which offers the possibility to study this class of objects from a new and complementary perspective, in particular, with improved constraints on the vertical structure of the disk. Using a radiative transfer model to predict line emission from a Keplerian flaring disk, Bujarrabal et al. (2009) derived a large-scale description of the physical conditions throughout the disk. After subtracting the model that best fit the observations, these authors found a significant residual emission situated about 1.3′′ (330 ± 70 AU) south of the central star, which they identified as a gas condensation, containing a mass between one and few times that of Jupiter. Hence, this source was proposed to be a candidate protoplanet, possibly resulting from a GI collpapse.