If we recall the tight, monotonic dependence of the position of galaxies along the SF sequence in the diagram with metallicity (as outlined in Section 3.1), we can interpret our global results of Figs 4 and 5 as a manifestation of the existence of an O/H versus N/O relation for SDSS star-forming galaxies, whose intrinsic scatter is reflected and, to some extent, translated into the observed distribution of emission line ratios within the [N ii]-BPT. A tight relationship between O/H and N/O abundances is indeed observed in both H ii regions and local galaxies, especially at M⋆ ≳ 109.5M⊙ (Vila Costas & Edmunds 1993; van Zee et al. 1998; Pérez-Montero & Contini 2009; Pilyugin et al. 2012; Andrews & Martini 2013; Hayden-Pawson et al. 2021), and it is set by the predominant nucleosynthetic origin of nitrogen from CNO burning of pre-existing stellar carbon and oxygen in low- and intermediate-mass stars experiencing the AGB phase (i.e. the ‘secondary’ nitrogen production mechanism, Kobayashi, Karakas & Umeda 2011; Ventura et al. 2013; Vincenzo et al. 2016); alternatively, Vincenzo & Kobayashi (2018) reproduced the observed N/O-O/H relation introducing failed supernovae (SNe) in massive stars within their cosmological simulations. Recently, such relationship between O/H and N/O has been suggested as even tighter than the one between M⋆ and N/O (Hayden-Pawson et al. 2021), in contrast to what claimed by previous studies (e.g. Andrews & Martini 2013; Masters et al. 2016). In light of our results, this would confirm that deviations in N/O at fixed O/H are more likely to be related to the offset from the SF sequence in the [N ii]-BPT than relative variations in M⋆, although the two are clearly physically correlated. The connection between the two diagrams is also readily evident if we look at the distribution of our galaxy sample in the N/O versus O/H diagram, as shown in Fig. 8 (where [N ii] λ6584/[O ii] λ3727, 29 is converted to N/O following the Te-based calibrations presented in Hayden-Pawson et al. 2021); here, each hexagonal bin is colour-coded by the average distance D of galaxies from the best-fitting line of the [N ii]-BPT, almost perfectly tracing the scatter around the median N/O versus O/H relation.


Braukmuller et al. (2018) proposed that all elements fall into one of four categories based on their condensation temperature: refractory elements (50% condensation temperature, Tc,50 > 1400 K), which exhibit approximately uniform enrichments in their Si-normalized concentrations in CC chondrites compared to CI chondrites by a factor of ∼1–1.4; main component elements (1300 K  Tc,50  1400 K), which have approximately the same Si-normalized elemental abundances in CC chondrites as CI chondrites (differ by a factor of ∼0.8–1.1); slope-volatile elements (800 K  Tc,50  1300 K), which exhibit monotonically decreasing Si-normalized concentrations with decreasing Tc,50 compared to CI chondrites; and plateau volatile elements (Tc,50  800 K), which display uniform depletions in Si-normalized concentrations compared to CI chondrites by a factor of ∼0.1–0.7 that are characteristic of each CC chondrite group. Given their uniform nature with Tc,50 and comparatively well-constrained isotopic and elemental compositions, we chose to focus on the concentrations of refractory, main component, and plateau volatile elements in this study. For the refractory and main component elements in CC chondrites, we examine the elemental and isotopic compositions of Ti and Cr, respectively, because these are lithophile elements whose isotopic compositions have been measured precisely for a large number of chondrites and their components (Trinquier et al. 2007, 2009; Qin et al. 2010; Olsen et al. 2016; Van Kooten et al. 2016; Gerber et al. 2017; Davis et al. 2018; Zhu et al. 2019; Schneider et al. 2020; Williams et al. 2020). For CC iron meteorites, we examine the isotopic compositions of Mo and Ni, respectively, because these are siderophile elements (so are therefore present in appreciable concentrations in iron meteorites, unlike Ti and Cr) whose compositions have also been relatively well studied in a number of iron meteorites as well as chondrites and their components (Burkhardt et al. 2011; Budde et al. 2016; Kruijer et al. 2017; Bermingham et al. 2018; Nanne et al. 2019; Budde et al. 2019; Worsham et al. 2019; Brennecka et al. 2020; Spitzer et al. 2020). For the plateau volatile elements, we examine the elemental compositions of six elements (Bi, Ag, Pb, Zn, Te, and Sn) that exhibit a number of desirable properties: their concentrations have been relatively well constrained in CC chondrites; they show a range of lithophile, siderophile, and chalcophile behaviors; their concentrations do not appear to be strongly dependent on redox state; they show minimal variability among NC chondrite groups. Our reasoning for not considering the isotopic compositions of these elements is discussed in Section 2.3. The adopted isotopic and chemical composition of each element used in this study in CC chondrites, CC iron meteorites, CAIs, CI chondrites, and NC chondrites are included in Table 1. Uncertainties on elemental concentrations have not been routinely reported throughout the literature, although these values are typically ±5 wt% (e.g., Lodders 2003; Palme et al. 2014). CAIs can be categorized into six groups based on their compositions (Stracke et al. 2012). For the purposes of this study, we adopt the composition of type I CAIs as the representative value of refractory objects because they are seemingly the most abundant type and lack the characteristic elemental depletions of other CAI groups (e.g., Stracke et al. 2012; Brennecka et al. 2020). We also focus largely on ordinary chondrites (OC) as representative NC meteorites rather than enstatite chondrites (EC) or Rumuruti chondrites (RC). This is because EC chondrites formed under more reducing conditions than OC and RC chondrites, which introduced a compositional signature for some elements to EC chondrites that is not present in OC, RC, or CC chondrites (presumably due to their formation in more oxidizing environments) so is not representative of large-scale mixing in the disk (Alexander 2019b). Additionally, the isotopic compositions of RC chondrites are sparsely measured compared to OC and EC chondrites. NC meteorites could have experienced a number of processes (e.g., mixing, chondrule formation, volatile loss, the addition of refractory materials, etc.) that gave these meteorites their specific chemical and isotopic signatures (Alexander 2019b). We do not explore these processes in this study and simply adopt the measured elemental and isotopic compositions of NC chondrites as potential end-members for the compositions of CC meteorites.


We now consider upcoming spectroscopic surveys. We consider two cases for the CMB lensing map, including (1) the full Planck CMB lensing map and (2) the Advanced ACTPol5 CMB lensing map. In both cases, we assume that the CMB lensing maps will be estimated using the temperature map and both E and B polarization maps, and we assume the B map only contains noise. We predict the noise in the Planck lensing map assuming the detector sensitivity and beam sizes listed in the Planck Bluebook (Planck Collaboration 2006). Advanced ACTPol will survey 20 000 deg2, and its increased temperature and polarization sensitivity will create a CMB lensing map that is an order of magnitude more sensitive than Planck. The specifications we use for Advanced ACTPol are listed in Table 3. For spectroscopic surveys, we consider the DESI emission line galaxy (ELG), LRG, and quasar surveys, as well as the Euclid Hα survey and the WFIRST Hα and O iii combined survey. The properties of the surveys are listed in Table 1. For DESI, we assume the same values as in the DESI Conceptual Design Report:6 bLRGD(z) = 1.7, bELGD(z) = 0.84, bQSOD(z) = 1.2, where D(z) is the growth factor. We also assume a 4 per cent error in β within Δz = 0.1 bins. Note that Advanced ACTPol's survey area overlaps with only ∼75 per cent of DESI's area; we take this into account in our DESI forecasts. For Euclid and WFIRST ELGs, we assume b(z) = 0.9 + 0.4z, a fit (Takada et al. 2014) to semi-analytic models (Orsi et al. 2010) that compares well with data. We determine the redshift distribution of Euclid Hα galaxies using the Hα luminosity function from Colbert et al. (2013) and assume a flux limit of 4× 10−16. This flux limit is in the middle of the range being considered, so the following Euclid forecasts can change accordingly. We also assume a 3 per cent error in β within Δz = 0.1 bins for Euclid and WFIRST (Amendola et al. 2013). For all subsequent forecasts, we assume EG measurements over angular scales 100 ≤ ℓ ≤ 500.


The gravitational potential of an eccentric companion at the quadrupole order can be decomposed as a sum over circular orbits (e.g. Storch & Lai 2013; Vick, Lai & Fuller 2017):
(5)$$\begin{eqnarray*}
U\left(\boldsymbol{\mathbf {r}}, t\right) = \sum \limits _{m=-2}^2 U_{2m} \left(\boldsymbol{\mathbf {r}}, t\right) ,
\end{eqnarray*}$$(6)$$\begin{eqnarray*}
U_{2m}\left(\boldsymbol{\mathbf {r}}, t\right) &=& -\frac{GM_2 W_{2m} r^2}{D(t)^3} Y_{2m}(\theta , \phi) e^{-imf\!\!\!\:(t)}, \\
&=& -\frac{GM_2W_{2m} r^2}{a^3}Y_{2m}\left(\theta , \phi \right) \sum \limits _{N = -\infty }^\infty \!\!F_{Nm}e^{-iN\Omega t} .
\end{eqnarray*}$$Here, the coordinate system is centered on the MS star, (r, θ, ϕ) are the radial, polar, and azimuthal coordinates of $\boldsymbol{\mathbf {r}}$ respectively, $W_{2 \pm 2} = \sqrt{3\pi /10}$, W2 ± 1 = 0, $W_{20} = -\sqrt{\pi / 5}$, D(t) is the instantaneous distance to the companion, f is the true anomaly, and Ylm denote the spherical harmonics. FNm denote the Hansen coefficients for l = 2 (also denoted $X^N_{2m}$ in Murray & Dermott 1999), which are the Fourier coefficients of the perturbing function, i.e.
(7)$$\begin{eqnarray*}
\frac{a^3}{D(t)^3} e^{-imf\!\!\!\:(t)} = \sum \limits _{N = -\infty }^\infty \!\!F_{Nm} e^{-iN\Omega t}.
\end{eqnarray*}$$The FNm can be written explicitly as an integral over the eccentric anomaly (Murray & Dermott 1999; Storch & Lai 2013):
(8)$$\begin{eqnarray*}
F_{Nm} = \frac{1}{\pi }\int \limits _{0}^{\pi } \frac{\cos \left[N\left(E - e\sin E\right) - mf(E)\right]}{\left(1 - e\cos E\right)^2}\,\,\mathrm{d}E.
\end{eqnarray*}$$By considering the effect of each summand in equation (5), the total torque on the star, energy transfer in the inertial frame, and energy transfer in the star’s corotating frame (which is also the tidal heating rate) can be obtained (Storch & Lai 2013; Vick et al. 2017):
(9)$$\begin{eqnarray*}
T = \sum \limits _{N = -\infty }^\infty F_{N2}^2 T_{\rm circ}\left(N\Omega - 2\Omega _{\rm s}\right),
\end{eqnarray*}$$(10)$$\begin{eqnarray*}
\dot{E}_{\rm in} &=& \frac{1}{2}\sum \limits _{N = -\infty }^\infty \Bigg [ \left(\frac{W_{20}}{W_{22}}\right)^2 N\Omega F_{N0}^2 T_{\rm circ}\left(N\Omega \right) \\
&&+\, N\Omega F_{N2}^2 T_{\rm circ}\left(N\Omega - 2\Omega _{\rm s}\right) \Bigg ] ,
\end{eqnarray*}$$(11)$$\begin{eqnarray*}
\dot{E}_{\rm rot} = \dot{E}_{\rm in} - \Omega _{\rm s} T .
\end{eqnarray*}$$Here, dots indicate time derivatives.


Although a correlation does exist, it is offset from the one-to-one line that one would expect, overestimating the number of spiral arms by approximately three. This may be due to how mass is assigned to the bulge and disc. We use photometric decompositions of Simard et al. (2011) and Mendel et al. (2014) to assign mass to the bulge and the disc. Such a model fits a classical bulge with n= 4 and an exponential disc. This may cause a systematic for two reasons. First, the photometric decomposition of galaxies may introduce a bias due to image resolution effects. The second issue is the pseudo- versus classical bulge argument – the model we use assumes an inner classical spherical bulge; bulges instead may be pseudo-bulges, which may not have a spherical shape, and profile well-described by a spherical Hernquist profile (Carollo et al. 1997; Gadotti & dos Anjos 2001; Kormendy et al. 2006; Fisher & Drory 2008; Gadotti 2009). Studying bulges and discs in detail is beyond the scope of this paper. Another possibility is that the assumption that spiral arms are measured at 2Rd may not be valid – if spiral arms were instead measured closer to the inner regions of galaxies, then this offset is negated. Unfortunately, the binary nature of visual morphological classifications, where arms either are or are not recorded, prevents further investigation of this point. Finally, there may be some spiral arms which are impossible to observe with visual morphology in the way presented in this paper. Of particular note is the case where the model predicts very high spiral arm numbers. In this case, the spiral arms may instead be wakelets which are difficult to observe visually; our observed arm number measurements may therefore be systematically low for these galaxies. Investigating which caveat, or which combination of caveats is responsible requires higher resolution imaging of galaxies than those used in this paper. Any study of this nature would be severely restricted in terms of sample size and completeness compared to the results we present in this paper.


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

6

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


Critical luminosity (Lcrit) is the luminosity above which a state transition from subcritical to supercritical takes place. The subcritical state (LX Lcrit) is known to be the low luminosity state whereas the supercritical state is high luminosity state (LX > Lcrit) (Becker et al. 2012). The critical luminosity is crucial to determine whether the radiation pressure of the emitting plasma is capable of decelerating the accretion flow (Basko & Sunyaev 1976; Becker et al. 2012). The luminosity during the 2020 giant outburst reached a record high, which was significantly higher than the critical luminosity (Reig & Nespoli 2013). The source entered a supercritical regime from a subcritical regime during the outburst. In the supercritical regime, radiation pressure is high enough to stop the accreting matter at a distance above the neutron star, forming a radiation-dominated shock (Basko & Sunyaev 1976; Becker et al. 2012). For the subcritical regime, accreted material reaches the neutron star surface through nuclear collisions with atmospheric protons or through Coulomb collision with thermal electrons (Harding 1994). These accretion regimes can also be probed by noting changes in the cyclotron line energies, pulse profiles, and changes in the spectral shape (Parmar, White, & Stella 1989; Reig & Nespoli 2013). During the transition from the subcritical to the supercritical regime, sources show two different branches in their hardness–intensity diagram (HID) which are known as horizontal branch (HB) and diagonal branch (DB) (Reig & Nespoli 2013). The HB implies the low-luminosity state of the source, which is represented by spectral changes and high X-ray variability. The DB corresponds to the high-luminosity state that appears when the X-ray luminosity is above the critical limit. The classification HB and DB depends on HID patterns that the source follows. The HB pattern is generally observed in the subcritical regime and the DB pattern is observed in the supercritical regime (Reig & Nespoli 2013).


In this work, we follow the method for measuring the IGM thermal state based on Voigt profile decomposition of the Ly α forest (Schaye et al. 1999; Ricotti et al. 2000; McDonald et al. 2001). In this approach, a transmission spectrum is treated as a superposition of multiple discrete Voigt profiles, with each line described by three parameters: redshift zabs, Doppler broadening b, and neutral hydrogen column density $N_{\rm H\, {\small I}}$. By studying the statistical properties of these parameters, i.e. the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution, one can recover the thermal information encoded in the absorption profiles. The majority of past applications of this method constrained the IGM thermal state by fitting the low-b-$N_{\rm H\, {\small I}}$ cutoff of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution (Schaye et al. 1999, 2000; Ricotti et al. 2000; McDonald et al. 2001; Rudie, Steidel & Pettini 2012; Boera et al. 2014; Bolton et al. 2014; Garzilli, Theuns & Schaye 2015, 2020; Hiss et al. 2018; Rorai et al. 2018). The motivation for this approach is that the Ly α lines are broadened by both thermal motion and non-thermal broadening resulting from combinations of Hubble flow, peculiar velocities, and turbulence. By isolating the narrow lines in the Ly α forest that constitutes the lower cutoff in $b-N_{{{{\rm H\, {\small I}}}}{}}$ distributions, of which the line-of-sight component of non-thermal broadening is expected to be zero, the broadening should be purely thermal, thus allowing one to constrain the IGM thermal state. However, this method has three crucial drawbacks. First, the IGM thermal state actually impacts all the lines besides just the narrowest lines. Therefore, by restricting attention to data in the distribution outskirts, this approach throws away information and reduces the sensitivity to the IGM thermal state significantly (Rorai et al. 2018; Hiss et al. 2019). Secondly, in practice, determining the location of the cutoff is vulnerable to systematic effects, such as contamination from the narrow metal lines (Hiss et al. 2018; Rorai et al. 2018). Lastly, the results from this approach critically depend on the choice of low-b cutoff fitting techniques, where different techniques might result in inconsistent T0 and γ measurements (Hiss et al. 2018; Rorai et al. 2018).


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


The ability to retrieve the polarized quantities of a radio source is entirely dependent on the ability to find radio sources within noisy images. It is of importance to planned future surveys to investigate suitable strategies for source-finding in linear polarization with interferometers such as LOFAR, which are very well suited for deep radio surveys (e.g. Hardcastle et al. 2016; Clarke et al. 2017), but are particularly technically challenging due to operation at low radio frequencies (Varenius et al. 2015), with potentially sub-arcsecond angular resolution (Moldón et al. 2015), at high sensitivity (Shimwell et al. 2016), and with the ability to make precise Faraday rotation measurements (Sotomayor-Beltran et al. 2013). Nevertheless, finding linearly polarized sources faces many hurdles: (i) at sub-arcminute resolution, the peak in linearly polarized intensity can be offset from the peak in total intensity (see e.g. fig. 1 in O'Sullivan et al. 2015), (ii) the statistics in polarized intensity, $P=\sqrt{Q^2+U^2}$, are Rician, rather than Gaussian, while all publicly available source-finders are geared towards Gaussian noise statistics, (iii) the full sensitivity is not provided in any single channel of Q, U, or P, and RM Synthesis is therefore required to retrieve the full point-source sensitivity from the data, (iv) sources detected in Q and U can have both positive and negative brightness, and these values oscillate and mix across the observing bandwidth due to Faraday rotation, and (v) in some cases, Q and U images can be more sensitive than I images, which in principle could lead to sources that can be found in P but not in I. Source-finding in circular polarization, Stokes V, is beyond the scope of this paper in which we focus on linear polarization, but also faces similar challenges due to the full sensitivity not being provided in a single channel and the process of Faraday conversion across the observing band. Moreover, the linear feeds used for observations at low radio frequencies with instruments such as LOFAR are more suitable for measuring circular rather than linear polarization, which further increases the difficulty of detecting faint linearly polarized sources.


With photometry in hand for the majority of our galaxy spectroscopy sample, we can also investigate velocity segregation effects as a function of galaxy luminosity. We use cluster galaxy brightness measurements in units relative to m*, a standard quantity that can be easily incorporated into both observational data and simulated clusters (Cole et al. 2001; Cohen 2002; Rudnick et al. 2006, 2009). Specifically, we use m* values computed from Bruzual & Charlot (2003) models in the same fashion as described in previous SPT publications (High et al. 2010; Song et al. 2012; Bleem et al. 2015). Figure 7 shows the distribution of cluster member galaxies with brightness measurements as described in Section 2.4 plotted relative to the characteristic magnitude, m*, for the full cluster member sample as well as the subsamples of cluster members of different spectral types. We use these data, in combination with the normalized peculiar velocities of each cluster member in the ensemble to plot the expectation value for the absolute peculiar velocity of cluster members as a function of brightness for all galaxies together, as well as for each of the passive, post-starburst, and star-forming galaxy subsets (Figure 8). It is clear that the brightest galaxies—independent of spectral type—universally prefer smaller absolute peculiar velocities, and that when we treat all galaxies together we see a strong drop in the absolute peculiar velocities of galaxies brighter than

, while galaxies fainter than this tend to remain approximately flat in absolute peculiar velocity as a function of brightness. There is no statistically significant evidence in our data for an evolution in the presence or of velocity luminosity segregation with redshift. Specifically, if we split our sample into two redshift bins at z = 0.45—which optimally balances the number of bright galaxies in the high and low bins—we see the strong drop in peculiar velocity for bright galaxies in each of the high and low-redshift bins.


About a quarter of the known exoplanets orbit at short distances (≲0.1 au) from their star (from the Exoplanet Encyclopaedia in December 2016; Schneider et al. 2011). Heating by the stellar energy can lead to the expansion of their upper atmospheric layers and their eventual escape. As a result of this expansion, the upper atmosphere produces a deeper absorption than the planetary disk alone when observed in the UV, in particular in the stellar Lyman-α (Ly-α) line of neutral hydrogen (e.g., Vidal-Madjar et al. 2003; Lecavelier des Etangs et al. 2012). Super-Earths and smaller planets display a large diversity in nature and composition (e.g., Seager et al. 2007; Rogers & Seager 2010; Fortney et al. 2013), which can only be investigated through observations of their atmospheres. The reduced scale height of the lower atmospheric layers makes them difficult to probe in the visible and the infrared. In contrast, very deep UV transit signatures can be produced by the upper atmospheres of small planets. The warm Neptune GJ436b, which is the lowest mass planet found evaporating to date (Ehrenreich et al. 2015), shows transit absorption depths up to 60% in the Ly-α line. The formation of such an extended exosphere is due in great part to the low mass of GJ436b and the gentle irradiation from its M-dwarf host (Bourrier et al. 2015, 2016b). Few attempts have been made to detect atmospheric escape from Earth-size planets, and Ly-α transit observations of the super-Earth 55 Cnc e (Ehrenreich et al. 2012) and HD 97658 b (Bourrier et al. 2016a) showed no evidence of hydrogen exospheres. In the case of 55 Cnc e, this non-detection hinted at the presence of a high-weight atmosphere – or the absence of an atmosphere – recently supported by the study of its brightness map in the IR (Demory et al. 2016). Understanding the conditions that can lead to the evaporation of Earth-size planets will be necessary to determine the stability of their atmospheres and their possible habitability. For example, large amounts of hydrogen in the upper atmosphere of a close-in terrestrial planet could indicate the presence of a steam envelope being photodissociated, and replenished by evaporating water oceans (Jura 2004; Léger et al. 2004).


Galaxy formation theory has developed dramatically over the last three decades. Λ cold dark matter (ΛCDM) has been established as the standard model for cosmological structure formation, and its parameters have been increasingly tightly constrained by observations. In parallel, simulations of galaxy formation within this standard model have grown in complexity in order to treat more accurately the many baryonic processes that impact the evolution of the galaxy population. Semi-analytic modelling is a particular simulation method which is optimized to connect the observed properties of the galaxy population – abundances, scaling relations, clustering and their evolution with redshift – to the astrophysical processes that drive the formation and evolution of individual galaxies (e.g. White 1989; Cole 1991; Lacey & Silk 1991; White & Frenk 1991; Kauffmann, White & Guiderdoni 1993; Cole et al. 1994; Kauffmann et al. 1999; Somerville & Primack 1999; Springel et al. 2001, 2005; Hatton et al. 2003; Kang et al. 2005; Lu et al. 2011; Benson 2012). Simple phenomenological descriptions of the relevant processes are needed, each typically involving uncertain efficiency and scaling parameters. These must be determined by comparison with observation or with more detailed simulations. As the range and quality of observational data have increased, so has the number of processes that must be included to model them adequately, and hence the number of adjustable parameters. In recent years, robust statistical methods have been introduced in order to sample the resulting high-dimensional parameter spaces and to determine the regions that are consistent with specific observational data sets. This development began with the work of Kampakoglou, Trotta & Silk (2008) and Henriques et al. (2009) and has since been extended to a wide range of models and sampling methods (Benson & Bower 2010; Bower et al. 2010; Henriques & Thomas 2010; Lu et al. 2011, 2012; Henriques et al. 2013; Mutch, Poole & Croton 2013; Benson 2014; Ruiz et al. 2015).


For the study of each of the individual reactions we have characterized the stationary points on their respective potential energy surfaces by means of density functional theory (DFT) calculations. We have employed the mPWB1K exchange and correlation functional of Zhao & Truhlar (2004) in combination with the def2-TZVP basis set (Weigend & Ahlrichs 2005). The main advantage of this functional for this investigation is that it was designed for the easy determination of activation energies. Minima and transition states (TSs) were optimized using the DL-FIND (Kästner et al. 2009) program of the ChemShell suite (Sherwood et al. 2003; Metz et al. 2014). A search of TS was done by means of potential energy surface scans and posterior optimization in cases where a kinetic barrier was predicted. Assessment of the nature of the stationary points was performed by computing the molecular Hessian of each. Additionally, we have addressed the validity of the DFT method by computing single-point calculations on the relevant DFT geometries at the CCSD(T)-F12/cc-PVTZ-F12 level of theory using Molpro 2015 (Werner et al. 2012, 2015). We have found excellent agreement between DFT and coupled cluster methods for the reaction barriers, with deviations of less than 1 kcal mol−1 in all cases. Furthermore, we have carried out intrinsic reaction coordinate (IRC) calculations to ensure a proper connection between our calculated TSs and their associated minima. For reactions with a barrier, we have computed both classical bimolecular reaction rate coefficients as well as tunneling-corrected ones. The inclusion of quantum tunneling in our calculations has been performed using semi-classical instanton theory (Rommel & Kästner 2011; Rommel et al. 2011), following a sequential cooling scheme for temperatures below the crossover temperature, and reduced instanton theory for temperatures above (McConnell & Kästner 2017). Crossover temperatures are defined—with

 being the frequency of the vibrational imaginary mode in the TS, and kB the Boltzmann constant—as
6


The stochastic gravitational-wave background (SGWB)—the primary goal of the search of the PTA collaborations—is expected to be dominant in the nanohertz band, which might originate from supermassive black hole binaries (SMBHBs; Rajagopal & Romani 1995; Sesana 2013), comic strings (Damour & Vilenkin 2005; Blanco-Pillado et al. 2018), the first phase transition (Caprini et al. 2010), and scalar-induced GWs (Yuan et al. 2019). Over the last few decades, the PTA collaborations have not found GW signals, but the increasingly sensitive data sets offer increasingly stringent constraints on the SGWB (van Haasteren et al. 2011; Shannon et al. 2013; Lentati et al. 2015; Shannon et al. 2015; Arzoumanian et al. 2016, 2018; Chen et al. 2020). Recently, the NANOGrav collaboration reported that there is strong evidence in favor of a stochastic common-spectrum process, which is modeled by a power-law spectrum among the pulsars, over the independent red noise processes of each pulsar, in their 12.5 yr data set (Arzoumanian et al. 2020). However, given the lack of statistically significant evidence for quadrupolar spatial correlations, it is inconclusive to claim the detection of an SGWB consistent with general relativity. Note that the tensor transverse (TT) modes giving rise to quadrupolar spatial correlations constitute only two of the six GW polarization modes that are allowed in a general metric theory of gravity, which also includes one scalar transverse (ST) mode, two vectorial longitudinal (VL) modes, and one scalar longitudinal (SL) mode. Later on, Chen et al. (2021) searched for nontensorial SGWBs in the NANOGrav 12.5 yr data set, and found strong Bayesian evidence that the common-spectrum reported by the NANOGrav collaboration had ST spatial correlations. More recently, the PPTA collaboration has also found a common-spectrum process in their second data release (DR2), with PPTA DR2 showing no significant evidence for, or against, TT spatial correlations (Goncharov et al. 2021a).


Fast radio bursts (FRBs) are cosmological radio transients with millisecond durations. Since the first FRB (FRB 010724, the Lorimer burst) was discovered in 2007 (Lorimer et al. 2007), hundreds of FRB sources have been detected, dozens of which are repeaters (e.g., the CHIME/FRB Collaboration et al. 2021). Recently, a Galactic FRB, FRB 200428, was detected to be associated with SGR J1935+2154 (Bochenek et al. 2020; CHIME/FRB Collaboration et al. 2020; Mereghetti et al. 2020; Li et al. 2021a; Ridnaia et al. 2021; Tavani et al. 2021), which suggests that at least some FRBs originate from magnetars born from the core collapse of massive stars (e.g., Popov & Postnov 2013; Katz 2016; Murase et al. 2016; Beloborodov 2017; Kumar et al. 2017; Yang & Zhang 2018, 2021; Metzger et al. 2019; Lu et al. 2020; Margalit et al. 2020; Wadiasingh et al. 2020; Wang et al. 2022; Zhang 2022). However, FRB 20200120E was found to be in a globular cluster of a nearby galaxy, M81 (Bhardwaj et al. 2021; Kirsten et al. 2022). This is in tension with the scenario that invokes active magnetars with ages ≲10 kyr formed in core-collapse supernovae (Kremer et al. 2021; Lu et al. 2022) and suggests that FRBs might originate from magnetars formed in compact binary mergers (Margalit et al. 2019; Wang et al. 2020; Zhong et al. 2020; Zhao et al. 2021). Therefore, the physical origin of FRBs is still not well constrained from the data (e.g., Cordes & Chatterjee 2019; Petroff et al. 2019; Zhang 2020; Xiao et al. 2021). The growing FRB detections start to shed light on the diversity among the phenomena. The repeaters presented in the first CHIME FRB catalog have relatively larger widths and narrower bandwidths compared with one-off FRBs (Pleunis et al. 2021). The behaviors of fluence with respect to peak flux exhibit statistically significant differences between bursts with long and short durations (Li et al. 2021c). Multiple origins for the FRB population seem increasingly likely.


The simplest approach to handling the problem of completeness is to be extremely conservative, and discard all data in regions of parameter space where the observations are not complete or nearly so. However, this invariably requires one to discard much of the available data. A somewhat more sophisticated approach is forward modelling: rather than deriving the mass and age distribution of the population from estimates of mass age for individual clusters, one could instead consider a proposed distribution of masses and ages, predict the resulting photometry distribution including the effects of incompleteness, and adjust parameters of the mass and age distribution until they match the observations. Approaches of this type are widely used in astronomy, for example to infer star formation histories or stellar mass distributions from observed colour–magnitude diagrams (CMDs; e.g. Dolphin 2002; Harris & Zaritsky 2009; Weisz et al. 2013; Conroy & van Dokkum 2016; see Cerviño 2013 for a review). However, methods of this type have not previously been applied to deriving the properties of populations of star clusters, at least in part due a unique challenge not present in other applications. In existing applications such as CMD fitting, the forward model is deterministic, i.e. for a given stellar mass, age, and other properties, there is a single predicted colour and magnitude. This is not the case for star clusters with masses ≲ 3000 M⊙, because such clusters are too small to fully sample the stellar initial mass function (IMF, e.g. Cerviño & Luridiana 2004, 2006; da Silva, Fumagalli & Krumholz 2012). As a result, two clusters of the same total mass and age can produce wildly different luminosities and colours. This means that the forward model is not deterministic, but instead depends on an additional random variable that couples non-linearly with the deterministic variables like cluster mass and age. This situation presents computational challenges that are not addressed by existing methods.


B335 is an isolated Bok globule with an embedded Class 0 protostar at a distance of 100 pc (Keene et al. 1980, 1983; Stutz et al. 2008; Olofsson & Olofsson 2009). The size of the dense core in B335 observed at millimeter wavelengths is ∼0.1 pc (Saito et al. 1999; Motte & André 2001; Shirley et al. 2002), and the core is slowly rotating (Saito et al. 1999; Yen et al. 2011; Kurono et al. 2013). Infalling and rotational motions on scales from 100 to 3000 au have been observed in molecular lines with single-dish telescopes and interferometers (Zhou et al. 1993; Choi et al. 1995; Zhou 1995; Saito et al. 1999; Evans et al. 2005, 2015; Yen et al. 2010, 2011, 2015b; Kurono et al. 2013). Nevertheless, no sign of Keplerian rotation was observed with the Atacama Large Millimeter/submillimeter Array (ALMA) at an angular resolution of 03 (30 au; Yen et al. 2015b), and the envelope rotation on a scale of 100–1000 au in B335 is an order of magnitude slower than in other Class 0 and I protostars surrounded by a Keplerian disk with a size of tens of au (Yen et al. 2015a). The presence of a small disk less than 10 au and the slow envelope rotation hints at the effects of the magnetic field on the gas kinematics in B335. In addition, ALMA observations in the C18O and H13CO+ lines show no detectable difference in the infalling velocities of neutral and ionized gas on a 100 au scale with a constraint on the upper limit of the ambipolar drift velocity of 0.3 km s−1, suggesting that the magnetic field likely remains well coupled with the matter in the inner envelope in B335 (Yen et al. 2018). The magnetic field structures on a 1000 au scale in B335 also show signs of being dragged toward the center and becoming pinched, as inferred from the ALMA polarimetric observations (Maury et al. 2018). Therefore, B335 is an excellent target to investigate the interplay between the magnetic field and gas motions and the effects of the magnetic field on the dynamics in collapsing dense cores.


The EFE mentioned in the previous section is due to the fact that the MOND equations (3) and (4) are non-linear and involve the total gravitational acceleration with respect to a pre-defined frame (e.g. the CMB frame). Decomposing the total gravitational field ∇Φ into an internal part $\boldsymbol g$ and an external field $\boldsymbol g_{\rm e}$ and using a similar decomposition for the Newtonian gravitational acceleration ($\nabla \boldsymbol \Phi _{\rm N}=\boldsymbol g_{\rm N}+\boldsymbol g_{{\rm Ne}}$) allows us to solve the equations by taking into account the external field. This must typically be done with a numerical Poisson solver (Wu et al. 2008; Angus et al. 2012; Lüghausen, Famaey & Kroupa 2015). Nevertheless, fits to rotation curves in MOND usually neglect the small corrections due to the non-spherical symmetry of the problem, in order to allow for a direct fit of the rotation curve. In the same spirit, and in order to get a first glimpse of the influence of the EFE on rotation curves, we generalize the one-dimensional solution, by using the following formula to fit rotation curves, namely equation (60) from Famaey & McGaugh (2012):

(6)

\begin{equation}
\boldsymbol g=\nu \left(\frac{|\boldsymbol g_{\rm N}+\boldsymbol g_{{\rm Ne}}|}{a_0}\right)\left(\boldsymbol g_{\rm N} + \boldsymbol g_{{\rm Ne}}\right)-\nu \left(\frac{g_{{\rm Ne}}}{a_0}\right)\boldsymbol g_{{\rm Ne}}\,.
\end{equation}

The 1D version of this formula has been shown to be a good approximation of the true 3D solution from a numerical Poisson solver for a random orientation of the external field, at least for computing the Galactic escape speed (Famaey et al. 2007; Wu et al. 2008). Further work should investigate the range of variation of the actual rotation curve compared to the one obtained in this way, for full numerical solutions of the modified Poisson equation and various orientations of the EFE. As mentioned in Famaey & McGaugh (2012), the EFE is negligible if ge g but can play a significant role when the gravitational field g ∼ ge a0. This condition is always reached at some point in the external part of the galaxies. In this case, the relation (6) shows that the EFE will induce a decrease in the internal gravitational field. In other words, the EFE can lead to a decrease of the external part of the rotation curves. We will study this effect more carefully in Section 3.


The two main problems arising when dealing with P are the typically low signal-to-noise ratio of the polarisation signal coming from ERS and the non-Gaussian distribution of its noise statistics. Regarding the former, as mentioned above, the typical polarisation fractions of ERS at frequencies below ∼10 GHz are at most 10%. This means that only a few ERS are bright enough to be detected in polarisation with present-day technology. A standard procedure to avoid false detections in polarisation is to detect sources in total intensity and then to try to estimate their polarisation properties in a non-blind way3. We follow this approach in this paper. Regarding the latter problem, assuming that the Q and U noises are Gaussian-distributed, P would have a non-Gaussian Rice distribution (Rice 1945). Rician distribution has strictly non-negative support and heavy tails, which firstly biases the estimation of the polarisation of the sources and secondly disrupts the intuitive interpretation of signal-to-noise in terms of σ thresholds which is used virtually everywhere else in radio astronomy. Simmons & Stewart (1985) discussed four estimators which attempted to correct for biasing in the degree of linear polarisation in the presence of low signal-to-noise ratios. More recently, Argüeso et al. (2009) studied the problem in the context of CMB astronomy and developed two methods for the detection and estimation of ERS in polarisation data: one that applies the Neyman-Pearson lemma to the Rice distribution, the Neyman-Pearson filter (NPF), and another based on pre-filtering before fusion of Q and U to obtain P, the filtered fusion (FF) method. That work found that under typical CMB-experiment settings, the FF outperforms the NPF both in terms of computational simplicity and accuracy, especially for low fluxes. López-Caniego et al. (2009) applied the FF to the Wilkinson Microwave Anisotropy Probe (WMAP) five-year data. The same method has been used to study the polarisation of the Planck Second Catalogue of Compact Sources (PCCS2, Planck Collaboration XXVI 2016) and of the QUIJOTE experiment wide survey source catalogue (Herranz et al. 2021). Alternatively, a novel method for the estimation of the polarisation intensity and angle of compact sources in the E and B modes of polarisation based on steerable wavelets has been recently proposed by Diego-Palazuelos et al. (2021).


The physical processes involved in the formation of massive O-type stars and their feedback mechanisms are still under debate (Zinnecker & Yorke 2007; Tan et al. 2014). The energetics of O-type stars can affect the origin of new low-mass and massive stars (Deharveng et al. 2010). The massive stars are often surrounded by the bubbles/rings/semi-ringlike structures traced at mid-infrared (MIR) 8.0 μm (Churchwell et al. 2006, 2007) and are also associated with the extended radio continuum emission (e.g., Deharveng et al. 2010). Note that the majority of the studies related to the MIR bubbles are mainly carried out for a single H ii region or several H ii regions on scales of a few parsecs (e.g., Zinnecker & Yorke 2007; Deharveng et al. 2010; Rathborne et al. 2011; Kendrew et al. 2012; Simpson et al. 2012; Tackenberg et al. 2012; Thompson et al. 2012; Tan et al. 2014; Dewangan et al. 2015a, 2015b; Xu et al. 2016a). However, to our knowledge, in the Milky Way, there is still a limited detailed multiwavelength study of large-scale systems (>25 pc) of several MIR bubbles/H ii regions containing O-type stars, and hence the origin of such extended systems of H ii regions remains unexplored. These systems could be candidates for “mini-starburst” (such as the W43 “mini-starburst” region; Motte et al. 2003). With the availability of the radio recombination line (RRL) and continuum observations (e.g., Lockman 1989; Condon et al. 1998; Anderson & Bania 2009; Jones & Dickey 2012), the MIR survey (e.g., Benjamin et al. 2003), the dust continuum survey at 870 μm (e.g., Schuller et al. 2009; Urquhart et al. 2018), and the 13CO line survey (e.g., Jackson et al. 2006; Anderson et al. 2009), it appears that the H ii regions located toward the Galactic plane and the inner Galaxy are the promising sites to investigate the extended systems of O-type stars. Such study will enable us to understand the physical conditions in a densely clustered environment linked with the luminous giant H ii regions/massive star-forming complexes/mini-starburst candidates in the Galaxy. However, in particular, in the direction of the inner Galaxy, the investigation of an extended system of H ii regions is often restricted by the near–far kinematic distance ambiguity (e.g., Anderson & Bania 2009; Jones & Dickey 2012; Urquhart et al. 2018). In recent years, significant effort has been devoted to resolving the distance ambiguity for H ii regions in the inner Galaxy (see Urquhart et al. 2018 and references therein). In this work, we aim to observationally investigate a large-scale system/configuration of several H ii regions powered by O-type stars and the origin of such a large system.


ASASSN-14li was discovered by the All Sky Automated Search for Supernova (ASASSN; Shappee et al. 2014) on ut 2014–11–22.63 (MJD 56983.6) as a 16.5 magnitude source in the V band (Jose et al. 2014; Holoien et al. 2016; Brown et al. 2017a). The position of the source was found to be consistent with the centre of the post-starburst galaxy PGC 043234, with a measured projected separation of 0.04 arcsec. This galaxy is at redshift z = 0.0206 with a luminosity distance of 90.3 Mpc (for cosmological parameters H0 = 73 kms−1 Mpc−1, Ωmatter = 0.27, and ΩΛ = 0.73). It was established through archival X-ray observations of PGC 043234 from the ROSAT All-Sky Survey (Voges et al. 1999) that the galaxy does not contain an efficiently accreting AGN, with the count rate implying a luminosity orders of magnitude below standard active nuclei (e.g. Miller et al. 2015). A small number (currently six) of confirmed TDEs, including ASASSN-14li, have also been detected at radio wavelengths and the population may form a bi-modal distribution, consisting of more common non-relativistic ‘thermal’ events and rarer relativistic jets. Three events (Swift J1644+57; Burrows et al. 2011; Zauderer et al. 2011, Swift J2058+05; Cenko et al. 2012, Swift J1112.2; Brown et al. 2017b) have isotropic ∼5 GHz luminosities of between 1040 and 1042 erg s−1 whereas the rest (IGR J12580+0134; Irwin et al. 2015, XMMSL1 J0740-85; Alexander et al. 2017, ASASSN-14li; van Velzen et al. 2016; Alexander et al. 2016) have luminosities in the range 1037 to 1039 erg s−1 at similar frequencies. The higher power events are believed to result from observing down the axis of a relativistic jet, resulting in the energy of photons being significantly boosted. Even accounting for boosting, these relativistic events have a higher total energy output than their thermal counterparts. The origin of the radio emission from the thermal events is currently uncertain, with transient jets (van Velzen et al. 2016), non-relativistic winds (Alexander et al. 2016), and shocks driven by unbound material (Krolik et al. 2016) all feasible scenarios. ASASSN-14li is by far the best studied of the ‘thermal’ TDE category, having been observed extensively at Optical, UV, X-ray (where ASASSN-14li is unusually loud for an optically selected TDE), and radio wavelengths. The high cadence X-ray and radio observations in particular allow for the X-ray/radio coupling to be probed.


Optical color-magnitude and near-infrared (NIR) color-color diagrams are used to classify our variable candidates. The 2MASS JHKs data are available for 93 stars, while for the remaining two stars, photometric data are adopted from the UKIDSS Galactic Plane Survey (Lucas et al. 2008). The 2MASS photometry is transformed to the California Institute of Technology (CIT) system using the relations provided on their website3 to compare with the evolutionary models. Figure 6 represents the J − H/H − K CCD based on 2MASS data, typically used to classify the YSOs. The YSOs from Rebull et al. (2011) and Ogura et al. (2002) are overplotted in colored symbols. The sequence of dwarf and giants from Bessell & Brett (1988), and the intrinsic locus of CTT stars (Meyer et al. 1997) are also overplotted. The three parallel lines are the reddening vectors drawn from the tip of the giant branch (left), from the base of the MS branch (middle), and from the tip of the intrinsic CTTSs line (right). The extinction ratios to derive these reddening vectors are

A

J
/
H
/
K

A
V

=
0.265
/
0.155
/
0.090

$ \frac{A_{J/H/K}}{A_V} = 0.265/0.155/0.090 $

, adopted from Cohen et al. (1981). In general, CTTSs with smaller NIR excess, WTTSs, and field stars (MS and giants) occupy the region between the left and middle reddening vectors. Figure 6 shows that most of the variables that are outliers in the proper motions and lie below the intrinsic CTTSs locus are the MS stars. Two variables (V173 and V177) are members based on their proper motions, but fall below the giant sequence. One of these, V173, does not have kinematic information. The CTTSs with large infrared excess are located in the region between the middle and right reddening vectors, while more moderate CTTSs with smaller infrared excess can also populate the region between left and middle reddening vectors, mixed with reddened WTTSs just above the CTT locus. Some contamination is expected depending on the reddening and IR excess, and also due to variability in single-epoch measurements.


It is harder to evaluate the behaviour of the young stellar population along the line of sight, since radial velocity measurements for our sample of Cepheids, needed for a thorough study, do not exist. Given this deficit, we provide only a simplified estimate using radial velocities of OBA-type stars from Evans & Howarth (2008). Since they belong to the same young population, we assume that they have a similar distance distribution and kinematics as the Cepheids. Fig. 16 shows the massive star sample in the plane of the sky. Except for the northernmost region (δ ≥ −72○), where no data exist, these stars cover a comparable area to the Cepheids (indicated as grey dots in the figure for comparison). The radial velocities show a distinct and well-known gradient across the SMC with higher velocities in the eastern part (see also fig. 5 of Evans & Howarth 2008). Such a gradient in radial velocity is also present in older (few Gyr) RGB stars (see fig. 9 of Dobbie et al. 2014). This gradient is commonly attributed to rotation of the SMC. Based on our results obtained for the Cepheids, we propose a different interpretation: this line-of-sight velocity gradient may instead be caused by the fact that the nearest parts of the galaxy, in the region of the SMC Wing, move with a higher radial velocity compared with the main body of the galaxy. Given the additional differences in tangential velocities, these outer parts might be in the process of being stripped from the SMC. Diaz & Bekki (2012) show in their simulations that tidal effects can produce a velocity gradient that is similar to that of a rotating disc. We stress again that this interpretation is based on the assumption that the Cepheid sample and the OBA-type stellar sample trace a similar three-dimensional distribution. For any conclusive answer, radial velocities of the Cepheid stars are required. Such measurements will be provided by the One Thousand and One Magellanic Fields (1001MC) survey (Cioni et al. 2019), which is a consortium survey with the forthcoming multi-object spectrograph 4MOST that will be mounted on the VISTA telescope.


Silicon carbide is the best-characterized presolar mineral. It was identified more than 30 yr ago (Bernatowicz et al. 1987) because it is tagged with noble gases of anomalous isotopic compositions (Lewis et al. 1994). Subsequently, it was found that the major elements C and Si, and numerous minor elements contained in presolar SiC, have highly anomalous isotopic compositions as well, the fingerprints of nucleosynthetic processes in their parent stars. Based on the isotopic compositions of C, N, and Si, SiC was divided into distinct populations (Zinner 2014). This includes the mainstream grains, which account for about 80%–90% of all grains (depending on grain size), and the minor types AB (originally defined as two distinct types A and B), C, X, Y, Z, and (putative) nova grains. The mainstream grains have 12C/13C ratios between 10 and 100 (solar: 89), and the 14N/15N ratios of most of them are higher than the solar ratio of 440, the ratio measured for the solar wind (Marty et al. 2011). In a plot of δ29Si versus δ30Si, the mainstream grains lie along a straight line defined by δ29Si = 1.37 × δ30Si–20 (Zinner et al. 2007), where δxSi = [(xSi/28Si)grain/(xSi/28Si)solar−1) × 1000, and x = 29 or 30, i.e., δxSi is the per mil deviation from the solar xSi/28Si ratio. δ30Si values of mainstream grains vary between about −50‰ and +150‰. The isotopic compositions of heavy elements show the signatures of slow neutron-capture nucleosynthesis (s-process, Käppeler et al. 2011), which points toward low-mass (1.5–3 M⊙) asymptotic giant branch (AGB) stars of about solar or supersolar metallicity as parent stars (e.g., Lugaro et al. 2018, and references therein). The minor type Y and Z grains (a few % of all SiC grains, depending on grain size), which fall to the 30Si-rich side of the Si mainstream line, were also proposed to originate from low-mass AGB stars, but with metallicities lower than solar (Hoppe et al. 1997; Amari et al. 2001b). This low-metallicity scenario, however, was recently questioned (Liu et al. 2019). The type C (∼0.1% of all SiC grains) and X grains (∼1% of all SiC grains) are believed to originate from core-collapse supernovae (CCSNe; Amari et al. 1992; Hoppe et al. 1996b; Nittler et al. 1996; Gyngard et al. 2010). These grains show strong depletions (X grains) or enrichments (C grains) in the heavy Si isotopes. Their 12C/13C ratios span a large range from 10 to >10,000; other characteristic features of X and C grains are enrichments in 15N and high initial 26Al/27Al ratios of typically >0.1. Putative nova grains (∼0.1% of all SiC grains) have low 12C/13C ratios of 10, low 14N/15N ratios of 40, and high initial 26Al/27Al ratios of up to 0.2 (Amari et al. 2001a); their origins in the outflows of nova explosions, however, were questioned and SNe were proposed for at least some of the putative nova grains instead (Nittler & Hoppe 2005; Pignatari et al. 2015; Liu et al. 2017a; Hoppe et al. 2018b).


Once corrected for dust attenuation, Hα luminosities can be transformed into star formation rates (SFR, in M⊙ yr-1) using a factor that depends on the assumed IMF and stellar model7: (10)\begin{equation} {SFR = k({\rm H}\alpha) \times L({\rm H}\alpha)_{\rm cor}} . \end{equation}SFR=k(Hα)×L(Hα)cor.We recall that this relation is valid only under the assumption that the mean star formation activity of the emitting galaxies is constant on a timescale of a few Myr, roughly comparable to the typical time spent by the stellar population responsible for the ionisation of the gas on the main sequence (Boselli et al. 2009; Boissier 2013; Boquien et al. 2014). The ionising stars are O and early-B stars, whose typical age is ≲107 yr. The stationarity condition is generally satisfied in massive, normal, star-forming galaxies undergoing secular evolution. In these objects, the total number of OB associations is significantly larger than the number of HII regions under formation and of OB stars reaching the final stage of their evolution, thus their total Hα luminosity is fairly constant with time. This might not be the case in strongly perturbed systems or in dwarf galaxies, where the total star formation activity can be dominated by individual giant HII regions (Boselli et al. 2009; Weisz et al. 2012), and the IMF is only stochastically sampled (Lee et al. 2009; Fumagalli et al. 2011; da Silva et al. 2014). The HRS sample is dominated by relatively massive galaxies undergoing secular evolution. For these objects, Eq. (10) can thus be applied. The sample, however, also includes galaxies in the Virgo cluster region, where the perturbation induced by the cluster environment might have affected their star formation rate (e.g. Boselli & Gavazzi 2006, 2014). Models and simulations have shown that in these objects the suppression of star formation occurs on timescales of a few hundred Myr (Boselli et al. 2006, 2008a,b, 2014d). These timescales are relatively long compared to the typical age of O-B stars. The recent work of Boquien et al. (2014) has clearly shown that the Lyman continuum emission tightly follows the rapid variations in the star formation activity of simulated galaxies down to timescales of a few Myrs. We can thus safely consider that the linear relation between the Hα luminosity and the star formation rate given in Eq. (10) is satisfied in the HRS sample.


Investigations of the turbulent nature of solar wind fluctuations have been ongoing for more than half a century (see, e.g., Bruno & Carbone 2016). Advances have been made consistently thanks to the increasingly accurate measurements of several dedicated space mission as well as to the enormous improvement of numerical calculation, new detailed models and theoretical frameworks, and the development of specific data analysis techniques. Nevertheless, the extremely complex nature of the system and the coexistence of multiple actors, scales, and dynamical regimes have led to a number of questions that remain open (Viall & Borovsky 2020). Among these, the very nature of the turbulent cascade of the solar wind flow and its relationship with the small-scale processes still need to be described in full (Tu & Marsch 1995; Bruno & Carbone 2013; Matthaeus & Velli 2011; Chen 2016). Magnetic field fluctuations have been characterized with great detail at magnetohydrodynamic and kinetic scales, for example, through spectral and high-order moments analysis (Tu & Marsch 1995; Bruno & Carbone 2013). The anisotropic nature of magnetic turbulence has also been addressed, and is still being debated, due to the limited access to three-dimensional measurements in space (see, e.g., Horbury et al. 2008, 2012; Sorriso-Valvo et al. 2010; Yordanova et al. 2015; Verdini et al. 2018; Telloni et al. 2019a; Oughton & Matthaeus 2020). Velocity fluctuations have been studied thoroughly (see, e.g., Sorriso-Valvo et al. 1999; Bruno & Carbone 2013), although the kinetic scales still remain quite unexplored for instrumental limitations, most notably in the sampling time resolution. Both the velocity and magnetic field show highly variable turbulence properties, with well developed spectra, strong intermittency (Sorriso-Valvo et al. 1999), anisotropy, and linear third-order moments scaling (Sorriso-Valvo et al. 2007; Carbone et al. 2011). The level of Alfvénic fluctuations (mostly but not exclusively found in fast streams, see e.g., D’Amicis et al. 2011; Bruno et al. 2019) are believed to be associated with the state of the turbulence. In particular, solar wind samples containing more Alfvénic fluctuations are typically associated with less developed turbulence, as inferred from both shallower spectra and reduced intermittency (see Bruno & Carbone 2013, and references therein). This is consistent with the expectation that uncorrelated Alfvénic fluctuations contribute to reduce the nonlinear cascade by sweeping away the interacting structures (Dobrowolny et al. 1980), as also confirmed by the observed anticorrelation between the turbulent energy cascade rate and the cross-helicity (Smith et al. 2009; Marino et al. 2011a,b).


The GBHT outburst light curves could be very complicated, and while the so-called ‘the main outburst’ could go through the spectral states described above, some GBHTs also show rebrightening episodes during the outburst decay (Kalemci et al. 2013) and/or an increase in brightness several days after the X-ray flux goes below the detection limits of the most observatories that are sometimes defined as mini-outbursts (Chen et al. 1997). A systematic multiwavelength study of GBHTs in the outburst decay by Kalemci et al. (2013) showed that for most of the systems, a rebrightening (secondary maximum or secondary flare) in OIR occurred ∼1–2 weeks after the soft-to-hard transition. Detection of rebrightening during the outburst decay supports the argument that the formation of a compact jet and its interaction with the accretion environment are imprinted on the multiwavelength behaviour of the GBHTs (Buxton & Bailyn 2004; Kalemci et al. 2005, 2013; Buxton et al. 2012; Dinçer et al. 2012; Corbel et al. 2013). Alternatively, the synchrotron radiation from the hot accretion flow model (Poutanen 1998; Veledina et al. 2013), or the irradiation from the secondary star or outer part of the disc could explain the brightness increase in the OIR bands. In contrast, there are limited number of pointed hard X-ray observations for the mini-outbursts (e.g. XTE J1752 − 223, SWIFT J1745 − 26, and V404 Cyg, Chun et al. 2013; Kalemci et al. 2014; Muñoz-Darias et al. 2017) since they have been observed frequently in the soft X-rays and optical (see Chen et al. 1997 for some historical examples, both in black holes and neutron stars). A recent study by Zhang et al. (2019) attempted a classification of the rebrightenings during/after the main outburst decay based on the the available fluxes and applied this scheme to Swift J1753.5 − 0127, which showed a mini-outburst in radio, optical, and X-rays. It can be seen that different flavours exist depending on whether the source reaches quiescence first. Some sources show multiple mini-outbursts after the initial outburst (e.g. XTE J1650 − 500, MAXI J1535 − 571, Tomsick et al. 2003; Cúneo et al. 2020). Although the origin of the mini-outbursts is still debated, an increased mass accretion triggered by the events during the evolution of the primary outburst through heating of the outer parts of the accretion disc (Ertan & Alpar 2002), or the companion star (Augusteijn et al. 1993), is known to be the likely explanations.


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

Orbiting SMBHBs produce a
and transient GW bursts


The Bayesian approach is indeed robust and optimal, within the context mentioned above. It focuses on the reconstruction of the LSS within the framework of the standard model of cosmology and for a given data base. However, most previous studies have not addressed the question how consistent is the assumed cosmological model with the observed data. This is not a trivial issue – the model needs to agree with the data so as to provide a solid foundation for the WF/CRs construction. Ideally, one should have started with establishing the agreement of the model with the data and only then reconstruct the LSS in the manner described above. However, history does not always proceeds in a linear fashion. The aim of the paper is to amend that situation and establish the likelihood of peculiar velocities data bases given the standard model of cosmology. The relevant methodology is straightforward and well established. One needs to calculate the likelihood function of the data given the model – namely the probability of the occurrence of the data within the framework of the assumed model (Jaffe & Kaiser 1995; Zaroubi et al. 1995; Hoffman 2001; Press et al. 2007). The likelihood function establishes the goodness-of-fit (GoF) of the data by the model. In the cosmological case and under the assumption of the linear regime, where the velocity field constitutes a random Gaussian vector field and the observational errors are normally distributed, the likelihood analysis amounts to calculating a χ2 statistics. This approach was indeed applied to velocity data bases (Jaffe & Kaiser 1995; Zaroubi et al. 1997, 2001). The application of the likelihood analysis to actual velocity data bases suffers however from one major drawback. The gravitational dynamics of structure formation induces non-linear contributions to the velocities of galaxies. These non-linear corrections render the parameter estimation and GoF analysis to be rather uncertain. The remedy to the problem involves the filtering of small scales to give linearized data. The likelihood analysis can then be safely applied to the linearized data. Here, we suggest such a small-scales filtering procedure and study the extent by which Cosmicflows-2 (CF2; Tully et al. 2013) is compatible with the Λ cold dark matter (ΛCDM) standard model of cosmology.


Classical imaging techniques were developed in the field to solve the RI reconstruction problem, such as clean and its multiscale variants (Högbom 1974; Bhatnagar & Corwnell 2004; Cornwell 2008; Stewart, Fenech & Muxlow 2011). In particular, clean builds a model image by iteratively removing point source components from the residuals of the acquired data (at each iteration). clean-based algorithms, however, are typically slow (generally requiring computationally demanding major cycles; cf. Clark clean), requiring fine-tuning and supervision, while providing suboptimal imaging quality (see e.g. Li, Cornwell & de Hoog 2011a; Carrillo, McEwen & Wiaux 2012). Another classical technique is the maximum entropy method (MEM) (Ables 1974; Gull & Daniell 1978), extended to RI imaging by Cornwell & Evans (1985). The MEM approach of Cornwell & Evans (1985) developed for RI imaging considers a regularization problem consisting of a relative entropic prior, a (Gaussian) likelihood term and an additional flux constraint. In principle, MEM requires less fine-tuning and supervision compared to clean and can therefore alleviate part of the shortcomings of clean-based algorithms. However, an optimal metric – expressed as an entropy functional – is not known in advance and therefore needs to be chosen individually (Starck et al. 2001; Maisinger, Hobson & Lasenby 2004). Indeed, it is widely known that MEM fails to reconstruct sharp and smooth image features simultaneously. Recently, the theory of compressed sensing (CS) has suggested the use of sparse representation and regularization approaches for the recovery of sparse signals from incomplete linear measurements (Donoho 2006; Candes & Wakin 2008; Candes et al. 2010), which has shown great success. CS techniques based on sparse regularization were ushered into RI imaging for image reconstruction (Suksmono 2009; Wiaux et al. 2009a,b; Wenger et al. 2010; Li et al. 2011a,b; McEwen & Wiaux 2011; Carrillo et al. 2012; Wolz et al. 2013; Carrillo, McEwen & Wiaux 2014; Dabbech et al. 2015; Garsden et al. 2015; Onose et al. 2016; Dabbech et al. 2017; Kartik et al. 2017; Onose, Dabbech & Wiaux 2017; Pratley et al. 2018) and have shown promising results and improvements compared to traditional approaches such as clean-based methods and MEM. In general, such approaches can recover sharp and smooth image features simultaneously (e.g. Carrillo et al. 2012). While sparse approaches have been shown to be highly effective, the best approach to image different sources remains an open question. Algorithms have been developed to scale sparse approaches to big-data (Carrillo et al. 2014; Onose et al. 2016; Cai, Pratley & McEwen 2017a; Kartik et al. 2017; Onose et al. 2017), such as that anticipated from the Square Kilometre Array (SKA1). However, clean-based methods, MEM, and CS-based methods, unfortunately, do not provide any uncertainty quantification about the accuracy of recovered images.


The right panel of Fig. 7 shows the relation between ΣSFR and R52. For each object, we computed ΣSFR = SFR/(2πR2), where R is a representative value of the galaxy radius. The latter is rather arbitrary and it depends on the chosen tracer, the depth, resolution, and wavelength of the observations. Here we adopted the ALMA sizes from circular Gaussian fitting for our sample, assuming R = FWHM/2. As mentioned in Sect. 3.2, this estimate combines all the available lines and continuum measurements, resulting in a size representative of the dust and gas content of each galaxy (Puglisi et al. 2019). We further recomputed the ΣSFR for the BzK galaxies in D15, using the Gaussian best-fit results of the rest-frame UV observations to be consistent with our estimates. For the SPT-SMGs, we used the sizes of Spilker et al. (2016), while we employed the 1.4 GHz radio measurements in Liu et al. (2015b) for the local spirals. For reference, we also show the mean values for the BzK galaxies, the local spirals, and ULIRGs as in D15. The best-fit model to the observed points returns a 60% flatter slope than in D15 (Table 3), but the trends are qualitatively similar. We restate that the choice of the tracer, the resolution, and depth of the observations play a major role in setting the exact values of the slope and intercept in our simple linear model, which should be thus taken with a grain of salt. This is particularly true for spatially resolved local objects, where we attempted to replicate the global, galaxy-scale measurements that can be obtained for distant objects. The observed data points in Fig. 7 qualitatively agree with the simulations by Narayanan & Krumholz (2014) and Bournaud et al. (2015), and they support the validity of ΣSFR as a good proxy for the gas conditions in galaxies. The total SFR is a worse predictor of the gas excitation conditions (Lu et al. 2014; Kamenetzky et al. 2016), since it does not correlate with the density and temperature probability distribution functions in clouds (Narayanan & Krumholz 2014). Interestingly, this seems to be partially confirmed by the linear regression analysis we applied here (Table 3): when modeling R52 as a function of LIR (∝SFR, Fig. 5) and ΣSFR, we do find similar slopes, but also a larger correlation coefficient ρ for ΣSFR than for LIR. However, LIR alone does correlate with the CO line luminosity ratio.


However, it is not straightforward to explain H2 formation in astronomical sources even when the catalytic roles of dust grains are introduced into models. Interstellar species are believed to be formed on cold grain surfaces via the so called Langmuir–Hinshelwood mechanism (Watson & Salpeter 1972; Pickles & Williams 1977; Hasegawa, Herbst & Leung 1992). To form H2, H atoms accrete on dust grains and then bind weakly with surfaces, which is known as physisorption. They can overcome the diffusion barrier and move on the grain surfaces via quantum tunnelling or thermal hopping. However, laboratory and theorectical studies showed that quantum tunnelling does not contribute much to the mobility of H atoms on silicate, carbonaceous or solid amorphous water (ASW) surfaces (Pirronello et al. 1997, 1999; Katz et al. 1999; Nyman 2021). If H atoms encounter other H atoms, then H2 molecules are formed. But H atoms can also desorb and leave grain surfaces. A hydrogen atom must reside on a grain long enough to find a partner H atom to form H2. As the dust temperature increases, the H atom desorption and diffusion rates also increase. So the temperature of grain surfaces must be sufficiently low so that an H atom can encounter another one before it desorbs. On the other hand, the temperature of grain surfaces must be high enough so that H atoms can diffuse on the grain surface. The parameter that measures how strongly species are to bound to grain surfaces is called desorption energy. It was found that if we assume a single H desorption energy in models, the dust temperature range over which efficient H2 formation occurs is narrow (6–10 K for olivine grains) (Katz et al. 1999). Moreover, it was found that the highest dust temperature at which H2 can be formed efficiently is less than 17 K (Katz et al. 1999). However, the grain surface temperature in the unshielded diffuse clouds, where hydrogen molecules are believed to be efficiently formed, is around 20 K (Li & Draine 2001).


It is much harder to localize and track the formation of current sheets in realistic black hole accretion flows in a larger domain and for a longer period because of the effects of the more complicated global dynamics governed by the central object, and due to the turbulence induced by the MRI. Both the evolution of accretion flows and the formation of current sheets therein strongly depend on the magnetic field geometry. We model an accretion disk around a rotating black hole, varying the initial conditions to study current sheet formation in different scenarios of magnetic field geometry. In the magnetically arrested disk (MAD; Igumenshchev et al. 2003; Narayan et al. 2003) scenario, the MRI and subsequent turbulence in the inner accretion disk are suppressed due to large-scale magnetic flux (see, e.g., White et al. 2019). In axisymmetric simulations as considered here, the arrested inflow is regularly broken by frequent bursts of accretion, allowing for a macroscopic equatorial current sheet to form and break in a periodic fashion. In a full 3D setup, magnetically buoyant structures are interchanged with less-magnetized dense fluid (Igumenshchev 2008; White et al. 2019), resulting in a magnetic Rayleigh–Taylor instability (Kruskal & Schwarzschild 1954) potentially sourcing interchange-type magnetic reconnection. In the Standard And Normal Evolution (SANE; Narayan et al. 2012; Sadowski et al. 2013) state, a fully turbulent accretion disk can develop due to a smaller magnetic flux (see, e.g., Porth et al. 2019), and current sheets can ubiquitously form and interact with the turbulent flow. Polarized synchrotron radiation observed by the Event Horizon Telescope (Event Horizon Telescope Collaboration et al. 2019a) can probe the field-line structure at event-horizon scales and put tighter constraints on the magnetization and address whether the accretion is in a SANE or a MAD state (Event Horizon Telescope Collaboration et al. 2019b).


In hydrodynamic and magnetohydrodynamic systems, different fluctuations interact with each other nonlinearly, generating turbulence (Matthaeus et al. 2015). One of the most important characteristics of turbulence is the existence of intermittency among various scales. Spatial intermittency manifests as coherent structures with large gradient at small scales. In ordinary fluids, coherent structures include a tangle of vortex filaments where vorticity is highly concentrated (Frisch 1995). In the turbulent plasma environments, examples of intermittent structures include current sheets, discontinuities, shock waves, and Alfvénic vortices (Veltri & Mangeney 1999; Sundkvist et al. 2007; Lion et al. 2016; Wang et al. 2019). The intermittency will influence the measured statistical properties of the fluctuating quantities. For example, the growth of flatness with decreasing scales indicates the existence of intermittency. Plenty of simulation works (Servidio et al. 2011; Karimabadi et al. 2013; Tenbarge & Howes 2013; Wan et al. 2015, 2016; Zhang et al. 2015) have indicated that dissipation, acceleration, and thermalization of turbulent plasmas mainly take place near intermittent structures on kinetic scale, while the actual physical mechanisms behind dissipation remain unclear. There are a variety of diagnostic approaches to measure intermittency. (1) Probability density functions (PDFs) of scale-dependent field increments develop heavy tails because of intermittency, and the tail is more enhanced with increasing intermittency (Marsch & Tu 1994). (2) The scale dependency of the normalized fourth-order moment, known as flatness,

, where δv = v(t + τ)−v(t), is an alternative representation. This quantity increases as the intermittency becomes more significant along with decreasing scales. (3) The p-th order structure function,

, will be larger than that for Gaussian PDF without intermittency and the scaling exponent, ζ(p), has a nonlinear form when intermittency presents. Based on such diagnostic approaches, the properties of intermittency in plasmas have been widely investigated in the solar atmosphere, magnetosheath, solar wind, termination shock, etc. (Burlaga 1991a, 1991b; Marsch & Liu 1993; Horbury et al. 1995; Macek et al. 2011, 2017; Chasapis et al. 2018). These observational analyses have revealed that intermittency is widely existing in the heliosphere and immensely influencing plasma dynamics.


A small number (currently six) of confirmed TDEs, including ASASSN-14li, have also been detected at radio wavelengths and the population may form a bi-modal distribution, consisting of more common non-relativistic ‘thermal’ events and rarer relativistic jets. Three events (Swift J1644+57

have isotropic ∼5 GHz luminosities of between 1040 and 1042 erg s−1

The higher power events are believed to result from observing down the axis of a relativistic jet, resulting in the energy of photons being significantly boosted.


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

10

10

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

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

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

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

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


On the other hand, a clear physical interpretation of the observed pulse broadening phenomenon requires a good understanding of the interstellar electron density structure. A power-law model of electron density fluctuations is commonly adopted in theoretical constructions on radio wave propagation (Lee & Jokipii 1976; Rickett 1977, 1990) and is compatible with observational indications (e.g., Armstrong et al. 1995). Recent advances in understanding the properties of magnetohydrodynamic (MHD) turbulence (Goldreich & Sridhar 1995; Lithwick & Goldreich 2001; Cho & Lazarian 2002, 2003) stimulate a renewed investigation on density statistics (Beresnyak et al. 2005; Kowal et al. 2007; Lazarian et al. 2008; Burkhart et al. 2009, 2010, 2015; Collins et al. 2012; Federrath & Klessen 2012), which provide important insight into key physical processes such as star formation in the turbulent and magnetized ISM (see reviews by, e.g., McKee & Ostriker 2007; Lazarian et al. 2015). The density spectrum in compressible astrophysical fluids was systematically studied in Kowal et al. (2007) by carrying out an extensive set of MHD numerical simulations with varying compressibility and magnetization. Instead of a single Kolmogorov slope with a power-law index of

, significant variations in the spectral slope of density fluctuations are present. For supersonic turbulence, their results are consistent with earlier findings in both magnetized (Beresnyak et al. 2005) and nonmagnetized (Kim & Ryu 2005) fluids. It shows that the density power spectrum becomes shallower as the sonic Mach number (

) increases, where VL is the turbulent velocity at the outer scale of turbulence and cs is the sound speed in the medium, and there is a significant excess of density structures at small scales in highly supersonic turbulence. This behavior is naturally expected as the gas is compressed in shocks by supersonic flows and the interacting shocks produce local density enhancements (Mac Low & Klessen 2004; Padoan et al. 2004b).


The only way to access the transitions which trace warmer molecular gas is to get above the atmosphere as did the Herschel Space Observatory The Herschel SPIRE Fourier Transform Spectrometer (FTS) was simultaneously sensitive to the J = 4−3 (EJ = 4 = 55 K) up to the J = 13−12 (EJ = 13 = 503 K) line of CO for local galaxies. With this access to higher energy CO transitions, Herschel gave us the tools to more finely discern the lower and higher excitation components of the multiphase molecular ISM. To more finely measure the excitation of the molecular ISM is to better understand energy exchange between the star formation and the ISM. Many studies of individual galaxies (Panuzzo et al. 2010; Rangwala et al. 2011; Hailey-Dunsheath et al. 2012; Kamenetzky et al. 2012; Spinoglio et al. 2012; Meijerink et al. 2013; Pellegrini et al. 2013; Rigopoulou et al. 2013; Israel et al. 2014; Papadopoulos et al. 2014; Rosenberg et al. 2014; Schirm et al. 2014; Glenn et al. 2015; Wu et al. 2015) and surveys (Papadopoulos et al. 2010, 2012a,b; Pereira-Santaella et al. 2013, 2014; Greve et al. 2014; Kamenetzky et al. 2014, 2016; Lu et al. 2014; Daddi et al. 2015; Israel, Rosenberg & van der Werf 2015; Liu et al. 2015; Mashian et al. 2015) have shown that the higher J lines of CO arise from warmer, denser gas than the cold gas responsible for the emission of for example CO J = 1−0. Though this warm gas is only a small fraction (∼10 per cent) of the total molecular mass, it is responsible for ∼90 per cent of the CO luminosity (Kamenetzky et al. 2014). This high CO luminosity cannot be explained by excitation from the ultraviolet (UV) light from young O and B stars in photon-dominated regions (PDRs); mechanical heating is often required. Theorists have attempted to use hydrodynamical galaxy simulations to produce galaxy-integrated spectral line energy distributions (SLEDs) of CO emission (Narayanan et al. 2008; Olsen et al. 2016), but we still lack a comprehensive picture of the mechanisms responsible for this emission. Furthermore, even higher J lines of CO than addressed here (above J = 13−12) have been detected, for example with Herschel PACS, indicating a third, even higher temperature component of molecular gas (NGC1068, Hailey-Dunsheath et al. 2012). The CO SLEDs from J = 14−13 through J = 30−29 show a large range in SLED shape, even among similar galaxies (Mashian et al. 2015).


The origin of the radio emission in radio-loud active galactic nuclei (RL AGN) is clear, luminous relativistic jets of magnetized plasma, which can extend far out, on the host galaxy scale and beyond. Conversely, radio-quiet (RQ) AGN are associated with radio emission which is typically 103 times weaker (as defined by Kellermann et al. 1989), in smaller structures (kpc-pc scale; e.g. Blundell et al. 1996; Nagar et al. 1999; Ulvestad et al. 2005a; Gallimore et al. 2006) with sub-relativistic velocities (e.g. Middelberg et al. 2004; Ulvestad, Antonucci & Barvainis 2005b) compared to RL AGN. The reduced sizes and low brightness of the radio emission of RQ AGN create a major challenge for detailed studies, in sharp contrast with the thoroughly studied RL AGN. The fewer radio studies of RQ AGN (e.g. Barvainis & Antonucci 1989; Kellermann et al. 1994; Barvainis, Lonsdale & Antonucci 1996; Kukula et al. 1998; Ulvestad et al. 2005a; Leipski et al. 2006; Doi et al. 2011; Padovani et al. 2011; Zakamska et al. 2016; Jarvis et al. 2019, 2021; Fawcett et al. 2020; Nyland et al. 2020; Smith et al. 2020b; Baldi et al. 2021a) generally lead to mixed results. This encourages to keep investigating it, as it indicates that the origin of the radio emission in RQ AGN is still an open question. If a number of different processes are indeed involved, then the radio band can be used to probe a range of physical processes, rather than being heavily dominated by a single process, as occurs in RL AGN (see Blandford, Meier & Readhead 2019 Panessa et al. 2019 for reviews). From large scale to small scale: (i) host galaxy star formation (SF) could account for the observed FIR-to-radio emission observed in active and non-active galaxies (Condon et al. 2013; Zakamska et al. 2016); (ii) an AGN-driven wind is expected to shock the interstellar gas, leading to particle acceleration and radio synchrotron emission, which may reach the observed flux level (Jiang et al. 2010); (iii) the intense radiation of the AGN photoionizes large volumes of ambient gas, as supported by the strength of the narrow and broad line emission observed in type-1 AGN, leading to thermal free–free emission in the radio band (Baskin & Laor 2021); (iv) a scaled-down jet, physically similar to the one in RL AGN, but much fainter, less energetic and slower (Barvainis et al. 1996; Gallimore et al. 2006; Talbot, Sijacki & Bourne 2021); (v) a tight radio/X-ray luminosity relation for AGN (∼10−5; Laor & Behar 2008) similar to coronally active stars (Güdel & Benz 1993; Güdel et al. 2002) suggests that coronal emission from magnetic activity above the accretion disc (Field & Rogers 1993; Gallimore, Baum & O’Dea 1997) may produce the observed radio emission.


The FOCAS and NIRSPEC spectra of PSO J006+39 were obtained at two different epochs separated by 1 yr and 9 months (by slightly less than 3 months in the quasar rest frame). Previously, we found that the PS1 y-band light curve of PSO J006+39 shows brightness variations with a peak-to-peak amplitude of ∼0.7 mag over ∼4 yr (Koptelova et al. 2017), which might be due to the flux variations of both continuum and Lyα line of PSO J006+39. To infer the brightness state of PSO J006+39 at the epochs of its FOCAS and NIRSPEC observations, we first calculated the spectral slope of the quasar continuum from the NIRSPEC spectrum with a wider wavelength coverage than that of the FOCAS spectrum. Using wavelength intervals of 11100–11300, 11400–11600, 13085–13400, and 14700–15200 Å we measured a spectral slope of αλ = −1.35 ± 0.26, where the quoted uncertainty is the statistical error of the fit. The fitted power law is shown in Figure 2 with a solid line. The estimated continuum slope is consistent but somewhat flatter than the typical slope of luminous quasars (Zheng & Malkan 1993; Vanden Berk et al. 2001; Selsing et al. 2016). We then fitted the FOCAS data using the power law with a fixed spectral slope of αλ = −1.35 and spectral windows of 9700–9850 and 10050–10100 Å. The spectral windows adopted for the analysis of the FOCAS and NIRSPEC spectra were taken to be similar to the rest-frame wavelength intervals commonly used to fit the continua of quasars (Vanden Berk et al. 2001; Decarli et al. 2010; Lusso et al. 2015) and less affected by the contribution from emission lines on the red side of the Big Blue Bump (BBB; e.g., Malkan 1983). The estimated continuum flux of PSO J006+39 at the epoch of its FOCAS observations is shown in Figure 2 with a dashed line. By comparing the continuum flux at the epochs of the FOCAS and NIRSPEC observations, we find that the brightness state of PSO J006+39 was different at these two epochs. PSO J006+39 was brighter by about 0.8 mag during the FOCAS observations than during the NIRSPEC observations. Thus, the continuum flux of PSO J006+39 might be different at different epochs depending on the brightness state of the quasar. Figure 2 also shows the fluxes of PSO J006+39 in the FOCAS Y, and NIRSPEC N2, N4, and N6 bands at the epochs of the FOCAS and NIRSPEC observations (see also Table 1).


The planetary physical properties that can be derived from measurements with the two most successful exoplanet detection techniques, that is, with the radial velocity method and the transit method, are the planet radius (if the planet transits its star), mass (a lower limit if the planet does not transit its star), and the orbital period and distance, eccentricity, and inclination (if the planet transits its star) (see Perryman 2018, and references therein). The upper atmospheres (above optically thick clouds) of giant exoplanets and those of smaller planets around M stars can be probed using spectroscopy during primary and/or secondary transits (Bean et al. 2010; Swain et al. 2009, 2008; Tinetti et al. 2007; Nakajima 1983). It appears to be virtually impossible to characterize the (lower) atmospheresand surfaces of small, Earth-like planets in the habitable zones of solar-type stars (Bétrémieux & Kaltenegger 2014; Misra et al. 2014; Kaltenegger & Traub 2009), in particular because the light of the parent star is refracted while traveling through the lower atmosphere of its planet and emerges forever out of reach of terrestrial telescopes (García Muñoz et al. 2012). The (lower) atmosphere and surface of a planet are crucial for determining the habitability of a planet, as they hold information about cloud composition, trace gases in disequilibrium and probably most importantly, liquid surface water (see, e.g., Schwieterman et al. 2018; Kiang et al. 2007a,b, and references therein). For such a characterization of terrestrial-type planets, direct observations of the thermal radiation that they emit or of the light of their parent star that they reflect are required. The numerical results that we present in this paper concern the reflected starlight. Because of the huge distances involved, any measured reflected starlight pertains to the (illuminated and visible part of the) planetary disk. It therefore is a disk-integrated signal.


Much of the recent work on this topic has focused on gathering observational evidence for hierarchical growth through the identification of stellar streams and tidal interactions, which are thought to be the hallmark of low-mass galaxies having been accreted by more massive galaxies. The Sagittarius dwarf galaxy (Ibata et al. 1994) and the stellar streams associated with it (Belokurov et al. 2006) are some of the most well-studied examples of this type of hierarchical accretion in the Milky Way. Recent data from the Gaia mission (Gaia Collaboration et al. 2016) and other large-scale surveys, as well as analyses that combine kinematic data with information about chemical abundances and/or specific stellar populations, have led to discoveries of additional substructures in the Galaxy and brought renewed attention to this topic (e.g., Belokurov et al. 2018; Deason et al. 2018; Helmi et al. 2018; Myeong et al. 2018). The Andromeda galaxy (M31) has been studied in detail as well. Structures formed from spatial overdensities of the red giant branch (RGB) population, e.g., the Giant Stellar Stream, have been found in the outer halo of M31 by using resolved RGB star maps (Ibata et al. 2001; Ferguson et al. 2002). Using the surface density of resolved RGB stars, it is possible to infer the surface brightness distribution of the underlying light; structures revealed by this technique, such as faint streams and clumps of RGB stars, suggest a rich history of accretion events and tidal interactions for M31. Deep observations of galaxies outside the Local Group have also revealed streams, shells, and satellites using resolved RGB stars and unresolved low surface brightness (LSB) features (e.g., Janowiecki et al. 2010; Crnojevic et al. 2016; Mihos et al. 2017). However, in galaxies well beyond the Local Group, RGB stars are unresolved and a different tracer of hierarchical assembly processes and tidal interactions is required. Globular clusters (GCs) have a number of properties that make them well suited for this task.