Observations of cold molecular gas are more promising since any activity from the AGN (radiation, outflows, or jets) will have an impact on the molecular gas reservoir first, and then on the SFR, which previous studies have focused on. The molecular gas provides an instantaneous measure of the raw fuel from which stars form and can be used as a more direct tracer of potential feedback effects. Over the last decade, large observational efforts have been devoted to map the molecular gas reservoir of galaxies (e.g., Daddi et al. 2010a; García-Burillo et al. 2012; Bauermeister et al. 2013; Bothwell et al. 2013; Tacconi et al. 2013, 2018; Genzel et al. 2015; Silverman et al. 2015; Decarli et al. 2016; Cicone et al. 2017; Saintonge et al. 2017; Fluetsch et al. 2019; Freundlich et al. 2019). These studies are largely based on observations of carbon monoxide (CO) rotational emission lines, used as a tracer of cold molecular hydrogen H2 (the ground-state rotational transition in particular traces the total molecular gas best), but there are also many studies based on dust emission (e.g., Tacconi et al. 2018 and references therein). The main targets of such CO campaigns have primarily been inactive1 galaxies that mostly lie on the main sequence of star-forming galaxies (e.g., Noeske et al. 2007; Schreiber et al. 2015), where the majority of the cosmic star-formation activity occurs. The fundamental relation between SFR and the molecular gas content of galaxies, the Schmidt-Kennicutt relation, provides precious information about how efficiently galaxies turn their gas into stars (Schmidt 1959; Kennicutt 1989). This star-formation law is usually presented in terms of surface densities, therefore requiring spatially resolved measurements of galaxies. However, in high-redshift studies, an integrated form of this relation with global measurements of the SFR and molecular mass is normally used (e.g., Carilli & Walter 2013; Sargent et al. 2014).


In regarding AGNs, the Te method tends to underestimate the oxygen abundance by an average value of about 0.6 dex in comparison to estimations based on strong-line methods and it produces subsolar O/H values for most of these objects (Dors et al. 2015; Dors, Freitas-Lemes & Âmores 2020). An alternative method to derive the metallicity or abundances in the nuclear regions of spiral galaxies is the extrapolation of the radial oxygen abundance. Along decades, results based on this indirect method have indicated Z near or slightly above the solar value in nuclear regions (Vila-Costas & Edmunds 1992; Zaritsky, Kennicutt & Huchra 1994; van Zee et al. 1998; Pilyugin, Vílchez & Contini 2004; Gusev et al. 2012; Dors et al. 2015; Zinchenko et al. 2019), in consonance with predictions of chemical evolution models (e.g. Mólla & Díaz 2005) and with the use of strong-line methods (e.g. Groves, Dopita & Sutherland 2004; Groves, Heckman & Kauffmann 2006; Feltre, Charlot & Gutkin 2016; Pérez-Montero et al. 2019; Thomas, Kewley & Dopita 2019; Dors et al. 2020). Therefore, Temethod does not seem to work for AGNs. The origin of the discrepancy between Z values calculated via Te method and via strong-line methods, the so-called Teproblem, could be attributed, in part, to the presence of heating/ionization by gas shock in the narrow-line region (NLR) of AGNs. In fact, Contini (2017) carried out detailed modelling of AGN optical emission lines by using the SUMA code (Contini & Aldrovandi 1983) and suggested the presence of gas shock with low velocity ($v \: \lesssim \: 400 \: \rm km \:s^{-1}$) in a sample of Seyfert 2 nuclei. This result is supported by recent spatially resolved observational studies of Seyfert 2 nuclei, in which the presence of gas outflows with velocity of the order of 100–300 $\rm km \: s^{-1}$ have been found (e.g. Riffel, Storchi-Bergmann & Riffel 2017; Riffel, Hekatelyne & Freitas 2018). Moreover, the Te problem can also be originated due to the use of an unappropriate calculation of the ionization correction factor (ICF) for oxygen in AGNs (Pérez-Montero et al. 2019; Dors et al. 2020).


The electronic computations were performed using the molpro (Molpro 2015, http://www.molpro.net) package. In a preliminary work, we used the complete active space self-consistent field (Knowles & Werner 1985; Werner & Knowles 1985) to examine the electronic wavefunction of the HNCO–He complex. These computations showed that this wavefunction is dominantly described by a unique electron configuration (with a weight ≥0.93) over the grid used for the generation of this PES. This justifies hence the use of monoconfigurational ab initio methods. Accordingly, we applied the recently established methodology by Hochlaf and co-workers for mapping multidimensional PESs of weakly bound molecular systems with high accuracy and relatively low computational cost (Lique, Klos & Hochlaf 2010; Halvick et al. 2011; Ajili et al. 2013; Mathivon, Linguerri & Hochlaf 2013; Kalugina et al. 2014; Mogren Al Mogren et al. 2014). Briefly, these electronic computations were carried out using the explicitly correlated coupled cluster method with single, double and perturbative treatment of triple excitations (CCSD(T)-F12) (Adler, Knizia & Werner 2007; Knizia, Adler & Werner 2009) in connection with the augmented correlation-consistent aug-cc-pVTZ basis set of Dunning and co-workers (Dunning 1989; Kendall, Dunning & Harrison 1992). In addition, molpro default choices for the density fitting and resolution of identity basis sets have been applied (Yousaf & Peterson 2008). Benchmarks by Hochlaf and co-workers (Lique et al. 2010; Halvick et al. 2011; Ajili et al. 2013; Mathivon et al. 2013; Kalugina et al. 2014; Mogren Al Mogren et al. 2014) showed that results obtained from this highly correlated approach are close to those deduced using standard coupled cluster techniques extrapolated to the complete basis set (CBS) limit, whereas a strong reduction in CPU time and disc occupancy are observed. For illustration, we performed CCSD(T)/aug-cc-pVXZ calculations (X = D, T, Q, 5) on the HNCO—He cluster. Then the energies were extrapolated to the CBS limit. The comparison between CCSD(T)-F12/aug-cc-pVTZ and CBS calculations is given in Table 1. It shows that the CCSD(T)-F12/aug-cc-pVTZ results are off by 4 per cent (at the maximum) with those deduced from CBS extrapolation. We compare also our results with those done using the CCSD(T)/aug-cc-pV5Z approach. We can clearly see that the CCSD(T)-F12/aug-cc-pVTZ approach offers a good agreement with the CCSD(T)/aug-cc-pV5Z calculations with a very reduced computational cost.


The comparisons show that except for GRBs 060707 and 060605, which have a very high vpeak, the LAE-LGRBs fall in the same parameter space as LyC leakers and follow the correlations between the indirect indicators found by Verhamme et al. (2017). Following their study, we can cut these plots into two regions corresponding to strong LyC leakers (fesc(LyC) > 5%, red rectangle) and weak LyC leakers (fesc(LyC)  5%, blue rectangle). All LAE-LGRBs fall in the category of the weak LyC leakers except for GRB 021004, which appears systematically to agree well with the region of the strong leakers. In panel b of Fig. 12, we also superimpose the distribution of [OIII]/[OII] ratio for the GRB sample of Krühler et al. (2015) and GRB 081121 reported here. For the majority of the GRBs, this ratio is about two, with seven cases at O32 > 4. GRB 021004 has a high value of O32 > 10 and is the strongest LAE of our golden sample (with fesc(Lyα) of 60%) in agreement with potential high fesc(LyC). Nevertheless, the Lyα profile of GRB 021004 is a single peak with no residual flux at the Lyα line center. This is not the typical line shape observed for confirmed LyC emitters, which have the tendency to show double- or triple-peak profiles (Verhamme et al. 2017; Rivera-Thorsen et al. 2017; Vanzella et al. 2020). Our shell-model fitting also suggests that the column densities are too high to allow LyC photons to escape. However, this model already predicted a similar HI column density (log(NHI/cm−2) ≈ 19−20) for four green pea galaxies out of the five with detected LyC emission reported in Yang et al. (2017). This suggests that LyC emission can escape through holes in the ISM even if the Lyα photons probe denser neutral gas. The only LAE-LGRB for which LyC leakage has been detected along the LGRB line of sight (

f
esc

(
LyC
)

=
0
.

35

−
0.11

+
0.10

$ f_{\mathrm{esc}}(\rm LyC) = 0.35^{+0.10}_{-0.11} $

) is GRB 191004B (Vielfaure et al. 2020). However, Fig. 12 (panel c) shows that it does not fall in the high escape fraction region, but in the lower left area. The reasons could be that (i) fesc(LyC) is lower at the scale of the galaxy than along the LGRB line of sight, and (ii) the indicators of strong LyC leakage evolves with redshift. As a comparison, the LyC emitters from Fletcher et al. (2019) are found out of the high escape region (red rectangle). They show lower rest-frame EW(Lyα) and higher vpeak than the local LyC emitters, whereas their escape fraction of ionizing photons is significantly higher (fesc(LyC) = 15 − 60%). This could also suggest that strong LyC leakers span a wider parameter space than predicted by the study of local LyC emitters. Overall, it is clear that this type of studies is still limited by the poor statistics, and the current results show the difficulty of characterizing LyC leakage based on these properties alone.


Galaxies are surrounded by vast gaseous haloes which extend well beyond the hosts’ stellar components: Early observations of quasar sight lines attributed the presence of absorption at multiple intermittent redshifts to gaseous haloes of intervening galaxies (e.g. Bergeron 1986; Bergeron & Boissé 1991; Lanzetta et al. 1995; Tripp, Savage & Jenkins 2000; Chen, Lanzetta & Webb 2001). In the past decade, owing to the rise of large spectroscopic surveys of galaxies with well-determined physical properties (e.g. SDSS), all sky UV surveys (e.g. GALEX), and improved sensitivity of UV spectrographs (e.g. COS), studies of the gaseous haloes of galaxies could systematically connect gas absorption properties to galaxy properties in statistically meaningful samples (e.g. Cooksey et al. 2010; Prochaska et al. 2011; Tumlinson et al. 2013; Liang & Chen 2014; Lehner, Howk & Wakker 2015). The aforementioned gaseous haloes are commonly referred to as the circum-galactic medium (CGM) and are ubiquitous in galaxies regardless of mass or star formation activity: even sub-L* galaxies (Bordoloi et al. 2014), and passive galaxies host a CGM (Thom et al. 2012). The current model of the CGM suggests the presence of a clumpy multiphase medium which extends beyond the virial radius of the host galaxy, with a declining radial density profile, containing a substantial amount of gas and metals (e.g. Werk et al. 2013, 2014; Liang & Chen 2014; Lehner et al. 2014, 2015; Prochaska et al. 2017). Observational studies targeting the CGM of L* galaxies showed that the CGM gas content is comparable to the mass of the interstellar medium (ISM; e.g. Chen et al. 2010; Tumlinson et al. 2011; Werk et al. 2014; Prochaska et al. 2017) and correlates positively with ISM properties (Borthakur et al. 2015). Additionally, CGM observations infer a significant amount of metals (e.g. Werk et al. 2013; Peeples et al. 2014) where CGM metallicities can extend to supersolar metallicities (Prochaska et al. 2017). The clumpy multiphase CGM consists of a warm gas T ∼ 104 − 5 K (clumpy in nature) embedded within a hot diffuse T ∼ 106 K medium (e.g. Heitsch & Putman 2009; Armillotta et al. 2017; Bordoloi et al. 2017). The multiphase structure of the CGM is corroborated by the variety of observed ionic species which survive at a vast range of temperatures: While the warm gas hosts the low ionization species (e.g. H i, Si ii, Si iii, C ii, C iv), the hot medium is home for the most highly ionized species (e.g. O vi, O vii). Additionally, the spectral line profiles of absorbers in the CGM can be reproduced by invoking a patchy medium (e.g. Stern et al. 2016; Werk et al. 2016), i.e. multiple high density gas clouds contribute to the optical depth along the line of sight thus leaving their kinematic imprint on the absorption line profile. For a review of the CGM, see Putman, Peek & Joung (2012) and Tumlinson, Peeples & Werk (2017).


The many unexpected surprises of comet 67P/Churyumov-Gerasimenko (hereafter 67P) revealed by the historic Rosetta mission highlight the importance of observing the evolution of comets throughout their orbits. One of the surprises was the drastic heterogeneity in both the major and minor volatile species in the coma that was observed early on in the mission (Hässig et al. 2015; Luspay-Kuti et al. 2015, hereafter ALK15). When Rosetta first arrived at comet 67P in August 2014, the Rosetta Orbiter Mass Spectrometer for Ion and Neutral Analysis/Double Focusing Mass Spectrometer (ROSINA/DFMS; Balsiger et al. 2007) detected large diurnal variations in the intensity profiles of various species in the coma from distances to the comet as far as 250 km. At this time, 67P was still at a distance of about 3 AU and inbound from the Sun. The intensity variations in the major and minor volatile species were found to be periodic, and were dependent on both the observing sub-spacecraft latitude and longitude (Hässig et al. 2015; Luspay-Kuti et al. (2015)). As reported in Hässig et al. (2015), the intensity of H2O in the coma dominated the overall signal, with maxima in the H2O signal every ~6 h, about twice during a rotation. Interestingly, however, CO2 and CO displayed a separate additional maximum when the H2O signal was near its minimum. This independent maximum in CO2 and CO only occurred at negative observing latitudes that are associated with a particular “view” of Rosetta at 67P, with the larger lobe blocking out the neck and head. At this time, 67P had not yet reached its first equinox (10 May 2015), and the poorly illuminated southern hemisphere was experiencing winter. In addition, the largest H2O activity was localized at the well-illuminated neck region, as also seen by the Microwave Instrument on the Rostta Orbiter (MIRO; Gulkis et al. 2015; Biver et al. 2015; Lee et al. 2015) and by the Visible InfraRed Thermal Imaging Spectrometer (VIRTIS; Bockelée-Morvan et al. 2015; Migliorini et al. 2016). VIRTIS also measured weak H2O production in regions with low solar illumination, while CO2 was outgassing from both illuminated and non-illuminated regions pre-inbound equinox (Bockelée-Morvan et al. 2015; Migliorini et al. 2016; Fink et al. 2016). The observed outgassing pattern of the major cometary species suggested that CO and CO2 may be sublimating from a depth below the diurnal skin depth.


We assume the time-scales we observe here are generated in the corona itself (and note that longer time-scale changes will be driven by the disc outside of the corona) and are made visible by a changing electron temperature and density as a result of local turbulence and coupling to mass accretion rate propagations through the flow from rout to rin. We note that we can discount variations in the seed photon population as the driver for changes in the power spectrum, as the UV emission from the disc is established to be considerably less variable than the corona in NLS1s (Leighly 1999; Smith & Vaughan 2007; Ai et al. 2013; Alston, Vaughan & Uttley 2013; Done & Jin 2016). We assume that the variability generated locally at each radius (rν) is at the viscous frequency (see Churazov et al. 2001) such that
(9)$$\begin{eqnarray}
r_{\nu } = \left[ \frac{2\pi \nu }{\alpha }\left(\frac{H}{R}\right)^{-2}\right]^{-2/3} ,
\end{eqnarray}$$where the frequency is in units of c/Rg (see e.g. Kato, Fukue & Mineshige 1998; Arévalo & Uttley 2006). In the above, α and $\frac{H}{R}$ are the dimensionless viscosity parameter of Shakura & Sunyaev (1973) and scale height of the accretion disc, respectively. We assume that our frequency range of interest, 0.01−1 mHz (i.e. the range over which we can practically fit to the data) corresponds to radii between the ISCO (rin) and some radius within the true outer edge of the corona (i.e. rout ≤ rcorona). The actual frequencies generated in our model therefore depend on the SMBH spin and the combination $\left(\frac{H}{R}\right)^2 \alpha$ (and somewhat on the SMBH mass – although here the range is small). Given the reported high spin values for these bright AGNs (Ogle et al. 2004; Fabian et al. 2013; Done & Jin 2016; Kara et al. 2017; Buisson et al. 2018b), we expect the ISCO to sit at ∼1.25Rg. For the corona at the ISCO to produce variability above our upper frequency limit of 1 mHz requires $\left(\frac{H}{R}\right)^2 \alpha \gtrsim 0.01$. We note that for the mass range subtended by our AGN sample (from 106.00 to 106.63 M⊙, see Table 2), should we instead assume zero spin (rin = 6Rg), the viscous frequency at rin is lower and we have strong curvature in our observed bandpass.


The kinetic energy stored in the CO shell can be estimated as $E_{\rm kin} = 0.5\, M_{\rm shell}\, V^2_{\rm exp}$, where Vexp is the expansion velocity of the shell and Mshell is the total (molecular, atomic, and ionized) shell mass. Adopting an expansion velocity equal to half the velocity interval where the structure is observed, Vexp = 7.0 ± 1.3 km s− 1 , the molecular mass given in Table 1 and the atomic and ionized masses estimated by Cichowolski et al. (2001), 1450 and 3000 M⊙, respectively, we obtain Ekin = (2.5 ± 1.0) × 1049 erg, assuming a 40 per cent error for the masses.. Although Cichowolski et al. (2001) concluded that WR 130 could have alone created the observed structure, it is important to note that they did not take into account the molecular mass present in the shell, which considerably increases the kinetic shell energy. Thus, we can compare now the new value obtained for Ekin with the mechanical energy deposited in the ISM by the wind of the WR star, Ew = (0.7–2.2) × 1050 erg (Cichowolski et al. 2001). We obtain ϵ = Ekin/Ew = 0.007–0.5. The ratio ϵ measures the energy conversion efficiency in the shell, and according to evolutionary models ϵ ≤ 0.2 (Koo & McKee 1992). Thus, not all the possible values of ϵ are compatible with the scenario where the energy injected during the WR phase is enough to create the structure. In this case, the contribution of the energy injected during the O-star phase and/or other massive stars, should be considered. As mentioned in the Introduction, WR 130 is a WNH star, and according to Smith & Conti (2008) its age would be of about 2–3 Myr and its initial mass of at least 60 M⊙. A rough estimation of the energy injected by such a star during its main sequence yields Ew = (2.5–3.5) × 1050 erg (de Jager, Nieuwenhuijzen & van der Hucht 1988), which would be enough to create the observed structure. We have nevertheless looked for the presence of other massive stars in the region. We queried the available catalogues such as the Galactic O-Star Catalog (Maíz Apellániz et al. 2013), the Early-Type Emission-Line Stars Catalogue (Wackerling 1970), the Catalogue of Be stars (Jaschek & Egret 1982), the H-alpha Stars in the Northern Milky Way Catalogue (Kohoutek & Wehmeyer 1997), and the Catalog of Galactic OB Stars (Reed 2003), for early-type and emission stars. No stars were found in any catalogue. The only massive star located nearby is, as mentioned by Cichowolski et al. (2001), an OB star, which has an uncertain spectral type and no distance estimate (Stock, Nassau & Stephenson 1960). It is located in projection not in the centre of the structure but on to the shell (there is a second OB star mentioned by Cichowolski et al. 2001 but its location is actually outside the structure, see fig. 1 of Cichowolski et al. 2001). Although we cannot completely rule out the possibility that the OB star may be playing a role in creating the shell structure, we think that the action of WR 130 is sufficient and most likely dominant in the region.


As MKT J170456.2–482100 is coincident with a star in a spectroscopic binary, it is possible that the companion star may be a pulsar or pulsating white dwarf, similar to AR Scorpii (Marsh et al. 2016). To investigate this possibility, we performed high-time resolution observations to search for pulsations over a range of periods spanning milliseconds to minutes. We observed the position of MKT J170456.2–482100 on utc 2019 January 30 with the ultra-wide-bandwidth (UWL) receiver deployed on the 64-m Parkes radio telescope in Australia. The output of the receiver is processed by the Medusa Graphics Processing Unit (GPU) cluster which produces 8-bit, full-Stokes filter banks with spectral and temporal resolutions of 1 MHz and 128 μs respectively over the $3328\, \mathrm{MHz}$ band from 0.740 to $4.03\, \mathrm{GHz}$. The data were recorded in psrfits format and processed using PSRCHIVE tools (Hotan, van Straten & Manchester 2004). Since our data were strongly affected by radio frequency interference (RFI) we used the clfd8 package described in (Morello et al. 2019) to perform more sophisticated RFI mitigation. Since radio waves are dispersed by free electrons in the interstellar medium along the line of sight, the data need to be corrected for this dispersion delay before any analyses can be made. This dispersion delay can be quantified by the dispersion measure (DM), which is the integrated free electron column density along the line of sight. We dedispersed the data over a range of trial DMs, $0.0 \le \mathrm{DM} \le 30.0$ pc cm$^{-3}$ in steps of 1 pc cm$^{-3}$ to account for the uncertainty in the distance to TYC 8332-2529-1. The DM range was estimated using various distances to the source (Bailer-Jones et al. 2018), and the NE2001 model (Cordes & Lazio 2002). For each trial DM, the resulting dedispersed time series was searched for long and short-period pulsations using both a Fast Folding Algorithm (FFA) and a Fast Fourier Transform (FFT), respectively.


The median value of the column density of OH in the first quadrant is 3.9 × 1014 cm-3 and for OH+ it is 0.68 × 1014 cm-3. In the fourth quadrant, the median column densities amount to 1.7 × 1014 cm-3 and 0.55 × 1014 cm-3, respectively. Column densities in excess of 1015 cm-2 (for OH) and above ~1014 cm-2 (for OH+) are rather the exception. The median N(OH) /N(OH+) ratio over all sightlines and velocity components is 3.3. While the formation of OH+ results from cosmic-ray induced reactions involving atomic and molecular hydrogen and atomic oxygen, the bottleneck expected for the formation of OH via ion-neutral chemistry is the availability of H2. The reaction of OH+ with H2 yields H3O+, via the two hydrogen abstraction reactions OH+(H2,H)H2O+(H2,H)H3O+ (see Appendix C). Then the dissociative recombination of H3O+ yields OH and H2O, with a branching ratio of ~74% to 83% in favor of OH (determined by ion storage ring experiments, Jensen et al. 2000; Neau et al. 2000), while less than ~1% forms O i . In the following, we attempt to confirm these predictions, that is, the bottleneck reaction OH+(H2,H)H2O+, and the N(OH) /N(H2O) ratio. As for the former, a strong anticorrespondence between the column densities of OH and OH+might naively be expected, where the availability of H2 tips the scales in favor of OH, while OH+ traces predominantly atomic gas (Hollenbach et al. 2012, further references therein). But even if a clear anticorrelation between OH and OH+ existed, it would be impossible to observe it. On a given sightline several clouds with high and low molecular hydrogen fractions \hbox{$f^{\rm N}_\HH = N(\HH)/(2N(\HH)+N($}fH2N=N(H2)/(2N(H2)+N(H i )) line up. Even across a single diffuse cloud, the N(OH) /N(OH+) ratio is expected to vary substantially, depending on the degree of self-shielding of H2 against the interstellar UV radiation field. To quantify the anticorrelation, we normalized the velocity-specific OH column density with the total OH and OH+ reservoir and obtained an abundance ratio r = Nv(OH)/(Nv(OH) + Nv(OH+) varying from zero (only OH+, no OH) to one, where all the OH+ abundance is exhausted owing to the formation of OH and (see below) water. (The normalization chosen here avoids the divergence of the distribution if OH has no spectral counterpart in OH+.) The resulting distribution (Fig. 12) indeed shows that these extremes are present in the data, although the second case is by an order of magnitude more frequent. We suggest two explanations for this. One reason is that if \hbox{$f^{\rm N}_\HH$}fH2N is too small, OH+ can be efficiently destroyed by the dissociative recombination with free electrons (Appendix C), while the formation of OH+ by the reaction chain H+(O,H)O+(H2,H)OH+ and the secondary, less important path H2+(H2,H)H3+(O,H2)OH+ become less efficient (see Appendix D) because less H2 is available. Another reason is that the fraction \hbox{$f^{\rm N}_\HH$}fH2N is larger in denser gas (cf. Table 3) where column densities are higher and absorption features easier to observe.


In principle, when ΔνZ>δν, with δν being the observed full width at half maximun (FWHM) of the line, the complete set of information concerning the magnetic field B can be derived. However, for most of the Zeeman detections, the Zeeman splitting ΔνZ turns out to be significantly smaller than δν. Indeed, even if we neglect the non-thermal line broadening due to typical processes occurring in star forming regions such as jets (with velocities up to hundreds of km s-1), outflows, and accreting/rotating disks (typically ≤10 km s-1), already the thermal broadening (even at kinetical temperatures lower than 10 K) is definitely larger than the Zeeman splitting (e.g., Frank et al. 2014). For instance, a typical linewidth of the coldest starless cores is ~0.1 km s-1  (e.g., di Francesco et al. 2007), indeed too broad to allow an observer to unveil the Zeeman effect. The expected B values in star forming regions range from ~100 μG, for low-mass objects (Li et al. 2014), to ~1 mG, as measured in regions hosting high-mass young stars (e.g., Pillai et al. 2016; Momjian & Sarma 2017). If we consider the N,J = 1, 1 ← 0, 1 transition (286.3 GHz), for which the largest Zeeman shift was obtained (Z = 0.87 Hz/μG), and we assume that B varies in the 0.1–1 mG range, we derive ΔνZ≃ values in the 87–870 Hz range, that is, 0.3–3 m s-1. Moving to higher frequencies and considering the SO N,J = 2, 2 ← 1, 2 transition at 309.5 GHz, we derive ΔνZ ≃ 61−610 Hz, that is, 0.06−0.59 m s-1. In conclusion, in such cases, only information about the LoS component of B, B∥, is obtained. In fact, the Stokes parameter Q and U spectra are usually too weak to be detected. The analysis is therefore limited to the Stokes V spectrum, which has the shape of the first derivative of the Stokes I spectrum and is proportional to (ΔνZ/δν)2 × B∥. According to Crutcher et al. (1993), Crutcher (2012), and Uchida et al. (2001), the standard procedure is to fit dI/dν to the observed V spectrum, with B∥ being the free parameter to be determined from the strength of the V spectrum. Furthermore, the direction (toward or away from the observer) of B∥ is obtained. Therefore, accurate laboratory (either experimental or theoretical) determination of the g factors might provide the opportunity to complete the missing information.


Neutral MF occurs as syn and anti conformers (also denoted Z and E rotamers) with Cs symmetry, with the syn rotamer being more stable (by ∼20 kJ mol−1) and well separated from the anti rotamer by a significant energy barrier of ∼35 kJ mol−1 for anti

 syn isomerization (Wilmshurst 1957; Curl 1959; Blom & Günthard 1981; Müller et al. 1983; Bagno & Scorrano 1996; Neill et al. 2011, 2012; Zeegers-Huyskens & Kryachko 2011; Ferro-Costas & Mosquera 2013). The zero-kinetic-energy photoelectron spectrum of MF provides an accurate estimate for its adiabatic ionization energy and vibrational frequencies of the radical cation ground state (Waterstradt et al. 1994). The electronic excitation spectrum of MF is very similar to that of acetic acid featuring three valence transitions (Nunes et al. 2010). In contrast to MF and its radical cation (MF+), only very limited information is available for H+MF. Theoretical studies indicate the preference for protonation at the carbonyl oxygen (CO) over the methyl ester (OMe) by around 80 kJ mol−1, and the CO-protonated tautomer has four rotamers within 20 kJ mol−1 (Zeegers-Huyskens & Kryachko 2011; Ferro-Costas & Mosquera 2013). Numerous mass spectrometric studies have investigated the production of H+MF via various ion–molecule reactions and its fragmentation by metastable decay and collisions (Harrison & Tsang 1976; Benoit & Harrison 1977; Hopkinson et al. 1979; van Baar et al. 1986; Horn et al. 2004; Lawson et al. 2012), and the measured proton affinity (PA) is reported as PA = 782.5 kJ mol−1 (Hunter & Lias 1998). However, the site of protonation and the rotational conformation of H+MF could not be established from these mass spectrometric measurements. The dominant fragment channel of H+MF is decarbonylation (loss of CO), whereby the C and O atoms come from the CO group. Significantly, there are no spectroscopic data available for H+MF and its clusters. To this end, our combined spectroscopic and DFT approach provides the first reliable experimental evidence for the preferred protonation site in the isolated molecule and the isomer assignment along with the intermolecular interaction of this prototypical protonated aliphatic ester with nonpolar ligands. There are a few experimental data for H+MF in the condensed phase. However, it is well known that solvation and counter ions can have a drastic effect on both the position and energetics of protonation in the various possible tautomers and rotamers. Previous 1H-NMR spectra of H+MF revealed three OH+ resonances in a super acid solution, demonstrating protonation at the CO group with three rotamers (although their configurations could not be established) (Fraenkel 1961; Olah et al. 1967). IR, Raman, and 1H/13C-NMR spectra of single crystal salts of H+MF with

 and

 show only a single isomer (the most stable (ts) conformer), which forms a strong ionic hydrogen bond (H band) between the OH+ group and the anion (Minkwitz et al. 2000). The characteristic OH stretch frequency is thus largely redshifted and thus not identified in both the IR and Raman spectra of the salts. Also, the IR intensities of the CH stretches are too weak to be observed.


We introduce the quantity ξ to represent a scaled product of equilibrium temperature (Teq) and surface gravity (g):
(14)$$\begin{eqnarray}
\xi = \left(\frac{T_{\text{eq}}}{1000~\text{K}}\right)\left(\frac{g}{g_{\rm J}}\right) ~,
\end{eqnarray}$$where gJ is the surface gravity of Jupiter. The calculated ξ values are listed in Table 4, along with the equilibrium temperature, surface gravity, and scale height for each planet. Fig. 6 shows the relative height of sodium for all 10 planets against ξ. The weight-combined results are shown in dark-blue, together with the unweighted results (light-blue) and literature values using the same HARPS/HARPS-N data (grey). The salmon-coloured points show recent results from other high-resolution spectrographs: WASP-69b with CARMENES (Khalafinejad et al. 2021), WASP-76b with ESPRESSO (Tabernero et al. 2021) and GRACES (Deibert et al. 2021), and WASP-121b with ESPRESSO (Borsa et al. 2021). We find that hNa is well described by an exponential trend of the form
(15)$$\begin{eqnarray}
h_{\lambda } = a\text{e}^{-b\xi } + c ~.
\end{eqnarray}$$As shown in Fig. 6, we fit this curve to the weight-combined results using the optimize.curve_fit function from scipy. The best-fitting values for the variables are: a = 1.70 ± 1.04, b = 5.04 ± 1.63, and c = 0.113 ± 0.013. The reduced chi-square of the fit across the full sample is $\chi ^2_\nu = 3.7$, much of which is skewed by two planets that deviate from the fit by more than 3σ (WASP-79b and HD 189733 b). The reduced chi-square when excluding these two planets is $\chi ^2_\nu = 1.2$. Since the exponential curve is asymptotic to the value of c, our results suggest that planets with ξ ≳ 1.25 are likely to have an upper limit on hNa of ∼0.113. The sodium features could potentially be muted due to other atmospheric effects, such as high-altitude clouds and hazes in lower temperature planets, or ionization of most of the sodium in extremely irradiated environments. Therefore, results lower than those given by equation (15) are also possible. The underlying physical processes behind this trend are not discussed in this current work, but these results motivate further observations to confirm the trend and theoretical studies to investigate possible physical mechanisms. Further refinement of this curve will be possible with more observations of low-ξ planets.


It is important to note that we have not classified our simulated galaxies by morphology itself in this paper, and more detailed analysis of the morphology, including kinematical decomposition, will be made in future work. In Fig. 4, we show the distributions of our morphology indicators, ETGΔs, LTGΔs, ETGΔt, and LTGΔt, with stellar mass. The top panel shows that LTGΔt  dominate at low mass, and ETGΔt, which have experienced a major merger within 1 Gyr, are more numerous above M* ∼ 5 × 1010M⊙; the ETGΔt fraction is ∼45 per cent and ∼85 per cent at M* ∼ 5 × 1010M⊙ and ∼1011M⊙, respectively. Since mergers are strong drivers of morphological change, this implies that our high-mass galaxies are mostly elliptical, which is in good agreement with observational results for ellipticals and S0 galaxies (e.g. Bernardi et al. 2010; Tempel et al. 2011). There is not a perfect correlation between galaxy morphology and tmerge, however, and the details of each individual merger are important. In the lower panel of Fig. 4, galaxies are separated by ΔSFMS. Galaxies that lie close to the SFMS (LTGΔs) are most numerous at lower masses, and constitute a declining fraction of the galaxy population with increasing mass, but the fraction of ETGΔs is not perfectly consistent with observations (e.g. Renzini & Peng 2015, ∼50 per cent and ∼75 per cent at log M* = 10.5 and 11). This means that our AGN feedback is probably not strong enough (see TK15a for more discussion). Our predicted distribution of gradients could be affected by these effects. Our galaxies that are classified as both LTGΔs and ETGΔt should be ellipticals, and their metallicity gradients may be too steep because of the lack of quenching of star formation. Therefore, we think our sample of ETGΔs is better for the comparison with observations of SAURON and ATLAS3D. For low-mass galaxies, the lack of resolution could result in underestimating gradients in general. However, our low-mass LTGΔs and LTGΔt galaxies, it could also overestimate the gradients in the case that the gradients would be measured along small star-forming discs, which are not resolved in our simulations.


The lifetime of molecular clouds (MCs) remains an active research topic in the study of the interstellar medium and star formation, and most recent studies, both observational and theoretical, place this lifetime at a few times 107 yr for clouds in the 105–106M⊙ mass range (e.g. Blitz & Shu 1980; Kawamura et al. 2009; Zamora-Avilés, Vázquez-Semadeni & Colín 2012; Zamora-Avilés & Vázquez-Semadeni 2014; Lee, Miville-Deschênes & Murray 2016). In addition, several observational studies have suggested that the star formation rate (SFR) of the clouds appears to increase over their lifetimes. For example, studies of young clusters embedded in moderate-mass MCs (∼104M⊙) (e.g. Palla & Stahler 1999, 2000; Da Rio et al. 2010) have shown that their age histograms contain a large majority of young (1–2 Myr) objects, but also a tail of older (up to several Myr) ones suggesting an accelerating star formation activity, sometimes followed by a subsequent decline (see also Povich et al. 2016; Schneider et al. 2018). In addition, Kawamura et al. (2009) reported a clear evolutionary process over the lifetime of giant molecular clouds (GMCs; of masses ∼105–106M⊙) in the Large Magellanic Cloud, evidenced by the increasing number of massive stars across the sequence of GMC ‘classes’ proposed by those authors. Finally, on the basis of the large scatter in the observed star formation efficiency (SFE) in Milky Way GMCs, Lee et al. (2016) have concluded that the SFR in those clouds must also be time variable. Numerical simulations of MC formation and evolution also exhibit time varying, increasing SFRs during their early stages (e.g. Vázquez-Semadeni et al. 2007; Hartmann, Ballesteros-Paredes & Heitsch 2012). Also, in the presence of stellar feedback, at late times the SFRs reach a maximum and begin to decrease again (e.g. Vázquez-Semadeni et al. 2010; Colín, Vázquez-Semadeni & Gómez 2013). Vázquez-Semadeni, González-Samaniego & Colín (2017) have recently shown that the simulations of Colín et al. (2013) in fact produce stellar age histograms highly resemblant of the observed ones (Palla & Stahler 1999, 2000; Da Rio et al. 2010), and reproduce observed radial age gradients in clusters (Getman et al. 2014) as well as bottom-heavy stellar initial mass functions (IMFs) in scattered regions of massive star formation (Povich et al. 2016).


Observations of splits in the MS and at the eMSTO of young and (at least) moderately massive Magellanic Cloud star clusters have demonstrated the presence of complex stellar populations, suggestive of variations in their stellar rotation properties (Milone et al. 2018a). The effects of stellar rotation on stellar populations have been observed in Galactic open clusters as well (Marino et al. 2018b). Nearly all of these young star clusters are sufficiently massive to host MPs among their MS stars. For example, NGC 1755, a young cluster with a mass of ∼104 M⊙ (Milone et al. 2016) or NGC 419, another young massive cluster with an age of 1.72 Gyr and a mass of ∼104 M⊙, are comparably massive with respect to other star clusters that show clear evidence of MPs (Martocchia et al. 2018a). Thus, clusters with minimum masses of order 104 M⊙ tend to show evidence of MPs. However, at present such a mass threshold has yet to be explained theoretically. If we assume that mass is an important driver of MP formation, then NGC 411 should also have shown clear evidence of chemical abundance variations among its RGB stars. However, we have found no such evidence in NGC 411, which challenges the idea that mass may be the only or even the main driver of MP formation. The similarity of the observed RGB width in NGC 411 with that expected for an SSP suggests an absence of significant chemical abundance variations. In fact, for NGC 411, NGC 1718, and NGC 2213 we derive maximum possible helium-abundance variations of δY = 0.003 ± 0.001(Y = 0.300), 0.002 ± 0.001(Y = 0.350), and 0.004 ± 0.002(Y = 0.300), respectively. We determined an upper limit to the nitrogen-abundance variation in NGC 411 of Δ[N/Fe] = 0.3 dex, although the available data did not allow us to determine useful upper limits for our other sample clusters. Combined with similar results for NGC 419, NGC 1806, and NGC 1846 (Martocchia et al. 2017), our result is indeed inconsistent with mass being the primary driver of MP formation, although it seems likely that a sizeable minimum mass is still required.


In this work we aim to explore the presence and properties of LSBGs in the environment of the NGC 1052 group of galaxies. This region is of particular interest in light of the “exotic” properties that recent works claim for some LSBGs found in this region. For instance, van Dokkum et al. (2018a) in [KKS2000] 04 (more commonly known as NGC 1052-DF2) and van Dokkum et al. (2019a) in NGC 1052-DF4 claimed the similarity between the observed baryonic matter and the dynamic matter obtained by the radial velocity dispersion of their GCs and also the stellar component (Emsellem et al. 2019; Danieli et al. 2019). This observational evidence would imply an extreme and unexpected deficit (even lack) of dark matter in these LSBGs. Taking into account that their metallicity content follows the usual stellar mass–metallicity relation for dwarf galaxies (Fensch et al. 2019; Ruiz-Lara et al. 2019), the possibility that they are tidal dwarf galaxies – galaxies formed by strong interactions with recycled material from massive host galaxies, high in metals, and intrinsically born with a lack of dark matter (see e.g., Duc 2012; Román et al. 2021) – is ruled out. The properties of these LSBGs have been the subject of much debate (see e.g., Martin et al. 2018; Ogiya 2018; Famaey et al. 2018; Kroupa et al. 2018; Lewis et al. 2020; Haslbauer et al. 2019; Müller et al. 2019; Nusser 2019; Montes et al. 2020, 2021). One hypothesis put forward by Trujillo et al. (2019) is that these LSBGs “lacking dark matter” could be at a closer distance than initially estimated by van Dokkum et al. (2018a, 2019a). This would not only make the stellar mass smaller (leaving room for a higher M/L fraction and therefore recovering a certain amount of dark matter, alleviating its strong deficit) but would also resolve the other anomalies that these LSBGs have related to their globular cluster luminosity function (GCLF) (e.g., Shen et al. 2021a), something considered a universal property of any galactic population, including LSBGs (e.g., Jordán et al. 2007; Villegas et al. 2010; Rejkuba 2012; Amorisco et al. 2018; Prole et al. 2019b). However, the distance to these galaxies is still the subject of intense debate (van Dokkum et al. 2018b, 2019b; Blakeslee & Cantiello 2018; Monelli & Trujillo 2019; Danieli et al. 2020; Shen et al. 2021b; Zonoozi et al. 2021) and there is currently no broad consensus on these distance values, with the remaining debated range of distances being approximately 12–22 Mpc.


HATLAS12-00 had already been identified as a candidate gravitationally lensed galaxy as a result of its high submm flux (i.e. F500 > 100 mJy), red Herschel colours and the lack of a bright optical or radio counterpart (see e.g. Negrello et al. 2010 for a discussion of the selection of lens candidates in H-ATLAS and other Herschel surveys). This source was therefore observed spectroscopically in the submm. A CO spectroscopic redshift of 3.26 was first suggested by Z-spec (Bradford et al. 2004) observations, then subsequently confirmed by observations by the CARMA interferometer (Leeuw et al., in preparation) and the Zpectrometer instrument (Harris et al. 2007) on the Greenbank Telescope (Harris et al. 2012; see also Fu et al. 2012). Additional followup observations in the optical, near-IR, submm and other wavelengths were targeted at the lensed z = 3.26 source and the foreground objects responsible for the lensing, resulting in detailed analyses of this lensing system by Fu et al. (2012) and Bussmann et al. (2013). Their conclusions are that the z = 3.26 source HATLAS12-00 is subject to gravitational lensing, with a magnification of 9.6 ± 0.5 in both the submm continuum and CO, and 16.7 ± 0.8 in the K′ band, by two foreground galaxies, one at a spectroscopically determined redshift of 1.22, and another with photometry suggesting that it lies at a similar redshift. The submm photometry of HATLAS12-00 at 890 μm acquired with the Submillimeter Array (SMA) as part of this programme (Fu et al. 2012; Bussmann et al. 2013) is fully consistent with the 870 μm and 850 μm fluxes derived for this source from the LABOCA and SCUBA2 data to be presented here. The spectral energy distribution (SED) of the lensed source, after correcting for the lensing amplification, is well matched by the optically thick SED model for Arp220 from Rangwala et al. (2011), with a lensing-corrected far-IR luminosity of 1.2 ± 0.2 × 1013 L⊙, and an implied star formation rate of 1400 ± 300  M⊙ yr−1. In many ways the unlensed properties of this object match those of the broader population of bright submm selected galaxies first discovered by the SCUBA submm imager (see e.g. Chapman et al. 2005; Clements et al. 2008; Michałowski, Hjorth & Watson 2010). The unlensed 870 μm flux of this object would be ∼7.7 mJy.

Compare/Contrast Compare/Contrast Compare/Contrast Compare/Contrast


Similar to Chen et al. (2017), we also follow Li & Draine (2001a) to derive upper limits on the abundance of the graphene C24 in the Galactic cirrus and in the diffuse ISM towards l = 44°20′, b = −0°20′ based on comparison of the observed IR emission with the calculated emission spectrum of C24. For the Galactic cirrus, the average emission per H has been measured by COBE/DIRBE (Arendt et al. 1998), COBE/FIRAS (Finkbeiner, Davis & Schlegel 1999), and Planck (Planck Collaboration XVII 2014). The diffuse ISM towards l = 44°20′, b = −0°20′ has been observed by COBE/DIRBE (Hauser et al. 1998). The Mid-Infrared Spectrograph (MIRS) aboard the Infrared Telescope in Space (IRTS) has also obtained the 4.7–11.7$\, {\rm \mu m}$ spectrum for the diffuse ISM towards l = 44°20′, b = −0°20′ (Onaka et al. 1996). As shown in Fig. 5(a), even locking up 20 $\, {\rm ppm}$ of C/H – the upper limit of graphene derived from the interstellar extinction – all in the specific graphene species C24, the 6.6, 9.8, and 20 $\, {\rm \mu m}$ emission features of C24 would still be hidden by the PAH features at 6.2, 7.7, 8.6, and 11.3 $\, {\rm\, \mu m}$ and would remain undetected by Spitzer or by the Short Wavelength Spectrometer (SWS) aboard the Infrared Space Observatory (ISO). This is also true for the diffuse ISM towards l = 44°20′, b = −0°20′. As illustrated in Fig. 5(b), as much as $\sim \, 20\, {\rm ppm}$ of C/H could also be tied up in the C24 graphene while the characteristic 6.6, 9.8, and 20 $\, {\rm \mu m}$ emission features of C24 are still not strong enough to be detected by IRTS. Therefore, for both the Galactic cirrus and the line of sight towards l = 44°20′, b = −0°20′, a upper limit of C/H ≲ 20 $\, {\rm ppm}$ is imposed by the COBE/DIRBE photometric data and the IRTS spectrum. Nevertheless, the actual abundance of C24 could be much lower than 20 $\, {\rm ppm}$ since, if graphene is indeed present in the ISM, it could span a wide range of sizes and charging states.


Molecular hydrogen H2 is conventionally believed to make up 17% of the interstellar medium (ISM) by mass in the Galaxy (e.g., Draine 2011, Table 1.2, not including He), but, unlike atomic hydrogen H i (at 60% by mass), H2 is not generally detectable in the cold, diffuse conditions that predominate the volume of the ISM. In order to determine the mass and structure of interstellar H2, emission from other “trace” molecules must be observed instead. The primary tracer for H2 in current use is the J = (1−0) ground-state rotational transition of 12CO at a wavelength of 3 mm. While this tracer has become widely adopted over the years (see, e.g., Heyer et al. 1998; Dame et al. 2001) and has been often defended as a reliable large-scale tracer for molecules in the ISM, it also remains the primary such tracer in common use. There are several reasons to be concerned about this. First, the critical volume density of the 12CO (1–0) transition at low optical depths is

; this means that gas at lower volume density will be less excited by collisions, thus emitting fewer photons, and may even effectively disappear from sensitivity-limited surveys. Second, in sufficient quantities to avoid the “excitation” problem, the 12CO signal is optically thick, so that direct calculation of column densities from line profile integrals is not possible. Instead, indirect methods of inferring the quantity of H2 must be used, such as the “X-factor” method (see, e.g., Bolatto et al. 2013, for a review). However, recent evidence from gamma rays and IR surveys has suggested that there are significant regions of the ISM apparently containing molecular gas that is not adequately traced by CO emission (see, e.g., Grenier et al. 2005). The “dark gas” appears not to be hidden optically thick H i (see Murray et al. 2018), and as such is most likely molecular. While several other molecular gas tracers have been studied (see, e.g., Jacob et al. 2019, on CH), these tracers may not be ideal for detecting low-density, diffuse portions of the large-scale ISM in emission owing to their high critical densities. A reliable alternative molecular tracer for diffuse gas is needed to confirm the identity of this “CO-dark” gas, as well as to provide information on its nature, kinematics, column density, and structure.


Stellar rotation is known to be related to the activity level; e.g. faster rotators tend to have larger star-spot coverages (e.g. Paper I), and stronger chromospheric emissions (e.g. Stauffer et al. 1997; Douglas et al. 2014; Newton et al. 2017; Paper II) and X-ray emissions (e.g. Pizzolato et al. 2003; Mamajek & Hillenbrand 2008); thus, a correlation between rotation and variation level should also be expected. In fact, Fig. 7 shows that there exists a large scatter in variation amplitude even for stars in the same cluster. It is reasonable to connect the scatter to the stellar rotation rate diversity, considering the fact that there exist noticeable differences in rotation periods between stars of the same temperature in young open clusters (e.g. Stauffer et al. 2016). To understand further on this scenario, we provided variation amplitudes as a function of temperature in Fig. 8, wherein shown are stars with known rotation periods. For comparison purpose, we also displayed the corresponding rotation periods in the upper panels. The periods were collected from the literature (Pleiades: Hartman et al. 2010; Covey et al. 2016; Rebull et al. 2016a; Praesepe: Agüeros et al. 2011; Delorme et al. 2011; Kovács et al. 2014; Rebull et al. 2017; Hyades: Hartman et al. 2011; Armstrong et al. 2015; Douglas et al. 2016); for a few stars in Praesepe, such as EPIC 211852399 and EPIC 211875458, the periods were obtained by us based on K2 data (see Appendix A). The colour contrast in Fig. 8 denotes the Rossby number, Ro, the normalized rotation period by the convective turnover time (the convective turnover time was estimated by using the correlation reported by Wright et al. 2011; see Paper I/II for details). It is known that the open cluster members mainly locate in two rotation sequences in the rotation–colour diagram (Barnes 2003), i.e. I (interface) and C (convective) sequence, corresponding to slow and fast rotators, respectively, as shown in the top panels in Fig. 8. The figure shows a tendency that GK-type C sequence stars in Pleiades have larger variation amplitude of EWH α compared to I sequence stars of the same temperature. We found no evident difference between different rotators among M-type Pleiades stars, partially because most of them are very fast rotators that reside in activity saturation regime (when Ro ≲ 0.1; e.g. Paper II). For Praesepe/Hyades sample, almost all GK-type stars rotate slowly (e.g. Ro ∼ 0.5), located in the I sequence (those stars with blue colours); there is no clear trend among these stars. Among M-type stars, some stars are fast rotators in C sequence (red or green colours), while others are slow rotators (in I sequence), as shown in the upper right panel of Fig. 8. Thus, there is a tendency that faster rotators have larger variation amplitude of EWH α. Unlike EWH α, TiO2n shows no clear difference among all sample stars with different rotation periods, probably due to its small intrinsic variation amplitude, which could be dominated by observational noise.


More recently, García-Bernete et al. (2022) found that the PAH molecules responsible for the 11.3 μm PAH emission band are more resilient in the hard environments often present in AGN. In particular, the authors found larger 11.3/7.7 μm and 11.3/6.2 μm PAH ratios in AGN-dominated systems compared to SF galaxies, indicating a larger fraction of neutral PAH molecules (as noted by Smith et al. 2007 using a sample of relatively weak AGN). However, these studies were limited by the spatial resolution (∼4″) and the low spectral resolution (R ∼ 60–130) of Spitzer/InfraRed Spectrograph (IRS). Previous sub-arcsecond angular resolution N-band (∼8–13 μm) ground-based spectroscopic studies investigated the 11.3 μm PAH feature in the nuclear and circumnuclear regions of AGN (e.g., Hönig et al. 2010; González-Martín et al. 2013; Alonso-Herrero et al. 2014, 2016; Ramos et al. 2014; Esquej et al. 2014; García-Bernete et al. 2015; Jensen et al. 2017; Esparza-Arredondo et al. 2018). However, these works were unable to provide definitive details regarding the effect of the AGN on the PAH molecules due to limited wavelength coverage and sensitivity. The changes in the PAH properties due to the presence of the AGN might be more prominent in their innermost regions of galaxies. Therefore, the unprecedented combination of high angular and spectral resolution (R ∼ 1500 − 3500) in the entire mid-IR range (4.9–28.1 μm) afforded by the James Webb Space Telescope (JWST)/Mid-Infrared Instrument (MIRI; Rieke et al. 2015; Wells et al. 2015; Wright et al. 2015) is key to investigating PAH properties. In this Letter we report on the first investigation of PAH emission in the nuclear regions of three luminous Seyfert (Sy) galaxies and compare them with emission from SF regions using JWST/MIRI Medium Resolution Spectrograph (MRS) data. This enables us, for the first time, to characterise the PAH properties of local luminous Sy galaxies (log (Lbol)> 44.46 erg s−1)1 at sub-arcsecond scales (∼0.45″, ∼142–245 pc).


We used the position and distance of the MCs in the FQS catalogue to describe the structure of the Milky Way in this poorly known portion of the third quadrant. In Fig. 16 we show the distribution of the clouds projected onto the Milky Way plane. At any Galactic longitude the clouds are grouped in three well-separated structures that trace the position of the spiral arms. The dispersion of the positions in each structure is given not only by the width of the arms but also by the uncertainty of the distance determination. Indeed, kinematic distances are affected by significant uncertainties due not only to the assumed Galactic rotation model but also to the unknown possible peculiar motions of the clouds themselves. In Fig. 16 we compare the positions of the clouds derived from FQS data with the expected locations of the spiral arms, adopting a log-periodic spiral form of the Galaxy (Reid et al. 2014). The pitch angle and the distance at a reference position of the three arms are taken from Xu et al. (2013) for the Local arm, Choi et al. (2014) for the Perseus arm, and Hachisuka et al. (2015) for the Outer arm. These authors used the positions of water masers derived from parallax measurements as part of the Bar and Spiral Structure Legacy (BeSSeL) survey to fit the parameters of the spiral arms. We found good agreement between the position of the FQS clouds and the modelled position of the Local and the Perseus arms, while the modelled Outer arm lies further than the observed clouds. We note that while the parameters of the Local and Perseus arms are derived by fitting about 20 water masers located in both the second and third quadrants, covering also the Galactic longitude of the FQS survey, the parameters of the Outer arm are derived from only 5 water masers, 4 of which are located in the second quadrant. Therefore it is not surprising that they might not be fully appropriate to describe the location of the Outer arm in the longitude range of the FQS survey of 220°  l   240°. In fact, an alternative model of the Outer arm from Hou & Han (2014), also shown in Fig. 16, seems in better agreement with the FQS results.


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


Studies of the radial n-capture-to-iron abundance gradients are very scarce so far. We can only search for a broad agreement of our results with several studies of abundance gradients with galactocentric distances (Rgc). da Silva et al. (2016) studied n-capture elements across the Galactic thin disc based on Cepheid variables. Because the Cepheids are young stars, their Rgc may be rather close to their birthplaces and Rmean. da Silva et al. (2016) supplemented their sample of 111 Cepheids with 324 more stars from other studies and found that the [Y/Fe] distribution is flat throughout the entire disc. In our study, we confirm this finding not only based on the whole thin-disc sample of stars and on a subsample of younger ≤4 Gyr stars, but also add another light s-process dominated element strontium. Like in our study, da Silva et al. (2016) also obtained positive [El/Fe] radial gradients for La, Ce, Nd, and Eu. The slopes are rather similar. For [Eu/Fe], they differ just by 0.002 dex kpc−1. More recently, Luck (2018b) also investigated the gradients of n-capture element abundance-to-iron ratios with respect to Rgc for a sample of 435 Cepheids. It is interesting to note that the [Ba/Fe] versus Rgc slope according to this Cepheid sample is also negative, as in our study. [Ba/Fe] is the only n-capture element-to-iron ratio with a negative radial gradient in our sample of stars and in Luck (2018b). Overbeek et al. (2016) investigated trends of Pr, Nd, and Eu to Fe abundance ratios with respect to Rgc using 23 open clusters. As in our study, they found that these elements have positive linear trends with galactocentric radius (the linear regression slopes are of about +0.04 dex kpc−1). They also suggested that the [El/Fe] relation of Pr and Nd, but not Eu, with the galactocentric radius may not be linear because the [El/Fe] of these elements appears to be enhanced around 10 kpc and drop around 12 kpc. Because only a small number of stars lie at these large radial distances, we cannot address this question. For the thick-disc stars, the radial abundance-to-iron slopes are negligible, as was found for α-process elements by Li et al. (2018), even though the production sites of α-elements and s-processes dominated elements are quite different.


There are three possible explanations for the origin of these systems: (1) they formed from the fragmentation of the same molecular cloud (Elmegreen & Elmegreen 1983), (2) they were generated in distinct molecular clouds and then became bound systems after a close encounter leading to a tidal capture (Vallenari, Bettoni & Chiosi 1998; Leon, Bergond & Vallenari 1999), or (3) they are the result of division of a single star-forming region (Goodwin & Whitworth 2004; Arnold et al. 2017). Their subsequent evolution may also have different outcomes. Dynamical models and N-body simulations (see, e.g., Barnes & Hut 1986; de Oliveira, Dottori & Bica 1998, and references therein) have shown that, depending on the initial conditions, a bound pair of clusters may either become unbound, because of significant mass-loss in the early phases of stellar evolution, or merge into a single and more massive cluster on a short time-scale (≈60 Myr) due to loss of angular momentum from escaping stars (see Portegies Zwart & Rusli 2007). The final product of a merger may be characterized by a variable degree of kinematic and morphologic complexity, mostly depending on the values of the impact parameter of the pre-merger binary system (de Oliveira, Bica & Dottori 2000; Priyatikanto et al. 2016). In some cases, the stellar system resulting from the merger event may show significant internal rotation (in fact, for many years this has been the preferred dynamical route to form rotating star clusters; see Sugimoto & Makino 1989; Makino, Akiyama & Sugimoto 1991; Okumura, Ebisuzaki & Makino 1991; de Oliveira, Dottori & Bica 1998). Merger of cluster pairs has been sometimes invoked to interpret the properties of particularly massive and dynamically complex clusters (e.g. see the study of ω Centauri by Lee et al. 1999, G1 by Baumgardt et al. 2003 and NGC  2419 by Brüns & Kroupa 2011), and, more in general, as an avenue to form clusters with multiple populations with different chemical abundances both in terms of iron and light elements (e.g. van den Bergh 1996; Catelan 1997; Amaro-Seoane et al. 2013; Gavagnin, Mapelli & Lake 2016; Hong et al. 2017).


Much of the progress in PPS has come from thorough Monte Carlo simulations that generate pulsars and test whether they fulfil the criteria for detection according to geometrical factors and sensitivity issues. It is then possible to develop and optimize a model for the underlying pulsar population, which informs us about the important intrinsic neutron star parameters and distribution, enabling predictions for future surveys. Usually, PPS studies follow two simple approaches. The first one is to take a ‘snapshot’ of the Galaxy as it appears today, where no assumptions are made regarding the prior evolution of the pulsar population. Instead, this population is generated assuming various distribution functions (typically spatial distribution, spin period P and,

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˙

$ \dot{E} $

- or Ṗ), which are optimized to match the observations. Inspired by earlier studies from Taylor & Manchester (1977) and Lyne et al. (1985), Lorimer et al. (2006) applied the snapshot approach to the canonical3 pulsar population to determine best-fitting probability density functions in Galactocentric radius (R), luminosity (L), height with respect to the Galactic plane (z), and the period P for the currently observed population of pulsars. Alternatively, one may consider ‘evolution’ strategies where the pulsars are evolved from birth up to the present era, starting from an initial spatial distribution, and an initial period and magnetic field distribution. A fine example of the latter genre is the comprehensive study of Faucher-Giguère & Kaspi (2006), which quite successfully reproduced the properties of the main part of the radio pulsar population using a model in which the luminosity has a power-law dependence on P and Ṗ. PPS studies can be also extended to the population of neutron stars observed in other bands, such as X-rays (see for instance Popov et al. 2010) and γ-rays. Indeed, with the broad increase in γ-ray pulsar numbers, a statistical treatment of the γ-ray population in combination with deep radio surveys of the Galactic plane is now feasible. Early works on radio-loud gamma-ray pulsar populations carried out before the Fermi era include Gonthier et al. (2002), (2004), (2007a,b). With the advent of Fermi/LAT, new studies emerged (see for instance Gonthier et al. 2018; Ravi et al. 2010; Takata et al. 2011; Watters & Romani 2011; Pierbattista et al. 2012), trying to constrain the geometry and the location of the gamma-ray emission sites. Watters & Romani (2011) showed that an initial spin period of P0 = 50 ms and a birth rate of one neutron star per 59 yr were required to reproduce the observed γ-ray population. They made the prediction that after ten years of operations, Fermi should detect ∼120 young γ-ray pulsars, of which about one half would be radio-quiet. Gonthier et al. (2004) included an exponentially decaying magnetic field with a 2.8 Myr timescale and displaying a satisfactory agreement with the P−Ṗ distribution at that time. Later, more accurate magnetic field decay models were elaborated, especially for magnetars, as presented in Viganò et al. (2013).


Independent measurements of distances and redshifts, z, allow astronomers to constrain cosmological models, since they both define the distance–redshift relation. When it was determined that type Ia supernovae (SNIa) could be standardized and therefore used to measure distances, this led to the discovery of the accelerated expansion of our Universe (Riess et al. 1998; Perlmutter et al. 1999). The combination of SNIa (Betoule et al. 2014), baryonic acoustic oscillations (Eisenstein et al. 2005; Alam et al. 2017), and the cosmic microwave background (CMB; Komatsu et al. 2011; Planck Collaboration et al. 2018) led to the emergence of the concordance Λ cold dark matter (ΛCDM) model, in which the energy density is dominated by dark energy as a cosmological constant Λ. In a flat Friedmann–Lemaître–Robertson–Walker universe, the comoving distance is defined as
(1)$$\begin{eqnarray*}
D(z) = \int _0^z \frac{c\mathrm{d}z}{H(z)},
\end{eqnarray*}$$ where, in the ΛCDM model,
(2)$$\begin{eqnarray*}
H(z) = H_0 \sqrt{\Omega _\mathrm{m} (1+z)^3 + 1-\Omega _\mathrm{m}}
\end{eqnarray*}$$is the Hubble parameter, H0 is the Hubble–Lemaître constant, and Ωm is the matter energy density at the current epoch. The luminosity and angular diameter distances are defined as
(3)$$\begin{eqnarray*}
D_\mathrm{L}(z) = (1+z) D(z)
\end{eqnarray*}$$(4)$$\begin{eqnarray*}
{\mathrm{ and}} \,D_\mathrm{A}(z) = \frac{R}{\theta }= \frac{D(z)}{(1+z)}.
\end{eqnarray*}$$Type Ia supernovae can only be used up to redshift of around 2 (Jones et al. 2013), and there are tensions between direct local measurements of the Hubble–Lemaître constant and model-dependent estimates using CMB observations (Planck Collaboration et al. 2018). Therefore, independent distance measurements to extragalactic objects are desired. We should emphasize here, that model-independent distance indicators can have various important applications in physical cosmology. In particular, to test different aspects of cosmological models and theories of gravity. For instance, we can use these model-independent measurements to test the FLRW metric (Clarkson, Bassett & Lu 2008; Wiltshire 2009; Shafieloo & Clarkson 2010; L’Huillier & Shafieloo 2017; Shafieloo, L’Huillier & Starobinsky 2018; Cao et al. 2019a; Qi et al. 2019a), to test general relativity and some modified gravity models (Cao et al. 2012; Shafieloo, Kim & Linder 2013a; Cao et al. 2015, 2017b; Qi et al. 2017; L’Huillier, Shafieloo & Kim 2018; Shafieloo et al. 2018; Xu et al. 2018; Chen, Sesana & Conselice 2019; L’Huillier et al. 2020), to test natural constants such as the speed of light (Cao et al. 2018), to test cosmic duality relationships, and to measure cosmic curvature (Shafieloo et al. 2013b; Cao et al. 2019b; Qi et al. 2019a, b; Zheng et al. 2020). Using a combination of such model-independent distance indicators can also be used to measure some key cosmological parameters such as the Hubble Constant (Liao et al. 2015; Suyu et al. 2017; Jee et al. 2019; Liao et al. 2019, 2020; Wong et al. 2019). Amongst the most energetic objects in our Universe are active Galactic nuclei (AGNs). AGNs are the nuclei of massive galaxies that sometimes produce relativistic jets of material launched from near a central supermassive black hole (SMBH). When these jets are not aligned close to our line of sight, AGNs are observed as radio galaxies, whereas if the jet is aligned to within a small angle to our line of sight, they are observed as blazars (Urry & Padovani 1995). Blazars and quasars are amongst the most consistently bright objects in our Universe and can be observed at redshifts as high as ∼7 (Mortlock et al. 2011). Attempts have been made to measure distances to AGNs in various ways, with some claiming deviations from the expected cosmology at high redshifts (Risaliti & Lusso 2017, 2019; Turner & Shabala 2019). Very long baseline interferometry (VLBI) has also been used to attempt to measure cosmological distances. The approach pioneered by Gurvits, Kellermann & Frey (1999) attempted to measure cosmological parameters by assuming that AGN could be used as a standardizable rod. Vishwakarma (2001) used this data set and compared it with supernovae data, and found it was not possible to differentiate different cosmological models with the VLBI data of Gurvits et al. (1999). Cao et al. (2015) revisited this technique and investigated the evolution of the standard rod by assuming a Planck cosmology. Cao et al. (2017a, c) then introduced a cosmology independent method for calibrating the standard rod and was able to provide reasonable constraints on cosmological parameters. Our approach differs from this by using the speed of light to normalize the rod. This approach was first attempted by Wiik & Valtaoja (2001), which found that that the apparent angular sizes of AGNs maximized at z ∼ 2. In this paper, we demonstrate the method on the famous nearby radio galaxy 3C 84 (NGC 1275) and discuss possible systematic errors. The source is known to exhibit extremely high energy emission despite not exhibiting strong relativistic effects (Jorstad et al. 2017; Liodakis et al. 2018), and has multiple independent measures of distance (Theureau et al. 2007; Hicken et al. 2009), thus making it an ideal source to test our methodology.


The first SMGs were detected using SCUBA at 850 μm (Smail et al. 1997; Barger et al. 1998; Hughes et al. 1998), which remains one of the prime wavelengths to detect these galaxies (e.g., Geach et al. 2017), thanks to a combination of available instruments, spectral window, and the negative k-correction at that wavelength. Other single-dish samples of SMGs have also been obtained at 1.1–1.3 mm using MAMBO (e.g., Eales et al. 2003; Bertoldi et al. 2007; Greve et al. 2008) and AzTEC (e.g., Aretxaga et al. 2011; Yun et al. 2012), at 1.4 mm/2 mm with the SPT (Vieira et al. 2010), and at 2 mm with GISMO (Staguhn et al. 2014; Magnelli et al. 2019). Selecting SMGs from observations at longer wavelengths is thought to favor galaxies at higher redshifts (e.g., Smolčić et al. 2012; Vieira et al. 2013; Staguhn et al. 2014; Magnelli et al. 2019; Hodge & da Cunha 2020), although it is difficult to compare the redshift distributions in an unbiased way (see, e.g., Zavala et al. 2014 for a discussion), and account for intrinsic variations of galaxy far-IR spectral energy distributions (SEDs). Nevertheless, the 2 mm band has been put forth as a potential candidate to detect high-redshift (z > 3) galaxies (e.g., Casey et al. 2018a, 2018b, 2019; Zavala et al. 2021). The negative k-correction is stronger at 2 mm than at 850 μm; thus, for a fixed SED, the 2 mm band should pick up more high-redshift galaxies than at 870 μm. In addition, better atmospheric transmission and larger fields of view can be achieved at 2 mm (but corresponding poorer resolution). Such an effort is currently ongoing (see Zavala et al. 2021 for first results). To understand the relationship between the populations detected at 850 μm and at 2 mm, we require a detailed characterization of the (sub)millimeter SEDs of these sources. Multiwavelength submillimeter observations are still rare, with most observations focusing on a single wavelength. Only a handful of sources observed at 2 mm have complementary shorter-wavelength detections (Staguhn et al. 2014; Magnelli et al. 2019). Thus, a more systematic multiwavelength dust continuum investigation is warranted in order to reveal the dust properties of (sub)millimeter-detected sources.


RFs can propagate from the magnetotail to Earth over a long distance more than 10 R
E together with BBFs behind them (Runov et al. 2009; Cao et al. 2010). Studies have suggested that RFs are crucial regions for particle acceleration, pitch-angle evolution, wave–particle interactions, and electromagnetic energy conversion during their Earthward propagation. For instance, rapid increases in energy fluxes of electrons and ions from tens to hundreds of keV are a typical feature of RF events (Khotyaintsev et al. 2011; Liu et al. 2013, 2018c, 2021a, 2022b; Zhou et al. 2018; Liu & Fu 2019; Gabrielse et al. 2021), pitch-angle distribution of suprathermal electrons can evolve dramatically around RFs (Runov et al. 2013; Liu et al. 2020), strong particle and wave activity can occur in the vicinity of RFs (Ono et al. 2009; Zhou et al. 2009, 2014; Fu et al. 2014; Breuillard et al. 2016; Greco et al. 2017; Yang et al. 2017), and RFs are associated with energy conversion from electromagnetic fields to particles (Sitnov et al. 2009; Huang et al. 2015; Khotyaintsev et al. 2017; Liu et al. 2018a, 2022a). The energetic plasma in the vicinity of RFs plays a key role in connecting the magnetotail with the inner magnetosphere because they carry a large amount of energy and can be injected into the inner magnetosphere to affect the ring current and radiation belt (Gabrielse et al. 2012; Duan et al. 2014; Turner et al. 2014). Possible mechanisms responsible for the energization of particles around RFs have been widely investigated based on both spacecraft observations and numerical simulations during the past decade. The strong convection electric field induced by the strong magnetic field gradient of RFs provides significant adiabatic acceleration of the ambient particles (Birn et al. 2004, 2013, 2015; Gabrielse et al. 2012, 2014, 2016; Ganushkina et al. 2013; Liu et al. 2016; Turner et al. 2016). Nonadiabatic effects, caused by particle reflection ahead of the RFs (Zhou et al. 2018), resonance with RFs (Ukhorskiy et al. 2013, 2017), and scattering by wave emissions (Zhou et al. 2009; Greco et al. 2017), are also significant for particle energization. These above studies usually assumed that the RF surface has a planar boundary at a typical thickness comparable to the ion gyroradius and below (Nakamura et al. 2002; Sergeev et al. 2009; Zhou et al. 2009; Schmid et al. 2011; Liu et al. 2013; Vapirev et al. 2013). Divin et al. (2015b) revealed that the RF surface is unstable to instabilities ranging from electron scales to ion scales. Simulation studies found that RFs can be unstable to interchange instability and that finger-like structures on ion–electron hybrid scales can develop at the RF (Vapirev et al. 2013). Such finger-like structures are found to play a role in modulating the electron acceleration process (Wu et al. 2018). Bai et al. (2022) also reported significant ion trapping acceleration at the RF with ion-scale ripples. Unlike these surface structures with ion or ion–electron hybrid scales, Liu et al. (2018b) recently reported that the RF layer has electron-scale density gradients, currents, and electric fields, based on the MMS mission, which consists of four spacecraft separated by 30 km. Such electron-scale ripple structure can be generated by lower hybrid drift instability (Divin et al. 2015b; Pan et al. 2018). Liu et al. (2021c) presented a detailed investigation of energy flux densities at two RFs with/without the electron-scale surface ripples and indicated that surface ripples may play an important role in the particle dynamics. But how such electron-scale RF structure impacts the electron energization and transport still remains unknown. In this paper, with the aid of observation-based test-particle simulation, we aim to investigate in detail the effect of the front surface ripples on the local electron dynamics.


We compare our results with a new reduction of observations from the Lowell Observatory SSS, which is running a long-term stellar activity survey complementary to the MWO HK Project. The SSS observes solar and stellar light with the same spectrograph, with the solar telescope consisting of an exposed optical fiber that observes the Sun as an unresolved source (Hall & Lockwood 1995; Hall et al. 2007). The basic measurement of SSS is the integrated flux in 1 Å bandpasses centered on the Ca ii H & K cores from continuum-normalized spectra, ϕHK, which can then be transformed to the S-index using a combination of empirical relationships derived from stellar observations:
7

where

 is the continuum flux scale for the Ca ii H & K wavelength region, which converts ϕHK to physical flux (erg cm−2 s−1).

 is a function of Strömgren

 and is taken from Hall (1996).

 (simply K in other works) is the conversion factor from the MWO HKP-2 H & K flux (numerator of Equation (1)) to physical flux (Rutten 1984). Ccf is a factor that removes the color term from S and is a function of Johnson

 (Rutten 1984). Finally, Teff is the effective temperature. See Hall et al. (2007) and Hall & Lockwood (1995) for details on the extensive work leading to this formulation. What is important to realize about this method of obtaining S is that it requires three measurements of solar properties,

,

, and

, along with the determination of one constant,

. The solar properties are taken from best estimates in the literature, which vary widely depending on the source used, and can dramatically affect the resulting SSSS for the Sun. Hall et al. (2007) used

,

, and

. The constant

 was empirically determined to be 0.97 ± 0.11 erg cm−2 s−1 in Hall et al. (2007) as the value that provides the best agreement between SSSS and

 from Baliunas et al. (1995) for an ensemble of stars and the Sun. This combination of parameters resulted in a mean SSSS of 0.170 for the Sun using observations covering cycle 23. A slightly different calibration of SSS data in Hall & Lockwood (2004) used a flux scale

 based on Johnson

, set to 0.65 for the Sun, and

 K. In Table 1 we estimated that this calibration resulted in a mean S = 0.168 for cycle 23. Hall et al. (2009), which included a revised reduction procedure and one year of data with the upgraded camera (see below), found

.


The properties of the persistent radio source associated with FRB 121102 may be constrained independently of the Faraday-rotating medium. We assume equipartition between the relativistic gas and magnetic field as is common in synchrotron sources3 (Readhead 1994). The source becomes self-absorbed at $1.5$ GHz for radius $R_{\rm per} < 0.05$ pc; this is thus the lower bound on the source size. European Very Long Baseline Interferometry (VLBI) Network observations of the source at 5 GHz set an upper bound on the source radius of Rper ≲ 0.35 pc (Marcote et al. 2017). This is consistent with the ${\approx } 30\, {{\rm per\, cent}}$ amplitude modulations observed in the source at 3 GHz (Chatterjee et al. 2017) being caused by refractive interstellar scintillation in the Milky Way interstellar medium (ISM; Walker 1998). For any radius within the allowed range (0.05  Rper/pc  0.35), we can determine the equipartition magnetic field, Beq, and the column of relativistic electrons, Nrel, using the standard expressions for synchrotron emissivity and absorption coefficients (Rybicki & Lightman 1979, their equations 6.36 and 6.53). We assume a power-law energy distribution of radiating electrons with somewhat shallow index of b = −1.5 that can account for the relatively flat spectrum of the source (Chatterjee et al. 2017). The peak Lorentz factor of the distribution, γmax, is chosen to correspond to the observed spectral break frequency of $\nu _{\rm max}=10$ GHz. If the lower Lorentz factor cut-off corresponds to emission at $\nu _{\rm min}=1$ GHz,4 then the equipartition magnetic field and electron column thus determined for minimum and maximum source sizes are $B_{\rm eq}\approx 140$ mG, $\gamma _{ \rm min}\approx 50$, γmax ≈ 160, $N_{\rm rel} \approx 0.95\, {\rm pc}\, {\rm cm}^{-3}$ for $R_{\rm per}=0.05$ pc, and $B_{\rm eq}\approx 27$ mG, $\gamma _{ \rm min}\approx 120$, γmax ≈ 370, $N_{\rm rel} \approx 0.1\, {\rm pc}\, {\rm cm}^{-3}$ for $R_{\rm per}=0.35$ pc. The reader can scale the equipartition field to other source sizes using Beq(R) ∝ R−6/7. The total energy contained in the relativistic electrons and the magnetic field (‘equipartition energy’) is ∼1049.1 and ∼1050.2 erg, respectively. If the relativistic electrons were injected in a one-off event, the synchrotron cooling rates at γmax yield source ages of $14$ yr for R = 0.05 pc and 60 yr for $R=0.35$ pc. The corresponding expansion velocities are $0.011\, c$ and $0.02\, c$, respectively.


After the cosmological recombination, the universe went into the dark ages during which the density fluctuations in the matter distribution grew, and after reaching a threshold, the matter collapsed to make the first bound objects. The nature of dark matter sets the timeline and characteristics of these first bound objects, which were the hosts for the first sources of light, so it is essential to see the impact of different dark matter models on the observables from the Cosmic Dawn and EoR. Then, the natural question that arises is whether one can use the differences in these observables, estimated for different dark matter models, in order to constrain the nature of dark matter. The present observational probes that allow us to have a peak in this epoch are the absorption spectra of high-redshift quasars (Loeb & Barkana 2001; White et al. 2003; Boera et al. 2019) and the Thomson scattering optical depth of the cosmic microwave background (CMB) radiation photons (Kaplinghat et al. 2003; Komatsu et al. 2011). However, these indirect probes provide very limited and weak constraints on the CD-EoR. The H i 21-cm line, which arises due to the hyperfine splitting of the ground state of the neutral hydrogen, is a direct and most promising probe to study this period. Motivated by this, a large number of radio interferometers, including the GMRT (Paciga et al. 2013), LOFAR (Ghara et al. 2020; Mertens et al. 2020), MWA (Barry et al. 2019; Li et al. 2019), and PAPER (Kolopanis et al. 2019), are attempting a statistical detection of this signal using the power spectrum statistic. In parallel, there is a complementary approach to detect the sky-averaged global 21-cm signal from the CD-EoR using experiments, e.g. the EDGES (Bowman et al. 2018), DARE (Burns et al. 2017), and SARAS (Singh et al. 2018). The next-generation interferometers like the SKA (Koopmans et al. 2015; Mellema et al. 2015) are expected to see a giant leap in the sensitivity, which will enable them to make tomographic images of the H i distribution across cosmic time.


However, the transition between the two extremes of modern (metal-rich) and primordial (metal-poor) star formation, and in particular the role of dust coupling and stellar radiation feedback at low metallicity, has thus far received limited exploration. Krumholz (2011) present analytical models for radiation feedback and predict a weak scaling of IMF peak mass with metallicity, while Myers et al. (2011) and Bate (2014, 2019) carry out radiation-hydrodynamic simulations of star formation over a metallicity range from $0.01{-}3\, Z_{\rm {\odot }}$ and find negligible effects on gas fragmentation. However, these studies do not explore lower metallicities, despite available evidence for the existence of a low-metallicity ISM in the past through the discovery of stars with metallicities as low as $10^{-4}\, \rm {Z_{\odot }}$ (Caffau et al. 2011; Starkenburg et al. 2018), as well as several others with $\rm {[Fe/H]} \lt -5$ (Christlieb et al. 2004; Keller et al. 2014; Frebel et al. 2015; Aguado et al. 2017, 2018; Ezzeddine et al. 2019; Nordlander et al. 2019). Coming from the opposite direction, Bromm et al. (2001), Omukai et al. (2005), and Omukai, Hosokawa & Yoshida (2010) consider the thermodynamics of gas of increasing metallicity, and find that dust and metal line cooling permits fragmentation to reach masses ≲1 M⊙ only once the metallicity exceeds ∼10−3.5 Z⊙. Dust is a more efficient coolant than metal lines, and permits fragmentation to lower masses at lower metallicity (e.g. Meece, Smith & O’Shea 2014; Chiaki & Yoshida 2020; Shima & Hosokawa 2021), but exactly by how much depends on the poorly known distribution of dust grain sizes in the early Universe (Schneider et al. 2006, 2012; Omukai et al. 2010; Schneider & Omukai 2010; Chiaki et al. 2015). However, the early Universe star formation models are fundamentally misanalogous to the modern ones that consider decreasing metallicity, in that the early Universe models consider dust solely as a coolant that enables fragmentation, whereas the modern ones assign it a more nuanced role, as both a source of cooling and later, once stellar feedback begins, a source of heating – a changeover that seems crucial to explaining why the IMF in the present-day Universe peaks at ${\sim}0.2\, \rm {M_{\odot }}$ rather than ${\sim}10^{-2}\, \rm {M_{\odot }}$ (Kroupa 2001; Chabrier 2003, 2005).


Binary neutron star (BNS) mergers have long been suspected to produce the central engines of short gamma-ray bursts (sGRBs) (Eichler et al. 1989). The link was firmly established in August 2017, after the combined detection of gravitational waves and an sGRB from the same BNS merger (Abbott et al. 2017a,b,c; Goldstein et al. 2017; Savchenko et al. 2017). The actual origin of the gamma-ray signal is still debated, coming from either an off-axis jet or from the shock breakout of a relativistic cocoon inflated by the jet itself (Kasliwal et al. 2017; Nakar & Piran 2017; Gottlieb, Nakar & Piran 2018a; Gottlieb et al. 2018b; Mooley et al. 2018a; Lundman & Beloborodov 2021). Nevertheless, the multiband observations of a rising afterglow (Alexander et al. 2017; Hallinan et al. 2017; Margutti et al. 2017, 2018; Troja et al. 2017, 2018, 2019; D’Avanzo P. et al. 2018; Lyman et al. 2018; Lamb et al. 2019) together with the detection of superluminal motion (Mooley et al. 2018b; Ghirlanda et al. 2019; Hotokezaka et al. 2019) have settled the presence of a jet that successfully broke out from the surrounding ejecta, observed off-axis with a viewing angle θobs ≈ 19° (Murguia-Berthier et al. 2017; Lamb, Mandel & Resmi 2018; Lazzati et al. 2018; Mooley et al. 2018a; Margutti & Chornock 2020). The information obtainable from afterglow observations is strongly dependent on the angular structure of the emerging jet. This structure might be mainly determined by the launching process (Kathirgamaraju et al. 2019) or it may arise as a consequence of the interaction with the surrounding environment during propagation. Therefore, an understanding of the processes that shape the jet could in principle provide insights into both jet formation, and the post-merger environment. Recent relativistic (magneto-) hydrodynamics simulations (Murguia-Berthier et al. 2014, 2017, 2021b; Geng et al. 2019; Beniamini et al. 2020b; Gottlieb, Levinson & Nakar 2020; Gottlieb & Nakar 2021; Gottlieb et al. 2021a; Gottlieb, Nakar & Bromberg 2021b; Hamidani & Ioka 2021; Lazzati et al. 2021; Nathanail et al. 2021; Pavan et al. 2021; Urrutia et al. 2021) have illustrated the importance of the ambient medium in shaping the jet, thereby highlighting the importance of understanding the remnant structure and ejecta properties. The joint events GW170817 and GRB170817A were followed by an additional electromagnetic transient spanning the spectral bands from UV to optical and IR on time-scales from days to weeks (Abbott et al. 2017b; Arcavi et al. 2017; Cowperthwaite et al. 2017; Drout et al. 2017; Evans et al. 2017; Pian et al. 2017; Smartt et al. 2017; Soares-Santos et al. 2017; Tanvir et al. 2017; Utsumi et al. 2017). The observed properties were consistent with the expectations for a thermal transient powered by the radioactive decay of freshly synthesized r-process elements (a so-called ‘macronova’ or ‘kilonova’ e.g. Li & Paczyński 1998; Kulkarni 2005; Rosswog 2005; Metzger et al. 2010; Roberts et al. 2011; Kasen, Badnell & Barnes 2013; Yu, Zhang & Gao 2013; Kasen, Fernández & Metzger 2015; Kasen et al. 2017; Metzger 2017; Perego, Radice & Bernuzzi 2017; Tanaka et al. 2017; Rosswog et al. 2018). Understanding the properties of this signal requires in-depth investigation of all the processes that can unbind material during and after a BNS merger, together with the available amount of free neutrons provided by each ejection channel. By now, several mass-ejection channels have been identified and they differ in terms of launch time, mass, electron fraction Ye, and velocity. During the merger ∼10−3 − 10−2 M⊙ of material are ejected dynamically (Rosswog et al. 1998, 1999; Rosswog & Davies 2002; Oechslin, Janka & Marek 2007; Bauswein, Goriely & Janka 2013; Radice et al. 2018a). On longer time-scales (∼1 s) a few 10−2 M⊙ of material can be unbound from the torus surrounding the remnant by the action of nuclear heating (Metzger, Piro & Quataert 2008; Fernandez & Metzger 2013; Fernandez et al. 2015; Just et al. 2015), magnetic (Siegel & Ciolfi 2015; Ciolfi et al. 2017; Siegel & Metzger 2017, 2018; Ciolfi & Kalinani 2020; Murguia-Berthier et al. 2021a), and viscous effects (Shibata, Kiuchi & Sekiguchi 2017; Fujibayashi et al. 2018, 2020; Radice et al. 2018b; Shibata & Hotokezaka 2019). Weak interactions play a key role since they can change the initially extremely low electron fraction and they are therefore of paramount importance for nucleosynthesis and the electromagnetic appearance of a BNS merger (Ruffert et al. 1997; Rosswog & Liebendörfer 2003; Dessart et al. 2009; Perego et al. 2014, 2017; Martin et al. 2015, 2018; Miller et al. 2019; Murguia-Berthier et al. 2021a).


Returning to the case of HL Tau, where the possible contribution of an infalling envelope is not an issue, how can one reconcile the strong indication of a dominant radial field component in the polarization map with the expectation that the bulk of the mm-wavelength emission originates near the disc mid-plane, where the azimuthal field component dominates? One possibility is that the non-negligible optical depth inferred in the bright emission rings of HL Tau at mm-wavelengths (Jin et al. 2016; Pinte et al. 2016) shifts the emission centroid to finite disc elevations where the magnetic field already has a measurable radial component. However, in view of the very small scale height inferred for the mm-emitting dust in this source, this is unlikely to be the main explanation. Perhaps a more likely possibility is that, even in this comparatively young source, the grains near the mid-plane, which dominate the total intensity, have already grown to sizes that exceed the maximum size $a_\mathrm{max} = \lambda /2\pi$ for producing polarized emission at wavelength λ (e.g. Cho & Lazarian 2007; for λ = 1.25 mm, amax = 0.2 mm), while the smaller grains (with sizes a amax), which contribute efficiently to the polarized flux, remain suspended at high elevations (where the field is predominantly radial). Another effect that could lower the polarized emission from grains that have settled to the mid-pane is the likelihood that grains become less elongated as they grow (e.g. Hughes et al. 2009), which would tend to reduce the value of the coefficient C in equation (2) (C → 0 as the grain axis ratio → 1).7 This interpretation is supported by the finding in the high-resolution observations of IRAS 4A (Cox et al. 2015) of an average polarization of 15 per cent at 8 mm and 10 per cent at 10 mm, with a peak fractional polarization of ∼20 per cent. If the intrinsic degree of mm-wavelength polarization in HL Tau is also of the order of 20 per cent, then it may be possible to explain the factor of ∼10 lower value of P measured in this source at 1.25 mm8 in terms of a dilution of the polarized emission from a ≲ 0.1 mm grains at high disc elevations by weakly polarized emission of larger grains residing near the mid-plane. In this scenario, most of the grains that are responsible for the mm-wavelength flux have settled to the mid-plane and grown to sizes a ≳ 1 mm.9 Although a fraction of these grains may have sizes in excess of 1 mm and would therefore emit less efficiently at that wavelength than a ≲ 1 mm grains (e.g. Miyake & Nakagawa 1993), the mid-plane region should still dominate the total mm-wavelength flux if most of the a ≳ 1 mm grains are concentrated there. Grains of size a ≲ 0.1 mm may be kept at high elevations by turbulent motions that can persist below the wind-driving surface layers (e.g. Simon et al. 2013, 2015; Bai 2015) as well as by the emerging outflows within these layers (see Safier 1993), with porosity effects (e.g. Ormel, Spaans & Tielens 2007) possibly also helping to mitigate gravity's pull towards the mid-plane. This scenario of course needs to be backed by detailed calculations and observational tests. One such test would be to obtain a polarization map of HL Tau at longer ( ≳ 1 cm) wavelengths: if the above picture is correct and the grains in the mid-plane region are aligned, such a map could reveal a stronger (or even dominant) contribution from the azimuthal and (especially if Λ0 ≪ 1) vertical field components.10 It is, however, conceivable that the large grains in this source are not well aligned because the radiative torque mechanism does not operate efficiently on them: this could happen if the characteristic wavelength of the anisotropic component of the local radiation field were much smaller than the mid-plane grain sizes (e.g. Cho & Lazarian 2007) or if the anisotropic radiation component inside the dust disc were weak due to finite optical depth effects. Note that the possibility of the mid-plane grains not being well aligned provides another reason for why the polarized mm-wavelength emission from this region could be weak.


What is the dominant mode of star formation for AGNs in general, and for quasars in particular? The main sequence gives a useful framework for discussing the evolutionary status of AGN host galaxies and their relation to the galaxy population at large. The existing literature in this field, however, is complicated enormously by the diverse strategies of AGN sample selection, the accuracy of the SFR and M* tracers, and the myriad choices of main-sequence prescription. While there is almost unanimous agreement that AGNs of low to moderate luminosity (Lbol ≲ 1045 erg s−1) at z ≈ 0–3 lie on or below the main sequence (e.g., Shao et al. 2010; Mullaney et al. 2012, 2015; Santini et al. 2012; Rosario et al. 2013a; Shimizu et al. 2015; Ellison et al. 2016; Leslie et al. 2016; Suh et al. 2017; Bernhard et al. 2019; Grimmett et al. 2020; Jackson et al. 2020), no consensus exists for AGNs with Lbol > 1045 erg s−1. The situation is particularly contentious at redshifts higher than ∼0.5, where luminous AGNs have been reported to be above (e.g., Rovilos et al. 2012; Florez et al. 2020; Kirkpatrick et al. 2020), on (e.g., Harrison et al. 2012; Xu et al. 2015; Stanley et al. 2017; Schulze et al. 2019), and below (e.g., Scholtz et al. 2018; Stemo et al. 2020) the main sequence. Fortunately, a better consensus of opinion can be found for luminous (Lbol ≳ 1045 erg s−1) AGNs at z ≲ 0.5. Most agree that low-redshift quasars are located largely on and above the main sequence (Husemann et al. 2014; Xu et al. 2015; Zhang et al. 2016; Stanley et al. 2017; Jarvis et al. 2020). Regardless of redshift, it appears that the magnitude of an AGN’s offset from the main sequence correlates positively with its luminosity (Bernhard et al. 2019; Grimmett et al. 2020). For their large sample of z ≈ 0.3 type 1 AGNs with uniform SFRs based on extinction-corrected [O II] λ3727 emission, Zhuang & Ho (2020) demonstrated that SFR systematically rises with increasing Lbol at fixed M*.


One of the fundamental tasks of the Galactic studies is to estimate the structure parameters of the major structure components. Bahcall & Soneira (1980) fit the observations with two structure components, namely a disc and a halo. Gilmore & Reid (1983) introduce a third component, namely a thick disc, confirmed in the earliest Besancon Galaxy Model (Crézé & Robin 1983). Since then, various methods and observations have been adopted to estimate parameters of the thin and thick discs and of the halo of our Galaxy. As the quantity and quality of data available continue to improve over the years, the model parameters derived have become more precise, numerically. Ironically, those numerically more precise results do not converge (see table 1 of Chang, Ko & Peng 2011, table 2 of López-Corredoira & Molgó 2014 and sections 5 and 6 of Bland-Hawthorn & Gerhard 2016, for a review). The scatters in density law parameters, such as scale lengths, scale heights and local densities of these Galactic components, as reported in the literature, are rather large. At least parts of the discrepancies are caused by degeneracy of model parameters, which in turn can be traced back to the different data sets adopted in the analyses. Those differing data sets either probe different sky areas (Bilir et al. 2006a; Du et al. 2006; Cabrera-Lavers et al. 2007; Ak et al. 2007; Yaz & Karaali 2010; Yaz Gökçe et al. 2015), are of different completeness magnitudes and therefore refer to different limiting distances (Karaali et al. 2007), or consist of stars of different populations of different absolute magnitudes (Karaali, Bilir & Hamzaolu 2004; Bilir et al. 2006b; Jurić et al. 2008; Jia et al. 2014). It should be noted that the analysis of Bovy et al. (2012), using the SEGUE spectroscopic survey, has given a new insight on the thin and thick disc structural parameters. This analysis provides estimate of their scale height and scale height as a function of metallicity and alpha abundance ratio. However, it relies on incomplete data (since it is spectroscopic) with relatively low range of Galactocentric radius as for the thin disc is concerned.