The first structures we consider are cosmic voids. Cosmic voids are defined as large underdense regions of the cosmic web, they are the largest structures in the Universe and make up most of its volume (Cautun et al. 2014; Falck & Neyrinck 2015). Historically, their existence was one of the earliest predictions of the concordance cosmological model (Hausman, Olson & Roth 1983), and their observational detection goes back to roughly 40 yr ago (Gregory, Thompson & Tifft 1978; Kirshner et al. 1981). Voids are in particular extremely underdense near their centres, and their spherically averaged density profile shows a characteristic shape (Colberg et al. 2005; Ricciardelli, Quilis & Planelles 2013; Hamaus, Sutter & Wandelt 2014a; Nadathur et al. 2014b; Ricciardelli, Quilis & Varela 2014). Recently, cosmic voids are becoming a promising cosmological probes: first they could represent a population of statistically ideal spheres with a homogeneous distribution at different redshifts which size evolution could be used to probe the expansion of the Universe using Alcock & Paczynski tests (Alcock & Paczynski 1979; Lavaux & Wandelt 2012; Sutter et al. 2012; Sutter et al. 2014b; Hamaus et al. 2015; Hamaus et al. 2016; Mao et al. 2017; Hamaus et al. 2022). Moreover, due to their low density, voids are naturally sensitive to dark energy and thus the interest to use them as probe of alternative Dark Energy models and modified gravity scenarios is increasing (Odrzywołek 2009; Lavaux & Wandelt 2010; D’Amico et al. 2011; Li 2011; Bos et al. 2012; Clampitt, Cai & Li 2013; Gibbons et al. 2014; Barreira et al. 2015; Cai, Padilla & Li 2015; Pisani et al. 2015; Zivick et al. 2015; Pollina et al. 2016; Baldi & Villaescusa-Navarro 2018), as well as the possibility of using them to put constraints on neutrinos masses (Massara et al. 2015; Kreisch et al. 2019; Contarini et al. 2021). Their imprint on the observed Cosmic Microwave Background (CMB) is also becoming an encouraging new cosmological probe, either through their Integrated Sachs-Wolfe (ISW) imprint (Baccigalupi, Amendola & Occhionero 1997; Baccigalupi 1999; Granett, Neyrinck & Szapudi 2008; Cai et al. 2014; Granett, Kovács & Hawken 2015; Hotchkiss et al. 2015; Ade et al. 2016; Nadathur & Crittenden 2016; Kovács et al. 2017; Kovács et al. 2019; Hang et al. 2021), or their lensing imprint (Cai et al. 2017; Raghunathan et al. 2020; Vielzeuf et al. 2021). Furthermore, the observed cold spot of the CMB could be explained as the imprint of the ISW sourced by very large voids along the line of sight (Rees, Sciama & Stobbs 1968; Kovac et al. 2013; Finelli et al. 2014; Nadathur et al. 2014a). Moreover, some works such as Jamieson & Loverde (2019) studied the properties of the voids via the separate universe technique. Finally, some studies tried to link high redshift intergalactic voids in the transmitted Lyman-α flux to the gas density (Viel, Colberg & Kim 2008). Because they are almost empty regions, their evolution during cosmic history is at most weakly non-linear and their properties could possibly be impacted by the primordial density fields from which they formed. This fact motivates us to investigate the effects of baryon-CDM relative perturbations on these objects and their statistics.


To determine the median spectral index and the variation within the sample we perform a bootstrap analysis, randomly drawing from our sample (with replacement) and median stacking both the LoTSS and FIRST cutouts independently to obtain a median peak pixel flux density measurement in each survey. This is then repeated 10 000 times to produce a distribution that also incorporates uncertainties due to sample variation. The 16th and 84th percentile of the resulting peak flux density distributions, together with the systematic flux scale density uncertainty of 5% (White et al. 1997) and 10% (Shimwell et al., in prep.) for the FIRST and LoTSS survey, respectively, are used to determine the error on the spectral index. This stacking procedure is done for all 93 quasars that overlap with FIRST (red) and for only the 35 sources detected by LoTSS with S/N > 2 that overlap with FIRST (grey), resulting in spectral indices of

−
0
.

29

−
0.09

+
0.10

$ -0.29^{+0.10}_{-0.09} $

 and

−
0
.

24

−
0.22

+
0.09

$ -0.24^{+0.09}_{-0.22} $

, respectively. Six of the FIRST detected quasars have spectral indices higher than these stacked values, which is as expected because these flat or positive spectral index quasars are naturally selected because of the FIRST flux limit of ∼144 μJy, which is shallower than the LOFAR flux limit assuming a negative spectral index. In general, LOFAR detected quasars are brighter at 144 MHz than the non-detected ones, therefore one might expect the stacked S/N > 2 sample to result in a steeper spectral index than when stacking all quasars. However, given the uncertainties on the median spectral index there is no significant deviation found between the two. In this work, we therefore assume a spectral index of −0.29±0.10 for the quasars not detected by FIRST when converting radio fluxes to luminosities. This spectral index is in line with the previous work of Gürkan et al. (2019), who found a median spectral index of −0.26 ± 0.02 for a large sample of optically selected quasars at z ≲ 3.


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


The E-MOSAICS project (Pfeffer et al. 2018; Kruijssen et al. 2019a) is a suite of cosmological, hydrodynamical simulations of galaxy formation in the Λ cold dark matter cosmogony that couples the MOSAICS model for star cluster formation and evolution (Kruijssen et al. 2011; Pfeffer et al. 2018) to the EAGLE model of galaxy formation and evolution (Crain et al. 2015; Schaye et al. 2015). The simulations are run with a highly modified version of the N-body, smoothed particle hydrodynamics code gadget3 (last described by Springel 2005). Bound galaxies (subhaloes) were identified within the simulations using the subfind algorithm (Springel et al. 2001; Dolag et al. 2009), in the same manner as in the EAGLE simulations (for details see Schaye et al. 2015). EAGLE includes subgrid routines describing radiative cooling (Wiersma, Schaye & Smith 2009a), star formation (Schaye & Dalla Vecchia 2008), stellar evolution, and mass-loss (Wiersma et al. 2009b), the seeding and growth of black holes (BHs) via gas accretion and BH–BH mergers (Rosas-Guevara et al. 2015), and feedback associated with star formation and BH growth (Booth & Schaye 2009). As current cosmological simulations lack the resolution and physics necessary to compute the feedback efficiencies from first principles, the stellar and active galactic nuclei feedback parameters are calibrated such that the simulations of cosmologically representative volumes reproduce the galaxy stellar mass function, galaxy sizes, and BH masses at z ≈ 0. The EAGLE simulations successfully reproduce a range of galaxy properties, including the stellar masses (Furlong et al. 2015) and sizes (Furlong et al. 2017) of galaxies, their luminosities and colours (Trayford et al. 2015), their cold gas properties (Lagos et al. 2015, 2016; Bahé et al. 2016; Marasco et al. 2016; Crain et al. 2017), and the properties of circumgalactic and intergalactic absorption systems (Rahmati et al. 2015, 2016; Oppenheimer et al. 2016; Turner et al. 2016, 2017). The simulations also largely reproduce the cosmic SFR density and relation between specific SFR and galaxy mass (Furlong et al. 2015). The simulations are therefore ideal for comparisons with observed galaxy populations.


The detailed kinematic reconstruction of the Sgr tidal debris by Law & Majewski (2010) used an initial total mass of

 M⊙ for the Sgr satellite. However, several studies point to a Sgr remnant mass significantly exceeding that value. Ibata et al. (1997) and Ibata & Lewis (1998) estimate lower bounds of 109 M⊙ for the mass of the dwarf today. With the discovery of previously unseen branches of the stream, the total luminosity budget of the progenitor galaxy is now believed to be on the order of 108 L⊙ (Niederste-Ostholt et al. 2010). As a result, recent studies have shifted to using dark-matter halo masses as large as 1011 M⊙ (Purcell et al. 2011; Gòmez et al. 2015) based on halo abundance matching arguments. Such high values are comparable to the mass of the LMC progenitor (see e.g., Jethwa et al. 2016; Peñarrubia et al. 2016) and imply a mass ratio relative to the MW on the order of 1:10. However, unlike the Magellanic Clouds, which may be on their first passage near the MW (Besla et al. 2007), Sgr is known to have experienced multiple close passages in the past. If true, such high Sgr progenitor masses would have important implications for the formation and evolution of the MW disk (e.g., Purcell et al. 2011; Gòmez et al. 2013; D’Onghia et al. 2016). Because the dynamical friction force is proportional to the square of the satellite mass, we expect drag to play a much more important role in slowing down the Sgr satellite and bringing it to closer galactocentric distances. Here, we perform an exploration across orbital angular momentum parameter space analogous to Section 3.1, this time using a Sgr progenitor mass of 6×1010 M⊙ according to the recent estimates of Gibbons et al. (2017). We consider two possibilities: a “slow sinking” scenario in which, as in Section 3, Sgr crosses the MW virial radius at

 (approximately 8 Gyr ago), and a “rapid sinking” scenario, in which we examine a first infall around

, about 4 Gyr ago.


Rather than AGN feedback, it is possible that the effects we are seeing are from a different process coeval or prior to the onset of AGN accretion. Several works have pointed out that AGN activity coincides with a recent starburst, with the AGN having significant accretion events at least ∼200 Myr after the starburst has occurred (Davies et al. 2007; Wild et al. 2007; Wild, Heckman & Charlot 2010; Yesuf et al. 2014) giving the neutral material time to propagate out to the impact parameters probed by COS-AGN (Heckman et al. 2017). With a sample of QSO sightlines probing the CGM around 17 low-redshift starburst and post-starburst galaxies, Heckman et al. (2017) have observed a similar signature of enhanced EWs of Ly α, Si iii, and C iv (the latter of which is not measured in our control sample) relative to a control-matched sample (matched in stellar mass and impact parameter). In the range of impact parameters and stellar masses probed by COS-AGN, the strength of our enhanced EW signature is consistent with the values probed by Heckman et al. (2017). However, the results of Heckman et al. (2017) show strong offsets in the kinematics of the gas from the host galaxy (≈100 km s−1; see fig. 5 from Heckman et al. 2017), whereas the COS-AGN sightlines do not (bottom panel of Fig. 6). Assuming that the AGN activity was triggered by the starburst, a minimum delay time of 200 Myr could allow for any starburst-driven winds to dissipate and kinematic offsets to no longer be present at the impact parameters of the COS-AGN sample. Although this starburst picture provides a possible explanation of our observations, we caution that starbursts are not the only astrophysical event linked to AGN accretion activity. For example, mergers that trigger the AGN (Ellison et al. 2011, 2013; Satyapal et al. 2014; Silverman et al. 2014; Goulding et al. 2018) could potentially affect the surrounding CGM gas. Past and future work focusing on the CGM of galaxy mergers can further test this result (Johnson et al. 2014; Hani et al. 2017; Bordoloi et al. in preparation).


A tidal disruption event (TDE) is an astronomical phenomenon that occurs when a star gets too close to a supermassive black hole in the galaxy center and is disrupted by the tidal force of the black hole. Part of stellar material is bound and accreted by the central black hole, resulting in bright optical, UV, and soft X-ray emission (Rees 1988; Lodato et al. 2015 and references therein). There are a growing number of candidate TDEs being discovered in soft X-ray, ultraviolet, and optical surveys; see Komossa (2015) for a recent review. Recently, three unusual TDE candidates have been discovered by Swift, i.e., Swift J164449.3+573451, Swift J2058.4+0516, and Swift J1112.2-8238 (hereafter Sw J1644+57, Sw J2058+05, and Sw J1112-82 for short, respectively), which have very bright nonthermal hard X-ray and radio emissions (Bloom et al. 2011; Burrows et al. 2011; Krimm et al. 2011a, 2011b; Zauderer et al. 2011; Cenko et al. 2012; Brown et al. 2015). The luminous nonthermal X-ray and radio emissions are thought to be produced by relativistic jets (Bloom et al. 2011; Burrows et al. 2011; Levan et al. 2011; Zauderer et al. 2011; Cao & Wang 2012; Metzger et al. 2012; Wang et al. 2014; Liu et al. 2015). Sw J1644+57 shows a highly variable light curve in X-rays, as observed by the X-ray Telescope on board Swift. At redshift

, the isotropic luminosity of the X-ray emission is as high as

 erg s−1. Sw J2058+05 exhibits a luminous, long-lived X-ray outburst with an isotropic peak luminosity of

 (at redshift

). Its total isotropic energy (0.3–10 keV) on a timescale of the first 2 months amounts to 1054 erg. Sw J1112-82 was initially also discovered by Swift/BAT (Burst Alert Telescope) in 2011 June as an unknown, long-lived (order of days) γ-ray transient source. It exhibits a similar bright X-ray flare, and its position is consistent with the nucleus of a faint galaxy at

 (Brown et al. 2015). The peak X/γ-ray luminosity of Sw J1112-82 exceeds

.


Kennicutt & Evans (2012) present a compilation of disk-averaged SFR and gas mass surface densities whose values have been calculated in a uniform manner across different galaxy types (including normal disk galaxies and dusty starburst galaxies selected in the IR) and find a power-law index of n ∼ 1.4. However, this result may be an artifact of combining galaxies of different interaction states. For a sample of z ∼ 1–3 MS galaxies, Tacconi et al. (2013) find an index consistent with unity and only a slight offset between their high-redshift sample and a low-redshift sample with similar masses. However, SMGs and other ultra-/luminous infrared galaxies (U/LIRGs) are further offset above the correlation for star-forming disk galaxies even when similar CO-to-H2 conversion factors are used for all galaxy populations (see also Bigiel et al. 2008; Daddi et al. 2010b; Genzel et al. 2010, 2015; Tacconi et al. 2018). In analyses of the resolved star formation properties of nearby disks, a near-unity index for the Schmidt–Kennicutt relation is also found in regimes where the molecular gas dominates the total gas mass surface density (Σgas >9 M⊙ pc−2; e.g., Bigiel et al. 2008, 2010; Schruba et al. 2011). The surface density version of the Schmidt–Kennicutt relation has been evaluated within only eight high-redshift galaxies: SMM J14011+0252 at z = 2.56 (Sharon et al. 2013), EGS 13011166 at z = 1.53 (Genzel et al. 2013), HLS 0918 at z = 5.24 (Rawle et al. 2014), GN20 at z = 4.05 (Hodge et al. 2015), PLCK G244.8+54.9 at z = 3.00 (Cañameras et al. 2017), AzTEC-1 at z = 4.34 (Tadaki et al. 2018), and the two components of HATLAS J084933 at z = 2.41 (Gómez et al. 2018).9

9
Freundlich et al. (2013) and Sharda et al. (2018) also examine the Schmidt–Kennicutt relation at z > 1, but they analyze individually resolved clumps within high-redshift galaxies rather than performing full pixel-by-pixel comparisons.
 These studies find a range of Schmidt–Kennicutt relation indices (n = 1–2). It is particularly worth noting that Genzel et al. (2013) find that their measured index depends strongly on which spatially resolved extinction correction they apply to their Hα measurements.


The detection criterion of having the full interval α ± σα inside the prior range [0.8, 1.2] (e.g., Ata et al. 2018; Chan et al. 2018) has commonly been employed in the literature. However, we can observe from these analyses that the distribution of the α parameter in general seems to be more Gaussian than what we find in our analyses (left panels in Figs. 3 and 4). A possible reason for this is the lower redshift we considered here, where the contribution from nonlinear effects is stronger. However, results from Villaescusa-Navarro et al. (2017), who investigated the BAO detection from 21 cm signal for the SKA case for the redshift range 0.35  z  3.05, also showed α distributions with clear deviations from a perfect Gaussian (but note the smaller number of simulations employed there, namely, 100). As pointed out by Chan et al. (2018) and Abbott et al. (2022), a natural consequence from having a (approximate) Gaussian distribution is a reasonable concordance among the three different error measurements, that is, ⟨σα⟩∼σ68 ∼ σstd. This is not our case, as can be seen from Tables 2 and 3 (as well as from Tables 4 and 5), indicating that ⟨σα⟩ is not meaningful or representative of the error in the α measurements for individual mock realizations (see also Figs. 3 and 4). Our results show that compared to ⟨σα⟩, the errors given by σ68 are overestimated by ∼18% to 33%, from the smallest to the highest z-bins when the ACF is used, but is underestimated by ∼50% for APS. Moreover, comparing the expected

σ
α
m

$ \sigma^m_\alpha $

 obtained fitting the mean Cℓ and ω(θ) to the average ⟨σα⟩, we find a reasonable agreement for intermediate and higher z-bins, but not for the lower z-bins, in particular, for the ACF estimator. In addition, although σstd agrees better with σ68, we still find non-negligible differences among them, which confirms our α distributions as non-Gaussian (a larger σstd indicates non-Gaussian tails). These reasons motivated our choice of using the α values instead of α ± σα ranges, which belong to the interval [0.8, 1.2] as a criterion for a BAO detection (defining the Nd fraction), as well as our choice of using the 68% spread of the α distributions, σ68, as the representative error in our measurements.


The clearest examples of host–AGN interaction are arguably found in nearby brightest cluster galaxies. The AGN in these systems have been shown to deposit vast amounts of energy into the surrounding intracluster medium via heating and (mega-parsec scale) jets both observationally and by means of modelling (e.g. Binney 2004; Scannapieco, Silk & Bouwens 2005; Gitti, Brighenti & McNamara 2012, for a review; English, Hardcastle & Krause 2016), which maintain the hot-gas reservoirs in these systems, prevent cooling flows, and thus suppress star formation (e.g. Binney & Tabor 1995; Li et al. 2015). In lower density environments (where the majority of galaxies live), the empirical picture is much less clear. Direct observational evidence for AGN feedback on galactic scales in such environments remains sparse. More specifically, while outflows have been observationally detected in a number of instances around AGN in various gas phases, most of these detections have been made in ultra-luminous infrared galaxies or some of the closest quasar–host galaxies (e.g. Rupke, Veilleux & Sanders 2005b; Nyland et al. 2013; Harrison et al. 2014), with only a few examples where the AGN have been shown to couple with kpc-scale outflows that are capable of impacting star-formation on galactic scales (for a review Cicone et al. 2014; Harrison 2017). Thus, it is still unclear to what extent the general AGN population could drive kpc-scale galactic outflows capable of possibly limiting or quenching star-formation in the local Universe. Indeed, recent observational work has cast doubt on the ability of AGN to directly regulate star formation in the nearby Universe. For example, Schawinski et al. (2014) found that black hole accretion occurs preferentially in quenched galaxies that experienced a rapid decay of their star-formation rates. Based on stellar population analysis, such a time delay between the peak of star formation and the onset of AGN activity has been reported to be of at least several dynamical time-scales (e.g. Kaviraj et al. 2015; Shabala et al. 2017, for radio and e.g. Schawinski et al. 2007; Kaviraj 2009; Wild, Heckman & Charlot 2010 for optical). AGN may therefore not play a significant direct role in regulating their associated star formation episodes as they would not couple directly to the cold-gas reservoir (see, e.g. the models of Kaviraj et al. 2011). Using observations for cold-gas outflows, this has been directly confirmed for radio AGN, which are found to couple mainly to residual gas in galaxies where the gas reservoir is already significantly depleted (e.g. Sarzi et al. 2016). A fuller understanding of the role of AGN in regulating star formation demands a direct study of whether outflows of neutral material (which are ultimately responsible for quenching star formation) are more likely launched in AGN hosts. Most importantly, a quantitative statement about the putative role of AGN in influencing the evolution of their host galaxy requires a study that employs a complete sample of such AGN in the local Universe. Performing such an analysis is the purpose of this paper.


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


In our study, we consider that the accretion disc is threaded by the poloidal magnetic field lines. The initial poloidal field lines are prescribed by implementing a vector potential Aϕ following Zanni et al. (2007) and Vourellis et al. (2019). The functional form of the vector potential is given by
(6)$$\begin{eqnarray}
A_\phi \propto \left(r \sin \theta \right)^{3/4} \frac{m^{5/4}}{\left(m^2 + \tan ^{-2}(\theta -\pi /2)\right)^{5/8}}.
\end{eqnarray}$$The parameter m(= 0.1) is related to the initial inclination of the field lines and it also determines the magnetic flux of the system. The parameter m play crucial role in the launching of Blandford–Payne type wind from the accretion disc (Blandford & Payne 1982; Dihingia et al. 2021). The initial strength of the poloidal magnetic field is determined by the choice of the plasma-β parameter at the truncation radius rtr on the equatorial plane as, $\beta _{\rm tr} = p_{\rm gas}^{\rm tr}/p_{\rm mag}^{\rm tr}$. Here, superscript ‘tr’ denotes quantities calculated at the r = rtr. Following our motivation, we carry out eight axisymmetric simulation models, by choosing different truncation radius (rtr), initial plasma-β (βtr), effective resolution (with AMR), and magnetic resistivity. For axisymmetric models, we consider the highest effective resolution to be 2048 × 1024 (with three refinement levels). The list of input parameters, effective resolution, and the final simulation time (tfinal) for all the simulation models are shown in the Table 1. Out of all these models, we consider 2D40AH to be our reference model for the sake of explanation and comparison. In Fig. 1, we show the initial density distribution (log (ρ/ρtr)) and the initial gas pressure distribution $(\log (p_{\rm gas}/p_{\rm gas}^{\rm tr}))$ for the reference model at panels (a) and (b), respectively. In panel Fig. 1(a), we also show the initial magnetic field lines in terms of grey lines. In Fig. 1(b), the white line represent the boundary of plasma-β = 1. In the figure, the density distribution follows equation (2) outside the truncation radius (rtr = 40). Near the equatorial plane, the matter distribution is gas pressure dominated, and far from the equatorial plane and inside the truncation radius, the matter distribution is magnetic pressure dominated.


As a first step to analysis of NU Ori’s magnetic field, least-squares deconvolution (LSD) profiles were extracted using a line mask developed from an extract stellar request from the Vienna Atomic Line Database 3 (VALD3; Piskunov et al. 1995; Ryabchikova et al. 1997, 2015; Kupka et al. 1999, 2000) using the stellar parameters determined for NU Ori Aa (Teff = 30.5 ± 0.5 kK, log g = 4.2 ± 0.1) by Simón-Díaz et al. (2011). These parameters were selected since Petit et al. (2008) identified the Aa component as the magnetic star, given that the Stokes V signature is much wider than the $v$sin i of the secondary component. The line mask was cleaned of all H lines, as well as lines strongly blended with H line wings, lines in spectral regions strongly affected by telluric contamination, lines blended with nebular or interstellar features, and lines in spectral regions affected by ripples. While He lines are often removed due to substantial differences between magnetometry results obtained from He versus metallic lines (e.g. Shultz et al. 2015, 2018b; Yakunin et al. 2015), in this case He lines were left in the mask since the majority of the Stokes V line flux comes from these lines, and the Stokes V profiles extracted using a line mask with He lines excluded did not result in detectable Zeeman signatures. Because of the very high $v$sin i of the Aa component, LSD profiles were extracted using a velocity range of ±600 km s−1 (in order to include enough continuum for normalization) and a velocity pixel size of 7.2 km s−1, or four times the average ESPaDOnS velocity pixel (thus raising the per pixel S/N by about a factor of 2). The significance of the signal in Stokes V was evaluated using false alarm probabilities (FAPs), with observations classified as definite detections (DDs), marginal detections (MDs), or non-detections (NDs) according to the criteria described by Donati, Semel & Rees (1992) and Donati et al. (1997). Since FAPs essentially evaluate the statistical significance of the Stokes V signal inside the stellar line by comparing it to the noise level, they are primarily sensitive to the amplitude of Stokes V, which unlike 〈B$z$〉 is not strongly dependent on rotational phase. FAPs are thus a complementary means of checking for the presence of a polarization signal, the principal advantage being that they can detect a magnetic field even at magnetic nulls, i.e. 〈B$z$〉 = 0.


Most GCs are now found to host multiple populations through photometry and spectroscopy (e.g., Carretta et al. 2010b; Mészáros et al. 2015; Milone et al. 2015; Piotto et al. 2015; Tang et al. 2017, 2018). Chemical abundances from spectroscopic data suggest that GCs have a group of so-called “second generation” (SG) stars with enhanced N and Na (sometimes He and Al), but depleted C and O (sometimes Mg). These kinds of stars presumably are only formed in the dense environments of GCs. Therefore, identifying field stars with an SG-like chemical pattern is a feasible way to find a link between field stars and GC ejection/dissolution. Thanks to large spectroscopic surveys, the search for these chemically peculiar stars is becoming more efficient. Using high spectral resolution surveys, multiple elements, like C, N, O, Na, Mg, and Al, can be measured, depending on the wavelength range and signal-to-noise ratio. Toward this, the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017) and Gaia-ESO survey have led to the discovery of a large group of N-rich field stars (Lind et al. 2015; Fernández-Trincado et al. 2016, 2017, 2019a; Martell et al. 2016; Schiavon et al. 2017). While high-resolution spectra give more elements for a detailed investigation of their chemical history, low-resolution spectra can supposedly extend the search for N-rich field stars toward fainter and more numerous samples (Martell & Grebel 2010; Martell et al. 2011; Koch et al. 2019). Simultaneously observing 4000 stars with fibers makes LAMOST an unprecedented machine in collecting low-resolution stellar spectra. Using the CN–CH band features around 4000 Å, we have identified ∼40 N-rich field stars8

8
Also called CN-strong, CH-normal stars in Paper I.
 in LAMOST DR3 (Tang et al. 2019, hereafter Paper I). The derived N abundances of these stars are clearly higher than those of the metal-poor field stars, indicating that (1) our sample is a bona fide sample of N-rich field stars and (2) the classical extra-mixing theory may not work for these stars. Moreover, a substantial fraction of retrograding N-rich field stars suggest that some N-rich field stars may be accreted. In this work, we expand our sample to ∼100 N-rich field stars in LAMOST DR5 (Section 2), making it more robust for drawing statistical conclusions, especially for the GC origin of these field stars. We put forward a detailed analysis of high-resolution chemical abundances and kinematics (Sections 3 and 4) to discuss the origins of these N-rich field stars (Section 5). As the second paper of this series, we will also call this present work Paper II.


The distribution function of the electrons inside the precursor can be formally determined through a Lorentz transform of the corresponding distribution function in the shock frame, and the latter can be obtained by solving a stationary transport equation with a loss term corresponding to the finite residence time spent in the precursor. Here, we approximate this distribution function in the precursor frame as follows: (3)\begin{equation} \frac{{\rm d}n_{\rm e\vert\rm p}}{{\rm  d}\gamma_{\rm e}}\,\simeq\,\frac{R^2}{r^2}\, \frac{\vert  s-1\vert}{\gamma_{\rm m\vert p}}\left(\frac{\gamma_{\rm e}}{\gamma_{\rm  m\vert p}}\right)^{-s}\, 2\Gamma_{\rm sh}^2n_{\rm  u}\,\Theta\left[r_{\rm p}(\gamma_{\rm e})-r\right].  \label{eq:dndg1} \end{equation}dne|pdγe ≃ R2r2 |s−1|γm|pγeγm|p−s 2Γsh2nu Θ[rp(γe)−r].The Heaviside function models the finite length scale up to which particles of a given Lorentz factor can travel. This precursor length scale is related to the (upstream frame) residence time tres through \hbox{$r_{\rm p}\,=\,R+c t_{\rm res}\left(1-\beta_{\rm sh}\right)\,\simeq\,R+ct_{\rm res}/(2\Gamma_{\rm sh}^2)$}rp = R+ctres1−βsh ≃ R+ctres/(2Γsh2). The residence time can be calculated as the time it takes to deflect the accelerated electron by an angle ~1/Γsh (Achterberg et al. 2001; Milosavljević & Nakar 2006; Pelletier et al. 2009). If the background magnetic field controls the transport of the accelerated electrons, this residence time is \hbox{$t_{\rm res}^{(1)}\,\simeq\,\Gamma_{\rm sh}^{-1}\gamma_{\rm e} m_{\rm e} c/(e B_{\rm u})$}tres(1) ≃ Γsh-1γemec/(eBu). In contrast, if pitch angle scattering in a micro-turbulence of length scale λδB governs the return of particles to the shock, \hbox{$t_{\rm res}^{(2)}\,\simeq\,\Gamma_{\rm sh}^{-2}\gamma_{\rm e}^2m_{\rm e}^2c^3/(\lambda_{\delta B}e^2\delta B_{\rm p}^2)$}tres(2) ≃ Γsh-2γe2me2c3/(λδBe2δBp2). Whether one or the other occurs depends on γe and the hierarchy between Bu and δBp. As the scattering frequency in a micro-turbulence scales as \hbox{$\gamma_{\rm e}^{-2}$}γe-2, while the gyrofrequency scales with \hbox{$\gamma_{\rm e}^{-1}$}γe-1, we expect the background field to control the residence time at higher energies. In order to bracket this realistic scenario, we consider in the following the above two extremes: (1) where regular deflection in a background field dominates at all energies and (2) where stochastic deflection in a small scale micro-turbulence of uniform energy density dominates at all energies. Correspondingly, we write \hbox{$r_{\rm p}(\gamma_{\rm e})=R+\Delta_i\gamma_{\rm e}^i$}rp(γe)=R+Δiγei, with i = 1,2 for models (1) or (2); \hbox{$\Delta_i=ct_{\rm res}^{(i)}/(2\Gamma_{\rm sh}^2)$}Δi=ctres(i)/(2Γsh2).


Many factors can affect the prevalence of AGN activity. One important question is how gas is brought down to the galaxy center to fuel supermassive black holes (SMBHs). In the literature, two kinds of mechanisms are proposed. One is the internal secular evolution process. The torque induced by non-axisymmetric galactic structures can drive slow and significant inflow (Kormendy & Kennicutt 2004; Hopkins & Quataert 2011; Sellwood 2014; Fanali et al. 2015). The galactic bar is one of the most prominent non-axisymmetric structures and it exists in about 40% of spiral galaxies (Oh et al. 2012). In addition, there is evidence demonstrating that bars can enhance star formation in the central regions of galaxies (e.g. Oh et al. 2012; Chown et al. 2019). However, the question of whether galactic bars can significantly affect AGN activity is still under debate (Arsenault 1989; Mulchaey & Regan 1997; Oh et al. 2012; Galloway et al. 2015; Goulding et al. 2017; Alonso et al. 2018). Other mechanisms, such as galaxy merger and interaction, are also expected to displace the angular momentum of the gas and transport the gas inward (e.g. Hopkins et al. 2006; Di Matteo et al. 2008; Bhowmick et al. 2020). Similarly to studies of secular evolution, observational evidence for this scenario is also mixed. Some studies have found significant environmental dependence of AGN activity (e.g. Koulouridis et al. 2006; Koss et al. 2010; Ellison et al. 2011; Sabater et al. 2013; Khabiboulline et al. 2014; Lackner et al. 2014; Satyapal et al. 2014; Hong et al. 2015; Kocevski et al. 2015; Goulding et al. 2018; Gao et al. 2020), while others have found no or only weak environmental effects (e.g. Grogin et al. 2005; Li et al. 2006a, 2008; Pierce et al. 2007; Ellison et al. 2008; Gabor et al. 2009; Darg et al. 2010; Wang & Li 2019; Man et al. 2019). The contradictory results may be caused by the difference in AGN selection criterion, observational bias, control sample, and environmental indicator used. As we show below, understanding the environmental effects on AGNs also requires knowledge about the evolutionary status of their host galaxies, as it can help us to better understand how to construct control samples and to adopt appropriate environmental indicators.


Nearly all of the cm-wavelength radio emission from star-forming galaxies, such as SMGs, is non-thermal synchrotron radiation from relativistic electrons accelerated in supernova (SN) remnants produced by the short-lived, high-mass OB-type stars (M ≳ 8 M⊙; main-sequence lifetime τMS ≲ 30 Myr). Because SNe trace the recent/on-going star formation, the radio synchrotron emission has the potential to trace the spatial scales on which star formation is occurring. This connection between radio emission and star formation is strongly supported by the close infrared (IR)-radio correlation observed in galaxies (e.g. Helou et al. 1985; Beck & Golla 1988; Xu et al. 1992; Condon 1992; Yun et al. 2001; Bell 2003; Tabatabaei et al. 2007; Murphy et al. 2008; Sargent et al. 2010; Morić et al. 2010; Dumas et al. 2011). On the basis of this correlation, the IR-emitting region of a star-forming galaxy is expected to be comparable in size to that of radio continuum emission. However, the most recent studies of the sizes of IR-emitting regions of SMGs based on continuum imaging observations with the Atacama Large Millimetre/submillimetre Array (ALMA) show that these are significantly smaller than SMG radio sizes presented in the literature (Simpson et al. 2015a; Ikarashi et al. 2015). A possible explanation for this discrepancy, as suggested by Simpson et al. (2015a), is cosmic ray (CR) diffusion in the galactic magnetic field away from their acceleration site, which would render larger radio sizes. To test this further here we present a study of radio sizes of SMGs from a well selected sample of SMGs in the Cosmic Evolution Survey (COSMOS; Scoville et al. 2007) deep field using radio data from the Karl G. Jansky Very Large Array (VLA)-COSMOS 3 GHz Large Project (1σ noise of 2.3 μJy beam-1, angular resolution \hbox{$0\farcs75$}0 .̋ 75; Smolčić et al., in prep.). We describe the SMG sample and the employed VLA data in detail in Sect. 2. The 3 GHz images are presented in Sect. 3, and the analysis (size measurements and radio spectral indices) are presented in Sect. 4. We compare our results with literature studies in Sect. 5, discuss the results in Sect. 6, and summarise the main results of the paper in Sect. 7.


As in Flowers et al. (2019), to compare our model transmission spectra directly against the Ehrenreich et al. (2020) results, we must calculate the transmission spectra as a function of orbital phase throughout the duration of transit. To account for orbital phase dependencies, we apply the following procedure:1.Account for phase-dependent backlighting of the planet (i.e., stellar limb-darkening effects). At different points of its transit, the planet will occult regions of its host star of varying brightness. Furthermore, at a fixed orbital phase, different regions of the planet’s limb will be backlit by varying intensities of stellar light. Similar to Flowers et al. (2019), we calculate the normalized stellar intensity at the center of each cell of the 2D projected planetary grid produced by our GCM at each modeled orbital phase of the planet. We use the quadratic limb-darkening coefficients reported by Ehrenreich et al. (2020) to establish the stellar center-to-limb intensity profile, and we take into account the 89.°623 orbital inclination of WASP-76b (Ehrenreich et al. 2020) to determine where the planet resides on the stellar disk as a function of its orbital phase. We make the assumption of constant impact parameter b over the course of transit.
9

9
In reality, a planet on an inclined orbit will not have a constant b over the entire duration of transit; rather, the planet’s distance from the stellar equator will be decreased at ingress and egress, reaching its maximum at center of transit. Our tests reveal that, for WASP-76b, the relative error induced by the constant b assumption is on the order of 4% in distance, which results in a change on the order of 1 m s−1 at the blueshift level (see Section 3.1). Hence, our b treatment is justified. This procedure allows us to calculate a backlighting factor f, which ranges from 0 to 1, effectively replacing the constant I

λ,0 from Equation (3) with a variable

Iλ,0×f(θ′,z,φ)

, for a given orbital phase φ and 2D projected polar angle

θ′

.2.Account for the decreasing of the continuum by interpolating a light curve produced by the batman code (Kreidberg 2015). Step 1 ensures that less light is transmitted through the planet’s atmosphere than a uniform stellar disk would emit. Step 2 further enforces that the inner, optically thick core of the planet is simulated crossing a limb-darkened star, as opposed to a star of uniform brightness.3.Account for the planet’s rotation over the course of transit. Because the planet is continually rotating as it travels across the face of its host star, we must transform the GCM coordinate system so that the correct observer-facing hemisphere is modeled at each instance during transit. For simplicity, we assume zero obliquity, which allows us to calculate the coordinate transform simply by assigning a linear offset to each planetary longitude; i.e., ϕ
rotated = ϕ + φ.


Galactic winds: Galactic winds driven by CRs have often been simulated in two limits: a diffusion-dominated regime, due possibly to ‘extrinsic confinement’, where CRs are scattered by extrinsic turbulence, and/or due to various wave damping mechanisms (e.g. ion neutral damping) and streaming-dominated ‘self confinement’, where CRs are confined by Alfven waves they produce via the gyroresonant streaming instability. In the diffusive ‘extrinsic confinement’ case, CRs do not heat the gas.19 In the streaming dominated ‘self confinement’ case, CR transport heats gas at a rate vA · ∇Pc. The diffusive case fits γ ray observations better, because CRs can propagate out of the galaxy faster (Chan et al. 2019). It is also much better at driving winds, because the CRs do not suffer strong energy losses via Alfven wave heating (Wiener et al. 2017b; Hopkins et al. 2020). However, we expect self-confinement to be very strong at the ∼GeV energies where CR energy peaks (Kulsrud & Pearce 1969; Farmer & Goldreich 2004; Wiener et al. 2013), while extrinsic compressible turbulence is strongly damped at small scales, and unlikely to efficiently scatter ∼GeV CRs (Yan & Lazarian 2002). Thus, CR winds should be streaming dominated and relatively inefficient. The CR staircase changes these dichotomies by changing the structure of the wind. We have seen how CR pressure can build up in streaming dominated simulations, due to trapping at bottlenecks. This increases mass outflow rates, similar to the effect of increased opacity in radiative outflows. In CR streaming simulations of isothermal winds where the CR acoustic instability arose, Quataert et al. (2022a) found an increase in wind mass loss rates by an order of magnitude, compared to analytic models without a CR staircase, illustrating the potential impact of CR staircases. High-resolution cosmological zoom simulations of CR staircases are actually well within reach. As seen in Appendix Section B, all that is required is that the diffusion length $l_{\rm diff} \sim \kappa /c_{\rm s} \sim 2 \, {\rm kpc} \, \left(\frac{\kappa }{10^{29} {\rm cm^2 s^{-1}}} \right)\left(\frac{c_{\rm s}}{150 \, {\rm km \, s^{-1}}} \right)^{-1}$ is resolved. However, to date only the FIRE collaboration has implemented the two moment method (capable of dealing with CR streaming) in such simulations, and – in contrast to, for instance, van de Voort et al. (2021) – the plasma β in their winds is too high for the acoustic instability to develop (Hopkins et al. 2020). But alternate setups where CR staircases appear are certainly numerically feasible.


MRI is considered to be the most promising mechanism driving angular-momentum transport in protoplanetary disks (Balbus & Hawley 1991; Brandenburg et al. 1995; Hawley et al. 1995; Balbus et al. 1996; Balbus & Hawley 1998). However, protoplanetary disks are cold, dense, and, therefore, poorly ionized. The low level of ionization tends to decouple the disk gas from magnetic fields, which generates non-ideal MHD effects: Ohmic dissipation, ambipolar diffusion (AD), and the Hall effect (e.g., Armitage 2011; Turner et al. 2014). These effects quench MRI in different ways: Ohmic dissipation originates from collisions between electrons and neutrals, AD from collisions between ions and neutrals, and the Hall effect from drift between electrons and ions (Fleming et al. 2000; Sano & Stone 2002; Bai & Stone 2011). Ohmic dissipation operates in high-density regions with weak field, AD dominates in highly ionized and low-density regions, and the Hall effect lies in between (Fleming & Stone 2003; Bai & Stone 2011; Bai 2014). So far, the effect of Ohmic dissipation has been best studied. Investigations show the layered accretion in the inner disk, where the midplane region is “dead” due to low ionization while the surface layer is “active” due to sufficient ionization (Gammie 1996; Jin 1996; Fleming et al. 2000; Fleming & Stone 2003; Turner et al. 2007; Ilgner & Nelson 2008; Oishi & Mac Low 2009; Okuzumi & Hirose 2011). Recent works that take into account both Ohmic dissipation and AD show that AD may render the surface layer and portions of the outer disk inactive (Bai & Stone 2011; Landry et al. 2013; Kalyaan et al. 2015). Bai & Stone (2013) find that MRI is completely suppressed in the inner disk and a strong magnetocentrifugal wind is launched. Three-dimensional simulations that include all three non-ideal MHD effects are also performed (Bai 2014, 2015; Lesur et al. 2014; Simon et al. 2015). In the inner disk, the influence of the Hall effect on midplane angular-momentum transport depends on the orientation of the vertical magnetic field with the disk rotation axis. When the field is aligned with the axis, the enhanced Maxwell stress promotes angular-momentum transport. When the field is anti-aligned with the axis, the midplane remains quiescent. In the outer disk, the Hall effect has little influence on the disk turbulence. Although the inclusion of AD and the Hall effect substantially changes the level of turbulence in the protoplanetary disks, the feature that the viscosity is low in the inner disk and high in the outer disk is still valid. In this study, we assume that gas giant planets form in situ via the core accretion scenario, which implies that their formation locations are always in the low-viscosity region. Since in this study we focus on the relation between photoevaporation and planet formation and gap opening by planets in the disk, we adopt Ohmic dissipation to represent the non-ideal MHD effects on the MRI. We consider that this simplification has little influence on our main calculation results.


An increasing number of recent works focus on the study of high-redshift Lyman-α emitters (LAEs), objects showing prominent rest-frame Lyα emission within a spectrum (usually) devoid of other line features (e.g. Cassata et al. 2011; Nakajima et al. 2018). The spectral properties of LAEs are usually interpreted as coming from young (≲50 Myr) and low-mass (M*   1010 M⊙) galaxies (e.g. Wilkins et al. 2011; Amorín et al. 2017; Hao et al. 2018; Santos et al. 2020) with small rest-frame UV half-light radii (R ≲ 1 − 2 Kpc, as in e.g. Møller & Warren 1998; Lai et al. 2008; Bond et al. 2012; Guaita et al. 2015; Kobayashi et al. 2016; Ribeiro et al. 2016; Bouwens et al. 2017a; Paulino-Afonso et al. 2018) which are actively star forming (SFR ∼ 1 − 100 M⊙ yr−1) and dust poor (dust attenuation AV   0.2, see e.g. Gawiser et al. 2006, 2007; Guaita et al. 2011; Nilsson et al. 2011; Bouwens et al. 2017b; Arrabal Haro et al. 2020). When observed at high redshift, isolated and grouped LAEs appear to represent the progenitors of present-day galaxies and clusters, respectively, providing extremely valuable insights into structure formation (e.g. Matsuda et al. 2004, 2005; Venemans et al. 2005; Gawiser et al. 2007; Overzier et al. 2008; Guaita et al. 2010; Mei et al. 2015; Bouwens et al. 2017b; Khostovan et al. 2019). A basic statistical tool to study the population of high-z LAEs is the description of their number density at a given redshift as a function of line luminosity (LLyα), namely the Lyα luminosity function (LF; see e.g. Gronke et al. 2015, for a theoretical approach). Several recent works have focused on the construction of the Lyα LF at z ≥ 2 (Gronwall et al. 2007; Ouchi et al. 2008; Blanc et al. 2011; Clément et al. 2012; Konno et al. 2016; Sobral et al. 2017, 2018a) by making use of deep observations of narrow sky regions (up to few squared degrees, as in e.g. Matthee et al. 2014, 2017b; Cassata et al. 2015; Ono et al. 2018). Their findings describe a Lyα LF that follows a Schechter function (Schechter 1976) at relatively faint line luminosity (i.e. LLyα ≲ 1042.5, see e.g. Ouchi et al. 2008; Konno et al. 2016; Sobral et al. 2016; Matthee et al. 2017a), a regime mostly occupied by low-mass star-forming galaxies (e.g. Hu et al. 1998; Kudritzki et al. 2000; Stiavelli et al. 2001; Santos et al. 2004; van Breukelen et al. 2005; Gawiser et al. 2007; Rauch et al. 2008; Guaita et al. 2011).


With the advent of the LOw Frequency ARray (LOFAR; Röttgering et al. 2011; van Haarlem et al. 2013) which combines a large field of view with high sensitivity on both small and large angular scales, we can now study the FIRC at lower frequencies where the contribution from thermal free-free emission is even less important than at 1.4 GHz. Operating between 30 and 230 MHz, LOFAR offers complementary information to the wealth of data collected at higher frequencies. Using deep LOFAR 150 MHz observations in the 7 deg2 Boötes field (Williams et al. 2016), Calistro Rivera et al. (2017) studied the FIRC at 150 MHz from z ∼ 0.05 out to z ∼ 2.5. They found fairly mild redshift evolution in the logarithmic IR to radio luminosity ratio in the form of qIR ∼ (1 + z)−0.22 ± 0.05. However, if the FIRC is non-linear (i.e. the logarithmic slope is different from one), then it implies that the qIR parameter would depend on luminosity. Therefore the reported redshift dependence of qIR may simply be a consequence of the non-linearity of the FIRC (Basu et al. 2015) as the mean SFR of galaxies is generally larger at higher redshifts (e.g., Hopkins & Beacom 2006; Madau & Dickinson 2014; Pearson et al. 2018; Liu et al. 2018; Wang et al. 2019). Based on LOFAR observations of the Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS; Eales et al. 2010) 142 deg2 North Galactic Pole (NGP) field (Hardcastle et al. 2016), Gürkan et al. (2018) found that a broken power-law (with a break around SFR ∼1 M⊙ yr−1) compared to a single power law is a better calibrator for the relationship between RC luminosity and SFR, possibly implying additional mechanisms for generating cosmic rays and/or magnetic fields. Also using LOFAR data in the NGP field, Read et al. (2018) found evidence for redshift evolution of the FIRC at 150 MHz. Heesen et al. (2019) studied the relation between radio emission and SFR surface density using spatially resolved LOFAR data of a few nearby spiral galaxies. They found a sublinear relation between the resolved RC emission and the SFR surface densities based on GALEX UV and Spitzer 24 μm data.


Coronal mass ejections (CMEs) are intense solar explosive eruptions during which large amounts of plasma and magnetic field from the solar atmosphere are ejected into interplanetary space. The interplanetary manifestations of CMEs (ICMEs; Kilpua et al. 2017) can be measured by a spacecraft at about 1 AU and exhibit the following characteristics: increase in total magnetic magnitude (Cane & Richardson 2003), helium abundance (Hirshberg et al. 1972; Zwickl et al. 1982; Richardson & Cane 2004), average iron ionization (Lepri et al. 2001; Lepri & Zurbuchen 2004), and O7+ abundance (Richardson & Cane 2004; Wang & Feng 2016); decrease in proton temperatures and proton densities (Gosling et al. 2001; Zhang et al. 2013); counterstreaming suprathermal electron (CSE) strahls and declining speed (Zwickl et al. 1982; Gosling et al. 1987; Shodhan et al. 2000; Burlaga et al. 2001). A subset of ICMEs was defined as magnetic cloud (MC) by Burlaga et al. (1981) empirically using the following properties: (1) the magnetic field strength is higher than average, (2) a smooth change in field direction as observed by a spacecraft passing through the cloud, and (3) low proton temperature compared to that of the ambient proton. Magnetic clouds usually have magnetic flux rope structures, and they are the main source of major geomagnetic storms (Burlaga et al. 1981; Webb et al. 2000; Huttunen et al. 2002; Zhang et al. 2007). Observations at 1 AU show that 30 − 40% of ICMEs are MCs, and this percentage depends on the solar cycle (Richardson & Cane 2004). However, CMEs are usually assumed to have magnetic flux rope structures near the Sun because of their helical shapes (Canfield et al. 1999; Liu et al. 2010; Rust & Kumar 1996). This begs the question of whether or not nonMC ICMEs also have flux rope structures. The journal of Solar Physics once made a special issue to address this question (Gopalswamy et al. 2013a). A comparative study of 23 MCs and 31 nonMC ICMEs was completed, and the source regions of the 54 ICMEs were located within ±15° longitude from the disk center. Yashiro et al. (2013) found no significant difference between the structures of the post-eruption arcades of MCs and nonMC ICMEs during launch. Gopalswamy et al. (2013b) observed that MCs and nonMC ICMEs have significant enhancement in Fe and O charge states, and Fe and O charge-state measurements are positively correlated with flare properties, including flare size and soft X-ray flare intensity. Their observations suggest that these CMEs have similar explosive environment and flux rope structures near the Sun. Furthermore, some studies indicate that CMEs associated with MCs tend to propagate along the Sun–Earth line, whereas nonMC events are deflected away from the Sun–Earth line (Kim et al. 2013; Mäkelä et al. 2013; Zhang et al. 2013). Therefore, many researchers believe that all ICMEs have magnetic flux rope structures and that the nonMC events are due to observational limitations, that is, that the observing spacecraft crosses the flanks of the ropes and therefore the ICMEs appear as nonMCs. This has been shown by some multi-satellite-observed ICMEs, namely spacecraft farther from the axis detect less clear flux rope signatures than centrally crossing spacecraft for the same event (Cane et al. 1997; Kilpua et al. 2011).


A charged particle moving in the electromagnetic field can feel Landau–Lifshitz radiation reaction force due to synchrotron radiation, thus modifying the motion of the charged particle significantly when taking into account the radiation reaction force. Recent observations have demonstrated that there is strong evidence that a magnetic field of several hundred Gauss exists in the vicinity of the supermassive black hole at the center of the Milky Way (Eatough et al. 2013). A dynamo mechanism from an accretion disk around a black hole accounts for the appearance of such a magnetic field (Punsly 2001; Brandenburg et al. 1995; Hawley et al. 1996). There is also clear evidence that the magnetic field on the surface of the neutron star can be up to 1014 G (Duncan & Thompson 1992; Paczyński 1992; Usov 1992; Thompson & Duncan 1995, 1996; Vasisht & Gotthelf 1997). The Landau–Lifshitz radiation reaction has been investigated in detail in Landau & Lifshitz (1975) in flat space, while, in curved space, the radiation reaction is described in Sokolov et al. (1978, 1983), DeWitt & Brehme (1960), and Tursunov et al. (2018). Thus, the radiation reaction force can affect the charged particles from the accretion disk around the black hole and the neutron star significantly. Radiation reactions have been an important element of pair creation scenarios in positron–electron plasma just above the pole of the event horizon (Hirotani & Pu 2016). Curvature radiation in black hole magnetosphere pair creation schemes is radiation resistance limited (Broderick & Tchekhovskoy 2015). Recently, a radiation reaction has also been applied to protonic acceleration in the vortex above the pole of the black hole (Ruffini et al. 2018). Radiation reactions are of fundamental importance in the evacuated vortex of black hole magnetospheres (Punsly 2001). In particular, if the field line angular velocity is set much less than the horizon angular velocity by distant plasma and a very tenuous plasma exists in the event horizon magnetosphere, then radiation resistance will determine the flow dynamics of accretion as well as the rotational energy extraction by a putative jet (Punsly 2001, 1991). The dynamics mentioned above cannot be revealed by MHD simulations with mass floors. The ad hoc injection of mass will damp any large waves that can break ideal MHD and prevent the associated large local electromagnetic forces from being achieved. Therefore, all existing numerical simulations of the black hole magnetosphere bypass the radiation reaction dominated dynamics as a consequence of numerical dissipation of waves and numerical diffusion in the MHD system in the evacuated vortex above the event horizon. Thus, a proper treatment of radiation reaction is critical for assessing the time evolution of these types of astrophysical systems. Numerical simulations using general relativistic magnetohydrodynamics (GRMHDs) are applied to investigate the physical process in accretion disks around neutron stars, as well as in microquasars (μQSOs), gamma-ray bursts, and active galactic nuclei. In curved spacetime, the dynamical evolution of the high energy disks made of ion–electron plasma in simulated GRMHD is usually performed without the contribution from Landau–Lifshitz radiation reaction force, which may play a crucial role. The method of particle-in-cell (Chen & Beloborodov 2014; Philippov & Spitkovsky 2014; Belyaev 2015; Cerutti et al. 2015, 2016; Philippov et al. 2015b) containing the radiation reaction forces has been investigated in flat space, while, in curved space, the same method with a radiation reaction has been achieved in Philippov et al. (2015a). Incorporating the radiation reaction into the relativistic magnetohydrodynamic equations governing the dynamics of plasma has been studied by Tam & Kiang (1979) and Berezhiani et al. (2004, 2008). In a recent study, Liu et al. (2018) achieved the one-fluid relativistic magnetohydrodynamics description of two-fluid plasma in which the Landau–Lifshitz radiation reaction is incorporated. However, numerical simulation with the radiation reaction from Liu et al. (2018) is not practical due to its highly nonlinear form at present, we expect that analytical investigations are essential and provide more motivation for future work. Thus, in this work, similar to Liu et al. (2018), we get the GRMHD equation for the one-fluid description of two-fluid plasma containing a Landau–Lifshitz radiation reaction in curved space, and these results could be applied to both positron–electron and proton–electron plasma.


The recent report by Buisson et al. (2020b) of the detection of Type-I bursts in Sw J1858 shows the presence of a neutron star primary. Therefore, here, we first consider whether Eddington-limited accretion in such a neutron star LMXB might explain the observed radio behaviour in Sw J1858. The neutron star LMXBs with the highest mass accretion rates are the Z-sources, which are thought to accrete near or at the Eddington luminosity, tracing out Z-shaped tracks in their X-ray colour–colour diagrams (Hasinger & van der Klis 1989; Homan et al. 2010). Z-sources can show strong changes in radio brightness, related to the branch they are positioned on in their colour–colour diagram track; they are radio brighter and more variable in the Horizontal Branch than in the Flaring and Normal Branches (Penninx et al. 1988; Hjellming et al. 1990a,b; Spencer et al. 2013; Motta & Fender 2019). Time-resolved radio studies of the different branches in Sco X-1 by Hjellming et al. (1990b) and Cyg X-2 by Hjellming et al. (1990a) show that these sources have similar levels of radio variability and luminosity to Sw J1858 during their radio-faint Flaring and lower Normal Branches. However, in the X-ray – radio luminosity plane, these sources are located to the right of Sw J1858, around the neutron star Eddington limit of 2 × 1038 erg s−1. For Sw J1858 to be similar to these sources, it would therefore have to be viewed a high inclination, reducing its observed X-ray flux and masking the Z-source variability properties through obscuration. However, a clear radio difference between Sw J1858 and the Z-sources is the radio spectral index: contrary to Sw J1858, Z-sources typically show steep spectra and are indeed associated with the launch of (resolved) discrete ejecta (Motta & Fender 2019). Also, in this scenario, Sw J1858 should not have resided in the much more radio bright Horizontal Branch during any of the observations, which is unlikely given the time-scales and commonness of transitions between the branches (Homan et al. 2010).


In general, the Hall time-scale for magnetic field evolution depends on the strength of the magnetic field, as seen in equation (4). For young NSs with fields below 1014 G, this time-scale may be longer than the observed SNR age. Therefore, magnetic field growth does not have a dramatic effect on these young NSs. However, many of these systems are observed to have a braking index n  3 (Espinoza 2012; Archibald et al. 2016). A possible explanation for these low braking indices may be through the emission of a relativistic particle wind (Thompson & Blaes 1998; Harding, Contopoulos & Kazanas 1999; Tong et al. 2013). However, the conclusive detection of wind nebulae around magnetars in particular is challenging due to the presence of dust-scattering haloes that accompany these X-ray bright, heavily absorbed objects (Esposito et al. 2013; Safi-Harb 2013). Only a handful of such nebulae have been proposed to be associated with highly magnetized NSs. For example, a wind nebula has been proposed to surround the magnetar Swift J1834.9–0846 in W41 (Younes et al. 2016), and the luminosity of a particle wind was estimated for SGR 1806–20 based on the X-ray and radio observations of the wind-powered nebula G10.0–0.3 (Thompson & Duncan 1996; Marsden, Rothschild & Lingenfelter 1999; Gaensler et al. 2005). In the pulsar wind model, relativistic particles load the magnetosphere with charge and distort the dipole field at large scales outside of the light cylinder. Besides affecting the NS spin-down, the emission of a relativistic wind can also offer an explanation for the significant timing noise that generally affects magnetar observations (Tsang & Konstantinos 2013). The HBPs J1119–6127 and J1846–0258 are clearly associated with pulsar wind nebulae (Gavriil et al. 2008; Kumar & Safi-Harb 2008; Ng et al. 2008; Safi-Harb & Kumar 2008; Safi-Harb 2013), suggesting that particle wind emission should play an important role in their evolution. We also expect that AXP and SGR evolution may be affected by wind emission due to candidate wind nebulae, but do not consider these models for the CCOs that do not show any evidence of PWN. However, we note that braking exclusively due to a steady particle wind produces a torque with a braking index n = 1, too low for the NSs with secure SNR associations in Table 1.


At large distances, the proper motions of the halo stars are either unreliable or generally unavailable, which hinders a direct measurement of their velocity dispersions. However, our off-centric location in the Galaxy means that the galactocentric radial (r) and heliocentric radial (s) directions are not the same. This difference is more significant in the inner halo, at a distance of r ≲ a couple of times of R0, where R0 is the distance of the Sun from the Galactic Centre. Hence, in the inner halo the observed line-of-sight velocities of the stars can be expressed in terms of all three orthogonal galactocentric velocities (vr, vθ, vϕ), or in other words the line-of-sight velocities have some contribution from the tangential galactocentric velocities. Provided we have a model that well represents the distribution of the halo stars, we can fit a model marginalized over the unknown tangential motions to the available four-dimensional data (position vector and a line-of-sight velocity), and thus estimate the velocity moments of the system. In the absence of proper motion, the approach of estimating moments of the velocities has been extensively used to predict the kinematics of the MW halo. For example, Sirko et al. (2004), Kafle et al. (2012), Kafle et al. (2013), Kafle et al. (2014) and King et al. (2015) fit an ellipsoidal distribution of velocities and similarly, Deason, Belokurov & Evans (2011a) apply an alternative power-law model to derive the halo kinematics. Using the marginalisation scheme, Kafle et al. (2012, 2013) studied halo Blue Horizontal Branch stars (BHBs), Kafle et al. (2014) studied both BHBs and K-Giant stars (KGs), while King et al. (2015) analysed a mixed bag of BHB and F-type stars to cumulatively construct the velocity dispersion and anisotropy of the outer halo. Interestingly, Kafle et al. (2012) found that the velocity anisotropy parameter of the Galactic halo is non-monotonic and has a prominent dip at a galactocentric radius of r ≃ 18 kpc. In their studies, King et al. (2015) find that the value of β at 15 ≲ R/kpc ≲ 25 is more tangentially biased, which they attribute to the difference in the spatial resolutions of the data sets and adopt a marginalization technique. A varying level of undulations in the anisotropy parameter has also been observed in simulated haloes (Rashkov et al. 2013; Loebman et al. 2017). There are a number of proposed scenarios that could explain such a feature, e.g. a transition from inner to outer halo or a local shell-like structure at the given radius. Moreover, it can also be due to the unrelaxed stars dispersed from the kinematically coherent satellite galaxies that are aligned with kinematically coherent planar structures; assuming that such planar structures have strong rotation as suggested by Ibata et al. (2013), Pawlowski, McGaugh & Jerjen (2015), Libeskind et al. (2015) and Ibata et al. (2015), etc. Recently, Loebman et al. (2017) suggest that a major merger as early as redshift z ∼ 1 can also result in a tangential dip in the value of β over a wide range of radii. While Bird & Flynn (2015) suggest that such a feature in the velocity anisotropy run of the halo is a transitory phase, Loebman et al. (2017) conclude that such dips are long-lived in the in situ stellar halo. In any case, there is currently no consensus view as to what causes such velocity anisotropy changes. Finally, in the outer halo there have been recent attempts to utilize multi-epoch Hubble Space Telescope data to estimate the halo velocity dispersion. In particular, recently Cunningham et al. (2016) used the Galactic foreground stars along the M31 galaxy and found that the halo is isotropic at r/kpc ∼ 25. In Fig. 10, we summarize the recent (this paper inclusive) measurements of the halo velocity anisotropy.


Next we chose an optimum cut-off radius for the detector FOV. The PSPC has a circular FOV with a radius 57′. The PSPC entrance window has a rib support structure with an inner ring at a radius corresponding to 20′ (Pfeffermann et al. 1987; Hasinger & Zamorani 2000). Both the ROSAT telescope angular resolution and its vignetting function are roughly constant within the inner 20′ ring, but degrade significantly towards larger off-axis angles. The combined detector and telescope PSFs are described in detail in Boese (2000). To the first order, the PSF at each off-axis angle can be approximated by a Gaussian function with a half power radius (HPR) of 13, 22, 52, 93, 130, and 180″, at off-axis angles of 0, 12, 24, 36, 48, and 57′, respectively (at 1 keV). The vignetting function at 1 keV drops almost linearly to about 50% at an off-axis angle of 50′. Taking into account all these effects, the HPR of the overall RASS PSF is 84″ (Boese 2000). This means that the classical confusion limit (40 beams per source) is reached at a source density of about 15 sources deg−2, which is exceeded in the high-exposure areas of our survey. In addition, we need to optimally discriminate between extended and point-like X-ray sources, calling for an angular resolution that is as high as possible. We therefore have to reduce the detector FOV. The sharpest imaging is achieved within the inner 20′ of the PSPC FOV, corresponding to the inner ring-like rib of the PSPC support structure (see Fig. 1). However, there is a trade-off between image sharpness and the number of photons required for detection and image characterization. In particular in the outer areas of our survey, where the RASS exposure times drop significantly, a 20′ FOV radius does not provide sufficient exposure time. Taking into account the various competing factors in this trade-off, we made a few tests varying the FOV cut-off radius, and finally decided on an optimum FOV radius of 30′. The PSPC detector coordinates have a pixel size of 0.934″. We thus removed all X-ray events from the dataset, which are further than 1925 pixels from the PSPC centre pixel coordinate [4119,3929]. A similar cut had to be applied to the modified PSPC instrument map (MOIMP), which is used later for the construction of the survey exposure map.


The B/T ratio of galaxies has been traditionally measured by modelling their surface brightness profile. Such modelling allows one to find the light-profiles of individual photometric components of galaxies and then measure their properties such as luminosity, shape, size etc. The earliest such works aimed at photometric decomposition of galaxies involved fitting for the azimuthally averaged 1D surface brightness profile (Kent 1985). However, this method leads to systematic errors as creation of 1D light profile by either averaging over the galaxy image or by taking a single cut along the major axis do not properly take into account non-axisymmetric features like a bar or isophotal twist (for more details see Gao & Ho 2017). Due to these shortcomings, techniques to fit the whole 2D image of the galaxy, pixel-by-pixel, were developed (Wadadekar, Robbason & Kembhavi 1999). There are now a number of implementations of 2D bulge disc decomposition available – gim2d: Simard (2010), galfit: Peng et al. (2002), imfit: Erwin (2015), profit: Robotham et al. (2016), budda: de Souza, Gadotti & dos Anjos (2004), gasp2d: Méndez-Abreu et al. (2008) – which fit the 2D images of galaxies. They usually employ different algorithms and methods to find the best-fitting model for a galaxy image. In the last two decades, some pipeline codes have been developed (pymorph: Vikram et al. (2010), galapagos: Barden et al. (2012)) to carry out bulge disc decomposition for large galaxy samples, in a mostly automated fashion. This 2D bulge-disc decomposition approach, while being powerful, is time consuming. The employed fitting algorithm and code carries out a search in parameter space defined by various model parameters and then finds the best fit. Most of the time, one also needs to carry out additional steps (masking other objects in the field and providing PSF images) before the actual fitting of galaxies can commence. Thus estimating the B/T ratio for a single galaxy involves a significant amount of time and computational cost. More importantly, the fitting procedure scales only linearly with the size of the galaxy sample. This limitation will be a major problem in the era of next generation sky surveys (e.g. LSST, Euclid sky surveys) which will observe several billion galaxies.


While these early studies demonstrated the viability of neutron star mergers as a major r-process site, they identified only one ejection channel: ‘dynamical ejecta’ that are tidally flung out by gravitational torques. Since they are never substantially heated, these ejecta carry their original β −equilibrium electron fraction from the original neutron star, Ye ≈ 0.05, and this enormous neutron-richness allows them to undergo a ‘fission cycling’ process (Goriely, Bauswein & Janka 2011; Korobkin et al. 2012), which produces a very robust r-process abundance distribution close to the solar pattern for A ≥ 130, but hardly any lighter r-process elements. Oechslin, Janka & Marek (2007) pointed out that there is a second channel of mass ejection that also happens on a dynamical time-scale: shock-heated matter from the interface where the stars come into contact. As of today, many more mass ejection channels have been discussed: matter that becomes unbound on secular time-scales (∼1 s) from the post-merger accretion torus (Beloborodov 2008; Metzger, Piro & Quataert 2008; Fernandez & Metzger 2013; Fernandez et al. 2015; Just et al. 2015; Siegel & Metzger 2017, 2018; Fernandez et al. 2019; Miller et al. 2019a), as MHD-driven winds (Siegel & Ciolfi 2015) and by viscous effects (Shibata, Kiuchi & Sekiguchi 2017; Radice et al. 2018a; Shibata & Hotokezaka 2019) from a long-lived neutron star merger remnant. Similar to the case of proto-neutron stars, the enormous neutrino luminosities (>1053 erg s−1) after a neutron star merger can also drive substantial matter outflows (Ruffert et al. 1997; Rosswog & Ramirez-Ruiz 2002; Dessart et al. 2009; Perego et al. 2014; Martin et al. 2015; Radice et al. 2018b). The secular torus ejecta contain approximately 40 per cent of the initial torus mass and, although the latter may vary substantially from case to case, they likely contribute the lion’s share to the total ejecta mass. Due to their different thermal histories and exposure times to neutrinos, the ejecta channels can have different electron fractions Ye and therefore different nucleosynthesis yields.1 For electron fractions below a critical value, $Y_{\rm e}^{\rm crit}\approx 0.25$ (Korobkin et al. 2012; Lippuner & Roberts 2015), lanthanides and actinides are efficiently produced, which, due to their open f-shells, have particularly high bound–bound opacities (Barnes & Kasen 2013; Kasen, Badnell & Barnes 2013; Tanaka & Hotokezaka 2013; Tanaka et al. 2020) and therefore lead to red transients that peak days after the merger. Ejecta with electron fractions above $Y_{\rm e}^{\rm crit}$, in contrast, only produce ‘lighter’ elements with lower opacities and thus result in bluer transients that peak after about 1 d. Opaque, low-Ye ejecta blocking the view on high-Ye ejecta can lead to a ‘lanthanide curtaining’ effect (Kasen, Fernández & Metzger 2015; Wollaeger et al. 2018), which will efficiently block blue light. Therefore, it is important to understand the layering, dynamics, interaction and potential mixing of different ejecta channels.


The X-ray transient MAXI J1820+070 was first detected on 2018 March 11 (Kawamuro et al. 2018) by the Monitor of All-sky X-ray Image (MAXI, Matsuoka et al. 2009) and was associated with the optical transient ASASSN-18ey (Denisenko 2018; Tucker et al. 2018). In the X-rays, the source flux exceeded 3 Crabs (Bozzo et al. 2018; Mereminskiy et al. 2018), and in the optical, the source reached a magnitude of mV = 12 − 13 (Littlefield 2018; Russell et al. 2018). The parallax of the source π = 0.3 ± 0.1 mas was presented in the Gaia DR2 catalogue (Gaia Collaboration 2018). This corresponds to a distance of

3
.

9

−
1.3

+
3.3

$ 3.9^{+3.3}_{-1.3} $

 kpc (Gandhi et al. 2018a). This unusually bright event allows a detailed investigation of multi-wavelength spectral and timing properties. The course of the outburst was monitored in radio (Trushkin et al. 2018; Polisensky et al. 2018), sub-millimeter (Tetarenko et al. 2018a), optical (Baglio et al. 2018), X-rays (Uttley et al. 2018), and γ-rays (Bozzo et al. 2018; Kuulkers et al. 2018). Because the object was sufficiently bright even for small telescopes, the target was almost continuously monitored, and a rich variety of phenomena was observed. Fast variability and powerful flares in the optical and infrared (Littlefield 2018; Sako et al. 2018; Gandhi et al. 2018b; Casella et al. 2018), optical, and X-ray quasi-periodic oscillations (Mereminskiy et al. 2018; Yu et al. 2018a,b; Buisson et al. 2018; Zampieri et al. 2018) as well as low linear polarisation (Berdyugin et al. 2018) were detected in the source. A 17 h photometric period was recently reported (Patterson et al. 2018) and was tentatively associated with the orbital or superhump period (previously, the source showed a 3.4 h periodicity, Richmond 2018). The X-ray spectral and timing properties as well as the optical-to-X-ray flux ratio suggests that the source is a black hole binary (Baglio et al. 2018; Mereminskiy et al. 2018).


It is generally believed that reionization started first in high-density regions, where the first luminous objects formed first. In the ‘bubble model’ of reionization (Furlanetto, Zaldarriaga & Hernquist 2004), the amount of star formation and the resulting ionizing photons are estimated using the excursion set model. Based on this idea, the so-called ‘seminumerical simulations’ have been developed. For example, Mesinger, Furlanetto & Cen (2011) developed the 21cmFAST,1 to simulate the evolution of the 3D density, ionization, and 21cm brightness temperature fields efficiently. The ‘bubble model’ considers spherical regions of increasingly smaller scales and identifies ionized bubbles by comparing the cumulative number of ionizing photons produced within the region with the number consumed in reionization process. It has been demonstrated that the statistical predictions of the ‘bubble model’ and the 21cmFAST agree fairly well with radiative–hydrodynamic simulations (Zahn et al. 2007; Mesinger et al. 2011; Zahn et al. 2011), at least when recombination, feedback, etc. are ignored. However, during most epochs of reionization, the topology of the ionization field is much more complicated than the isolated bubbles configuration. The bubbles start to connect with each other as early as when the global ionized fraction is just about 10 per cent, and the Universe starts the percolation process when the ionized fraction gets ∼30 per cent (see e.g. Furlanetto & Oh 2016; Chen et al. 2018). Inspired by the bubble model, the 21cmFAST determines the ionization state of each point by comparing the expected ionizing photon production in the surrounding region with the required number, but it allows non-spherical geometry for the ionized regions. In order to give a better description of the evolution of neutral regions after percolation, Xu et al. (2014) developed the so-called ‘island model’, assuming isolated neutral islands topology. The island model also takes into account an ionizing background that is inevitable during the late EoR (Furlanetto & Oh 2005; McQuinn, Oh & Faucher-Giguère 2011; Emberson, Thomas & Alvarez 2013). Based on the ‘island model’, a seminumerical code named islandFAST was developed to mimic the islands evolution during the last stage of reionization (Xu et al. 2017). In the islandFAST, the effect of small-scale absorbers is taken into account empirically by adopting a fitting formula for the evolution of mean free path (MFP) of ionizing photons (Songaila & Cowie 2010), based on the observed number density of Lyman limit systems up to redshift 6. Before the completion of reionization, the MFP is limited by both the underdense islands and the overdense absorbers. The evolution of the ionization field and the intensity of the ionizing background are derived self-consistently by an iterative procedure to ensure convergence in the total effective MFP of the ionizing photons.


Over the last decade, the radial and vertical dependences of the metallicity-alpha-element distribution have been studied in more and more detail with increasingly larger samples (e.g., Bensby et al. 2011; Anders et al. 2014; Nidever et al. 2014; Hayden et al. 2015; Queiroz et al. 2020). Figure 6 is mostly consistent with similar plots shown in the above papers. In the inner 10 kpc, it displays two over-densities, a high alpha-element (here [Mg/Fe]), and a low one. Between Rg = 6 and 10 kpc, the two over-densities define two different sequences. In Appendix E, we note that when the sample is restricted to a ±500 pc layer around the Galactic plane, two close but separated sequences are observed in the Rg ∈ [4, 6] kpc interval. Because of their scale height (Bovy et al. 2012), kinematics (Bensby et al. 2003), and age properties (Haywood et al. 2013), these two sequences are associated with the thick disc (high-alpha) and thin disc (low-alpha), respectively. Moving inward of Rg = 4 − 6 kpc, Fig. 6 shows that the two over-densities connect through a zone of lower density to form a single sequence. This is in agreement with the observations of Hayden et al. (2015), Bensby et al. (2017), Zasowski et al. (2019), Bovy et al. (2019), and Lian et al. (2020a,b), who also report a single sequence in the inner disc and/or in the bulge/bar area. Conversely, Rojas-Arriagada et al. (2019) and Queiroz et al. (2020) observe two sequences in the inner regions. In Appendix F, we compare the distributions of different APOGEE DR16 alpha elements in the ([Fe/H], [α/Fe]) plane (restricting the sample to the stars contained in the Rg ∈ [0, 2] kpc interval). The different elements produce different patterns: the global alpha-element abundance5 and oxygen show a double sequence, while magnesium, silicon, and calcium present a single sequence. This could explain, at least partly, why Queiroz et al. (2020), who use a combined α-element abundance, observe a double sequence, while we see a single one with magnesium. However, this does not explain the discrepancy with Rojas-Arriagada et al. (2019), who also used magnesium. Beyond Rg = 10 kpc, the high-alpha sequence gradually vanishes. This is in agreement with the finding that the thick disc has a shorter scale length than the thin disc (Bensby et al. 2011; Cheng et al. 2012; Bovy et al. 2012). It should be emphasised that in this paragraph the term ‘sequence’ is used in the geometrical sense. It does not presuppose the number of chemical tracks that form the sequence or sequences. In particular, based on Fig. 6, it can not be excluded that the single geometrical sequence observed in the inner disc be made of two chemical tracks, with the low-alpha one restricted to a narrow metallicity range. We discuss and propose an interpretation of the inner disc sequence in Sect. 5.


It is a pressing question as to how the radiation that is observed in relativistic jets in active galactic nuclei (AGNs) is generated (e.g., Blandford & Königl 1979; Marscher 1980; Zensus 1997; Laing & Bridle 2002; Honda 2010; Levinson & Rieger 2011; Mościbrodzka et al. 2011; Ito et al. 2013; Mason et al. 2013; Potter & Cotter 2013; Hovatta et al. 2014; Scott & Stewart 2014; Shih & Stockton 2014; Wang et al. 2014; Turner & Shabala 2015; Asada et al. 2016; Hirotani et al. 2016; Koay et al. 2016; Khabibullin et al. 2016; Prieto et al. 2016). Although there is a common consensus that the emitters are energetic particles, how these particles are accelerated to such high energies, how they dissipate their energy, and how they are transported with the jets themselves are still the subject of feverish investigation (e.g., Blandford & Eichler 1987). It is argued that relativistic outflows from black holes are associated with accretion flows (Blandford 1976; Fender et al. 2004; Meier 2005; Ferreira et al. 2006; Trump et al. 2011; Pu et al. 2012; Wu et al. 2013; Ishibashi et al. 2014; Sbarrato et al. 2014). In the case of collimated relativistic jets, magnetic fields must play an important role (Camenzind 1986a, 1986b, 1987; Fendt & Greiner 2001; Vlahakis & Königl 2004; Komissarov et al. 2007; Lyubarsky 2009; Nakamura & Asada 2013; Homan et al. 2015), and it is argued that jets are powered at the expense of the black hole, wherein energy is extracted from a reservoir of rotational energy from the black hole itself, either by electromagnetic means (Blandford & Znajek 1977; Komissarov 2004, 2005; Toma & Takahara 2014) or through magnetohydrodynamical processes (Phinney 1983; Takahashi et al. 1990; Koide et al. 2002; McKinney & Gammie 2004; Hawley & Krolik 2006). Models have been proposed for both of these cases, and they both in principle possess certain testable predictions. In particular, for the latter, numerical GRMHD simulations (e.g., McKinney 2006) and analytical GRMHD studies (e.g., Takahashi et al. 1990; Pu et al. 2016) consistently show the presence of a stagnation or separation surface (a separatrix). This surface separates the (inner) inflow region from the (outer) outflow region, both of which follow the same global, black-hole-threading magnetic field lines. The relatively slow radial velocities near the stagnation surface imply a high concentration of fluid particles. If energetic particles are injected in the vicinity of the stagnation surface or near the black hole event horizon, they must accumulate in high concentrations near the stagnation surface, provided that the cooling timescale is not significantly shorter than the dynamical timescale of the jet fluid flow. This surface is a unique feature of relativistic GRMHD jets and in contrast to an ideal force-free magnetic jet (e.g., McKinney & Narayan 2007; Tchekhovskoy et al. 2008; Broderick & Loeb 2009).


The first transit of HD 21749b was identified by both the MIT Quick Look Pipeline (which searches for planet candidates in the 30 minutes Full Frame Images) and the Science Processing Operations Center (SPOC) pipeline based at the NASA Ames Research Center (Jenkins et al. 2016). No other matching transits were found in the publicly released data from sectors 1 and 2. After TOI 186.01 was alerted, we searched for archival spectroscopy of this very bright star and found 59 High-accuracy Radial-velocity Planet Searcher (HARPS) radial velocities (RVs) in the European Southern Observatory (ESO) archive (see Section 2.4). A periodogram of these RVs showed a clear signal at 35.57 days, but the TESS photometry and the RHK index (Boro Saikia et al. 2018) indicate a stellar rotation period of around 35 days, calling for caution. If the strongest period in the RVs did correspond to the planet, then we expected to see additional transits in sectors 3 and 4. Once the sector 3 data were released, we discovered that a momentum dump29

29
“Momentum dumps” consist of resetting the momentum wheel speed every 2.5–3 days and are used to mitigate the noisier-than-expected measurements of the spacecraft momentum wheel speeds at higher wheel speeds (see https://archive.stsci.edu/files/live/sites/mast/files/home/missions-and-data/active-missions/tess/_documents/TESS_Instrument_Handbook_v0.1.pdf for details). Momentum dumps require brief interruptions to Fine Pointing mode, during which an increase in the flux dispersion is noticeable in the science data, so data acquired during these intervals are excluded from our analysis.
 occurred approximately 35.6 days after the sector 1 transit (see Figure 1). We did not let this unexpected turn of events foil our search efforts, and upon close inspection of the light curve we succeeded in recovering a partial transit (including egress) immediately following the momentum dump. Finally, we observed a third transit in sector 4, thus allowing for a robust ephemeris determination (see Section 3.3). Serendipitously, when applied to the first three sectors of the HD 21749 light curve, the SPOC pipeline yielded an additional planet candidate with a period of 7.9 days (TOI 186.02).


The simulation model Run1-hr of Meyer et al. (2018) begins with the gravitational collapse of $100\, \rm M_{\odot }$ of pre-stellar rotating molecular material on to the stellar embryo. At the end of the free-fall collapse phase, the infalling material ends on a centrifugally-balanced disc, from which the gas is subsequently transferred to the growing protostar. Fig. 1 plots the accretion rate history on to the central massive protostar (solid blue line, in $\rm M_{\odot }\, \rm yr^{-1}$) together with the evolution of the protostellar mass (dashed red line, in $\rm M_{\odot }$) that is calculated as the integrated disc-to-star mass transfer rate through the sink cell. The vertical thin black line indicates the onset of disc formation, when the free-fall collapse of the envelope material on to the protostar stops and the star begins to gain its mass exclusively via accretion from its surrounding disc. After the initial infall of material, the collapse of the parent pre-stellar core material generates an initial increase of the mass flux through the inner boundary at a time ${\approx } 2\, \rm kyr$. The accretion rate then reaches the standard value predicted for MYSOs of $10^{-3}\, \rm M_{\odot }\, \rm yr^{-1}$ (Hosokawa & Omukai 2009) up to the onset of the disc formation happening at ${\approx } 12\, \rm kyr$. Variabilities in the accretion flow begin right after the disc formation and the accretion rate history exhibit numerous peaks of growing intensity as the MYSO becomes heavier. This is not caused by different inner boundary conditions, but simply reflects the time-dependent azimuthal anisotropies induced in the accretion flow by the disc evolution. The efficient gravitational instabilities produce complex substructures in the disc, such as overdense spiral arms in which gaseous clumps of various morphologies form at radii of ${\sim } 100\, \rm au$ and inward-migrate down to the central protostar. This produces luminosity outbursts via the mechanism revealed in Meyer et al. (2017) for massive stars. These outbursts are responsible for step-like increases in the stellar mass evolution (see thick dotted red line) due to the fast accretion of dense circumstellar material inside the sink cell. A more detailed description of the evolution of circumstellar discs around young massive stars irradiating their self-gravitating discs can be found in our precedent study (Meyer et al. 2018). In Fig. 1, several magenta dots mark the time instances of the chosen simulation snapshots considered in this study. Note that the young star becomes, by definition, a massive object when $M_{\star }=8\, \rm M_{\odot }$. Hence, our selected disc models are all in the high-mass regime.


A large proportion of systems where one planet or more is orbiting closer to its host star than Mercury to the Sun have been observed. Tidal interactions play a key role in the orbital configuration of these very compact systems since they are likely to circularize orbits, align spins, and synchronize periods (Zahn 1977; Mathis & Remus 2013; Ogilvie 2014). These interactions consists in an exchange of angular momentum between the orbit and the spins of the celestial bodies. This exchange is the consequence of the dissipation of tidal flows. The kinetic energy of these tidal flows is converted into heat through tidal dissipation. Since the planet is synchronized within a timescale of a few thousand years, the stellar tide drives the secular orbital evolution (Guillot et al. 1996; Rasio et al. 1996; Leconte et al. 2010). In this work, we neglect the impact of the dissipation in the radiative zone. In stellar convection zones, there are two kinds of tides and both are dissipated by the turbulent friction applied by convective eddies. On the one hand, the equilibrium tide is the large-scale velocity field associated with tidal deformation, the so-called tidal bulge. This nonwave-like entity corresponds to the hydrostatic adjustment of the star to the gravitational perturbation (Zahn 1966; Remus et al. 2012). The friction applied by convective motions delays the response of the star to the perturbation (e.g., Zahn 1989; Ogilvie & Lesur 2012; Mathis et al. 2016). This results in a lag angle between the axes of the tidal bulge and the line of centers. This angle increases with dissipation magnitude. Hansen (2012) calibrated its value for several stellar masses by constraining the dissipation using observations of planetary systems. Since lower-mass stars have deeper convective envelopes, they dissipate more energy than higher-mass stars. On the other hand, in rotating bodies such as stars, at low tidal frequencies, the Coriolis acceleration acting on this equlibrium tide excites inertial modes (Ogilvie & Lin 2007). Their ensemble, the dynamical tide, constitutes the wavelike part of the tidal response. Its dissipation strongly depends on internal structure since it arises from the reflection of inertial modes on the radiative, stably stratified core (Ogilvie 2013; Mathis 2015). The dynamical tide may also vary over several orders of magnitude with rotation since inertial waves are restored by the Coriolis force. At low frequencies, dissipation of the dynamical tide is several orders of magnitude higher than the dissipation of the equilibrium tide (Ogilvie & Lin 2007).


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


GRB 170817A, the short GRB directly associated with the first gravitational wave signal GW170817 from a binary neutron star merger, is a great example presenting afterglow spectra with a beautiful single power-law extending from radio to X-ray (Abbott et al. 2017a, b; Goldstein et al. 2017; Savchenko et al. 2017). A successful launch of a relativistic jet in GRB 170817A is supported by the detection of superluminal motion of a compact radio source (Mooley et al. 2018b; Ghirlanda et al. 2019). The jet was observed from off-axis (i.e. the jet axis and the line of sight was misaligned), leading to a faint gamma-ray emission (Abbott et al. 2017c; Ioka & Nakamura 2018, 2019; Salafia & Ghirlanda 2022, and references therein) and early rising afterglow light curves (Alexander et al. 2017; Hallinan et al. 2017; Margutti et al. 2017; Troja et al. 2017). The slow rising afterglow light curves also rejected a uniform top-hat jet (Mooley et al. 2018a; Troja et al. 2018) and revealed a launch of a structured jet, while various jet structures can explain the observations (see, however, Lamb, Levan & Tanvir (2020) for an alternative scenario with a refreshed shock in an off-axis uniform jet). Often assumed structured jets are a Gaussian jet or a power-law jet (D’Avanzo et al. 2018; Gill & Granot 2018; Lamb & Kobayashi 2018; Lyman et al. 2018; Resmi et al. 2018; Ghirlanda et al. 2019; Lamb et al. 2019; Troja et al. 2019, 2020; Ryan et al. 2020). Other non-trivial jet structures such as hollow-cone jets and spindle jets are also possible candidates as recently discovered by Takahashi & Ioka (2020, 2021), while the consistency of a hollow-cone jet was also confirmed by Nathanail et al. (2020, 2021). As predicted by Troja et al. (2018), the rapid decline of the afterglow after the peak (Mooley et al. 2018c; Lamb et al. 2019; Hajela et al. 2020; Makhathini et al. 2021; Troja et al. 2020; Balasubramanian et al. 2021) revealed a distinctive signature of a successfully launched structured jet, setting it apart from a chocked jet scenario. The observed electron power-law index derived from the afterglow spectrum falls within the range predicted in a theory of particle acceleration at trans-relativistic shock (Keshet & Waxman 2005) as mentioned by Margutti et al. (2018) and is consistent with being constant in time within observational errors (D’Avanzo et al. 2018; Dobie et al. 2018; Margutti et al. 2018; Fong et al. 2019; Kilpatrick et al. 2022).