The recoiling supermassive black hole (rSMBH) carries it the broad-line region (BLR) along with it and leaves the stellar nucleus behind; it can be observable for tens of Myr as an offset AGN (Madau & Quataert 2004; Loeb 2007, Blecha et al. 2011, 2016). We therefore expect two observational characteristics: (i) the rSMBH could be observed spatially offset with respect to the stellar center of the host galaxy, and (ii) the broad emission lines could have a measurable velocity offset with respect to the systemic velocity. So far, there have been more than a dozen reports of rSMBH candidates. Some examples of rSMBH candidates are SDSS J092712.65+294344.0 (Komossa et al. 2008), SDSS J105041.35+345631.3 (Shields et al. 2009), M87 (Batcheldor et al. 2010), QSO E1821+643 (Robinson et al. 2010), CXOC J100043.1+020637 (Civano et al. 2010), CXO J122518.6+144545 (Jonker et al. 2010), a half-dozen SDSS QSOs (Eracleous et al. 2012), 10 nearby core elliptical galaxies (Lena et al. 2014), NGC 3115 (Menezes et al. 2014), 5 SDSS AGNs (Comerford et al. 2015), and 26 SDSS QSOs (Kim et al. 2016). Except for CXOC J100043.1+020637, most of the rSMBH candidates described to date either have a spatial offset or a velocity offset, but not both. The source CXOC J100043.1+020637 has two compact sources separated by ∼2.5 kpc and has a velocity offset of ∼1200 km s−1 (Civano et al. 2010). Chandra observations find that the southeastern source, which has a point-like morphology typical of a bright AGN, is responsible for the whole X-ray emission in this system (Civano et al. 2012). The northwestern source has a more extended profile in the optical band, with a scale length of ∼0.5 kpc. Recent 3 GHz Karl G. Jansky Very Large Array (VLA) observations find that the entire observed 3 GHz radio emission can be associated with the southeastern nucleus (Novak et al. 2015). The observations favored an explanation within the rSMBH picture, but the presence of an obscured and radio-quiet SMBH in the northwestern source is not ruled out (i.e., Blecha et al. 2013; Wrobel et al. 2014).


The non-gravitational interaction in the dark sector, precisely between dark matter and dark energy is a phenomenological concept that was originally thought to explain the different values of the time-independent cosmological constant (Wetterich 1995), but later on, such concept was found to be very useful to explain the cosmic coincidence problem (Amendola 2000; Chimento et al. 2003; Cai & Wang 2005; Hu & Ling 2006; del Campo, Herrera & Pavón 2008, 2009). Certainly, this led to a large amount of investigations towards this direction where the dark sectors have direct interaction (Billyard & Coley 2000; Barrow & Mota 2003; Barrow & Clifton 2006; Skordis et al. 2006; Koivisto & Mota 2008b; Quartin et al. 2008; Chimento 2010; Valiviita, Maartens & Majerotto 2010; Koivisto, Mota & Zumalacarregui 2012; Thorsrud, Mota & Hervik 2012; Akrami et al. 2013; Faraoni, Dent & Saridakis 2014; Yang & Xu 2014a,b,c; Duniya, Bertacca & Maartens 2015; Pan, Bhattacharya & Chakraborty 2015; Valiviita & Palmgren 2015; Mukherjee & Banerjee 2017; Pan & Sharov 2017; Santos et al. 2017; Sharov et al. 2017; Pan, Mukherjee & Banerjee 2018; also see Pan & Chakraborty 2013; Chen et al. 2014; Pan & Chakraborty 2014; Shahalam et al. 2015, 2017; Cai, Tamanini & Yang 2017; Kumar & Nunes 2017a; Odintsov, Oikonomou & Tretyakov 2017). Such interacting scenarios have good motivation if the particle physics theory is considered because from the particle physics view, mutual interaction between any two fields is a natural phenomenon, irrespective of the nature of the fields. Although the interacting dynamics is complicated and a generalized cosmic scenario, it recovers the non-interaction cosmology as a special case. Thus, the theory of non-gravitational interaction between dark matter and dark energy is a generalized version of the non-interacting dark matter and dark energy cosmologies. Interestingly enough, the observational data at recent time found that the direct interaction between dark matter and dark energy cannot be excluded (Salvatelli et al. 2014; Kumar & Nunes 2016; Nunes, Pan & Saridakis 2016; Yang et al. 2016; Kumar & Nunes 2017b; van de Bruck, Mifsud & Morrice 2017; Yang, Banerjee & Pan 2017a; Yang, Pan & Mota 2017b; Yang, Pan & Barrow 2018). Moreover, very recently, it has been reported that the current tension on the local Hubble constant can be alleviated with the introduction of dark matter and dark energy interactions (Kumar & Nunes 2016; Di Valentino, Melchiorri & Mena 2017). Additionally, the crossing of phantom barrier has also been found to be an easy consequence of the non-gravitational interaction. Thus, the theory of interacting dark energy might be considered to be an appealing field of research and indeed a hot topic for the next generation of the astronomical surveys.


The comparison with other hot corinos is not easy since we have a limited number of lines, in contrast to well-known sources that have been more extensively observed with ALMA and NOEMA, such as IRAS 16293-2422 (Jørgensen et al. 2016), NGC1333 IRAS 2A and 4A (Taquet et al. 2015; López-Sepulcre et al. 2017). In general, we find a similar inventory ofCOMs but with lower abundances in B1b-S. We are going to discuss only some trends and ratios between them. For example, one similarity with hot corinos are the higher abundances of O-bearing COMs with respect to N-bearing COMs. We observe a similar trend in B1b-S, where the highest abundances are obtained for CH3OCOH, CH3OCH3, and CH3CHO, while NH2CN and NH2CHO show the lowest abundances. Cyanamide has been recently detected towards the low-mass protostars IRAS 16293-2422 and NGC 1333 IRAS2A (Coutens et al. 2018), with observed NH2CN to NH2CHO ratios of 0.2and 0.02, respectively. These values are in the range of those observed towards the molecular clouds in the Galactic centre but lower than in Orion KL (Coutens et al. 2018). We obtain in B1b-S anabundance ratio of 0.25, similar to IRAS 16293-2422. Of the three possible isomers of C2 H4O2, we have detected CH3OCOH and CH2OHCHO. The observed CH3OCOH to CH2OHCHO ratio in B1b-S, ~20, is similar to that observed in the low-mass protostars in NGC 1333 and IRAS 16293-2422 (Taquet et al. 2015; Jørgensen et al. 2012). Acetic acid (CH3COOH) is the most stable but the least abundant of the three isomers (Lattelais et al. 2010). It has been observed in IRAS 16293-2422 with a ratio with respect to glycolaldehyde of ~11 (Jørgensen et al. 2016), consistent with the 5–15 upper limits in B1b-S. Glycolaldehyde and its corresponding alcohol, ethylene glycol, show similar abundances in B1b-S, slightly higher for CH2OHCHO. This is in contrast to other hot cores and hot corinos (Fuente et al. 2014; Jørgensen et al. 2016; Favre et al. 2017). However, since detections of these species are based on just a few lines, in particular for glycolaldehyde, column densities may be not well constrained and it is difficult to make definite conclusions. We have detected CH3CH2OCOH for the first time in a low-mass protostar, with a relatively high abundance of 10−11. This detection shows that the molecular complexity is high in young hot corinos and other species with a larger number of atoms could be present. It is noteworthy that this species has not been previously observed in the well-known hot corinos IRAS 16293-2422 and NGC 133IRAS4A. We have checked in the ALMA spectral line survey of IRAS 16293-2422 (PILS, Jørgensen et al. 2016), and no clear features are seen, although the observed frequencies are different. It is possible that the high level of line confusion and wide linewidths prevent the detection of weak lines in these more evolved sources.


The filtered MHD equations read
11

12

where we sum over repeated indices, and
13

14

15

16

denote the inertial (I), Maxwell (M), advective (A), and dynamo (D) subfilter-scale stresses, respectively. Despite their common origin through the electric field in the induction equation, we here treat

 and

 separately, in order to disentangle the effects of magnetic-field-line advection, encoded in

, and magnetic-field-line stretching, encoded in

. Usually, the magnetic subscale stress refers to the difference

 (Aluie 2017; Offermans et al. 2018). Equations (11) and (12) differ from expressions for the filtered MHD equations found elsewhere by an additional projection of the coupling terms. The latter ensures that the dynamics defined by Equations (11) and (12) are confined to the same finite-dimensional subspace Ωℓ of the original domain Ω (Buzzicotti et al. 2018; Offermans et al. 2018). At first sight, this formulation suggests that the corresponding evolution equations for kinetic and magnetic energy feature terms are not Galilean invariant, which ought to be avoided as the measured subfilter-scale energy transfers otherwise include unphysical fluctuations (Aluie & Eyink 2009a, 2009b; Buzzicotti et al. 2018). However, the energy balance equations can be expressed in an alternative way by including terms that vanish under spatial averaging and ensure Galilean invariance of all terms (Buzzicotti et al. 2018; Offermans et al. 2018). For a statistically stationary evolution, the spatiotemporally averaged energy budget can then be written as
17

18

where

 and

 are the filtered kinetic and magnetic dissipation rates, respectively, and

 are terms that convert kinetic to magnetic energy

 and vice versa

, and
19

20

21

22

denote the four proper energy fluxes, in the sense that they vanish in the limit ℓ → 0, as can be seen from Equations (13)–(16). If positive, the inertial and Maxwell fluxes,

 and

 transfer kinetic energy from scales larger than or equal to ℓ to scales smaller than ℓ and vice versa if negative, while the advective and dynamo fluxes,

 and

, do so with magnetic energy. Note that there is no interscale energy conversion as the conversion terms

 and

 only involve filtered fields; as such they are known as resolved-scale conversion terms (Aluie 2017). The total energy flux is then given by the sum
23


The young starburst inferred by the detections of high ionization emission line of He II λ4686 and the blue WR bump in this and previous works (Guseva et al. 2000; Brinchmann, Kunth & Durret 2008) is confirmed by the age estimates made here for the bright and faint regions in Mrk 22 as ∼4 and ∼10 Myr, respectively. Unlike previous works, we carried out abundance analysis for both the regions separately. We found an appreciable metallicity difference of ∼0.5 dex between the bright region [12 + log (O/H) ∼ 8] and the faint region [12 + log(O/H) ∼ 7.5]. The separation between two regions is ∼0.6 kpc. Typical metallicity gradients in normal spiral galaxies have been found between −0.009 and −0.231 dex kpc−1, with an average gradient of −0.06 dex kpc−1 (Zaritsky, Kennicutt & Huchra 1994). The observed metallicity difference between the two regions in Mrk 22 is too large to be explained as a normal galactic metallicity gradient. The chemical composition as measured from the gas-phase metallicity [12 + log(O/H)] shows various degree of spatial variations in different types of dwarf galaxies. For instance, shallow gradient in metallicity is seen in SBS 0335−052 (Papaderos et al. 2006) while no significant variations were seen in Mrk 35 (Cairós et al. 2007). A study on a large sample indicates that normal BCD galaxies are chemically homogeneous (Kobulnicky & Skillman 1996; Papaderos et al. 2006; Kehrig et al. 2008; Cairós et al. 2009; Pérez-Montero & Contini 2009; Pérez-Montero et al. 2011; Hägele et al. 2011; García-Benito & Pérez-Montero 2012; Lagos & Papaderos 2013). On the other hand, the metallicity of extremely metal-poor galaxies is usually not homogeneous within the galaxy, with the low metallicity seen in regions of intense star formation (Papaderos et al. 2006; Izotov & Thuan 2009; Levesque et al. 2011; Sánchez Almeida et al. 2013, 2014, 2015). However, large metallicity gradients are not common in dwarf galaxies. The simplest explanation for large metallicity difference in a single system is a recent merger of two galaxies with different metallicity. In a few cases, significantly large metallicity differences between star-forming regions in dwarf galaxies were seen and understood in terms of recent tidal interactions or mergers (López-Sánchez, Esteban & Rodríguez 2004a,b; López-Sánchez, Esteban & García-Rojas 2006; López-Sánchez & Esteban 2009, 2010). The evolution in terms of metallicities in interacting dwarf galaxies is fairly complex as it can depend on various factors such as mixing of metals with the interstellar medium (ISM), possible outflows of metals, and inflow of metal-poor gas in tidally interacting systems.


Figure 1a shows for each cluster a visualization of the resulting background-subtracted color-magnitude diagram, produced with an approach similar to that of van der Burg et al. (2016). Specifically, we subtracted the residual background contamination as follows: 1) We start from a candidate cluster member sample obtained as discussed in Sect. 3.1, and a control field sample from the GOODS-S field (see Sect. 2.3) that is selected in the same manner. 2) For each galaxy in the candidate member sample, we calculate a “weight” that corresponds to the statistical excess of the candidate member sample over the control field density at the magnitude and colors of the given galaxy. Weights are calculated as follows (see van der Burg et al. 2016, for a more detailed description): first, all candidate member weights are initially set to 1. Then, for each galaxy in the control field sample we subtract the corresponding “background contamination” from the candidate member sample by appropriately reducing the weights of all candidate members that lie within a distance in the color (m814–m140) – color (m140–[3.6]) – magnitude (m140) space given by their photometric uncertainties (1σ), with a minimum distance of 0.3 mag, effectively resulting in a smoothing of galaxy densities in the color-color-magnitude space. If no galaxies are found within this distance, we double the search distance, and then if necessary increase the search distance to 1.3 times the distance to the closest galaxy. This criterion allows the full subtraction of the background contamination estimated from all galaxies in the control field sample, while reducing the weights of those candidate members that are more similar to the galaxies in the control field. For each considered control-field galaxy, the weights of all selected candidate members identified with the above criterion are reduced so that the contribution of the considered field galaxy (normalized by the areas of the probed cluster region and of the control field) is removed. At the end of this procedure, the contributions of all galaxies from the field sample have been subtracted from the candidate member sample.


So far, only one ancient and massive intruder has been identified unambiguously, with its body now nothing but an enormous cloud of tidal wreckage scattered throughout the inner Milky Way. The existence of a vast debris structure left behind by this merger event, known today as the Gaia-Sausage/Enceladus (GS/E), was suggested before Gaia (see Evans 2020, for the historical development). In particular, Deason et al. (2013) argued that the rapid transition in the Galactic stellar halo structural properties at break radius of 20–30 kpc is likely associated with the apocentric pileup of a relatively early (8–10 Gyr ago) and single massive accretion event. It is hypothesized that the progenitor dwarf galaxy was massive enough for its orbit to shrink and radialize quickly as a result of a complex interplay between dynamical deceleration, host recoiling, and self-friction (Vasiliev et al. 2022). Sinking deep in the heart of the Milky Way, the dwarf sprayed the bulk of its stars in a region enclosed by its last apocenter, i.e., some ∼30 kpc (see Deason et al. 2018). As a result, the region of the Galactic halo within this so-called break radius (see Deason et al. 2011) is inundated with the GS/E stars, consistently showing up as the most striking substructure even in relatively small volumes around the Sun (see examples of pre-Gaia hints in, e.g., Chiba & Yoshii 1998; Brook et al. 2003; Meza et al. 2005; Nissen & Schuster 2010; Hawkins et al. 2015). Subsequently, the Gaia data made crystal clear the unusually strong radial anisotropy of the relatively metal-rich GS/E debris and helped to reveal its dominance in the solar neighborhood (see Belokurov et al. 2018; Haywood et al. 2018b; Myeong et al. 2018b). The genesis of the GS/E debris cloud was also unambiguously confirmed by its unique chemical fingerprint (see, e.g., Helmi et al. 2018; Mackereth et al. 2019) and the large group of globular clusters (GCs) associated with it (see, e.g., Myeong et al. 2018c, 2019; Massari et al. 2019). Close to the Sun, the GS/E structure has been thoroughly scrutinized both kinematically and chemically (see Evans et al. 2019; Necib et al. 2019; Sahlholdt et al. 2019; Das et al. 2020; Feuillet et al. 2020, 2021; Kordopatis et al. 2020; Molaro et al. 2020; Monty et al. 2020; Aguado et al. 2021a; Buder et al. 2021a; Bonifacio et al. 2021; Carollo & Chiba 2021; Matsuno et al. 2021). Outside of the solar neighborhood, fewer studies exist; nonetheless, the global structure of the GS/E cloud is starting to come into focus (see, e.g., Iorio & Belokurov 2019; Lancaster et al. 2019; Simion et al. 2019; Naidu et al. 2020; Balbinot & Helmi 2021; Bird et al. 2021; Iorio & Belokurov 2021; Wu et al. 2022).


Our N-body planet-formation simulations utilize the well-established Mercury6 Hybrid integration package (Chambers 1999). While the resolution of our simplified numerical models is admittedly low compared to many contemporary models of planet formation (e.g., Morishima et al. 2010; Carter et al. 2015; Woo et al. 2021), this is acceptable for our purposes as the goal of our study is broadly investigate planet formation around M-dwarfs and follow the dynamical evolution of debris (i.e., collisional fragments and leftover planetesimals: Genda et al. 2012; Stewart & Leinhardt 2012; Quintana et al. 2016; Clement et al. 2019b) generated and stranded during the ultimate epoch of giant impacts in these systems. Thus, we limit the number of simulation particles employed in our initial simulation set and do not include a pebble accretion model to minimize compute time and perform a broad parameter space sweep before switching to higher-resolution models in our investigation of post-formation bombardment (Section 2.2). Moreover, as the initial conditions for planet formation around low-mass stars remain poorly understood and largely unconstrained, we begin our investigation by deviating only slightly from the accepted paradigm of rocky planet accretion in the solar system (e.g., Chambers & Wetherill 1998; Chambers 2001; Hansen 2009). An important limitation of this methodology is the absence of a gas-disk model in our simulations. If short-period planets around M-dwarfs form in situ, their growth is sufficiently rapid that it must have coincided with the gas-disk phase (unless planetesimal formation is delayed for some reason (Ogihara et al. 2015, see Section 4 for a more detailed discussion of these caveats). We plan to expound upon the results of this preliminary study in future work with more detailed models and artificial gas-disk treatments (e.g., Clement et al. 2020) specifically tuned to form specific systems of M-dwarf-hosted planets (e.g., Ormel et al. 2017; Coleman et al. 2019; Schoonenberg et al. 2019).


However, the intrinsic effects caused by the unknown emission and acceleration mechanisms in the source could mitigate or enhance the LIV-induced time delay, which would impact the accuracy of the resulting constraints on LIV. A key challenge is then to distinguish an intrinsic time lag at the source from a delay induced by LIV. Long GRBs usually have significantly positive or negative intrinsic spectral lags and should not be used for LIV searches until reasonable progress is made on the modeling of the emission and acceleration mechanisms (Chen et al. 2005; Ukwatta et al. 2012; Bernardini et al. 2015), while short GRBs are consistent with null or negligible intrinsic spectral lag and are therefore an ideal tool to measure the LIV effect (Norris & Bonnell 2006; Bernardini et al. 2015, 2017; Xiao et al. 2022). Currently, in addition to short GRBs, active galactic nucleus (AGN) flares and gamma-ray pulsars are two other classes of astrophysical sources that have no significant intrinsic lag in general and are often used for LIV tests (Biller et al. 1999; Kaaret 1999; Aharonian et al. 2008; MAGIC Collaboration et al. 2017). It should be noted, however, that there is also evidence of intrinsic lags in some cases of AGN flares and pulsars. For example, MAGIC Collaboration during an observational campaign regarding Mkn 501 blazar found an indication of about 4 minutes time delay between the peaks at E  0.25 TeV and E > 1.2 TeV (MAGIC Collaboration et al. 2008), which may indicate a progressive acceleration of electrons in the emitting plasma blob. A robust method to study the correlations between arrival times and energy, based on a likelihood function built from the physical picture assumed for the emission, propagation, and detection of the photons was proposed by Martínez & Errando (2009). In the case of pulsars, there are some lags if the energy range is extended too much toward low energies (e.g., radio versus TeV). No real progress on the topic of intrinsic effects will be made without accurate models for production and acceleration mechanisms for each type of source. Perennes et al. (2020) first attempted to gain knowledge on source-intrinsic spectral lags of flaring AGNs at high and very high energies and on short timescales relevant for LIV searches, using leptonic AGN flare modeling. Concerning GRBs, some ways have been proposed to reduce the impact of intrinsic effects, e.g., fitting the observed spectral lags of statistical samples of GRBs at a range of different redshifts (Ellis et al. 2006; Bernardini et al. 2017; Xiao et al. 2022), or using only a limited observer-frame energy bands range corresponding to the fixed source-frame energy bands (Wei & Wu 2017). Anyway, there is no reason to think that the low and high-energy photons should be emitted simultaneously at the source, and while detecting distinct signals at different energy channels, we have no idea which one was sent first. Previous studies usually assumed that the intrinsic time delays are either an unknown constant for all GRBs considered or scale with the photon energy E according to some power-law function (Ellis et al. 2006; Biesiada & Piórkowska 2009a; Zhang & Ma 2015; Wei et al. 2017a; Acciari et al. 2020; Pan et al. 2020; Du et al. 2021).


We modelled the TESS photometry and HARPS RV measurements and accounted for the gravitational interactions between the adopted components of the system using a photodynamical model. The TESS transits are the most numerous of the transit observations and dominate the determination of the planet-to-star radius ratio. For simplicity, we did not model the transit observations with other instruments. The planet positions and velocities in time were obtained through an n-body integration. The sky-projected positions were used to compute the light curve (Mandel & Agol 2002) using a quadratic limb-darkening law (Manduca et al. 1977) that we parametrised following Kipping (2013). The light-time effect (Irwin 1952) was included in the model. To account for the integration time, the model was over-sampled by a factor 3 and was then binned back to match the cadence of the data points (Kipping 2010). The line-of-sight projected velocity of the star issued from the n-body integration was used to model the RV measurements. We used the n-body code REBOUND (Rein & Liu 2012) with the WHFast integrator (Rein & Tamayo 2015) and an integration step of 0.005 days, which resulted in a model error smaller than 1 ppm for the photometric model. The model was parametrised using the stellar mass and radius, planet-to-star mass ratios, planet b-to-star radius ratio, and Jacobi orbital elements (Table 3) at reference time, tref = 2458 370.418461 BJDTDB. Due to the symmetry of the problem, we fixed the longitude of the ascending node of the interior planet ΩB at tref to 180°, and we limited its inclination to ic  90°. We used a GP regression model with an approximate Matern kernel (celerite, Foreman-Mackey et al. 2017) for the model of the error terms of the transit light curves, and the QPC kernel (Perger et al. 2021; Ambikasaran et al. 2015) for the RVs. For the photometric dataset, we added a transit normalisation factor and a jitter parameter. For the RV, we added a systemic RV and a jitter parameter. In total, the model has 28 free parameters. We used normal priors for the stellar mass and radius from Sect. 3, non-informative sinusoidal priors for the orbital inclinations (uniform in cos i), and non-informative uniform prior distributions for the rest of the parameters. The joint posterior distribution was sampled using the emcee algorithm (Goodman & Weare 2010; Foreman-Mackey et al. 2013) with 200 walkers with starting points based on the results of Sect. 4.2. We ran 1.2×106 steps of the emcee algorithm and used the last 200 000 steps for the final inference. In Table 3, we list the prior, the median, and the 68% CI of the inferred marginal distributions of the system parameters.


The magnetic field in the crust of a neutron star is simple. In the crust, ions are fixed in a lattice, while only the electrons are mobile. These dynamics may be described based on electron magnetohydrodynamics. The evolution of the magnetic field owing to the Hall drift and Ohmic dissipation has been studied in several researchers. The magnetic fields are numerically simulated on a secular time-scale (refer Pons & Geppert 2007; Kojima & Kisaka 2012; Viganò et al. 2013; Gourgouliatos et al. 2013; Gourgouliatos & Cumming 2014, for axially symmetric cases). Recently, three-dimensional calculations of the evolution have been performed (Wood & Hollerbach 2015; Gourgouliatos, Wood & Hollerbach 2016; Gourgouliatos & Hollerbach 2018). The simulation shows that non-axisymmetric features such as magnetic hotspots produced by an initial perturbation persist over a long time-scale ∼106 yr. Small-scale features are likely to decay owing to the action of Ohmic dissipation, but they seem to be steadily supported by the Hall effect. This effect becomes more important as the field-strength increases. At the same time, magnetic stress causes deformations in the ion lattice. The crust responds elastically when the deviation is within a critical limit. Beyond this limit, the crust cracks or responds plastically. The effect of elastic deformation on the crustal magnetic-field evolution has been studied (Bransgrove, Levin & Beloborodov 2018). Sudden crust breaking could produce a magnetar outburst and/or a fast radio burst (Li, Levin & Beloborodov 2016; Baiko & Chugunov 2018; Suvorov & Kokkotas 2019). Plastic flow beyond the critical point is crucial for long-term evolution (Lander 2016), and a coupled system between the flow and magnetic field can be solved numerically in a two-dimensional square box of a crust-depth size (Lander & Gourgouliatos 2019). Their simulation shows significant motion near the surface at a rate of 10–100 cm yr−1 for a certain viscosity range. At 103 yr, the path-length reaches ∼1 km, which is the size of the simulation in plane-parallel geometry. The magnetic-field structure comprises a poloidal loop field confined in a two-dimensional box. It is important to examine the effect of the plastic flow on the global features. In particular, changes in the external dipole field in 103–105 yr are interesting.


Theoretical features of CB-SMBHs have been predicted for observations; however, observational data can be alternatively explained by complicated broad-line region (BLR) models around a single black hole. Thus, they are still elusive, though there is growing evidence for the appearance of CB-SMBHs. As one of the several signatures of CB-SMBHs, radial velocity curves of double-peaked Hβ emission line have been suggested by Popović et al. (2000), Shen & Loeb (2010), Tsalmantza et al. (2011) and Popović (2012),  but the asymmetry is a better tracer than the double-peakedness in the reverberations (Shen & Loeb 2010). Candidates with this feature are NGC 4151 (Bon et al. 2012) and NGC 5548 (Li et al. 2016a, 2016b), which show opposite motions of red and blue peaks. A large sample of active galactic nuclei (AGNs) with double-peaked Hβ profiles built up by Eracleous et al. (2012) has been monitored for systematic shifts of the two peaks for a couple of years (Runnoe et al. 2017). Periodical variations could be regarded as a signature of binary black holes, such as OJ 287 (Valtonen et al. 2008), PG 1320 (Graham et al. 2015), Akn 120 (Li et al. 2017), and others (Liu et al. 2015; Zheng et al. 2016; Dorn-Wallenstein et al. 2017). It usually takes at least three times the period to determine the periodicity of varying AGNs, such as, more than 10 yr to justify their periodicity if the orbital periods are 3 yr or so (Li & Wang 2018). An X-shaped radio jet has been suggested as a signature of binary black holes (Merritt & Ekers 2002; Cheung 2007), but only one could be plausible (Kharb et al. 2017). A deficit of UV emissions of spectral energy distributions is formed by the interaction between the secondary and circumbinary disks (Hayasaki et al. 2008; Schnittman 2011a, 2011b; Sesana et al. 2012; Roedig et al. 2014). However, there are alternative explanations for these phenomena, such as a processing jet as an alternative explanation of AGN periodical variabilities (since most of them are radio-loud AGNs), dust extinction for the UV deficit in Mrk 231 (Ye et al. 2016; but see Leighly et al. 2016), elliptical disks (Eracleous et al. 1995), and hot spots (e.g., Jovanović et al. 2010) or spiral arms (e.g., Storchi-Bergmann et al. 2017) for the double-peaked profiles of the broad Hβ line. Three candidates with double-peaked profiles, Arp 102B, 3C 390.3, and 3C 332, have been excluded by long-term monitoring campaigns (Eracleous et al. 1997). No CB-SMBHs have been unambiguously identified so far.


We have used the Code Investigating GALaxy Emission (CIGALE; Burgarella et al. 2005; Noll et al. 2009; Boquien et al. 2019) SED fitting package to model the full SED of ADFS-27. We have run the code on all spatially integrated photometry from Table 2 for the entire galaxy and also on the two source components ADFS-27N and S individually, using only the photometry in those bands where the emission is resolved into both sources. We ran two series of fits, with star formation histories (SFHs) limited either to approximately the age of the universe at z = 5.655 (i.e., ≤1.0 Gyr) or to an age of ≤0.2 Gyr, as is characteristic for young dusty starbursts (e.g., Greve et al. 2005; Bergvall et al. 2016). We sampled standard ranges for all main parameters within CIGALE and used a Bruzual & Charlot (2003) single stellar population and a Chabrier (2003) stellar initial mass function with a “delayed” SFH (i.e., where SFR(t) ∝ t/τ2 × exp(−t/τ), and the fit parameter τ is the time at which the SFR peaks; Boquien et al. 2019; see also Burgarella et al. 2020) for all fits. We fixed the power-law slope of the dust attenuation law to −0.7 for both the interstellar medium and birth clouds and assumed a polycyclic aromatic hydrocarbon (PAH) mass fraction (which is not directly constrained by the data) of qPAH = 3.9% (i.e., similar to dust found in the Milky Way and nearby galaxies with near-solar metallicity; e.g., Draine & Li 2007, and references therein).13

13
We allowed for a range in metallicity in our fits, but the metallicity remains difficult to constrain directly without rest-frame optical spectroscopy.
 This is consistent with the range of qPAH = 0.47%–3.9% found for a sample of infrared-luminous galaxies at z = 0.5–4 (Magdis et al. 2012).14

14
The uncertainty due to this assumption is fully captured by the error bars for the most relevant parameters, like Mdust.
 For ADFS-27 as a whole and for ADFS-27S (which is detected in the near-infrared bands), the best-fit parameters for both series agree within the uncertainties. We thus adopt those from the series with less constraints on the SFH in the following, and we only use those from the other series in the evaluation of the true uncertainties. For ADFS-27N (which is not detected in the near-infrared bands), the series with more stringent constraints on the SFH appears to provide more reasonable results and thus are adopted in the following.


The Galactic Center (GC) and the Central Molecular Zone (CMZ) in particular represent an environment with conditions that are not to be found anywhere else on large scales in the Milky Way. The CMZ received its name from the presence of a large reservoir of dense (

 cm−2) and molecular gas of a few times 107 M⊙ (Oka et al. 1998; Morris & Serabyn 1996; Ferrière et al. 2007) and covers the central ∼500 pc of the GC region. The large amount of molecular gas is found to be accompanied by a relatively high star formation rate (SFR) of ∼0.1 M⊙ yr−1 (Longmore et al. 2013a; Barnes et al. 2017). Star formation (SF) laws that build on the assumption of a constant gas-depletion time of 1 Gyr can fit the observed SFR (Bigiel et al. 2010; Leroy et al. 2008, 2015). However, these relations are derived from gas at much lower densities than observed in the CMZ. Density-dependent SF laws, on the other hand, strongly overpredict the SFR (Longmore et al. 2013a) at ∼0.4 M⊙ yr−1 (Kennicutt 1998; Krumholz & McKee 2005; Krumholz et al. 2012) to ∼0.8 M⊙ yr−1 Lada et al. (2010, 2012). Thus, the star formation efficiency (SFE) in the CMZ is significantly lower than expected for the observed gas densities. The complex interplay of energetic processes in the GC allows for different potential answers to this problem of low SFE, but none of these processes alone can explain the discrepancy (Kruijssen et al. 2014). A general picture of episodic starbursts in gas rings in galactic centers introduced by Krumholz & Kruijssen (2015) and Krumholz et al. (2017) might solve the SFE problem in the particular case of the CMZ and set the framework for another intriguing feature of the GC: a ring-like structure of dust and molecular gas. This structure (see Figure 1 for an overview) is projected onto an infinity (

) shape that follows several arcs, the most prominent being the so-called “dust ridge” stretching from the massive molecular cloud G0.253+0.016 (“the Brick”) to the star-forming region Sgr B2 (Lis et al. 1999). It might be continued via an

 arc and another loop at negative longitude ([

],

]) passing through the star-forming region Sgr C. The syntax

 denotes the four quadrants in Galactic coordinates at positive/negative Galactic longitude (l) and latitude (b). Clouds at

 and

 are thought to be located in front of Sgr A*, i.e., the near side of the GC that is visible in silhouette against the background, whereas most of the

 and

 gas is more likely to be on the far side, i.e., behind Sgr A* (Bally et al. 2010; Molinari et al. 2011).


In the interstellar medium, CH3OH  and other “saturated” (hydrogen-rich) molecules are primarily believed to be formed on the surface of dust grains (Tielens & Hagen 1982; Charnley et al. 1992; Watanabe & Kouchi 2002), where CH3OH and NH3  are among the most abundant mantle species present relative to H2O, as measured in both low and high-mass young stellar objects (YSOs) and cold cloud cores (Tielens & Allamandola 1987; Dartois et al. 1999; Pontoppidan et al. 2004; Gibb et al. 2004; Boogert et al. 2008; Öberg et al. 2011). Notably, for CH3OH, the high abundances measured for maser sources are inconsistent with those predicted by gas-phase formation models (Menten et al. 1986; Hartquist et al. 1995). To get the CH3OH  off of the dust grains and into the gas phase in the observed large quantities then requires a mechanism to liberate the CH3OH  from the grain mantles. Proposed mechanisms include thermal desorption via heating from an embedded protostar, shocks, or cosmic rays (requiring grain temperatures ≳90 K Tielens 1995; Brown & Bolina 2007), or nonthermal desorption processes including photodesorption via far-UV photons from cosmic ray interactions (Prasad & Tarafdar 1983; D’Hendecourt et al. 1985; Öberg et al. 2009a), grain sputtering, wherein the ice mantles of grains are dislodged via collisions (often in shocks) with other grains, neutrals, ions, or cosmic rays (Johnson et al. 1991; Caselli et al. 1997), and finally exothermic chemical reactions on the grain surfaces Duley & Williams (1993), Roberts et al. (2007). In particular, the presence of molecules formed on grains in relatively cool and dense environments requires an efficient nonthermal desorption process (Willacy & Williams 1993; Roberts et al. 2007; Öberg et al. 2009b; Caselli et al. 2012). In the CMZ, the abundance of 36 GHz CH3OH  sources has been suggested to be due to photodesorption from cosmic rays in this region Yusef-Zadeh et al. (2013a). We reconsider this in the light of our new, high-resolution observations.


The classical framework in which theoretical galactic studies are performed these days is the Λ cold dark matter (ΛCDM) paradigm. However, both the cosmological constant Λ and the CDM part of the model could also be related to a modification of gravity. On galaxy scales, the model is indeed plagued by severe problems, the most famous ones being the cusp–core problem (de Blok 2010; Oman et al. 2015, but see also Read et al. 2016), the too-big-to fail problem (Boylan-Kolchin, Bullock & Kaplinghat 2011; Papastergis et al. 2015; Pawlowski et al. 2015) or the satellite planes problem (Kroupa, Theis & Boily 2005; Metz, Kroupa & Jerjen 2007; Metz, Kroupa & Libeskind 2008; Pawlowski, Pflamm-Altenburg & Kroupa 2012; Ibata et al. 2013, 2014; Pawlowski et al. 2015). There is also a more general problem linked to the finely tuned relation between the distribution of baryons and the gravitational field in galaxies, as encapsulated in various scaling relations involving a universal acceleration constant a0 ≈ 10−10 m s−2, including the tight baryonic Tully–Fisher relation (McGaugh et al. 2000; Lelli, McGaugh & Schombert 2016a; Papastergis, Adams & van der Hulst 2016), the diversity of shapes of rotation curves at a given maximum velocity scale (Oman et al. 2015) or the relation between the stellar and dynamical surface densities in the central regions of galaxies (Lelli et al. 2016b; Milgrom 2016), and many others (Famaey & McGaugh 2012). All this points to things happening as if the effects usually attributed to CDM on galaxy scales were actually due to a modified force law. The a priori simplest explanation for this would be that gravity is indeed effectively different in the weak field regime and accounts for the effects usually attributed to CDM. This paradigm is known as modified Newtonian dynamics (MOND), or Milgromian dynamics, suggested more than 30 years ago by Milgrom (1983). It predicted all the observed galaxy scaling relations well before they were precisely assessed by observations (Famaey & McGaugh 2012). Nevertheless, this paradigm cannot be complete, as a full theory of gravitation, also valid on cosmological scales, has not yet been found. But while successful on galaxy scales, the MOND paradigm has still been far from being fully explored even on these scales where it is currently successful. Hence, there is still potential for falsification of this paradigm in its a priori domain of validity. The main reason for this lack of exploration of all predictions of MOND on galaxy scales is its non-linear nature, and the previous lack of numerical codes devised to model galaxies in this framework.


Over 2500 known pulsars have been included in the database of the Australia Telescope National Facility (ATNF1

1

http://www.atnf.csiro.au/research/pulsar/psrcat

), whose parameters can be queried and visualized, and more fascinating pulsars are waiting to be discovered (Manchester et al. 2005; Bates et al. 2012; Ng et al. 2015). Many of these stars have very stable rotation periods. Among them, the rotation periods of “normal” pulsars vary from a few tens of milliseconds to a few seconds, and the derivatives of their periods are between 10−17 and 10−13 (Manchester et al. 2001; Lorimer et al. 2006); they are called cosmic “lighthouses” because their broadband emission and steady rotation sweep out a beam of radiation across the sky. These lighthouse-like pulsars can radiate photon signals with stable periods and profiles, thus playing an important role in studying the evolution law of stars (Faucher-Giguere & Kaspi 2006), exploring the interstellar medium (ISM; Daniel et al. 2000; Bogovalov et al. 2005), detecting gravitational waves (Hobbs et al. 2009), establishing timing references (Hobbs et al. 2012) and realizing deep-space navigation (Sheikh et al. 2006; Emadzadeh & Speyer 2011). On-orbit application research on pulsars is being performed worldwide (Vikhlinin et al. 2009; Ge et al. 2012; Kaya et al. 2014). However, pulsars are far from the Earth, and compared with the receiving areas of gigantic ground-based radio observatories, that of an X-ray detector is more limited; therefore, the received photon signals are always submerged in observation noise. Meanwhile, compared with radio signals, which are more susceptible to interference from artificial signals, other forms of ground signals and photon signals from other stars, X-ray signals are almost immune to interference because of their small field of view and high energy. However, we cannot completely rule out the possibility of interference from instruments and other stars. The above factors hamper research on pulsar searches and timing observations. Therefore, it is quite important to study noise and interference mitigation methods for pulsar signals.


Be stars are believed to rotate at ~60−80% of their critical velocity (Porter 1996; Rivinius et al. 2006). Earlier observations of the V850 Cen Hα line (Parkes et al. 1980; Corbet et al. 1986) detected a shell-type profile of the emission line, that is a double-peaked profile in which the central absorption extends below the stellar continuum flux. According to the seminal model by Struve (1931, yet largely accepted; see Rivinius et al. 2013, for a more recent review), shell-type profiles imply an inclination angle of i ~ 90° (i.e. an edge-on system). During our campaign we did not observe shell-type emission lines (see Fig. 2). Therefore, based on a qualitative comparison with Fig. 1 of Rivinius et al. (2013), the profiles detected in this work support a large (60° ≲  i  ≲ 80°) inclination angle, yet not an edge-on view. Later, more physical models (Hummel 1994; Hanuschik 1996; Hummel & Hanuschik 1997) also support a large inclination angle. However, we should note here that line profile shapes do not always give unambiguous information about the disk inclination angle (Silaj et al. 2010; Quirrenbach et al. 1997). In any case, transient shell lines do not demand a tilt of the disk plane. For example, shell profiles need a geometrically thick medium to form. Therefore, the Hα line profiles observed in the present work may simply be due to a decrease of the disk density, with respect to previous conditions. Assuming typical values of the mass and radius of a B2 type star as M⋆ = 9.9 M⊙, R⋆ = 5.4 R⊙ (Townsend et al. 2004; Pasinetti-Fracassini et al. 2000; Sugizaki et al. 2015), the critical velocity of rotation is (4)\begin{equation} V_{\rm break}=\sqrt{\frac{GM_\star}{R_\star}}\approx475\,\rm km\,s^{-1}. \end{equation}Vbreak=GM⋆R⋆≈475 km s-1.With an inclination angle i = 90° and Vsini = 330 km s-1, the resulting critical fraction is w = V/Vbreak ≈ 0.69. On the other hand, assuming w = 0.8 and Vsini = 330 km s-1, the resulting inclination angle is i ~ 60°, which is still consistent with the inclination inferred by the Hα line profile. We therefore conclude that, at least during our observations, a more conservative range for the inclination angle of V850 Cen is 60° ≲  i  ≲ 90° and that V850 Cen is likely rotating at 0.69 ≲  w  ≲ 0.80.


Unlike BH–BH mergers, binary neutron star (BNS) merger mechanisms are expected to yield an optical counterparts powered by the radioactive decay of rapid neutron capture process (r-process) elements synthesized in the merger ejecta (Li & Paczyński 1998; Metzger et al. 2010) or by the cooling of shock-heated material around the neutron star (NS; Piro & Kollmeier 2018). On 2017 August 17, the LVC detected the first and best example of a BNS merger: GW170817 (Abbott et al. 2017a). Only two seconds after its detection, a short gamma-ray burst (GRB 170817A) was detected (Connaughton et al. 2017; Goldstein et al. 2017). GRB 170817A was followed by the discovery of the optical counterpart Swope Supernova Survey 17a [SSS17a (AT 2017gfo)] ∼11 h later in the galaxy NGC 4993 (Coulter et al. 2017) and later confirmed by others teams (Abbott et al. 2017c; Arcavi et al. 2017; Covino et al. 2017; Díaz et al. 2017; Drout et al. 2017; Kilpatrick et al. 2017; Lipunov et al. 2017; McCully et al. 2017; Pian et al. 2017; Shappee et al. 2017; Smartt et al. 2017; Soares-Santos et al. 2017; Troja et al. 2017; Utsumi et al. 2017; Valenti et al. 2017). The combination of EM and GW information on the BNS can be used to constrain the mass and the radii of NS (Margalit & Metzger 2017) or their equation of state (Bauswein & Janka 2012; Annala et al. 2018). Also, observations of the optical–infrared (IR) ‘kilonova’ counterpart (Chornock et al. 2017; Cowperthwaite et al. 2017; Drout et al. 2017; Kilpatrick et al. 2017; Nicholl et al. 2017; Shappee et al. 2017; Valenti et al. 2017; Villar et al. 2017) provided the first observational confirmation that NS mergers produce the majority of the r-process elements heavier than iron (Burbidge et al. 1957; Cameron 1957; Kasen et al. 2017; Pian et al. 2017; Metzger 2019). They also permit tests of theoretical kilonova models. For example, Drout et al. (2017) showed that the temperatures cooled from 10 000 to 5100 K in between 12 and 36 h after the event, confirming model predictions. Also, Shappee et al. (2017) used spectra taken 11.76 and 12.72 h after the merger to show that the photosphere was expanding at ∼0.3c.


The formation and evolution of S0 galaxies are very important for understanding the formation and evolution of galaxies, but they are still an open question (e.g., the recent review by D’Onofrio et al. 2015). Currently, there are two possible scenarios on the origin of S0 galaxies. One is that S0 galaxies are transformed from spiral galaxies, where spirals lose their gas and star formation is rapidly quenched. The other is that S0 galaxies are intrinsically different from spiral galaxies since their formation (Kormendy & Kennicutt 2004; Barway et al. 2009; van den Bergh 2009). The transformation origin may be associated with intra-cluster medium and neighboring galaxies, via minor mergers, slow encounters, galaxy harassments (Moore et al. 1996), or tidal effects in the dense environment (Gunn & Gott 1972; Larson et al. 1980; Dressler & Sandage 1983; Mihos & Hernquist 1994; Moore et al. 1998, 1999; Neistein et al. 1999; Shioya et al. 2002). A lot of studies have discussed the environmental dependence of galaxy evolution. Generally speaking, early-type galaxies tend to be in dense environments and have low star-formation rates (SFRs; Dressler 1980; Balogh et al. 1997, 1998, 2000; Poggianti et al. 1999; Treu et al. 2003). The fraction of S0 galaxies in the field is only about 15%, while spirals are the majority (Naim et al. 1995). Within the group environment, spirals and S0s are both about 40%–45% (Postman & Geller 1984). Furthermore, S0s become dominant in dense environments, the fraction grows up to 60% in clusters (Dressler 1980; Postman & Geller 1984). Dressler et al. (1997), Fasano et al. (2000), and Desai et al. (2007) also found that the galaxy morphological distributions change abruptly in clusters at

, about 50 ∼ 70% of spirals at high redshift (z > 0.4) are transformed into S0s, while a fraction of ellipticals, about 25%, remains nearly constant between z = 0.8 and z = 0.0. However, Wilman et al. (2009) showed that the fraction of S0s in groups is the same as in clusters but it is much higher than in the field at z = 0.4, which might suggest that S0s are formed in groups or subgroups.


The early studies of the cooling of hypernuclear stars did not include the high-mass astrophysical constraint on the EoS of hypernuclear matter (Haensel & Gnedin 1994; Schaab, Balberg & Schaffner-Bielich 1998; Tsuruta et al. 2009). In Paper I we started a systematic study of the cooling of hypernuclear compact stars on the basis of modern density functionals mentioned above. Several works have appeared since then in this context: Grigorian, Voskresensky & Maslov (2018) used the ‘nuclear medium cooling’ scenario (Schaab et al. 1997; Blaschke, Grigorian & Voskresensky 2004) to account for hyperons using an EoS based on the DFT (Maslov et al. 2015), pion-mediated enhanced neutrino emissivities for the modified Urca and bremsstrahlung processes, vanishing P-wave neutron pairing, and phenomenological crust–core temperature relation. The pion-mediated enhanced neutrino emissivities and vanishing P-wave neutron pairing are the key factors that distinguish their models from those in Paper I. Nevertheless, the remainder of the physical input, for example, the crust–core temperature relation, is not identical to ours. Note that Paper I does not implement the minimal cooling scenario (Page et al. 2004) as it allows for the dUrca process among nucleons and hyperons, uses pair-breaking processes with dressed (in-medium) vertices, and covers a wide range of masses up to the maximum mass of Mmax/M⊙ ∼ 2, which implies a varying cooling behaviour for the mass hierarchy (see, in particular, the conclusion Section of Paper I). The same problem was also addressed by Negreiros et al. (2018) using hyperonic EoS based on the FSU class of relativistic density functional models which feature massive objects and are tuned to available data on hypernuclei (Tolos, Centelles & Ramos2017a,b). In these models, the main cooling agents are the (Λ, p) and (n, p) dUrca processes which were regulated by variations of proton and neutron superfluid gaps. In particular the density range over which the proton S-wave gap is non-zero has been explored with the aim to obtain a satisfactory agreement with the data. The main difference with respect to Paper I is the absence of pairing in the hyperonic sector. Combined, the emerging new generation of cooling models of hypernuclear stars have the potential to further constraining the physics of dense nuclear matter, especially its composition.


Magnetic field fluctuations in the solar wind are highly turbulent. The measured power spectral density (PSD) of the fluctuating magnetic field always exhibits power laws k−α, where k is the wavenumber, and α is the spectral index. A single spacecraft measures the PSD as a function of f−α in the frequency domain, which can be converted to the spatial domain under the Taylor hypothesis. According to the physical processes at different scales, the PSD in the solar wind can be divided into several segments, which can be fitted with different α. The inertial range, which is dominated by magnetohydrodynamic (MHD) turbulence, follows the cascade models with spectral indices αi from around 3/2 to 5/3 (Bruno & Carbone 2013; Chen et al. 2020). The PSDs become steepened below the ion scales (ion thermal gyroradius ρi or ion inertial length di), where kinetic mechanisms should be taken into account. Sometimes a sharp transition range is observed with αt ∼ 4 (Sahraoui et al. 2010; Bowen et al. 2020a). This transition range may be caused by imbalanced turbulence (Voitenko & Keyser 2016; Meyrand et al. 2021), energy dissipation of kinetic waves (Howes et al. 2008), ion-scale coherent structures (Lion et al. 2016), or a reconnection dominated range (Mallet et al. 2017). At smaller scales, a flatter sub-ion kinetic range forms with the spectral index αk ∼ 7/3, which can be explained as the MHD Alfvénic turbulence developing into a type of kinetic wave turbulence, e.g., kinetic Alfvén waves (KAWs; Schekochihin et al. 2009) or whistler waves (Cho & Lazarian 2004). Intermittency in the kinetic range could lead to an −8/3 spectrum (Boldyrev & Perez 2012; Zhao et al. 2016). Ion-cyclotron-wave (ICW) turbulence could lead to a steeper −11/3 spectrum (Krishan & Mahajan 2004; Galtier & Buchlin 2007; Meyrand & Galtier 2012; Schekochihin et al. 2019).The kinetic range always behaves as the KAW turbulence with the slope of −2.8 in the near-Earth space (Bale et al. 2005; Chen et al. 2013; Chen 2016). The spectral indices increase again beyond the electron kinetic scales in observations, indicating the conversion of turbulence energy to electrons (Sahraoui et al. 2009; Alexandrova et al. 2012; Chen et al. 2019) or transitions to a further cascade (Schekochihin et al. 2009; Chen & Boldyrev 2017). In simulations, Meyrand & Galtier (2013) obtained a −8/3 spectrum at electron scales under the 3D electron–MHD model.


The main goal of this paper is to use the JAM method to measure the parameters MBH, (M/L)TOT, and βz of the central region of the galaxy NGC 4546. To do this, we obtained AO assisted IFU observations from the Near-Infrared Integral Field Spectrometer (NIFS), installed on the Gemini North Telescope, and also archive photometric observations performed with the Wide Field and Planetary Camera 2 (WFPC2), installed on the Hubble Space Telescope (HST). NGC 4546 (see Fig. 1) is an SB0 galaxy (de Vaucouleurs et al. 1991) with magnitude Mk = −23.30 (Skrutskie et al. 2006, K band) and is located at a distance of 14 Mpc (Tully et al. 2013; 1 arcsec = 68 pc). It hosts a type 1 LINER AGN at the centre (Ricci, Steiner & Menezes 2014b). This object was also classified as a fast rotator by Emsellem et al. (2011). Gas discs in molecular, neutral, and ionized forms are all counter rotating with respect to the stellar disc (Galletta 1987; Bettoni, Galletta & Oosterloo 1991; Sage & Galletta 1994; Sarzi et al. 2006; Ricci, Steiner & Menezes 2014a). Cappellari et al. (2013a) used JAM to model the stellar kinematics of NGC 4546 using a SAURON data cube of this galaxy from the ATLAS3D project (Cappellari et al. 2011). Although their procedure was very important to determine global parameters for the stellar dynamics of NGC 4546, such as (M/L)TOT and βz within 1 effective radius (1 Reff = 22 arcsec, Cappellari et al. 2013a), the spatial resolution of the data cubes from the ATLAS3D project is not high enough to resolve the sphere-of-influence radius of this object. Assuming $R_{\mathrm{ soi}} \, = \, GM_{\mathrm{ BH}} / \sigma _e^2$, where σe is the velocity dispersion within 1 effective radius and using the MBH × σ relation of Saglia et al. (2016), we calculate Rsoi = 18 pc (0.26 arcsec) for σe = 188 km s−1 (Cappellari et al. 2013a). We will show that Rsoi is resolved by our NIFS observations. Thus, this paper will complement the JAM results of Cappellari et al. (2013a) for NGC 4546, but for the vicinity of its SMBH, i.e. using AO assisted IFU data within a field of view (FOV) of 200 × 200 pc2.


Finally, to calculate Σ(rp), we need to build an accurate model for ξhm on radial scales between 0.1$\, h^{-1}\, {\mathrm{Mpc}}$ and ${\sim}100\, h^{-1}\, {\mathrm{Mpc}}$. We adopt the two-component model of ξhm developed by Zu et al. (2014; a modified version proposed by Hayashi & White 2008):
(6)$$\begin{eqnarray*}
\xi _{\mathrm{hm}}(r) &=& \left\lbrace \begin{array}{ll}\xi _\mathrm{1h} & \quad \mbox{if}\ \xi _\mathrm{1h} \geqslant \xi _\mathrm{2h},\\
\xi _\mathrm{2h} & \quad \mbox{if}\ \xi _\mathrm{1h} \lt \xi _\mathrm{2h},\\
\end{array} \right.\nonumber \\
\xi _\mathrm{1h} &=& \frac{\rho _\mathrm{NFW}(r|M_h)}{\rho _\mathrm{m}} - 1, \nonumber \\
\xi _\mathrm{2h} &=& b \,\, \xi _{\mathrm{mm}}.
\end{eqnarray*}$$Here, ξ1h and ξ2h are the so-called ‘1-halo’ and ‘2-halo’ terms in the halo model (Cooray & Sheth 2002), ρNFW(r|Mh, c) is the NFW density profile of halo mass Mh and concentration c, b is the average halo bias, and ξmm is the non-linear matter–matter autocorrelation function predicted at Planck cosmology (Takahashi et al. 2012). Zu et al. (2014) found that this simple model provides an adequate description of the halo–matter cross-correlation measured from simulations at the level of a few per cent on scales of our concern (i.e. below the halo radius). For massive haloes, several studies found that the average density profile in the inner region of haloes deviates from the NFW shape and the Einasto profile is more accurate (Dutton & Macciò 2014; Klypin et al. 2016). However, since we are only fitting to scales above $0.1\, h^{-1}\, {\mathrm{Mpc}}$, the difference between NFW and Einasto should be negligible. We have also ignored the extra lensing effect caused by the stellar mass of the BCGs, which has negligible contribution on scales above $0.1\, h^{-1}\, {\mathrm{Mpc}}$. The uncertainties of the predicted ΔΣ can be as large as $10{{\ \rm per\ cent}}$ around the transition between the 1-halo and 2-halo scales ($2{-}4\, h^{-1}\, {\mathrm{Mpc}}$; see the fig. 5 of Zu et al. 2014), but we are only concerned with the measurement of halo mass and concentration, which are inferred primarily from scales below the transition scale, and the large-scale bias, which is estimated from scales above $10\, h^{-1}\, {\mathrm{Mpc}}$. Additional, our statistical uncertainties of weak lensing at those scales is around ${~}10{{\ \rm per\ cent}}$. Therefore, the impact of relatively large uncertainties in the transitional regime on our conclusions should be negligible. For future modelling of cluster weak lensing signals of per cent level uncertainties, the transitional behaviour can be potentially improved by using the scheme proposed by Garcia et al. (2020) and emulators developed by Salcedo et al. (2020).


We have tested the pixel-ICA algorithm, i.e., a non-parametric method proposed by Morello et al. (2014, 2015) to detrend Spitzer/IRAC primary transit observations, on simulated data sets. Systematics similar to the ones present in Spitzer/IRAC data sets are obtained by combining instrumental jitter with inter- or intra-pixel sensitivity variations. A variety of jitter timeseries is used to test the pixel-ICA method with:

1.
periodic signals with different frequencies, phasing, and shape;

2.
non-stationary signals with varying amplitudes or frequencies;

3.
sudden change.

The detrending performances of pixel-ICA method have been compared with division by a polynomial function of the centroid, in this paper PCD method, and PLD method (Deming et al. 2015). Here we summarize the main results found:

1.
Pixel-ICA algorithm can detrend non-stationary signals and sudden changes, as well as periodic signals with different frequencies and phasing, relative to the transit.

2.
Inter-pixel effects are well-detrended with pixel-ICA method.

3.
Even if the instrument PSF is not entirely within the array of pixels, pixel-ICA leads to results which are consistent at ∼1σ with the input parameters.

4.
In most cases, pixel-ICA outperforms PCD method, especially if the instrument PSF is narrow, or it is not entirely within the photometric aperture.

5.
Intra-pixel effects are only detectable if the PSF is relatively small.

6.
Intra-pixel effects cannot be totally detrended by any of the three methods, but pixel-ICA, in most cases, outperforms PCD method, which is largely case-dependent. Also, pixel-ICA method provides consistent results within the error bars.

7.
It is possible to fit the astrophysical signal after detrending or together with the other components. The only differences are registered if at least one of the non-transit components has a similar shape at the time of transit, in which case the first approach is preferable, but the two results were consistent within 1σ.

8.
The PLD method, updated to include cross-term between pixel fluctuations and the astrophysical signals, lead to very similar results than pixel-ICA, particularly if the astrophysical signal is fitted together with the other components.

In conclusion, we have found in a variety of simulated cases that pixel-ICA performs as well or better than other methods used in the literature, in particular polynomial centroid corrections and PLD (Deming et al. 2015). The main advantage of pixel-ICA over other methods relies on its purely statistical foundation without the need of imposing prior knowledge on the instrument systematics, therefore avoiding a potential source of error. The results of this paper, together with previous analyses of real Spitzer/IRAC data sets (Morello et al. 2014, 2015), suggest that photometric precision and repeatability at the level of one part in 104 can be achieved with current infrared space instruments.


We investigate the possibility of our clouds corotating within a ‘cold-flow disc’, in which material that is accreting on to the galaxy arises due to filamentary structure from the cosmic web to form an extended disc structure. As done previously by Kacprzak et al. (2010b), we investigate this by employing a simple halo model from Steidel et al. (2002) with the updated values for i and position angle (PA). In order to determine if all the low-, intermediate-, and high-ionization clouds can be explained by a corotating thick disc, we set the lagging scale height term to hv = 1000 kpc. This term is related to the location above the mid-plane where the lagging halo velocity component begins to matter and vlos becomes dominated by an exponentially declining term. Following previous studies (e.g. Steidel et al. 2002; Kacprzak et al. 2010a,b, 2011b, 2019; French & Wakker 2020; Nateghi et al. 2021) we are forcing the disc to be a thick, nearly rigid rotator, where material far above the disc plane is rotating along with the disc. This places our low- and high-ionization clouds high above the galactic disc at a high angle. The line-of-sight distance (Dlos) and line-of-sight velocity (vlos) can be found in Fig. 9. The figure shows that much of the low-, intermediate-, and high-ionization clouds (except Cloud #1) can be explained by a corotating thick disc, but the low-metallicity subsystem cannot be. Using such a large value for hv may be extreme, but it clearly illustrates the contrast between the low-metallicity subsystem and the other gas phases. In short, it is not at all possible that the low-metallicity subsystem is due to a cold-flow disc. Using a more plausible (smaller) value for hν will not affect the disparity between the low-metallicity subsystem and the other gas phases. We find that even by adopting a non-physically motivated scale height of hv = 10 kpc (adopted from Ho et al. 2017), we can still explain the metal-enriched clouds with a corotating thick disc (except Cloud #1 and Cloud #2), but we are still unable to explain the low-metallicity subsystem. This agrees with recent simulations in which high angular momentum gas accretes via a cold-flow disc, creating large corotating gaseous structures in the galaxy halo (Stewart et al. 2013, 2017). The Q0454−220 system also agrees with observations of galaxy/absorber pairs, which have been found to exhibit disc-like or accretion kinematics over a large range of impact parameters (e.g. Burchett et al. 2013; Bouché et al. 2016; Ho et al. 2017; Rahmani et al. 2018).


The origin of the extreme magnetic fields of magnetars is still an important open question as several scenarios have been proposed, such as a convective dynamo in a fast rotating proto-neutron star (PNS) (Thompson & Duncan 1993; Raynaud et al. 2020; Raynaud, Cerdá-Durán & Guilet 2022), the Tayler-Spruit dynamo following fallback (Barrere et al. 2022), amplification in main-sequence stellar mergers (Schneider et al. 2019), or the fossil field scenario (Ferrario & Wickramasinghe 2006). To shed light on this question, it is important to assess the efficiency of each of the dynamo mechanisms in the conditions specific to a PNS. The impact of different ingredients on the MRI has been studied in recent years: the shear parameter (Masada et al. 2012), neutrino viscosity and drag (Guilet, Müller & Janka 2015), stable stratification (Guilet & Müller 2015; Reboul-Salze et al. 2021b), and spherical geometry (Reboul-Salze et al. 2021a). A remaining open question is the dependence on diffusion coefficients. Local disc simulations have shown that the efficiency of the MRI is strongly correlated to the magnetic Prandtl number Pm (the ratio of viscosity to resistivity) when Pm ∼ 0.1−16 (Fromang et al. 2007; Lesur & Longaretti 2007; Simon & Hawley 2009; Longaretti & Lesur 2010; Shi, Stone & Huang 2016; Potter & Balbus 2017) and plateaus at Pm  0.1 with an imposed external magnetic field (Meheut et al. 2015). Low and high Pm regimes are computationally challenging because a high numerical resolution is needed to resolve the small viscous (low Pm) or resistive (high Pm) scale. The regime of low Pm has attracted particular attention because it is relevant to most regions of accretion discs as well as to liquid metals (laboratory experiments and Earth core), but the opposite regime of large Pm has not been targeted specifically by previous studies of the MRI. This regime is relevant to PNSs (Thompson & Duncan 1993; Guilet et al. 2015; Lander 2021), neutron star merger remnants (Rossi, Armitage & Menou 2008), which exhibit physical conditions similar to PNSs (Guilet et al. 2017), interstellar and intergalactic media (Schekochihin et al. 2004), and to the inner parts of some accretion discs (Balbus & Henri 2008; Potter & Balbus 2014, 2017). In the latter case, the Pm dependence of the MRI may drive an instability leading to variability in the accretion rate (Potter & Balbus 2014, 2017; Kawanaka & Masada 2019).


The EWs were measured with the methods described in Vásquez et al. (2015). As in Paper I, we used the sum of the EWs of the two strongest CaT lines (λ8542, λ8662) as a metallicity estimator, following the Ca II triplet method of Armandroff & Da Costa (1991). Different functions have been tested in the literature to measure the EWs of the CaT lines, depending on the metallicity regime. For metal-poor stars ([Fe/H] ≲ −0.7 dex) a Gaussian function was used with excellent results (Armandroff & Da Costa 1991), while a more general function (such as a Moffat function or the sum of a Gaussian and Lorentzian, G + L) is needed to fit the strong wings of the CaT lines observed in metal-rich stars (Rutledge et al. 1997; Cole et al. 2004). Following our previous work (Gullieuszik et al. 2009; Saviane et al. 2012) we have adopted here a G+L profile fit. To measure the EWs, each spectrum was normalised with a low-order polynomial using the IRAF continuum task, and set to the rest frame by correcting for the observed radial velocity. The two strongest CaT lines were fitted by a G+L profile using a non-linear least squares fitting routine part of the R programming language. Five clusters from the sample of Saviane et al. (2012) covering a wide metallicity range were re-reduced and analysed with our code to ensure that our EWs measurements are on the same scale as the template clusters used to define the metallicity calibration. Figure 5 shows the comparison between our EWs measurements and the line strengths measured by Saviane et al. (2012) (in both cases the sum of the two strongest lines) for the five calibration clusters. The observed scatter is consistent with the internal errors of the EW measurements, computed as in Vásquez et al. (2015). The measurements show a small deviation from the unity relation, which is more evident at low metallicity. A linear fit to this trend gives the relation: ΣEW(S12) = 0.97 ΣEW(this work) + 0.21, with an rms about the fit of 0.13 Å. This fit is shown in Fig. 5 as a dashed black line. For internal consistency, all EWs in this work have been adjusted to the measurement scale of Saviane et al. (2012) by using this relation. In Table 3 we provide the coordinates, radial velocities, and the sum of the equivalent widths for the cluster member stars, both measured (“m”) and corrected (“c”) to the system of Saviane et al. 2012.


We use the Hβ λ4861 velocities to standardize the SNe II because the majority of the high redshift spectra (SDSS-II and SNLS samples) are noisy and taken at early phases where the Fe ii absorption lines are not visible. Errors on the Hβ velocities were obtained by measuring many times the minimum of the absorption changing the continuum fit. Both quantities are listed in Table 1. To find the best epoch to use the SCM we need the velocities for different epochs. As proposed by Hamuy (2001) and used in all SNe II cosmology works (Nugent et al. 2006; Poznanski et al. 2009; D’Andrea et al. 2010; Olivares et al. 2010; Poznanski et al. 2010; Rodríguez et al. 2014; de Jaeger et al. 2015) we do an interpolation/extrapolation using a power law of the form
9

where A and γ are two free parameters obtained by least-squares minimization for each individual SN and t is the epoch since the explosion. To derive the velocity error following the work done by de Jaeger et al. (2015), a Monte Carlo simulation is performed, varying randomly each velocity measurement according to the observed velocity uncertainties over more than 2000 simulations. Following Poznanski et al. (2009), we add in quadrature to the velocity uncertainty of every SN II a value of 150 km s−1 to account for unknown host-galaxy peculiar velocities. For the SNe II with one spectrum the same power law is used but this time with a fixed γ, which is derived using only the CSP-I sample for which we have many spectra per SN and a better fit can be achieved. We find a median value of γ = −0.407 ± 0.173. It is important to note that in the majority of other SN II cosmology works, the authors used the same power law for all of the SNe, whereas in our work the γ is different for all SNe II with more than two spectra. Additionally, in Section 6.4, we show the possibility of using a new relation between A and γ in order to derive the velocity when only one spectrum is acquired without assuming the same power-law exponent.


HD 141569 is a Herbig star classified as a B9-A0 spectral type (Augereau & Papaloizou 2004), with an effective temperature of 9750 ± 250 K, an estimated age of 7.2 ± 0.02 Myr, a luminosity between 16.60 ± 1.07 L⊙ (Vioque et al. 2018) and 27.0 ± 3.6 L⊙ (Di Folco et al. 2020), a mass of 2.14 ± 0.01M⊙, and a Gaia distance of 110 ± 1 pc (Arun et al. 2019)2. It is a non-flaring disk system with little mid-IR excess classified as a group-II source (Meeus et al. 2001). It is the only known pre-main sequence star characterized by a hybrid disk (Wyatt et al. 2015; Péricaud et al. 2017; Di Folco et al. 2020), an evolutionary disk state between the protoplanetary and debris-disk regimes. Near-IR imaging spatially resolved an optically thin disk consisting of two rings located at about ~ 280 and ~ 455 au from the star Augereau et al. (1999); Weinberger et al. (1999); Biller et al. (2015). A more complex system is shown in the visible, consisting of multiple rings and outer spirals that could be explained through perturbations by two nearby (~ 7.5 arcsec) M dwarfs, or by planetary perturbations (Augereau & Papaloizou 2004; Wyatt 2005; Reche et al. 2009). Fisher et al. (2000) found a warm disk component up to 110 au at 10.8 and 18.2 μm, later confirmed by Marsh et al. (2002). The short-wavelength counterpart of this component was detected by Mawet et al. (2017) through L′ imaging and ranging between 20 and 85 au. Emission at 8.6 μm was detected by Thi et al. (2014), and was interpreted as emission from polycyclic aromatic hydrocarbons (PAHs). NOEMA and ALMA observations in the millimeter range showed continuum emission equally shared between a compact (≲ 50 au) and a smooth extended dust component (~350 au), with large millimeter grains dominating the inner regions and smaller grains in the outer ones (Di Folco et al. 2020). Finally, inner disk features were detected by SPHERE in the Y, J, H, and K bands (Perrot et al. 2016) and by Keck/NIRC2 in the L′ band (Currie et al. 2016) at physical separations of 45, 61, and 88 au. These results point out the high morphological complexity of the outer disk in the HD 141569 system.


Several physical processes affect galaxies inside clusters in a simultaneous way. One of these mechanisms is the ram pressure stripping (e.g. Gunn & Gott 1972; Abadi, Moore & Bower 1999; Book & Benson 2010; Steinhauser, Schindler & Springel 2016). This process can remove an important fraction of the cold gas from galaxies, resulting in the inhibition of star formation. Although this mechanism is more effective at the central regions of massive clusters, it has been reported in less massive systems (e.g. Rasmussen, Ponman & Mulchaey 2006; Jaffé et al. 2012; Hess & Wilcots 2013). Ram pressure stripping occurs as galaxies move at high speeds through the hot ionized gas of the intracluster medium, which collides with the cold gas of the galaxies and removes it. The warm gas from the galactic halo can also be removed by the gas of the intracluster medium, a process known as starvation (e.g. Larson, Tinsley & Caldwell 1980; Balogh, Navarro & Morris 2000; McCarthy et al. 2008; Bekki 2009; Bahé et al. 2013; Vijayaraghavan & Ricker 2015). This process can cut-off further gas cooling from the galaxy’s halo gas that fuels future star formation. Kawata & Mulchaey (2008) predicted that starvation can act in galaxy groups as well. Another physical process that works on galaxies in their passage through the deep potential well of the cluster is tidal stripping (e.g. Zwicky 1951; Gnedin 2003a; Villalobos, De Lucia & Murante 2014). It can induce a central star formation burst (Byrd & Valtonen 2001), bar instabilities (Łokas et al. 2016), changes in the pattern of the spiral arms (Semczuk, Łokas & del Pino 2017), and truncate dark matter haloes (e.g. Gao et al. 2004; Limousin et al. 2009). In the outskirts of clusters, mechanisms like galaxy–galaxy interaction, known as harassment, are more effective (e.g. Moore et al. 1996; Moore, Lake & Katz 1998; Gnedin 2003b; Smith et al. 2015). Most of the processes mentioned above tend to decrease or to completely suppress the star formation in galaxies. As a consequence, galaxies in clusters are typically red, early-type, with an old stellar population, and have little or none star formation at all.


One of the major endeavors of modern observational cosmology is to paint a coherent picture of the history of the universe. To this end, the final frontier remains the identification and characterization of the first sources that appeared in the universe, those which played a significant role in reionizing the intergalactic medium from a neutral state to a fully ionized one over the first billion years (corresponding to redshifts of 6 ≲ z ≲ 12). Extragalactic surveys (of deep fields as well as lensing clusters; Grogin et al. 2011; Koekemoer et al. 2011; Bradley et al. 2012; Ellis et al. 2013; Bradley et al. 2014; Schmidt et al. 2014; Treu et al. 2015; Lotz et al. 2017; Salmon et al. 2018; Coe et al. 2019) with the Hubble Space Telescope (HST) have yielded impressive gains in the number of galaxy candidates at redshifts z = 7–10, with samples reaching over 1000 objects, and revolutionized our understanding of galaxy evolution therein. Complementing these observations, the spectroscopic confirmation (e.g., Finkelstein et al. 2013; Oesch et al. 2015; Zitrin et al. 2015; Roberts-Borsani et al. 2016; Hoag et al. 2017; Stark et al. 2017; Hashimoto et al. 2018) and characterization (e.g., Laporte et al. 2017; Mainali et al. 2018; Endsley et al. 2021) of over a dozen sources has seen impressive advances with ground-based spectroscopy (e.g., probing the rest-frame UV and FIR with Keck/MOSFIRE, VLT/X-Shooter, and ALMA), particularly for the brightest and rarest objects. For the rest-frame optical, however, the Spitzer Space Telescope has, until now, afforded the only realistic means for statistical analyses. However, the Infrared Array Camera’s (IRAC) coarse spatial resolution and the limited depth probed by many surveys make robust and uncontaminated constraints on galaxy properties a challenging feat. Further advances with current facilities are challenging owing to the limited wavelength coverage of HST and the observed faintness of star-forming galaxies as one approaches redshifts of z > 10. The imminent arrival of the James Webb Space Telescope (JWST) has the potential to detect galaxies well beyond the current frontier of z ∼ 12 (e.g., Behroozi et al. 2020) thanks to the unprecedented resolution and sensitivity of its near-IR (NIR) imaging and spectroscopic capabilities, and revolutionize our current understanding of galaxy evolution.


Regardless of whether the NGC 6334 filament will form massive stars, our ArTéMiS result that the filament inner width is within a factor of 2 of 0.1 pc has interesting implications. Our NGC 6334 study is clearly insufficient to prove that interstellar filaments have a truly universal inner width, but it shows that the finding obtained with Herschel in nearby clouds is not limited to filaments in low-mass star-forming regions. It is quite remarkable that the NGC 6334 filament has almost the same inner width as the faint subcritical filaments in Polaris (cf. Men’shchikov et al. 2010; Arzoumanian et al. 2011), the marginally supercritical filaments in Musca and Taurus (Cox et al. 2016; Palmeirim et al. 2013), or the lower-mass supercritical filaments in Serpens South and Vela C (Hill et al. 2012), despite being three orders of magnitude, two orders of magnitude, and at least a factor of ~3 denser and more massive than these filaments, respectively (see Table 1). While not all of these filaments may have necessarily formed in the same way, this suggests that a common physical mechanism is responsible for setting the filament width at the formation stage and that the subsequent evolution of dense filaments, through accretion of background cloud material (cf. Heitsch 2013; Hennebelle & André 2013) for example, is such that the inner width remains at least approximately conserved with time. A promising mechanism for creating dense filaments, which may be quite generic especially in massive star-forming complexes, is based on multiple episodes of large-scale supersonic compression due to interaction of expanding bubbles (Inutsuka et al. 2015). With about seven bubble-like HII regions per square degree (Russeil et al. 2013, see also Fig. 2), there is ample opportunity for this mechanism to operate in NGC 6334. More specifically, at least in projection, the NGC 6334 filament appears to be part of an arc-like structure centered on the HII region Gum 63 (see Fig. 2a), suggesting the filament may partly result from the expansion of the associated bubble. Interestingly, the background column density is one order of magnitude higher for the NGC 6334 filament than for the other filaments of Table 1, which is suggestive of a significantly stronger compression. More observational studies are needed to investigate the structure and environment of a larger number of filaments in massive star-forming regions to determine whether the characteristics of the NGC 6334 filament are generic. More theoretical work is also needed to better understand the physics controlling the width of interstellar filaments.


The purpose of this paper is to demonstrate a complementary approach to single-dish IM experiments, capable of the statistical detection of H i field and therefore the fluctuations in the underlying matter field by measuring the H i power spectrum with interferometric observations. Interferometers have inherent advantages over single-dish measurements. Besides providing high angular resolutions, they are less sensitive to systematics which poses a major problem to the autocorrelation power. However, the smallest k-modes accessible to an interferometer is determined by the shortest baselines which may hinder probing the BAO scales. Interferometers such as CHIME (Bandura et al. 2014), TIANLAI (Xu, Wang & Chen 2014), and HIRAX (Newburgh et al. 2016) are custom designed to probe the BAO scales using the 21 cm signal in the redshift range z ∼ 0.5–2. In this paper, we study the feasibility of detecting the cosmological 21 cm signal with MeerKAT and present forecasts on the statistical measurement of H i with MeerKAT L-band (856 MHz  ν  1712 MHz) observations on quasi-linear scales. We present the sensitivity estimates at z ∼ 0.27 from our newly developed simulation pipeline, which is our first attempt towards the measurement of H i power spectrum with MeerKAT. Our pipeline is based on the methods being developed for similar statistical measurement of H i from the Epoch of Reionization from a series of experiments at lower radio frequencies such as LOFAR (Van Haarlem et al. 2013), GMRT (Paciga et al. 2013), PAPER (Parsons et al. 2014), HERA (DeBoer et al. 2017), and MWA (Tingay et al. 2013). We show that with MIGHTEE (Jarvis et al. 2016; Maddox et al. 2021), one of MeerKAT’s large survey projects, we can achieve constraints on the H i power spectrum at z = 0.27. There are implicit advantages with such survey projects with a specific emission line. First, it provides a one to one correspondence between observed frequency and redshift, thereby delivering a very high redshift resolution. Secondly, these are generally less time consuming compared to an optical spectroscopic galaxy survey which requires very high sensitivity to detect individual galaxies.


The GMC associated with G305 is one of the most massive and luminous clouds in the Milky Way (Fig. 1). It is located in the Galactic plane at l ~ 305°, b ~ 0° and at a kinematic distance of 4 kpc (derived from a combinationof radio and Hα observationsby Clark & Porter (2004); Davies et al. (2012) measured its spectrophotometric distance to be 3.8 ± 0.6 kpc and most recently Borissova et al. (2019) measured the Gaia DR2 average distance to be 3.7 ± 1.2 kpc); this places it in the Scutum-Crux spiral arm. Given this distance, the complex has a diameter of ~ 30 pc (Clark & Porter 2004) and a molecular mass of ~6 × 105 M⊙ (Hindson et al. 2010). The G305 complex consists of a large central cavity that has been cleared by the winds from massive stars belonging to two visible central clusters (Danks 1 and 2) and the Wolf-Rayet star (WR48a; Clark & Porter 2004; Davies et al. 2012). The cavity is surrounded by a thick layer of molecular gas (traced by CO and NH3 emission; Hindson et al. 2010, 2013). Radio continuum observations by Hindson et al. (2012) have revealed that the cavity is filled with ionized gas and identified six ultra-compact HII (UC HII) regions and also one bright rimmed cloud (BRC) at the periphery of the cavity, indicating molecular gas irradiated by UV radiation (Sugitani & Ogura 1994; Thompson et al. 2004), which may cause implosion (Bertoldi 1989) or evaporation. A number of studies havereported star formation tracers (water and methanol masers, HII regions and massive young stellar objects, MYSOs; Clark & Porter 2004; Lumsden et al. 2013; Urquhart et al. 2014; Green et al. 2009, 2012). Furthermore, Hindson et al. (2010) found the concentration of star formation tracers to be enhanced inside a clump of NH3 bearing molecular gas that faces the ionizing sources, which is consistent with the hypothesis that the star formation has been triggered. Analysis of the stellar clusters in the complex reveals them to have ages of 1.5 Myr for Danks 1 and 3 Myr for Danks 2,with the former possibly being triggered by the latter (Davies et al. 2012). Additionally, a diffuse population of evolved massive stars was also found to exist within the confines of the G305 complex that had formed around the same time as the two clusters (Leistra et al. 2005; Shara et al. 2009; Mauerhan et al. 2011; Davies et al. 2012; Faimali et al. 2012; Borissova et al. 2019).


In Figure 8, we also find small differences in the [Na, Al, O/Fe] abundance ratios between the stars in the bright and faint RC groups, although it is not as clear as in the case of [Na, Al, O/H] abundances. In particular, unlike Figure 7, stars in the bRC group are more enhanced in [Na/Fe] but appear to be more depleted in [Al/Fe] and [O/Fe] than those in the fRC group. The mean differences are 0.053 ± 0.021 dex, 0.032 ± 0.018 dex, and 0.071 ± 0.045 dex in [Na/Fe], [Al/Fe], and [O/Fe], respectively, which are marginally significant at p-values of 0.22, 0.18, and 0.23. When the relative fraction of RC stars is taken into account (27%; see Section 4), the difference in [Na/Fe] between the genuine RC stars would correspond to Δ[Na/Fe] ∼ 0.20 dex, which is comparable to that expected from our chemical evolution model for the bulge stars (Δ[Na/Fe] = 0.2 ∼ 0.3 dex; Kim & Lee 2018; Lee et al. 2019).10

10
The previous study by Lee et al. (2019) noted a clear separation of the two groups according to Na abundance among bright RGB stars in the outer bulge. The apparent lack of such a distinct difference between the two groups in this study may be due to a larger uncertainty on abundances of relatively faint sample stars.
 The overall chemical patterns, however, are not identical to those observed in typical GCs, where the later-generation stars are more enhanced in [Na, Al/Fe] and more depleted in [O, Mg/Fe] than the first-generation stars at a given metallicity, although the trend of [Na, Al O/Fe] between the two RCs is less clear. Figure 9 shows the comparison of stars in this study with stars in metal-rich GCs ([Fe/H] > −1.0) on the Na–O diagram. The stars used in this study have a different distribution from stars in GCs. Although the bRC group is slightly more enhanced in [Na/Fe] and more depleted in [O/Fe] than the fRC group, the [Na/Fe] variation of RC stars is smaller than that of GC stars. This discrepancy might imply the different chemical evolution between stars in the bulge and typical GCs. We note, however, that even though we employ only metal-rich GC stars for the comparison, the majority of stars are still far more metal-poor ([Fe/H]  −0.5) than stars in the bulge. Because the relatively small [Na/Fe] variation is expected from the chemical evolution model for metal-rich bulge stars and the O-depletion is indistinct in some metal-rich GCs, such as NGC 6121 and 47 Tuc (see Kim & Lee 2018; Lee et al. 2019), the direct comparison of bulge stars with similarly metal-rich GCs on the Na–O plane would require further spectroscopic observations for such GCs in the bulge.


Using the constrained hyperbolic divergence cleaning scheme with variable cleaning speed from Tricco et al. (2016), we can keep the divergence error low in all cases. The mean normalized divergence error, ⟨ϵdivB⟩=⟨h|∇ ⋅ B|/|B|⟩, is typically of order 10−5 − 10−3. In Fig. 17, we show the normalized divergence error maps for several test problems. Again we see that the divergence cleaning works extremely well here, the maximum error is generally around 10−2. Comparing to Hopkins (2016, their Fig. 4), we find that the errors are smaller than their MFM simulations with the Dedner et al. (2002) cleaning in general, with an exception for the outskirt of the advection loop (where the magnetic field is essentially zero and thus not important for the result). The improvement is probably due to the more advanced constrained cleaning method (Tricco et al. 2016). The normalized divergence error for the μ = 10 cloud-collapse case at the jet launching time is shown in Fig. 18. Here, the divergence cleaning still performs very well in the disc, along the jets and for the majority of the regions where the outflow interacts with the ambient gas, especially when the divergence error is compared to the total gas pressure (right panel). The result is similar to the Dedner cleaning in Hopkins (2016), although our error is somewhat larger at the tip of the jets where the gas is shocked. However, we note that the comparison is not direct in this case as the jets may develop differently. Overall, the result from cleaning is still worse than the constrained transport or constrained gradient schemes (Hopkins 2016). For SPMHD, as shown in Tricco & Price (2012), divergence errors can be reduced to machine precision (or more practically to a certain tolerance value) using cleaning, with the help of a sub-cycling routine. However, local adjustments are required to determine the number of iterations for each particle to efficiently subcycle the cleaning in the simulation. This is because certain regions are more affected than others and because divergence is spread to nearby neighbours. Conceivably, if vector potentials (Stasyszyn & Elstner 2015) could work for a wider range of problems this could be an interesting avenue as well. However, the exploration of these methods in detail is beyond the scope of this work.


Lower limit on μ: at the highest accretion rates, to observe pulsations, the magnetic field must be at least high enough to truncate the accretion disc at or above the neutron star surface. Thus by setting rt = Rs we obtain the lower limit on the dipole moment as

(5)

\begin{equation}
\mu _{\rm min} = \gamma _{\rm B}^{-1/2}(GM)^{1/4}\dot{M}_{\rm max}^{1/2}R_{\rm s}^{7/4}.
\end{equation}

We assume the mass accretion rate can be estimated from the bolometric luminosity as $L = GM\dot{M}/R_{\rm s}$, and estimate L from the observed luminosity in the X-ray band by applying a bolometric correction factor (L = ϵbolLX). The typical reported values of the bolometric correction factor have a range of ϵbol ∼ 1–2 (Gilfanov et al. 1998; Galloway et al. 2002, 2008; Campana et al. 2003; Migliari & Fender 2006; Casella et al. 2008). The mass accretion rate then follows as

(6)

\begin{eqnarray}
\dot{M} &=& 10^{16} \mbox{ g s}^{-1} \left( \frac{ \epsilon _{\rm bol} L_{\rm X}}{1.87 \times 10^{36}\mbox{ erg s}^{-1}} \right)\nonumber\\
&&\times\,\left( \frac{M}{1.4 \,\mathrm{M}_{\odot }} \right)^{-1} \left(\frac{R_{\rm s}}{10 \mbox{ km}}\right).
\end{eqnarray}

Expressing the X-ray luminosity in terms of the observed X-ray flux and the assumed distance (LX = 4πd2F), we obtain the lower limit on the magnetic moment

(7)

\begin{eqnarray}
\mu _{\rm min} &=& 9.36 \times 10^{24} \mbox{ G cm}^{-3} \left( \frac{ \gamma _{\rm B} }{ 1 } \right)^{-1/2} \left( \frac{ \epsilon _{\rm bol} }{ 1 } \right)^{1/2} \nonumber \\
&&\times \left( \frac{ F_{\rm max}}{10^{-10}\, \mbox{erg}\mbox{ cm}^{-2}\mbox{ s}^{-1}} \right)^{1/2} \left( \frac{d}{10 \mbox{ kpc}}\right) \nonumber \\
&&\times \left(\frac{M}{1.4 \,\mathrm{M}_{\odot }}\right)^{-1/4} \left( \frac{R_{\rm s}}{10 \mbox{ km}}\right)^{9/4},
\end{eqnarray}

where Fmax is the highest observed X-ray flux with pulsation and we adopted the boundary values of γB and ϵbol that give the lowest magnetic moment. For a detailed discussion of these assumptions we again refer to Section 4.


Douchin & Haensel (2001; DH) formulated a unified EoS for NS on the basis of the SLy4 Skyrme nuclear effective force (Chabanat et al. 1998), where some parameters of the Skyrme interaction were adjusted to reproduce the Wiringa et al. calculation of neutron matter (Wiringa et al. 1988) above saturation density. Hence, the DH EoS contains certain microscopic input. In the DH model the inner crust was treated in the CLDM approach. More recently, unified EoSs for NS have been derived by the Brussels-Montreal group (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013). They are based on the BSk family of Skyrme nuclear effective forces (Goriely et al. 2010). Each force is fitted to the known masses of nuclei and adjusted among other constraints to reproduce a different microscopic EoS of neutron matter with different stiffness at high density. The inner crust is treated in the extended Thomas-Fermi approach with trial nucleon density profiles including perturbatively shell corrections for protons via the Strutinsky integral method. Analytical fits of these neutron-star EoSs have been constructed in order to facilitate their inclusion in astrophysical simulations (Potekhin et al. 2013). Quantal Hartree calculations for the NS crust have been systematically performed by (Shen et al. 2011b,a). This approach uses a virial expansion at low density and a RMF effective interaction at intermediate and high densities, and the EoS of the whole NS has been tabulated for different RMF parameter sets. Also recently, a complete EoS for supernova matter has been developed within the statistical model (Hempel & Schaffner-Bielich 2010). We shall adopt here the EoS of the BSk21 model (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013; Goriely et al. 2010) as a representative example of contemporary EoS for the complete NS structure, and a comparison with the other EoSs of the BSk family (Chamel et al. 2011; Pearson et al. 2012; Fantina et al. 2013; Potekhin et al. 2013) and the RMF family (Shen et al. 2011b,a) shall be left for future study.


Cassiopeia A (Cas A) is a Galactic SNR located $3.4 \, {\rm kpc}$ away (Reed et al. 1995), with an age of approximately $330 \, {\rm yr}$ (Fesen et al. 2006) and a radius of $1.7 \, {\rm pc}$ (Reed et al. 1995). It provides a unique laboratory to test the efficiency of dust condensation in SN ejecta, and the subsequent destruction of dust by the reverse shock, and as such has been studied extensively in the past. IR/sub-mm observations have led to derived dust masses ranging from ${\sim } 10^{-4} \, {\rm M}_\odot$ of hot ($T \sim 100 \, {\rm K}$) dust (Arendt, Dwek & Moseley 1999; Douvion, Lagage & Pantin 2001) to $2{\text{-}}4 \, {\rm M}_\odot$ of cold dust emitting at sub-mm wavelengths (Dunne et al. 2003), although this higher mass has been attributed to foreground dust emission in the ISM (Krause et al. 2004). Analyses of integrated fluxes from Spitzer and Herschel observations (Rho et al. 2008; Barlow et al. 2010; Arendt et al. 2014) found ${\sim } 0.01 \, {\rm M}_\odot$ of hot dust, with ${\sim } 0.1 \, {\rm M}_\odot$ of cold, unshocked dust present in the central regions, in agreement with simulations of the dust formation and evolution in Cas A by Nozawa et al. (2010). Dunne et al. (2009) suggested the observed polarization of the sub-mm emission could be explained by ${\sim } 1 \, {\rm M}_\odot$ of cold dust, similar to the value of $1.1 \, {\rm M}_\odot$ given by Bevan et al. (2017) as the most likely mass based on the shape of emission-line profiles affected by extinction. De Looze et al. (2017) utilized spatially resolved Herschel and Spitzer observations of Cas A to fit the dust continuum emission, following the removal of line and synchrotron contamination, using a four-component model including ISM dust emission and three SNR dust temperature components. They found a large mass of unshocked cold dust in the centre of the SNR (up to $0.6 \, {\rm M}_\odot$), significantly above previous estimates based on the IR/sub-mm emission.


In this study, the 272 eV suprathermal electron pitch-angle distributions (PADs) measured by ACE are used. The electron PADs are obtained from the Solar Wind Electron Proton Alpha Monitor (SWEPAM) with angular and time resolutions of 9° and 64 s respectively (McComas et al. 1998). Here we examined 16 s average magnetic field, 64 s average plasma, 1 h average O7+/O6+ ratio, and mean Fe charge state ⟨Fe⟩ data from 1998 to 2008 measured by ACE and identified 272 ICMEs in total. The ICMEs were identified by the following process: (1) We take the events in previous ICME lists of Jian et al. (2006), Chi et al. (2016), and Richardson & Cane (2004)1 as candidate ICMEs. (2) Some lists also report short-duration ( 10 h) structures as ICMEs. As the origin of these smaller-scale ICMEs and flux ropes are still debated (Feng et al. 2007; Rouillard et al. 2011; Janvier et al. 2014; Feng & Wang 2015; Wang et al. 2019), we excluded them from this study. (3) The high Fe charge states (⟨Fe⟩ ≥ 12) and abnormally high O7+/O6+ ratio (≥1) are the result of flare-related heating in the corona (Lepri & Zurbuchen 2004; Reinard 2005), and therefore they are independently reliable ICME indicators (Feng & Wang 2015). If the candidate ICMEs have high Fe charge states and/or abnormally high O7+/O6+ ratio, they are identified as ICMEs. (4) If the candidate ICMEs have no high Fe charge states and abnormally high O7+/O6+ ratio, we look for the following five characteristics: declining speed (apparent expansion), increasing total magnetic magnitude and helium abundance (He/P > 0.06) (Richardson & Cane 2004), and decreasing proton temperatures and proton densities. If the candidate ICMEs have three or more of the above characteristics they are identified as ICMEs. Given that magnetic flux ropes are special field topologies characterized by bundles of helical magnetic-field lines collectively spiraling around a common axis, the essential observational properties of magnetic flux ropes should be enhanced magnetic field strength and smooth rotations (Feng et al. 2008, 2010), namely, measured enhanced magnetic field strength, the center-enhanced magnetic components, and bipolar curve magnetic components. Therefore, if an ICME was found to have enhanced magnetic field strength, both center-enhanced and bipolar field components, it was identified as MC. Among the 272 ICMEs, 101 (37.1%) events were identified as MCs. All 272 ICMEs are listed in Table A.1. The second and third columns show the start and end times, the fourth column gives the duration of the ICMEs, and the fifth column provides the types of ICMEs (MC or nonMC).