adsabs/FOCAL huggingface dataset:
The polarized emission of these OH masers was studied several times in the past (e.g., Fish et al. 2005, 2006; Green et al. 2007; Fish & Reid 2007; Fish & Sjouwerman 2010). Fish et al. (2005) detected linearly polarized emission toward 24 OH maser spots at 1.665 GHz with the VLBA (⟨Pl⟩ = 36%). From these detections, they measured a mean polarization angle of + 59°. Under the assumption that the magnetic field is perpendicular to the linear polarization vectors, the magnetic field is orientated on the plane of the sky with an angle 

$\Phi_{\rm{B}}^{\rm{1.6~GHz~OH}}={-}31$



Φ
B

1.6 GHz OH

=−31

°. From the 6.0 GHz OH masers, the linearly polarized emission was also detected, which led Green et al. (2007) and Fish & Sjouwerman (2010) to measure ⟨Pl⟩ = 13.6% and 19%, respectively. Green et al. (2007) measured a mean linear polarization angle of − 58° (

$\Phi_{\rm{B}}^{\rm{6.0~GHz~OH}}={+}32$



Φ
B

6.0 GHz OH

=+32

°) with the Multi-Element Radio Linked Interferometer Network (MERLIN), while Fish & Sjouwerman (2010) measured ⟨χ⟩ = −60° (

$\Phi_{\rm{B}}^{\rm{6.0~GHz~OH}}={+}30$



Φ
B

6.0 GHz OH

=+30

°) with a global VLBI network. In addition, from the right circular and left circular polarization spectra of the 1.6 and 6.0 GHz OH masers, it was possible to measure the magnetic field strength. From 11 and 10 Zeeman pairs of 1.7 GHz OH masers, a magnetic field on the plane of the sky B|| = −3.3 mG (Fish et al. 2005) and −4.5 mG (Fish & Reid 2007) was measured, respectively; while from 7, 6, and 11 Zeeman pairs of 6.0 GHz OH masers, B|| = −5.6 mG (Fish et al. 2006), − 3.5 mG (Green et al. 2007), and −4.8 mG (Fish & Sjouwerman 2010) was estimated, respectively. Green et al. (2007) reported a linearly polarized emission from two 6.7 GHz CH3OH maser features with the MERLIN (beam size 43 mas× 43 mas). In particular, for their features C (

$V_{\rm{lsr}}^{\rm{C}}={+}14.62$



V

lsr
C

=+14.62

 km s−1, IC = 53.56 Jy beam−1, 

$\Delta v{_{\textrm{L}}}^{\rm{C}}=0.27$


Δv{_L}^C=0.27

 km s−1, 

$P_{\rm{l}}^{\rm{C}}=0.2\%$



P
l
C

=0.2%

) and D (

$V_{\rm{lsr}}^{\rm{D}}={+}14.62$



V

lsr
D

=+14.62

 km s−1, ID = 20.03 Jy beam−1, 

$\Delta v_{\textrm{L}}^{\rm{D}}=0.27$


Δ
v
L
D

=0.27

 km s−1, 

$P_{\rm{l}}^{\rm{D}}=1.3\%$



P
l
D

=1.3%

), they measured a linear polarization angle of χC = +20.6° and χD = −76.7°, respectively.Green et al. (2007) also reported the very first Zeeman-splitting measurement for 6.7 GHz CH3OH maser emission using the cross-correlation method (Modjaz et al. 2005); for maser feature D, they measured 

$P_{\rm{V}}^{\rm{D}}=0.6\%$



P
V
D

=0.6%

 and ΔVZD = 0.9 ± 0.3 m s−1.
Citation: Green et al. 2007
Citation function: Background
Citation: Green et al. (2007)
Citation function: Compare/Contrast; Compare/Contrast
Citation: Green et al. (2007)
Citation function: Compare/Contrast
Citation: Green et al. (2007)
Citation function: Compare/Contrast
Citation: Green et al. 2007
Citation function: Compare/Contrast; Compare/Contrast
Citation: Green et al. (2007)
Citation function: Compare/Contrast; Compare/Contrast
We compute the integrated polarized emission of our radio relic following the formalism of Burn (1966): 
(6)$$\begin{eqnarray*}
P_{\mathrm{pol}}(\lambda ^2) = \frac{\sum \limits _{\mathrm{los}} P_{\mathrm{tot}} \Pi \exp \left(2i \left(\epsilon _{\mathrm{int}} + \mathrm{RM}\lambda ^2 \right) \right) \mathrm{d}s}{\sum \limits _{\mathrm{los}} P_{\mathrm{tot}} \mathrm{d}s},\end{eqnarray*}$$using the emission per volume in each simulation cell Ptot, the intrinsic degree of polarization Π and the intrinsic angle of polarization ϵint. RMλ2 accounts for Faraday rotation. The intrinsic degree of polarization Π at observing frequency νobs is computed using the parallel and perpendicular components of the radio emission, equations (3) and (4) (e.g. Rybicki & Lightman 1986): 
(7)$$\begin{eqnarray*}
\Pi = \frac{P_{\parallel }-P_{\perp }}{P_{\parallel }+P_{\perp }}.\end{eqnarray*}$$The intrinsic angle of polarization, ϵint, is computed with respect to the horizontal axis of the projected maps. Each simulation cell can be considered to be filled with a uniform magnetic field and, in this case, the intrinsic angle of polarization is perpendicular to the direction of the projected magnetic field. If the emission is going through a magnetized medium, the intrinsic angle of polarization is Faraday rotated. In equation (6), RMλ2 determines the amount of Faraday rotation. Here, λ is the wavelength corresponding to the observation frequency and RM is the rotation measure (RM) of the ambient medium. The RM at a distance x from the observer is computed as: 
(8)$$\begin{eqnarray*}
\mathrm{RM}= 812 \int _{0}^x \frac{n_\mathrm{e}}{10^{-3} \ \mathrm{cm}^{-3}} \frac{B_{\mathrm{para}}}{\mu \mathrm{G}} \frac{\mathrm{d}l}{\mathrm{kpc}} \ \left[\mathrm{\frac{rad}{m^2}}\right].\end{eqnarray*}$$The integral is taken along the LoS. ne and Bpara are the thermal electron number density and parallel magnetic field component, respectively, along the LoS. Faraday rotation occurs either outside of the emitting region, external Faraday rotation, or inside the source, internal Faraday rotation.
Citation: Rybicki & Lightman 1986
Citation function: Uses; Uses
Table 1 provides the details of the X-ray observations of Holmberg IX X-1 presented in this work. Our data reduction largely follows the procedures outlined in Walton et al. (2014). The XMM-Newton data for epochs 1 and 2 were re-reduced using SAS v14.0.0 in exactly the same manner as described in our previous work for both the EPIC-pn and EPIC-MOS detectors (Strüder et al. 2001; Turner et al. 2001), using more recent calibration files (up to date as of 2015 July). Our new Suzaku observations (epochs 3–6) were also reduced with  HEASOFT v6.18 in the same manner as the epoch 1 data; as before, we only used the XIS detectors (Koyama et al. 2007) given the high-energy NuSTAR coverage. The only major update to our data reduction procedure in comparison to Walton et al. (2014) is for the NuSTAR data. The standard science data (mode 1) were reduced with  NUSTARDAS v1.5.1 in the same manner as in that work, again with updated calibration files (NuSTAR CALDB 20150316). However, in order to maximize the signal-to-noise ratio (S/N), in this work we also make use of the spacecraft science data (mode 6) following the procedure outlined in Walton et al. (2016c; see also the NuSTAR Users Guide11

11

http://heasarc.gsfc.nasa.gov/docs/nustar/analysis/nustar_swguide.pdf

). In brief, spacecraft science mode refers to data recorded during periods of the observation in which the X-ray source is still visible, but the star tracker on the optics bench cannot return a good aspect solution. During such times, the star trackers on the spacecraft bus are used instead. For these observations, this provides an additional ∼20%–40% good exposure (depending on the observation). The inclusion of the mode 6 data allows us to fit the NuSTAR data for Holmberg IX X-1 from 3 to 40 keV for all epochs. As in Walton et al. (2014), we model the XMM-Newton spectra over the 0.3–10.0 keV range, and the Suzaku data over the 0.6–10.0 keV range for the front-illuminated XIS units (XIS0, XIS3) and the 0.7–9.0 keV range for the back-illuminated XIS1, excluding 1.7–2.1 keV owing to known calibration issues around the instrumental edges.
Citation: Koyama et al. 2007
Citation function: Uses; Uses
The shape of the fireball is an open question. Thompson & Duncan (2001) considered spherical or cylindrical structures, but the exact shape trapped in a realistic magnetar field structure, which may sustain local twists, is unclear. Feroci et al. (2001) showed that the time-dependence of the X-ray luminosity Lx(t) for the light curve of the giant flare from SGR 1900+14 on 1998 August 27 was well fit by the following function:

(1)

\begin{equation}
L_{\rm x}(t) = L_{\rm x}(0)\left(1 - \frac{t}{\tau _\mathrm{evap}}\right)^\chi ,
\end{equation}

where τevap is an evaporation time-scale. The parameter χ = a/(1 − a) can be related, in a simple model where the fireball has uniform energy density and surface flux, to the shape of the fireball (Thompson & Duncan 2001). For the 1998 giant flare from SGR 1900+14, the best-fitting value was a = 0.75 (Feroci et al. 2001), while for the 2004 December 27 giant flare of SGR 1806–20, Hurley et al. (2005) found a = 0.6. A homogeneous fireball cannot have a value higher than a = 2/3, which is also the value for a homogeneous sphere, so these results show that the SGR 1900+14 fireball may have a more complex structure (Thompson & Duncan 2001). In this paper, we choose to model the magnetic field as a pure dipole, which is sufficient to explore the generic character of outflows and fireballs, and their coupling. This choice leads to a torus-shaped fireball, as that is the only shape that can be trapped in the closed field-lines of a dipole field. We use the equations for a dipolar magnetic field in full general relativity given by Wasserman & Shapiro (1983). When considered in two dimensions (as our model geometry has rotational symmetry) the boundary of the fireball lies along a single closed field line, which is determined by a single parameter. We choose to use the diameter of the torus-shaped fireball as this parameter, defined as the equatorial radius of the outermost field line minus the radius of the star. We let the diameter vary between one and one hundred kilometres (∼0.1–10 stellar radii), to cover all possible fireball sizes.
Citation: Feroci et al. (2001)
Citation function: Background
Citation: Feroci et al. 2001
Citation function: Compare/Contrast; Compare/Contrast
Star-forming galaxies 'At all the (relatively low, z≲1\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym}
				\usepackage{amsfonts}
				\usepackage{amssymb}
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$z\lesssim 1$$\end{document}) redshifts probed by present facilities, radio-emitting star-forming galaxies appear in all respect identical to star-forming galaxies selected at any other wavelength, with spectral types ranging from spirals to irregulars and dwarfs. Although only ≲10-4\documentclass[12pt]{minimal}
				\usepackage{amsmath}
				\usepackage{wasysym}
				\usepackage{amsfonts}
				\usepackage{amssymb}
				\usepackage{amsbsy}
				\usepackage{mathrsfs}
				\usepackage{upgreek}
				\setlength{\oddsidemargin}{-69pt}
				\begin{document}$$\lesssim 10^{-4}$$\end{document} of the bolometric luminosity produced by a non-AGN powered galaxy is radiated at radio wavelengths (Condon 1992), the importance of radio selection for star-forming galaxies relies on the fact that it can provide estimates of the star-formation activity of such sources in a way which is unaffected by the presence of dust up to the earliest epochs. To do that, a solid calibration of the relation between radio luminosity and infrared luminosity (or alternatively SFR) is mandatory. This is why a lot of effort has been put in the recent years to provide calibrations as precise as possible at all redshifts and for all galaxy types. From an observational point of view, it has been found at least in the local universe that radio and infrared luminosities show an incredibly tight, approximately linear, correlation over more than five orders of magnitude in infrared luminosity (e.g., Helou et al. 1985; De Jong et al. 1985; Condon 1992; Yun et al. 2001), irrespective of galaxy type and level of star-forming activity, as long as the galaxy hosts episodes of star-formation. This relation, originally found at 1.4 GHz, has also been observed to hold at different frequencies (e.g., Delhaize et al. 2017; Gürkan et al. 2018). The theoretical reasons behind it are still not fully understood, as many factors involved in the process of shaping a galaxy should intervene to produce at least some modifications which are not (yet) clearly visible in the available data.
Citation: Condon 1992; Condon 1992
Citation function: Background; Background; Background; Background
Observations of the Lyman series forests in z ≳ 6 quasars indicate that the IGM is already highly ionized by z ∼ 6 (e.g., Fan et al. 2006; Bosman et al. 2018; Eilers et al. 2018, 2019; Yang et al. 2020), although the final completion of reionization might extend down to z ∼ 5.5 (e.g., Becker et al. 2015; Davies et al. 2018a; Kulkarni et al. 2019; Keating et al. 2020; Nasir & D’Aloisio 2020). However, the Lyman series forests are very sensitive to neutral hydrogen and saturate even at low IGM neutral fraction (i.e., 





). On the other hand, if the neutral fraction is of order unity, one would expect to see appreciable absorption redward of the wavelength of the Lyα emission line, resulting in a damping wing profile (e.g., Miralda-Escudé 1998) due to significant optical depth on the Lorentzian wing of the Lyα absorption. The first quasar with a damping wing detection is ULAS J1120+0641 (Mortlock et al. 2011) at z = 7.09, although different analyses yielded different constraints on 





 (Bolton et al. 2011; Mortlock et al. 2011; Bosman & Becker 2015; Greig et al. 2017; Davies et al. 2018b), ranging from 





 to 





 at z ∼ 7.1. Recently, the spectrum of quasar ULAS J1342+0928 (Bañados et al. 2018) at z = 7.54 shows a robust detection of the damping wing signal (Bañados et al. 2018; Davies et al. 2018b; Greig et al. 2019; Ďurovčíková et al. 2020), yielding 





 at z ∼ 7.5. Compared to other probes of reionization history, such as cosmic microwave background (CMB) polarization (Planck Collaboration et al. 2018) and Lyα emission line visibility in high-redshift galaxies (e.g., Ouchi et al. 2010; Mason et al. 2018), a main advantage of IGM damping wing measurement is that it can be applied to individual quasar sight lines, thereby constraining not only the average neutral fraction, but also its scatter in different regions of the IGM. However, the damping wing experiment is only feasible at very high redshifts where the IGM is relatively neutral, and current damping wing analyses have been limited to these two sight lines due to the lack of bright quasars at z ≳ 7. Thus, it is crucial to investigate the damping wing experiment along more z > 7 quasar sight lines.
Citation: Bolton et al. 2011
Citation function: Differences; Differences
The linearized equation of motion (see derivation of Equation (A12)) for the unmagnetized case is given by (also refer to Christensen-Dalsgaard 2003):
9





where cs(r), ρ0(r), and g(r) are the sound speed, density, and gravity (directed radially inward), respectively, and 





 denotes the covariant spatial derivative operator. For all ensuing calculations and derivations, we write Equation (9) in the form 





, where the magnetically unperturbed wave operator 





 is self-adjoint (Goedbloed & Poedts 2004). To solve for the eigenmodes of the unperturbed model S, the boundary conditions employed are: (a) 





 and the Eulerian pressure perturbation at r = 0 are finite, and (b) the Lagrangian pressure perturbation at r = R⊙ vanishes (see Section 17.6 in Cox 1980). As already mentioned earlier, the Cowling approximation is used, and hence, the gravitational Poisson equation is not needed while finding the eigenmodes. We suppress the subscript “0” in the unperturbed eigenfunctions 





 and eigenfrequencies ωk,0 for the rest of this paper. Unless specified otherwise, any instance of ωk or 





 should be assumed to imply eigenfrequencies and eigenfunctions of Equation (9), respectively. The Sun is treated as a fluid body with a vanishing shear modulus and, hence, is unable to sustain shear waves (although the presence of magnetic fields complicates this assumption). Thus, the eigenfunctions of the background model contain no toroidal components (see Chapter 8 of Dahlen & Tromp 1998), rendering them purely spheroidal. We write the displacement field 





 in the basis of vector spherical harmonics (and thereafter GSH) as follows:
10







11





Here, 





 denote spherical polar coordinates, with basis vectors 





 and 





 where n is the radial order, ℓ is the angular degree, and m is the azimuthal order. The dimensionless lateral covariant derivative operator is denoted by 





. The basis vectors in spherical polar coordinates are related to those in the GSH basis via
12
Citation: Goedbloed & Poedts 2004
Citation function: Uses
Citation: Cox 1980
Citation function: Uses
A gravitational wave (GW) event originated by the merger of a binary neutron star (BNS) system was detected for the first time by aLIGO/Virgo (GW 170817; Abbott et al. 2017a), and was found to be associated to the weak short gamma-ray burst (GRB) GRB 170817A detected by the Fermi and INTEGRAL satellites (Goldstein et al. 2017; Savchenko et al. 2017), marking the dawn of multi-messenger astronomy (Abbott et al. 2017b). The proximity of the event ~41 Mpc; Hjorth et al. 2017, Cantiello et al. 2018) and the relative accuracy of the localisation (~30 deg2, thanks to the joint LIGO and Virgo operation) led to a rapid (Δt  11 h) identification of a relatively bright optical electromagnetic counterpart (EM), named AT2017gfo, in the galaxy NGC 4993 (Arcavi et al. 2017; Coulter et al. 2017; Lipunov et al. 2017; Melandri et al. 2017; Tanvir et al. 2017; Soares-Santos et al. 2017; Valenti et al. 2017). The analysis and modelling of the spectral characteristics of this source, together with their evolution with time, resulted in a good match with the expectations for a “kilonova” (i.e. the emission due to radioactive decay of heavy nuclei produced through rapid neutron capture; Li & Paczyński 1998), providing the first compelling observational evidence for the existence of such elusive transient sources (Cowperthwaite et al. 2017; Drout et al. 2017; Evans et al. 2017; Kasliwal et al. 2017; Nicholl et al. 2017; Pian et al. 2017; Smartt et al. 2017; Villar et al. 2017). While the bright kilonova associated to GW 170817 has been widely studied and its main properties relatively well determined, the observations of the short GRB 170817A are more challenging for the current theoretical frameworks. Indeed, the properties of this short GRB appear puzzling in the context of observations collected over the past decades (Berger 2014; D’Avanzo 2015; Ghirlanda et al. 2015). The prompt γ-ray luminosity was significantly fainter (by a factor ~2500) than typical short bursts (see, e.g. D’Avanzo et al. 2014). A faint afterglow was detected in the X-ray and radio bands only at relatively late times (starting from ~9 and 16 d after the GW/GRB trigger, respectively; Alexander et al. 2017; Haggard et al. 2017; Hallinan et al. 2017; Margutti et al. 2017; Troja et al. 2017a), while earlier observations provided only upper limits in these bands (Evans et al. 2017; Hallinan et al. 2017).
Citation: Coulter et al. 2017
Citation function: Background; Background
To explore the link between angular momentum and local gravitational instability in nearby star-forming spirals, we need a reliable disc instability diagnostic. Contrary to what is commonly assumed, the gas Toomre parameter is not a reliable diagnostic: stars, and not molecular or atomic gas, are the primary driver of disc instabilities in spiral galaxies, at least at the spatial resolution of current extragalactic surveys (Romeo & Mogotsi 2017). This is confirmed by other investigations (Marchuk 2018; Marchuk & Sotnikova 2018; Mogotsi & Romeo 2018), and is true even for a powerful starburst+Seyfert galaxy like NGC 1068 (Romeo & Fathi 2016). The stellar Toomre parameter is a more reliable diagnostic, but it does not include the stabilizing effect of disc thickness, which is important and should be taken into account (Romeo & Falstad 2013). The simplest diagnostic that does this accurately is the Romeo–Falstad $\mathcal {Q}_{N}$ stability parameter for one-component (N = 1) stellar (⋆) discs, which we consider as a function of galactocentric distance R: 
(1)
\begin{eqnarray*}
\mathcal {Q}_{\star }(R)= Q_{\star }(R)\, T_{\star }\, ,
\end{eqnarray*}
where Q⋆ = κσ⋆/πGΣ⋆ is the stellar Toomre parameter (σ denotes the radial velocity dispersion), and T⋆ is a factor that encapsulates the stabilizing effect of disc thickness for the whole range of velocity dispersion anisotropy (σ$z$/σR) observed in galactic discs: 
(2)
\begin{eqnarray*}
T_{\star }= \left\lbrace \begin{array}{ll}\displaystyle 1+0.6\left(\frac{\sigma _{z}}{\sigma _{R}}\right)_{\star }^{2} &amp;\quad \text{if }0\le (\sigma _{z}/\sigma _{R})_{\star }\le 0.5\, , \\
{\displaystyle 0.8+0.7\left(\frac{\sigma _{z}}{\sigma _{R}}\right)_{\star }} &amp;\quad \text{if }0.5\le (\sigma _{z}/\sigma _{R})_{\star }\le 1\, . \end{array} \right.
\end{eqnarray*}
Observations do not yet constrain the radial variation of (σ$z$/σR)⋆, hence that of T⋆ (Gerssen & Shapiro Griffin 2012; Marchuk & Sotnikova 2017; Pinna et al. 2018).
Citation: Romeo & Falstad 2013
Citation function: Compare/Contrast; Uses
Accreting supermassive BHs can have a profound impact on the evolution of the host galaxies (see review by Alexander & Hickox 2012), as testified by the observed tight relationships between the relic BH masses and the physical properties of the hosts, most noticeably the stellar mass or velocity dispersion of the bulge component (e.g., Magorrian et al. 1998; Ferrarese & Merritt 2000; Gebhardt et al. 2000; Tremaine et al. 2002; Kormendy & Ho 2013; McConnell & Ma 2013; Reines & Volonteri 2015; Shankar et al. 2016, 2020a; Sahu et al. 2019; Zhu et al. 2021). These suggest that (apart from short-time stochastic fluctuations) the BH and the bulge stellar mass must have coevolved over comparable timescales, possibly determined by the energy feedback from the BH itself on the gas/dust content of the host (see Tinsley 1980; Silk & Rees 1998; Fabian 1999; King 2005; Lapi et al. 2006, 2014, 2018; for a review, see King & Pounds 2015). In fact, targeted X-ray observations in the high-redshift star-forming progenitors of local massive galaxies have started to reveal the early growth of a dust-enshrouded (super)massive BH in their nuclear regions (e.g., Mullaney et al. 2012; Page et al. 2012; Delvecchio et al. 2014; Rodighiero et al. 2015, 2019; Fiore et al. 2017; Stanley et al. 2015, 2017; Massardi et al. 2018; Combes et al. 2019; D’Amato et al. 2020) before it attains a high enough mass and power to manifest as a bright AGN and eventually reduce/quench star formation and partly evacuate gas and dust from the host (e.g., Granato et al. 2001, 2004; Lapi et al. 2011,2014, 2018). Another, albeit more indirect, indication of coevolution for the bulk of the BH and the host stellar mass comes from the similarity between the activity timescales of the central BH to the transition timescale of (green valley) galaxies from the blue cloud to the red sequence (see Wang et al. 2017; Lin et al. 2021, 2022; this is true apart from rejuvenations at late cosmic times; see Martin-Navarro et al. 2022).
Citation: Tinsley 1980
Citation function: Background
Citation: Alexander & Hickox 2012
Citation function: Background
Citation: Kormendy & Ho 2013; Mullaney et al. 2012
Citation function: Background; Background
Citation: Granato et al. 2001
Citation function: Background
Citation: Wang et al. 2017
Citation function: Background