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.


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.


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.


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.


Star-forming galaxies 'At all the (relatively low, z≲1\documentclass[12pt]{minimal}
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				\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}
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				\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.


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.


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


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).


Gough’s (1977a) concept of averaging over convective eddies is based on Spiegel’s (1963) finding that the linearized equations of motions for determining the convective growth rate σ of a convective eddy, i.e. the rate with which the convective fluctuations grow with time, satisfy a variational equation for σ, if the locally defined superadiabatic temperature gradient β(r0) is replaced by the averaged, i.e. non-local, value (Gough 1977a,b)
(2)
\begin{eqnarray*}
{\cal B}(r)=\frac{2}{\ell }\int \beta (r_0)\cos ^2\left[\pi (r_0-r)/\ell \right]\, {\rm d}r_0\, .
\end{eqnarray*}
In expression (2), the averaging is obtained by taking account of contributions from convective eddies centred at r0 and the range of integration is the vertical extent ℓ, which scales with the local pressure scale height. Based on Spiegel’s finding on the convective growth rate, Gough (1977a) suggested similar expressions for the averaged, non-local, convective heat, ${\cal {F_{\mathrm{c}}}}$, and momentum, $\mathcal {P}_{\rm t}$, fluxes, with β(r0) in equation (2) being replaced by the locally computed convective fluxes Fc(r0) and pt(r0), respectively. This would, however, lead to a system of integro-differential equations for the stellar structure, which would be difficult to solve numerically. Gough (1977a) suggested therefore to approximate the kernel ${\cal K}:=2\cos ^2[\pi (r_0-r)/\ell ]$ in equation (2) by the expression ${\cal K}\simeq a\exp (-a|r_0-r|/\ell)/2$, and setting the integration limits formally to ±∞, which leads to an integral expression that represents the solution to the second-order differential equation
(3)
\begin{eqnarray*}
\frac{{\rm d}^2{\cal {F_{\mathrm{c}}}}}{{\rm d}\ln p^2}=\frac{a^2}{\alpha ^2}\left({\cal {F_{\mathrm{c}}}}-{F_{\mathrm{c}}}\right)\,
\end{eqnarray*}
(Gough 1977a; Balmforth 1992a; Houdek & Dupret 2015) for the non-local convective heat flux, ${\cal {F_{\mathrm{c}}}}$, for example, where ln p (p is total pressure) is now the new independent depth variable (as implemented in the calculations), α ≔ −ℓdln p/dr is the mixing-length parameter, and a is another dimensionless, non-local, parameter. Similar expressions are obtained for the averaged, non-local, superadiabatic temperature gradient, $\cal B$, and turbulent pressure, $\cal P_{\mathrm{t}}$, introducing the remaining non-local (dimensionless) parameters b and c, respectively. These non-local parameters control the spatial coherence of the ensemble of eddies contributing to the total heat (a) and momentum (c) fluxes, and the degree to which the turbulent fluxes are coupled to the local stratification (b). Roughly speaking, the parameters a, b, and c control the degree of ‘non-locality’ of convection; low values imply highly non-local solutions, and in the limit a, b, c → ∞ the system of equations formally reduces to the local formulation (except near the boundaries of convection zones, where the local equations are singular). Theoretical values for the dimensionless, non-local, parameters a, b, and c can be obtained by demanding that the terms in a Taylor expansion about r of the exact, 2cos 2[π(r0 − r)/ℓ], and approximate, aexp (− a|r0 − r|/ℓ)/2, kernels differ only at fourth order, resulting in a theoretical estimate for a ≃ 7.8 (Gough 1977a). The standard mixing-length assumption of assigning a unique scale to turbulent eddies at any given location can, however, cause too much smoothing, leading to larger values for a, b, or c (Houdek & Gough 2002). Therefore, values for a, b, and c, which typically differ, need to be determined from calibration in a similar way as it is common for the mixing-length parameter, α, in stellar evolutionary theory.1It should be mentioned that our adopted non-local convection formulation does not treat the overshoot regions correctly, where the non-local enthalpy flux, $\cal {F_{\mathrm{c}}}$, remains positive although it should be negative. The overshoot regions may therefore not be suitable for calibrating the non-local parameters to 3D simulation results (see also discussion in Section 5.2). The effect of such positive $\cal {F_{\mathrm{c}}}$ values in the overshoot regions on the damping rates and eigenfrequencies is, however, negligible.


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} &\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 }} &\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).


One of the important findings of the COS-Halos survey is that

 is omnipresent in the halos of SF galaxies which harbor a major reservoir of galactic metals (i.e., Tumlinson et al. 2011a). Outflows from the SF galaxies are thought to be the origin of highly ionized oxygen in the CGM. However, the outflows need not be active at the time of observations. Active outflows that are detected primarily via low-ions (e.g.,

,

,

) absorption in the spectra of host-galaxies (i.e., the “down-the-barrel” outflows) are also found to be ubiquitous at both high and low redshifts (Shapley et al. 2003; Martin 2005; Rupke et al. 2005; Veilleux et al. 2005; Rubin et al. 2010, 2014). Despite the ubiquity of winds, several basic questions that are key to quantifying galaxy feedback remain unanswered. How far do they propagate? What is the baryon mass that are processed through them? What is the mass-flow rate through winds? What are the mass loading factors and kinetic power of the winds? To what degree are metals processed through them? This is essentially because the location of the outflow with respect to host-galaxy is an unknown in “down-the-barrel” outflows. Galaxy outflow probed by a background QSO has the advantage of having the minimum distance between host-galaxy and outflowing material. For example, by analyzing a post-starburst outflow from a galaxy at

 detected in the spectra of QSO PG 1206+459 at an impact parameter of ∼68 kpc, Tripp et al. (2011) have shown that the entrained gas mass could be as large as ∼ few

 Numerous strong and large velocity spread (

 km s−1) metal absorption lines along with solar to super-solar metallicities in different absorption components suggest that the absorber is tracing an active outflow. Such wide velocity spread

 absorbers at low-z are also reported by Tumlinson et al. (2011b) and Muzahid (2014). In both these cases metallicity of the

 bearing gas is low (e.g.,

) which suggest that

 is probably tracing an “ancient outflow” (Ford et al. 2014) rather than an active wind. Interestingly, strong

 is detected in PG 1206+459 which is not present in the latter two systems. We note that the location of the absorbing gas with respect to the host-galaxy’s projected major and minor axes are not known for any of these strong

 absorbers.


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).


Theoretical and observational work argue for a strong correlation between the NIR size and the AGN luminosity (Suganuma et al. 2006; Kishimoto et al. 2011; Koshida et al. 2014; GRAVITY Collaboration 2019). In the standard picture, the NIR emission originates from the dust sublimation region, which is determined by the dust sublimation temperature Tsub. The temperature at which dust sublimates depends on the grain size and composition and ranges from Tsub ≈ 1500 K for silicate (Si) grains to Tsub ≈ 2000 K for graphite (C) grains (Baskin & Laor 2018). By assuming a grain size distribution typical for the interstellar medium (ISM), the mean sublimation distance can be calculated for graphite and silicate dust as

R
≈

a
X

×

L

46

1
/
2

$ R\approx a_{\mathrm{X}}\times L_{46}^{1/2} $

 [pc] with aC = 0.5 and aSi = 1.3 (e.g. Barvainis 1987; Netzer 2015; for grain size dependence see Baskin & Laor 2018). However, there is evidence both from SED fitting (Mor & Netzer 2012) and from dust reverberation mapping (Kishimoto et al. 2007; Koshida et al. 2014) that, close to the AGN, one may find only larger graphite grains. Since, at the same distance from the AGN, large grains are cooler than small grains, one might naturally expect to find a distribution of large graphite grains at the smallest radii. In addition changes in the brightness of the AGN may lead to changes in the dust sublimation radius (Kishimoto et al. 2013) or instead, depending on the dust distribution, its temperature (Schnülle et al. 2015). As such, the sublimation radius is really rather a sublimation region according to grain size and species (e.g. Hönig & Kishimoto 2017; Baskin & Laor 2018). Empirical studies have found R2.2 μm ≈ 0.4 pc × (LAGN/1046 erg s−1)1/2 (assuming the V-band to Rsub relation from Koshida et al. 2014, and using the conversion LAGN ∼ 8L5500 Å from Netzer 2015), which corresponds to a good approximation to the sublimation radius of graphite. For NGC 1068 the observed relation from Koshida et al. (2014) predicts a dust sublimation radius in the range R2.2 μm ≈ 0.08–0.27 pc, for the luminosity range quoted in Table 1.


It is expected that the polarization properties produced by the thermal–nonthermal electrons have wide applications to many kinds of synchrotron sources. Here, we propose some examples. Covino et al. (2017) detected the low-level linear polarization of AT 2017gfo/GW170817 during the kilonova phase. Although the measured polarization seems to be due to the Galactic dust along the line of sight, we think that future synchrotron polarization detections for electromagnetic counterparts of gravitational wave events can be applied to further investigate compact object merger systems and constrain detailed physics of gravitational wave events. Fast radio burst (FRB) 140514 has the linear polarization limit of

 and the circular polarization degree of 21 ± 7% (Petroff et al. 2015). The development of the radio polarization measurements on FRBs are carried out to reveal the FRB origin. Covino & Götz (2016) summarized the polarization observation of GRB prompt and afterglow emissions, and the GRB jet geometry related to the polarization was also mentioned. Steele et al. (2017) presented the optical polarization results of some GRBs, and the linear polarization degrees are relatively low (see also the recent report of Wiersema & Covino 2018 on GRB 180205A). Moreover, the circular polarization was detected in GRB 121024A (Wiersema et al. 2014). Spectropolarimetric detection of either supernova Ia (SN Ia) or core-collapse supernova was performed (Tanaka et al. 2012; Porter et al. 2016). The polarization properties can be helpful to further explore SN explosion mechanisms. Thermal electrons cannot be ignored in the celestial objects mentioned above, and we should consider the thermal electron contribution to the synchrotron polarization. Moreover, some objects, such as kilonova, GRB, and SN as mentioned above, have dense environments (D’Elia et al. 2007; Kasen et al. 2013; Tanaka & Hotokezaka 2013; Buckey et al. 2018; Yang et al. 2018). Polarization radiative transfer should be taken into account when we consider the polarization measurements in the optical and radio bands. In this paper, we do not attempt to reproduce these different polarization properties with exact modeling parameters. However, these polarization detections of the different populations encourage us to further explore the possibility of applying our scenario, when we assume that all of these kinds of sources are dominated by the synchrotron radiation.


Recent work by Tseliakhovich & Hirata (2010) showed that, at the time of recombination, baryons were moving in a coherent manner (on scales of ≲3 Mpc comoving) with respect to the dark matter and had an rms velocity of ∼30 km s−1. Since, on small scales, the baryons effectively displayed a streaming motion with respect to the dark matter component, their relative velocity is usually referred to as a ‘stream velocity’ in the literature, and we adopt this convention throughout this work. Tseliakhovich & Hirata (2010) also argued that, since shortly after recombination the temperature of the baryons (and hence the sound speed) drops precipitously, the streaming motion of the baryons becomes supersonic and it can potentially have a dramatic impact on structure formation. Subsequent studies, both theoretical and numerical, showed that the large stream velocity of baryons has profound implications on the total number density of haloes (Tseliakhovich & Hirata 2010; Maio, Koopman & Ciardi 2011; Stacy, Bromm & Loeb 2011; Tseliakhovich, Barkana & Hirata 2011; Fialkov et al. 2012; Naoz, Yoshida & Gnedin 2012; O'Leary & McQuinn 2012; Bovy & Dvorkin 2013; Tanaka, Li & Haiman 2013; Tanaka & Li 2014; Asaba, Ichiki & Tashiro 2016), the size of the haloes that are able to retain gas at a given redshift (Naoz, Yoshida & Gnedin 2013), the overall gas fraction in haloes (Dalal, Pen & Seljak 2010; Greif et al. 2011; Maio et al. 2011; Tseliakhovich et al. 2011; Fialkov et al. 2012; Naoz et al. 2012, 2013; O'Leary & McQuinn 2012; Richardson, Scannapieco & Thacker 2013; Asaba et al. 2016), the gas density and temperature profiles (Greif et al. 2011; Liu & Wang 2011; Fialkov et al. 2012; O'Leary & McQuinn 2012; Richardson et al. 2013), the halo mass threshold in which star formation occurs (Liu & Wang 2011; Maio et al. 2011; Greif et al. 2011; Fialkov et al. 2012; O'Leary & McQuinn 2012; Bovy & Dvorkin 2013), as well as black hole evolution (Tanaka et al. 2013; Tanaka & Li 2014; Latif, Niemeyer & Schleicher 2014) and magnetic fields (Naoz & Narayan 2013). A thorough review of the implications of the stream velocity on structure formation is presented in Fialkov (2014).


Gohil & Ballantyne (2017) showed that the AGN obscuration phenomenon depends on the gas fraction in NSDs. With a higher gas fraction, a greater amount of gas is available to accrete, which increases a column of gas in annulus Σmp and, in turn, controls expansion of the atmosphere. The overall gas fraction (f0) in galaxies is observed to be increasing with redshift. f0 is related to the depletion time and the specific star-formation rate (sSFR) through
(16)
\begin{eqnarray}
f_0(z)=\frac{1}{1+[t_{\rm dep}(z){\rm sSFR}(z)]^{-1}}.
\end{eqnarray}
The depletion time is estimated to be (Saintonge et al. 2013)
(17)
\begin{eqnarray}
t_{\rm dep}=1.5(1+z)^{\alpha } [{\rm Gyr}],
\end{eqnarray}
with α = −1.0 (Tacconi et al. 2013). Lilly et al. (2013) provide an analytical expression for the evolution of sSFR, given by
(18)
\begin{eqnarray}
{\rm sSFR}(M_*,z)= \left\lbrace \begin{array}{@{}l@{\quad }l@{}}0.07\Big (\frac{M_*}{10^{10.5} \, \mathrm{M}_{\odot }}\Big )^{-0.1} (1+z)^3\ \ & z<2,\\
 0.30\Big (\frac{M_*}{10^{10.5} \, \mathrm{M}_{\odot }}\Big )^{-0.1} (1+z)^{5/3}\ \ & z\ge 2, \end{array}\right.
\end{eqnarray}
which was motivated by observational data (e.g. Daddi et al. 2007; Elbaz et al. 2007; Noeske et al. 2007; Pannella et al. 2009; Stark et al. 2013). Since there is a weak dependence on the galaxy mass M*, we choose M* = 1010.5 M⊙. Then the distribution of the gas fraction (Φf) is assumed to be Gaussian around f0 and is given by
(19)
\begin{eqnarray}
\Phi _{\rm f}(z,f)=\frac{1}{\sqrt{2 {\pi} }\sigma _{\rm f}}\exp \Big [-\frac{(f-f_0)^2}{2\sigma _{\rm f}^2}\Big ].
\end{eqnarray}
The dispersion σf is estimated to be 0.2 by roughly fitting a Gaussian to the results of Tacconi et al. (2013). Finally, we can compute the weights Wf of input parameter f ≡ fg, out from
(20)
\begin{eqnarray}
W_{\rm f}(z,f)=\frac{\Phi _{\rm f}(z,f)}{\sum \limits _{k}\Phi _{\rm f}(z,f_k)},
\end{eqnarray}
where
(21)
\begin{eqnarray}
f_k\in [0.2,0.4,0.6,0.8].
\end{eqnarray}
The right panel of Fig. 1 shows the evolution of 20, 40, 60 and 80 per cent gas fraction with redshift, represented by black, red, blue and green curves, respectively. At low redshift, NSDs with low gas fraction dominate the sample, while NSDs with a 40 per cent gas fraction dominate at 1  z  2. Beyond z = 2, NSDs with a 60 per cent gas fraction dominate. Wf of NSDs with low gas fraction decrease overall with redshift and the reverse is true for NSDs with high gas fraction (60 and 80 per cent). Similarly to the observational evidence, the figure illustrates that the dominant gas fraction increases with z and its evolution flattens out at higher redshift.


PHL 1811 itself has an estimated Eddington ratio of

 (Leighly et al. 2007b). PHL 1811, along with several PHL 1811 analogs and WLQs with rest-frame optical spectra (J1521+5202, 2QZ J2154–3056, and the two high-redshift WLQs in Shemmer et al. 2010), have weak or undetected [O iii]

 narrow emission lines, suggestive of high Eddington ratios (e.g., Boroson & Green 1992; Shen & Ho 2014). Moreover, several studies have found that as

 increases, the C iv REW generally decreases and the C iv blueshift also increases (e.g., Bachev et al. 2004; Baskin & Laor 2004; Richards et al. 2011; Shen & Ho 2014; Sulentic et al. 2014; Shemmer & Lieber 2015). In these correlations, there is only limited sampling in the super-Eddington or low (

 Å) C iv REW regime, but the overall trends suggest that the Eddington ratio grows as one moves from typical quasars toward WLQs in the C iv REW versus blueshift space (Figure 3(a)). By the nature of our selection of the PHL 1811 analogs and WLQs, demanding that the BELR does not produce normal emission lines, we may have recovered effectively a population of quasars with (extremely) high Eddington ratios. It is difficult to measure

 directly for our exceptional objects, as the SMBH masses estimated from the line-based virial method are likely highly uncertain and perhaps systematically in error (Section 5.3). However, based on the empirical Γ

 relations, our joint spectral analysis of the X-ray normal subsample in Sections 5.2 and 5.3 does indicate a high Eddington ratio (

) in general for our quasars.33

33
Narrow-line Seyfert 1 galaxies (NLS1s) also generally have steep X-ray spectra and high Eddington ratios. PHL 1811 itself is considered a NLS1 (Leighly et al. 2001), and NIR spectroscopy of a limited sample of WLQs shows that they have in general narrow Hβ and strong optical Fe ii emission (see Section 5.1 of Plotkin et al. 2015), similar to NLS1s. However, as the line widths and REWs have likely dependences on luminosity, our PHL 1811 analogs and WLQs are not directly comparable to local, less-luminous NLS1s.


Phinney (1989) was the first to recognize that

 is not exactly the maximum orbital pericenter for a complete tidal disruption, a distance we would like to name the “physical tidal radius” (we assign it the symbol

). To remedy the neglect of internal stellar structure, he suggested that

 could be estimated by applying to

 a correction factor based on the star’s apsidal motion constant and its dimensionless binding energy. For this reason,

 is sometimes reinterpreted to be

, but without evaluating how it might differ from

 (Stone et al. 2013). Several groups have tried to include stellar structure in the calculation of

, but employing purely Newtonian dynamics on polytropic stars (e.g., Luminet & Carter 1986; Khokhlov et al. 1993; Guillochon & Ramirez-Ruiz 2013; Mainetti et al. 2017). Recently, there have been efforts beginning from genuine main-sequence stellar structures, but still restricted to Newtonian dynamics, and examining a limited range of stellar masses (only 1

 in Goicovic et al. 2019,

 and

 at several ages in Law-Smith et al. 2019,

,

, and

 at three different ages in Golightly et al. 2019). Others have explored the dependence on black hole mass induced by relativistic effects, but without any reference to internal stellar structure or the hydrodynamics of disruption (e.g., Ivanov & Chernyakova 2006; Kesden 2012; Servin & Kesden 2017). Earlier works employed a post-Newtonain approximation (e.g., Ayal et al. 2000) or explored the use of relativistic hydrodynamics simulations for strong encounters of polytropic stars, but without stellar self-gravity (e.g., Laguna et al. 1993). In some cases, relativistic effects were approximated by a “generalized Newtonian potential” (e.g., Gafton et al. 2015; Gafton & Rosswog 2019) or in terms of genuine relativistic dynamics (e.g., Frolov et al. 1994), but assuming a polytropic structure for the star and computing stellar self-gravity in an entirely Newtonian fashion (in the last case, fixing it to its initial stellar surface value). Many of these explorations of

 also computed the energy distribution dM/dE and explored the relation between the remnant mass and orbital pericenter in partial disruptions; in one case (Manukian et al. 2013), they also examined the remnants’ orbital properties. However, all this work was subject to the limitations already enumerated.


Figure 1 presents the Stokes I image from W43-MM1. The continuum emission shows a fragmented filament extending from the north to the south–west. Two bright sources at the center, A and B1, completely dominate the energy budget in W43-MM1 (with integrated fluxes of ∼2.0 and 0.5 Jy, which correspond to

 of the total flux recovered), over a number of additional fragments extending to the south–west. Also, additional sources to the east and west have been detected. Comparing with the SMA results from Sridharan et al. (2014) and the PdBI 1 mm results from Louvet et al. (2014), the ALMA observations reproduce quite well the overall morphology of W43-MM1, but with better resolution. The noise in the ALMA map is

 with a peak of 503 mJy

 obtained from Gaussian fitting. We used the getsources algorithm (Men'shchikov et al. 2012) to successfully extract 14 sources from our ALMA data (see Table 1 and Figure 1). The extraction was later compared to other methods such as clumpfind (Williams et al. 1994), FellWalker, and Reinhold (Berry et al. 2007) obtaining a good agreement with the selection produced by getsources. We used the source positions and sizes derived using getsources as initial guess for a Gaussian 2D fitting (using CASA imfit algorithm) in order to derive accurate fluxes from the extracted sources.14

14
We found that getsources tends to underestimate the recovered fluxes from our data.
 Also, we kept the same source nomenclature used by Sridharan et al. (2014), but adding numbers where higher multiplicity was discovered with respect to the SMA map. Using the standard procedure to calculate masses from dust emission (Hildebrand 1983), we computed masses for all 15 sources in our catalog assuming a dust opacity of

 cm2 g−1 (Ossenkopf & Henning 1994), a gas to dust ratio of 1:100, and a dust temperature of

 K (Bally et al. 2010), with the exception of the hot core, source A, where we used a range between

 K. Although the SMA detected CH3CN emission toward B1 and C, it was unresolved and not sufficient to derived temperatures; hence, we used

 K for these sources. Herpin et al. (2012) modeled an spectral energy distribution and derived a temperature profile for source A using all the publicly available data on W43-MM1 to date. Their model suggests a temperature of ∼150 K at 2500 au distance (05 radial;

 size) and ∼70 K at about 8000 au distance (07 radial; 14 size), which are the length scales sampled by ALMA. However, if larger spatial scales than our source size are considered, the temperature might be lower and on the order of 30 K (as suggested by Bally et al. 2010). These scales (

) are consistent with Herschel primary beam at 160 μm and, of course, larger than our deconvolved source sizes and synthesized beam. Therefore, and using this temperature range, our derived mass for source A is between 312 and 146 M

(with the exception of the 30 K temperature derived mass of 728 M

). These estimates put source A below other massive clumps such as the SDC335-MM1 mass estimate of 545 M

(Peretto et al. 2013) and G31.41+0.31 with a mass estimate of 577 M

 (Girart et al. 2009).15

15
Note that in this massive core a magnetic field strength of 10 mG was derived using n(H2) =

 cm−3.
 However, these mass estimates were derived from observations sampling larger length scales than our ALMA W43 observations. The deconvolved size of SDC335-MM1 is about 0.054, which is two times the size of source A or four times the area. A simple estimate assuming an

 density profile, will give about 272 M

 per source A size for SDC335-MM1 and about 205 M

 per source A size for G31.41+0.31.


The ALMA data were obtained in Cycle 3 through proposal 2015.1.00540.S (PI: R. A. A. Bowler). We observed the six brightest LBGs at 6.5  $z$  7.5 presented in Bowler et al. (2012, 2014). The galaxies are all within the COSMOS field (Scoville et al. 2007a),1 and were initially selected in the near-IR YJHKs data based on the UltraVISTA2 survey data release 2 (McCracken et al. 2012). The coordinates of the six galaxies, which defined each ALMA pointing, and their photometric redshifts are shown in Table 1. The galaxies were selected via SED fitting and are secure $z$ > 6.5 objects as demonstrated by the sharp spectral break observed in the photometric data at ${\simeq } 1\, {\mu} {\rm m}$ (Fig. A1). The strength of the break ($z - Y \gt 2\, {\rm mag}$) observed in the sample cannot be reproduced by the common low-redshift or brown-dwarf contaminants (e.g. Ouchi et al. 2010; Bouwens et al. 2011; Bowler et al. 2012). Each target was observed for 10 min in Band 6 (centred at $233\, {\rm GHz}$ or $1.29\, {\rm mm}$; corresponding to ∼170 ${\mu}$m in the rest frame). The integration time was chosen to provide limits on the ratio of FIR to UV luminosity sufficient to distinguish between the previous results at $z$ > 5 from Watson et al. (2015) and Capak et al. (2015). The data were taken in a compact configuration C36-2, with a maximum baseline of 330 m, on 2016 January 25. In order to maximize continuum sensitivity, the correlator was set up in time division mode with 2 GHz bandwidth across each of four spectral windows (centred at 224, 226, 240, 242 GHz) in two polarizations. The data were reduced with the ALMA pipeline of casa version 4.5.1. Calibration was performed by ALMA personnel using J1058+0133, J0948+0022, and Ganymede for bandpass, phase, and flux calibration, respectively. We then processed the data through the imaging pipeline, collapsing the full 8 GHz bandwidth and both polarizations into a single-continuum image of each field, initially using natural weighting of baselines to obtain the optimal root-mean-square (rms) sensitivity for point sources. Imaging was achieved using the tclean task, and the data were cleaned by defining a mask for any source in the field with a peak signal-to-noise ratio (SNR) > 3 that also corresponds to a Hubble Space Telescope(HST)-detected galaxy (whether the target or serendipitous), with a clean threshold of 60 ${\mu}$Jy (≃ 2 × rms). The natural weighted images have a beam size of 1.1 × 1.4 arcsec full width at half-maximum (FWHM) and reach an average rms sensitivity of $27\, {\mu} {\rm Jy}\,{\rm beam}^{-1}$, with small deviations of $2 \, {\mu} {\rm Jy}\,{\rm beam}^{-1}$ between the different pointings. To increase the sensitivity to extended flux, we also tried imaging the targets with a 1 arcsec taper, which results in a beam size of 1.4 × 1.7 arcsec and rms sensitivity of $31\, {\mu} {\rm Jy}\,{\rm beam}^{-1}$. As the natural weighted images have a smaller beam and better rms sensitivity, we chose to present this weighting throughout the paper, however comment on the tapered results where relevant. We measured fluxes using two complementary methods. First, fluxes were measured from the peak flux within an aperture of radius 1 arcsec from the HST/WFC3 centroid. The peak flux assumes that the source is unresolved in the ALMA data. For the stacks and the detected individual source, we also measured the total flux using a Gaussian fit. In the case of a non-detection at the 3σ level for the individual LBGs, we conservatively provide 2σ upper limits calculated as $f_{\rm peak} + 2\, \times \, {\rm rms}$.


A non-vanishing α1 adds to the polarization of the orbit in the same way as a non-vanishing α3, and analogous to equation (13) one finds for the change of the orbital eccentricity vector
(17)
\begin{eqnarray*}
\dot{\boldsymbol {e}} = \dot{\boldsymbol {e}}_{\hat{\alpha }_1} + \dot{\boldsymbol {e}}_{\hat{\alpha }_3} + \dot{\omega }_{\rm PN}\, \hat{\boldsymbol {k}} \times {\boldsymbol {e}} \, ,
\end{eqnarray*}
where
(18)
\begin{eqnarray*}
\dot{\boldsymbol {e}}_{\hat{\alpha }_1} \simeq \frac{\hat{\alpha }_1}{4c^2} \, \frac{M_{\rm p}- M_{\rm c}}{M_{\rm p}+ M_{\rm c}} \, n_{\rm b} \mathcal {V}_O \, {\boldsymbol w}_\perp
\end{eqnarray*}
(Damour & Esposito-Farèse 1992b) and
(19)
\begin{eqnarray*}
\dot{\boldsymbol {e}}_{\hat{\alpha }_3} \simeq \frac{3}{2\mathcal {V}_O}\, {\boldsymbol {a}}_{\hat{\alpha }_3} \times \hat{\boldsymbol {k}} = -\hat{\alpha }_3 \pi \, \frac{s_{\rm p}\nu }{\mathcal {V}_O} \, {\boldsymbol w}_\perp
\end{eqnarray*}
(Bell & Damour 1996). The velocity ${\boldsymbol w}$⊥ is the projection of the systemic CMB frame velocity into the orbital plane of the binary pulsar. To independently constrain $\hat{\alpha }_3$ from PSR J1713+0747 timing, we will include the $\hat{\alpha }_1$ limits obtained from PSR J1738+0333 by Shao & Wex (2012) in our analysis. Conversely, owing to its small orbital period, PSR J1738+0333’s possible $\hat{\alpha }_3$ effects would be much smaller than its $\hat{\alpha }_1$ effects and would have insignificant impact on the $\hat{\alpha }_1$ limits derived from this system. There is one assumption, however, that we have to make here. Since PSR J1713+0747 and PSR J1738+0333 have different masses, and therefore different sensitivities sp, we cannot assume that they would lead to identical $\hat{\alpha }_1$. For this reason, our analysis only applies to deviations from GR which exhibit only a moderate mass dependence of the strong-field parameter $\hat{\alpha }_1$, at least for neutron stars in the range of 1.3–1.5 M⊙.


In our spectroscopic analysis, we also quantify the reflection strength for each source. It is therefore interesting to compare our results to the typical assumptions made in CXB population-synthesis models. Indeed, they generally implement relatively similar assumptions. The reflection is always assumed to have a constant value

 within each population (e.g., Ballantyne et al. 2006; Treister et al. 2009; Akylas et al. 2012; Ueda et al. 2014) or possibly a function of the degree of obscuration (e.g., G07; Ueda et al. 2014; Esposito & Walter 2016) with no dispersion around a mean value. On average, we find median reflection values that are: (1) significantly lower (

) than those assumed (

) by CXB models and (2) exhibit a rather broad distribution with a median value relative to the whole sample of ∼0.4 (Table 6). Furthermore, we measure a significant anti-correlation with unabsorbed and intrinsic luminosities (the latter being more pronounced; see Figure 8 (lower panels) and Table 6). This trend is further confirmed by the findings of our companion paper on stacked NuSTAR spectra (DM17). In this context, we find sources with lower unabsorbed luminosities to have a median reflection (

) a factor of two stronger than more luminous ones (

). The broad R distribution reaches 50% percentile values a factor of two larger. When using intrinsic coronal luminosities, the differences exacerbates further by a factor of about two. A similar trend has been largely ignored by models; the one exception being the G07 model, for which QSOs have been assumed to have no reflection. G07 also assumes higher R for Type-1 sources (R = 1.3) compared to Type-2s (R = 0.88) in order to mimic a orientation-dependent disk reflection. Ueda et al. (2014) instead assumes a flat R = 0.5 from the disk and a torus-based contribution in the context of a luminosity- and redshift-dependent unified scenario in order to reproduce a total R = 1 for Seyfert galaxies.


Over the past decades, our understanding of the EoR has deepened from advances in the observational frontier of galaxies in the early universe. Dedicated surveys of high-redshift galaxies using the Hubble Space Telescope (HST) have measured a large sample of galaxies out to redshift as high as z ∼ 8 (Bouwens et al. 2015b; Finkelstein et al. 2015), which with the help of gravitational lensing has allowed the rest-frame ultraviolet (UV) galaxy luminosity function to be accurately constrained to a limiting magnitude of

M

UV

AB

≳
−
15

 (Atek et al. 2015; Bouwens et al. 2017; Yue et al. 2018). It is expected that, by the advent of the James Webb Space Telescope (JWST), not only the currently limited sample size of 9 ≲ z ≲ 12 galaxies and candidates (Ellis et al. 2013; Oesch et al. 2014, 2016, 2018) but also the constraints on the faint-end slope evolution of the UV luminosity function will be considerably enhanced (Mason et al. 2015; Yung et al. 2019). Combined with the Thomson scattering optical depth τes = 0.055 ± 0.009 inferred from the cosmic microwave background (CMB) temperature and polarization power spectra by Planck Collaboration et al. (2016a), the SFH based on a plausible faint-end extrapolation of the luminosity function suggests that the global reionization history could be explained by the “known” high-z galaxy population. If the average escape fraction of their ionizing photons into the intergalactic medium (IGM) is in the range of 10%–20% (e.g., Mason et al. 2015; Robertson et al. 2015; Bouwens et al. 2015a; Sun & Furlanetto 2016; Madau 2017; Naidu et al. 2020), there will be no need to invoke additional ionizing sources such as Population III stars and quasars. Nevertheless, the uncertainty associated with such an extrapolation indicates a fundamental limitation of surveys of individual objects—sources too faint compared with the instrument sensitivity, such as dwarf galaxies, are entirely missed by galaxy surveys, even though a significant fraction, if not the majority, of the ionizing photons are contributed by them (Wise et al. 2014; Trebitsch et al. 2018; but see also Naidu et al. 2020).


Millimeter-to-submillimeter emission tells us much about these hidden galactic nuclei, for physical scales of several parsecs to several 100 pc in this work. First, these wavelengths contain various emission lines tracing the dominant (by mass) interstellar medium in these systems, that is, cold-to-warm molecular gas (∼10 to a few 100 K). The lines tell us the physical conditions and kinematics of the gas and thereby tell us about the fueling and feedback of the nuclear activities as well as the mass distribution in the nuclei. Second, the short millimeter and submillimeter continuum is usually dominated by thermal emission from dust. It is this dust continuum that carries the vast majority of the bolometric luminosity of these nuclei. Because of that, high-resolution information available at sub/millimeter wavelengths is very useful to characterize the nuclei, complementing spatially unresolved observations at the far-IR where the continuum spectrum peaks. Third, the dust in these nuclei is moderately opaque (the opacity is around the order of unity) at sub/millimeter wavelengths to produce bright emission, and yet it also makes the nuclei penetrable except at the very center in extreme cases. As a guide, τ
1 mm = 1 corresponds to

NH2∼1025.5

 cm−2 for an environment similar to the Galactic disk (Planck Collaboration et al. 2014; Galliano et al. 2018). The structure of the nuclei can thus be probed more easily in the sub/millimeter than at far-IR and shorter wavelengths. At the same time, the continuum emission carries information about the dust opacity and hence the obscuring column density. Fourth, rotational lines from vibrationally excited HCN at sub/millimeter wavelengths can be an indicator and probe of the NGC 4418/Arp 220-type nuclei with significant obscuration (Sakamoto et al. 2009; Aalto et al. 2015, 2019; Imanishi et al. 2019). These nuclei are opaque enough to trap infrared photons to increase their inner temperature (i.e., the greenhouse effect), and the enhanced infrared radiation vibrationally excites molecules such as HCN (González-Alfonso & Sakamoto 2019). Their rotational lines in the sub/millimeter have a chance to leak out of the dusty nuclei and indicate their hot interior since dust opacity is lower at longer wavelengths. And finally, the Atacama Large Millimeter/submillimeter Array (ALMA) has dramatically enhanced our capability for high-resolution and high-sensitivity observations at sub/millimeter wavelengths. A characteristic ALMA resolution of 0.″1 is on the order of 10 pc at nearby hidden galactic nuclei at tens of megaparsecs. While the resolution does not match the accretion disks around supermassive black holes (r ≪ 1 pc), it is only an order of magnitude larger than that of young massive star clusters (Longmore et al. 2014) and corresponds to the outer radii of molecular tori around AGN (Combes et al. 2019). Therefore, ALMA observations are good at probing the obscuring interstellar medium around AGN (if any), circumnuclear star formation, and their effects on the circumnuclear material.


We should examine whether our picture is consistent with previous studies at a higher radio luminosity regime,

logL1.4GHz>27

. It is natural to assume that the unification between radio galaxies (HzRGs) and RLQSOs works at this regime. Actually, observational evidence for the unification has been found in this luminosity regime (Wylezalek et al. 2013). Hyperluminous radio galaxies/RLQSOs with

logL1.4GHz>27

 are expected to reside in the galaxy denser regions according to the L
jet − Σ relation,
16

16
The L
jet − Σ relation would break down in the extremely high-density regions, as a very large velocity dispersion of galaxies in the massive structures reduces the merger frequency; thus, SMBH spin and mass growth would be slow. as shown by arrow

C

 in Figure 7. There is definitive evidence that hyperluminous radio galaxies exist in the rich galaxy overdense regions (Venemans et al. 2007; Falder et al. 2010; Wylezalek et al. 2013; Hatch et al. 2014; Husband et al. 2016). For instance, Venemans et al. (2007) examined the environments of eight radio galaxies with log L
1.4 GHz ≥ 27.3 at z ∼ 2−5 and found six of them in overdense regions. These radio galaxies with available optical spectra are classified as either HERGs, RLQSOs, or dust-obscured RLQSOs (Eales & Rawlings 1993; Venemans et al. 2007; Drouart et al. 2016; Nesvadba et al. 2017). Hatch et al. (2014) also found that radio-loud AGNs with log L
1.4 GHz > 27.2 are significantly more present in high-density regions than radio-quiet AGNs at z ∼ 1−3. Falder et al. (2010) found that there is a positive correlation between the radio luminosities and the ambient environments of HzRGs and RLQSOs with log L
1.4 GHz = 26.65–28.65 at z ∼ 1. A similar trend is also found for seven luminous radio galaxies at z ∼ 2.2 (Husband et al. 2016). The faintest radio galaxy with log L
1.4 GHz = 26.6 in Husband et al. (2016) resides in the lowest-density region, which is comparable to that of blank fields (Figure 3), and the others with log L
1.4 GHz > 27 reside in the denser regions. On the other hand, Zeballos et al. (2018) found that some of the HzRGs with log L
1.4 GHz > 27 do not reside in the overdense regions of SMGs. However, Zeballos et al. (2018) could not deny the possibility that the overdense regions around those radio galaxies are buried due to the sample variance. In future, we could assess hyperluminous radio galaxy environments at z ∼ 4; as the survey area of the HSC-SSP will reach ∼1000 deg2, about 10 hyperluminous radio galaxies are expected to be found, assuming the radio galaxy luminosity function of Dunlop & Peacock (1990).


The SFR of a gaseous clump with a density gradient is higher than if that same clump was made of uniform-density gas (Tan et al. 2006; Girichidis et al. 2011; Elmegreen 2011; Parmentier 2014, 2019). Centrally concentrated clumps actually process their gas into stars at a pace faster than expected based on their mean freefall time, because the density of their central regions is higher than the clump gas mean density. Parmentier (2019) refers to the ratio between the SFR of a clump with a density gradient, SFRclump, and the SFR of its top-hat equivalent, SFRTH, as the magnification factor ζ (see Equation (8) in Parmentier 2019):
1

The SFR of a clump can thus be written as (see Section 2 in Parmentier 2019, for a discussion)
2

In this equation, mgas is the gas mass hosted by the clump,1

1
The clump total mass mclump consists of the gas mass mgas and the mass mstars of the stars it has formed.
 and

 is the mean freefall time of the clump gas:
3

The latter is defined based on the clump gas mean density
4

with rclump the radius containing the clump gas mass mgas. ζ is the magnification factor, which quantifies by how much the density gradient of a clump enhances its SFR compared with what is expected based on its mean freefall time

. Equation (2) therefore allows one to disentangle the contribution of the density gradient, embodied by the ζ factor, from that of the star formation efficiency per freefall time itself. Parmentier (2019) coins

 the intrinsic star formation efficiency per freefall time since it is independent of the clump density gradient.2

2
This is as opposed to the (globally) measured star formation efficiency per freefall time, defined as

 (Parmentier 2019).
 For a top-hat profile, ζ = 1 and the SFR obeys
5

Note that the gas density of the top-hat equivalent is equal to the gas mean density

 of the centrally concentrated clump (same gas mass mgas enclosed within the same clump radius rclump).


Various models of the gas and dust distribution in the GC exist: a simple bar model (Morris & Serabyn 1996); variations of a spiral arm model in which the apparent ring is formed by the inner part of two spiral arms (Sofue 1995; Sawada et al. 2004; Rodríguez-Fernández & Combes 2008; Rodríguez-Fernández 2011; Ridley et al. 2017); a closed, twisted elliptical ring detected in dust emission (Molinari et al. 2011), and a sequence of open-ended gas streams (Kruijssen et al. 2015, hereafter K15). K15 highlight the impossibility of closed orbits in extended gravitational potentials and provide a better fit to single-dish ammonia emission in position–position–velocity (PPV) space, as was confirmed by Henshaw et al. (2016b) for three molecular species in single-dish observations. Thus, we focus on this model and call it the “stream model” in contrast to the “ring model” and the “spiral arm” model. According to the stream model, the stream of GC molecular clouds oscillates radially and vertically, and can be traced for ∼1.5 revolutions around the GC. The radial oscillation periodically brings dense molecular gas closer (r ∼ 60 pc at pericenter) to the gravitational center (traced by Sgr A*) and deeper into the potential, whereas the apocenter lies at r ∼ 120 pc. As the CMZ clouds slowly evolve toward low virial ratios as the turbulent energy dissipates (Krumholz & Kruijssen 2015; Walker et al. 2015; Henshaw et al. 2016a), it is statistically more likely that cloud collapse occurs at the pericenter where the compressive tidal forces are strongest along the orbit and thus a cloud receives the final nudge for the transition to self-gravitation. Subsequent SF stages will then occur downstream from the pericenter passages and could potentially be observed as an SF sequence if the orbit is sufficiently sampled with molecular clouds that start to collapse at a similar point of their orbits. This model of triggered star formation was first proposed by Longmore et al. (2013b) based on the observation of different evolutionary SF stages along the dust ridge. The two young stellar clusters in the GC, Arches and Quintuplet, may also support this model as their orbits and ages are consistent with formation at a common point after collapse of their respective parent clouds at a pericenter passage (Figure 1 of Stolte et al. 2014; Kruijssen et al. 2015). In addition to stars and star formation tracers, cloud properties are also expected to show evolutionary behavior along the gas streams; this has not been thoroughly tested yet. Weak hints toward rising gas temperatures in the dust ridge are suggested by Ginsburg et al. (2016), while a recent paper by Kauffmann et al. (2017b) based on N2H+ data from the Galactic Center Molecular Cloud Survey can neither confirm nor exclude the possibility of triggered evolution when examining mass-size relation and SF suppression. Both analyses were based on a low number of measurements (∼35 measurements in dust ridge clouds in Ginsburg et al. 2016 and six clouds in Kauffmann et al. 2017b) and lack the statistical power to detect potential evolution in the presence of scatter.


With only

 as a free parameter, different studies suggest that

 = 10%–20% at z > 6 is necessary for galaxies to fully ionize the universe (Bolton & Haehnelt 2007b; Finkelstein et al. 2012; Kuhlen & Faucher-Giguère 2012; Bouwens et al. 2015a, 2015c; Mitra et al. 2015; Robertson et al. 2015; Khaire et al. 2016; Price et al. 2016). Simulations do not agree on

 at high redshifts and find either very high (e.g., Sharma et al. 2016) or very low values (e.g., Gnedin et al. 2008; Ma et al. 2015). Furthermore, they predict a strong dependence on the mass of dark matter halos and star formation (e.g., Wise & Cen 2009; Razoumov & Sommer-Larsen 2010). Direct observational constraints on

 in the EoR are not possible because of the increasing opacity of the IGM to LyC photons at z > 4 (e.g., Madau 1995; Inoue et al. 2014). Except for one strong LyC emitter at z = 3.2 with

 > 50% (de Barros et al. 2016; Vanzella et al. 2016b), the handful of confirmed LyC emitters at z  3 all show consistently

 ≲ 8% (Steidel et al. 2001; Leitet et al. 2013; Borthakur et al. 2014; Cooke et al. 2014; Siana et al. 2015; Izotov et al. 2016a, 2016b; Leitherer et al. 2016; Smith et al. 2016). The numerous non-detections listed in the literature show upper limits of

 ∼ 2%–5% over large ranges of redshift (Vanzella et al. 2010; Sandberg et al. 2015; Grazian et al. 2016; Guaita et al. 2016; Rutkowski et al. 2016; Vasei et al. 2016). If galaxies are responsible for ionizing the universe at z > 6, then clearly their population-averaged LyC escape fraction needs to increase substantially with redshift by at least a factor of two (see also Inoue et al. 2006). What methods can we use to access

 observationally in the EoR? Radiative transfer models suggest a correlation between the ratio

/

 and

 in density-bound H ii regions (e.g., Nakajima & Ouchi 2014), and a handful of recent observational studies verify this positive correlation (de Barros et al. 2016; Izotov et al. 2016a, 2016b; Vanzella et al. 2016a, 2016b). The increased

/Hβ ratios found in z > 5 galaxies (e.g., Stanway et al. 2014; Roberts-Borsani et al. 2015; Faisst et al. 2016a) hint toward an increasing

/

 ratio for the global population of galaxies at high redshifts and therefore could be the smoking gun for a strong evolution in

(z). Currently, the

 line cannot be measured spectroscopically at z > 4, and the use of broad-band photometry to determine

 line strengths is degenerate with the 4000 Å Balmer break, which is a strong function of age and other galaxy parameters. However, local analogs of high-redshift galaxies can be used to probe the physical properties of these galaxies.


To detect supernova neutrinos with the KamLAND data, a cluster of DC events is required: two DC events within a 10 s window. The very low DC rate enables us to use the minimum cluster condition (two DC events). An accidental DC event cluster is a background for supernova neutrinos. Based on the DC event studies, we evaluate the number of accidental cluster events (

≡nclusteraccidental

) via Monte-Carlo (MC) simulation. Accidental cluster rates and accumulation of

nclusteraccidental

 are shown in Figure 1. Before distillation campaigns, the DC event is mainly caused by reactor -

ν¯e

, and 13C(α, n)16O interaction has a secondary contribution (Abe et al. 2008). After distillation campaigns, the DC event by 13C(α, n)16O interaction decreases but reactor -

ν¯e

 is still a dominant component (Gando et al. 2011). Japanese reactors were shut down after the Great East Japan Earthquake in 2011. In the reactor-off phase (Gando et al. 2013), the rate of reactor -

ν¯e

 events is decreased. These trends of DC event rate are also shown in Figure 1. In an energy region above 10 MeV, fast neutrons and atmospheric neutrinos have dominant contribution on the number of DC events (Abe et al. 2022b). Typically, the DC candidate rate is ∼1 day−1 in the reactor-on phase and 0.1 day−1 in the reactor-off phase. Usually, we call a KamLAND data set a “run,” which consists of typically 24 hr data. The number of expected DC events is estimated in run by run and the number of accidental clusters is calculated from that. Taking into account that time differences between each run are more than 10 s, there should be no accidental clusters that occur across two runs. As a result, the accumulated number of accidental clusters is

nclusteraccidental=0.32−0.04+0.02

 clusters, and this rate is 0.023 cluster yr−1 on average. The error of

nclusteraccidental

 includes systematic uncertainties of the number of expected DC events by reactor -

ν¯e

, atmospheric neutrino, and fast neutron.


One factor that we have not taken into account so far is that the strength of an AGN may affect how strong the corresponding emission from the NLR is. Thus, it may be the case that lower-luminosity or lower-accretion-rate AGNs are more easily overwhelmed by star formation. Therefore, we next explore whether correctly and incorrectly classified X-ray AGNs differ in their intrinsic AGN properties. One of the indicators of the accretion strength of an AGN in the optical regime is the luminosity of the forbidden [O iii] line,

, which scales with the bolometric luminosity of the AGN (Mulchaey et al. 1994; Heckman et al. 2005; LaMassa et al. 2010; Azadi et al. 2017; Glikman et al. 2018). A related quantity,

 divided by the fourth power of the stellar velocity dispersion, σ4, can provide an estimate of the Eddington ratio of the AGN (Kewley et al. 2006). Trump et al. (2015) suggested that higher sSFR galaxies must have more efficient AGNs in order to be classified as BPT–AGNs because of the relative contributions from star formation. We show

 and

 versus stellar mass in Figures 8 and 9, respectively, with the BPT star-forming galaxies from GSWLC-M1 composing the backgrounds in Figures 8(a) and 9(a) and the BPT–AGNs from GSWLC-M1 making up the backgrounds in Figures 8(b) and 9(b). In Figures 8 and 9, there appear to be two distinct sequences for the two BPT types when mass is included, where in Figure 8(a), the background BPT star-forming galaxies form one sequence where

 appears to correlate with stellar mass, including galaxies with masses up to

, while the star-forming galaxies in Figure 9(a) do not show a strong dependence of proxy Eddington ratio with stellar mass, which is expected because

 from star-forming galaxies primarily comes from star formation. The BPT–AGNs form sequences in Figures 8(b) and 9(b) that have no apparent dependence on mass with masses ranging roughly from

. The existence of these two sequences is apparently the case because of the different sources of [O iii] emission that are dominant in BPT star-forming galaxies versus BPT–AGNs. The majority of the BPT–H ii are more consistent with the background star-forming galaxies in Figures 8(a) and 9(a), whereas the BPT–AGNs all appear consistent with the background BPT–AGNs shown in Figures 8(b) and 9(b), which is to be expected if the NLR dominates [O iii] emission. Six BPT–H ii are more consistent with the background BPT–AGNs in Figures 8(b) and 9(b), and if the NLR is indeed the source of their [O iii] emission, their Eddington ratios are much lower than the average BPT–AGNs, suggesting that they have relatively inefficient accretion. We will return to these outliers in Section 3.2.3.


The disk-wind outflows that accompany highly super-Eddington accretion carry a total mass-loss rate

Ṁw

, which nearly equals the entire mass-transfer rate, i.e.,

Ṁw∼Ṁ

 (e.g., Blandford & Begelman 1999; Hashizume et al. 2015), with only a small fraction making its way down to the BH/NS surface. Depending on the radial scale of their launching point in the disk or binary, the outflows can possess a range of speeds, from values similar to the binary orbital velocity, v
orb ≲ 100 km s−1, to the transrelativistic speeds v
j ≳ 0.3c that characterize jet-like outflows from the innermost radii of the disk (and similar to those observed in SS 433 and ULX; e.g., Jeffrey et al. 2016 and references therein). In ADIOS models for the radial disk structure (Blandford & Begelman 1999; Margalit & Metzger 2016), the mass accretion rate decreases as a power law with radius

Ṁ∝rp

 for

r∈[rin,rout≲Rtr]

, where r
out ≫ r
in. Assuming the outflows local to each annulus in the disk reach an asymptotic velocity equal to the local disk escape velocity, the kinetic energy-averaged wind velocity is given by (e.g., Metzger 2012)
6

vw≈p1−pGM•rinrinroutp≈0.05cM•10M⊙0.3rin6rg−0.2routR⊙−0.3,

where in the second equality we have normalized r
in to gravitational radius r
g = GM
•/c
2 and take p = 0.6 (as supported by hydrodynamical simulations of radiatively inefficient accretion flows; e.g., Yuan & Narayan 2014; Hu et al. 2022). In what follows, we take v
w ∼ 0.03c as a fiducial value, consistent with that expected for a main-sequence or moderately evolved donor star feeding a relatively compact accretion flow, r
out ∼ R
⊙. However, lower value v
w ≲ 0.01 c may be appropriate for a giant donor star (r
out ≳ 102
R
⊙) or for larger values of p. The kinetic luminosity of the wind is then
7

Lw≈12Ṁwvw2≈1042ergs−1Ṁw105ṀEdd×M•10M⊙vw,92ergs−1,

where v
w,9 = v
w/(109 cm s−1) and hereafter we adopt the short-hand notation Y
x ≡ Y/10x for quantities given in cgs units. In analytic estimates hereafter, we shall typically fix the value of M
• = 10M
⊙ and use L
w and

Ṁw

 interchangeably.


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

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

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


J0815+4729 is a main-sequence star (T

eff

=
6215
±
82

 K,

log
g

 = 4.7±0.5) with a metallicity of [Fe/H] ≤ −5.8 dex. Finding unevolved stars at this extremely low metallicity is very important since their stellar surface composition is not expected to be significantly modified by any internal mixing processes as in giant stars (Spite et al. 2005). J0815+4729 is similar to HE 1327–2326 in regard to its carbon enhancement, effective temperature, and metallicity. HE 1327–2326 is considered a turn-off/subgiant star, while J0815+4729 appears to be a dwarf. The ISIS spectrum of HE 1327–2326 indicates a metallicity of [Fe/H] ∼ −4.9 since the stellar Ca line is blended in that spectrum with the ISM features (Aguado et al. 2017b). However, the authors proposed a simple analysis taking into account the ISM absorption based on the UVES spectrum of HE 1327–2326. For J0815+4729, we require a high-resolution spectrum to clearly isolate the stellar Ca feature from possible additional ISM lines, and thus together with the detection of Fe lines, to establish the metallicity of this star. There are two other confirmed dwarf stars in this metallicity regime: one without any detectable carbon, J1029+1729 (Caffau et al. 2011), and another carbon-enhanced unevolved star, J1035+0641 (Bonifacio et al. 2015). The majority of extremely metal-poor stars shows overabundances of carbon, [C/Fe] > 0.7, and it appears that carbon-enhanced metal-poor (CEMP) stars split into two groups, with dramatically different carbon abundances (see, e.g., Beers & Christlieb 2005; Allende Prieto et al. 2015; Bonifacio et al. 2015 and references therein). The two carbon bands (high and low) studied have different origins. On the one hand, CEMP stars in the high-carbon band (A(C) ∼ 8.2) are probably produced by mass transfer from a binary companion, most likely an AGB star (Starkenburg et al. 2014). On the other hand, objects lying in the low-carbon band (A(C) ∼ 6.8) are thought to show the original carbon abundance inherited by the star from the ISM (Stancliffe 2009; Bonifacio et al. 2015; Abate et al. 2016). J0815+4729 has an abundance ratio of

[

C

/

Fe

]

≥
+
5.0

 dex  corresponding to A(C) ∼ 7.7 dex (adopting [Fe/H] ≤ −5.8). In Figure 4 (bottom panel), we show the carbon abundance ratio [C/Fe] for all stars at [Fe/H]  −4.5. All stars in this metallicity regime are considered to belong to the low-carbon band (Bonifacio et al. 2015), except for J0815+4729, which appears to be in between the low- and high-carbon bands. Both metallicity and carbon abundance are considered upper and lower limits, respectively. High-resolution spectra would be very useful to measure other elemental abundances and investigate the properties of the first supernovae. In particular, the barium abundance, or that of any other s-element, is not measurable from ISIS or OSIRIS spectra, and this is required to determine whether J0815+4729 is a CEMP-s, CEMP-r, or i-process star (Hampel et al. 2016). If we establish the abundance pattern, we will learn about the progenitor properties. Finally, the radial velocity accuracy from medium-resolution data is not enough to discard variations among different exposures, which would be indicative of binarity.


The distributions of separations at apoapsis and periapsis from our LSMC analysis shown in the left panel of Fig. 11 indicate a range at 68%∼18–57 au. If the companion is coplanar with the outer disk, a ∼0.25 M⊙ companion with a 50 au apoapsis and e ∼ 0.5 − 0.7 would in principle create a region of orbital instability extending out to ∼100 au (Holman & Wiegert 1999), which is the innermost possible location for the outer disk (e.g., Fukagawa et al. 2006; Casassus et al. 2012; Rameau et al. 2012; Rodigas et al. 2014; Avenhaus et al. 2017). Nevertheless, the inclination and longitude of node of HD 142527B disagree with those of the outer circumstellar disk (i = 28°, Ω = 160°, Verhoeff et al. 2011; Perez et al. 2015), as has been reported by Lacour et al. (2016). This result would at first sight rule out that HD 142527B is responsible for the outer disk truncation. However, recent hydrodynamical simulations have shown that for an eccentric companion with an almost polar inclination to the outer disk that approaches its periapsis passage, the interactions of companion and disk can reproduce several of the main observed disk features, such as its large cavity, and with the correct position angles, its spiral features and shadows (Price et al. 2018). This orbital configuration is broadly consistent with the results from our orbital analysis. On the other hand, the orbital plane of the companion is close to the plane of the inner circumstellar disk, as previously suggested by Lacour et al. (2016). The inner disk has a position angle of 110 ± 10° from CO(6-5) kinematics measured with ALMA (Casassus et al. 2015). Its mean radius is estimated to be about 10 au from near-infrared interferometric observations (Anthonioz et al., in prep.). From MIR imaging and SED modeling, Verhoeff et al. (2011) derived a maximum radial extension for the inner disk up to 30 au. However, Avenhaus et al. (2014) imaged the inner circumstellar environment down to ∼0.1″ (15 au) in polarized scattered light with NaCo, but did not detect traces of an inner disk. More recently, Avenhaus et al. (2017) imaged the disk in visible polarized light with SPHERE down to 25 mas (∼4 au) and found evidence for dust scattering close to the star, although it remains unclear if this scattering is related to the inner disk because of geometrical discrepancies with predictions from a modeling of the shadows projected onto the outer disk (Marino et al. 2015). Using our orbital analysis of the companion, we derived the distribution of its separation at periapsis (Fig. 11, right panel) and find a 68% confidence interval of ∼10 − 12 au. This results indicates that the shape of the inner disk is strongly affected by HD 142527B.


We first assess the mass–size relation regulated by collision-induced turbulence, i.e. the mass–size relation of clumps in the molecular ring. In our clump–clump collision scenario, the turbulent energy injected by the collisions cascades down to small scales and counterbalances self-gravity to produce a rough virial equilibrium (i.e. the clumps are able to maintain virialization; see Section 5.1). These virialized clumps should always have their energy dissipation rates (per unit mass) $\dot{\epsilon }_{\rm diss,clump}=\frac{1}{4}\frac{\sigma _{\rm obs,los}^3}{R_{\rm clump}}$ (equation 14) match their virial energy dissipation rates (per unit mass)
(33)$$\begin{eqnarray}
\dot{\epsilon }_{\rm diss,vir} =\frac{1}{4}\left(\alpha _{\rm vir,crit}\, GM_{\rm clump}/5\right)^{3/2}R_{\rm clump}^{-5/2}
\end{eqnarray}$$(Li 2017b), i.e. $\dot{\epsilon }_{\rm diss,clump}\approx \dot{\epsilon }_{\rm diss,vir}$, where as before αvir, crit ≈ 2 is the boundary between gravitationally bound and unbound objects (Kauffmann et al. 2013, 2017). The virial energy dissipation rate (per unit mass) $\dot{\epsilon }_{\rm diss,vir}$ is the energy dissipation rate (per unit mass) a molecular gas structure would have if it were virialized. We therefore expect
(34)$$\begin{eqnarray}
\dot{\epsilon }_{\rm diss,vir}\approx \dot{\epsilon }_{\rm diss,clump}\approx \dot{\epsilon }_{\rm inject,coll}
\end{eqnarray}$$for the clumps in the molecular ring of NGC 404, where we have used $\dot{\epsilon }_{\rm diss,clump}\approx \dot{\epsilon }_{\rm inject,coll}$, i.e. the energy dissipation rates (per unit mass) of clumps are approximately equal to the energy dissipation rates (per unit mass) from clump–clump collisions in the molecular ring (see Section 4.4). We indeed find very good agreements between the estimated $\dot{\epsilon }_{\rm diss,vir}$, the measured $\dot{\epsilon }_{\rm diss,clump}$, and our predicted $\dot{\epsilon }_{\rm inject,coll}$ in the molecular ring (see panel c of Fig. 9), providing more evidence that the turbulence induced by clump–clump collisions can support and maintain molecular ring clumps in virial equilibrium.


As we see, in the magnetospheres of Crab-like pulsars the Cherenkov drift resonance might lead to the hard X-rays. In the previous section, we have seen that this emission inevitably leads to the non-vanishing pitch angles (see equation 14), generating the synchrotron emission. In Fig. 2 we show the behaviour of energy of synchrotron photons, $\epsilon _{_{{\rm GeV}}}$ versus γb in the interval [0.5; 1] × 107 for different values of Lorentz factors of the plasma component: γp = 1 (solid line), γp = 10 (dashed line), γp = 50 (dash–dotted line). We have taken into account the dipolar character of the magnetic field, $B\approx 3.2\times 10^{19}\times \sqrt{P\dot{P}}\times R^3/R_{lc}^3$ G (Goldreich & Julian 1969), where R = 106 cm is the neutron star's radius. The rest of the parameters is: $P = P_{_{{\rm Cr}}}$, $\dot{P}=\dot{P}_{_{{\rm Cr}}}$, $n_b = n_{_{GJ}}$, where $n_{_{GJ}} = B/Pec$ is the Goldreich–Julian number density (Goldreich & Julian 1969). As it is evident from the plots by increasing γp, the resulting emission energy increases as well, which directly follows from the analytical behaviour, $\epsilon _{_{{\rm GeV}}}\propto \gamma _p^{1/8}$ (this can be seen by combining equations 8, 12–14). We see that the QLD by means of the feedback of ChDI guarantees the synchrotron emission over 100 GeV. We can roughly estimate the possible VHE luminosity by multiplying the number of particles involved in the process with the single emission power, $P_{{\rm syn}}\approx 2e^4\gamma _b^2B^2\langle \psi \rangle ^2/3m^2c^3$. It is worth noting that the thickness of the layer, d, where the electrons accelerate to the highest energies, is of the order of Rlc/2γb. Then, by taking into account the corresponding number of particles, $4\pi R_{lc}^2n_{_{GJ}}d$, one can show that in the emission energy band 150 GeV the highest energy electrons lead to the bulk luminosity of the order of 1033 erg s−1 which is in a good agreement with observations (Lessard et al. 2000; Albert et al. 2008).


The Barnard 5 (B5) dark cloud is located at the North-East of the Perseus complex (235 pc; Hirota et al. 2008). It contains four known protostars of which the most prominent is the Class I protostar IRS1. SCUBA continuum emission maps at 850 μm carried out with the JCMT only revealed dust emission towards known protostars and at about 2–4 arcmin north from IRS 1 (Hatchell et al. 2005) whilst molecular maps of CO, NH3, and other species show several chemically differentiated clumps (S. B. Charnley, in prep.). Methanol emission in B5 displays a particularly interesting distribution since it shows a bright so-called methanol hotspot at about 250 arcsec north-west from IRS 1, a region showing no infrared sources and no detected sub-mm continuum emission (see Fig. 1 in Hatchell et al. 2005; Wirstrom et al. 2014). The subsequent detection of abundant water, with absolute abundances of about 10-8, with the Herschel Space Observatory by Wirstrom et al. (2014) suggests that efficient non-thermal processes triggering the evaporation of icy methanol and water are at work. The methanol hotspot therefore represents an ideal target to detect cold COMs in dark clouds since they are supposed to be formed from methanol, either at the surface of interstellar grains, or directly in the gas phase after the evaporation of methanol. The Perseus molecular cloud was recently mapped with Herschel as part as the Gould Belt Survey key program (André et al. 2010) using the photometers PACS and SPIRE in five bands between 70 μm and 500 μm.Figure 1 presents the Barnard 5 molecular cloud as seen by Herschel/SPIRE at 250 μm. The Herschel data has been retrieved from the Herschel Science Archive. The data were calibrated and processed with the Herschel pipeline and are considered as a level-3 data product. Dust emission is compared with the integrated intensity map of the A+-CH3OH 30 − 20 transition as observed with the IRAM 30 m telescope (this work).The methanol hotspot is located between the two dense cores East 189 and East 286 (Sadavoy, priv. comm.) revealed by Herschel for the first time, and the methanol emission peaks at the edge of core East 189. East 189 and East 286 have the following properties derived through a fitting of their observed spectral energy distribution: M = 0.5M⊙, Td = 12 K, R = 3.6 × 10-2 pc, nH = 3 × 104 cm-3, and M = 0.7M⊙, Td = 9.9 K, R = 2.7 × 10-2 pc, nH = 1.2 × 105 cm-3 (Sadavoy  2013).


Next, we fit the emission lines using the code described in detail in Dong et al. (2005). The optical spectra show strong, narrow emission lines such as [O ii] λ3727, [O i]

,

, [N ii]

, and [S ii]

 [O iii]

 is instead weak. As we verified above, broad

 is evidently presented (see also Greene & Ho 2007; Dong et al. 2012). The SDSS data are used to fit the blue part such as in the

+[O iii] region (as not covered by the MMT spectrum), and the MMT data for the red part such as [O i] lines, the

+[N ii] region, and [S ii] lines. We fit the MMT spectrum first. Every narrow or broad component of the emission lines is modeled with Gaussians, starting with one Gaussian and adding in more if the fit can be improved significantly according to the F-test. The [S ii]

 doublet lines are assumed to have the same profile and fixed in separation by their laboratory wavelength; the same is applied to [N ii]

 doublet lines, and to [O i]

 and [O i]

 emission lines. The flux ratio of the [N ii] doublet

 is fixed to the theoretical value of 2.96 (e.g., Acker et al. 1989; Storey & Zeippen 2000). In the best-fit model, it turns out that one Gaussian is used for the broad component of

, while two Gaussians for the narrow component of

, each line of the [N ii], and [S ii] doublet and the two [O i] lines, respectively. The reduced

 is 1.21 for the

+[N ii] region. Note that the [N ii]

 and [S ii] doublet lines show asymmetric line profiles clearly in the MMT spectrum, which are actually common in high-resolution spectra (Xiao et al. 2011); thus these narrow lines, and narrow

 also, need two Gaussians to model. Then we fit the

+[O iii] region based on the SDSS spectrum. As the spectral signal-to-noise (S/N) of this region is not high and the

 emission line is much weaker than

, we assume the broad and narrow components of

 have the same profiles as the respective components of

. The [O iii]

 doublet lines are assumed to have the same profile, and the flux ratio of

 is fixed to the theoretical value of 2.98 (e.g., Storey & Zeippen 2000; Dimitrijević et al. 2007); the best-fit model turns out to adopt two Gaussians for each [O iii] doublet line. The reduced

 is 0.95 for the

+[O iii] region. [O ii] λ3727 is fit independently, and one Gaussian is sufficient to model. We also fit the

 lines of the N and S branches of the extended emission. One Gaussian is statistically sufficient for either branch, with reduced

 of 0.95 (N) and 0.97 (S), respectively. The best-fit line parameters, centroid, FWHM (corrected for instrumental broadening), and flux of every branch agree well with those directly integrated/measured from the spectra.


The de-projected distance that corresponds to the core-position changes of Markarian 421 is approximately 3.5 ∼ 8.7 pc (equivalent to (1.0 − 2.6) × 105 Schwarzschild radii (Rs)) for a jet-viewing angle of 2°–5° (Lico et al. 2012). One of the leading models for explaining the blazar phenomenon is the so-called internal-shock model, in which discrete ejecta with higher speeds catch up with the preceding slower ejecta, and the collision leads to a shock wave in the colliding ejecta (Spada et al. 2001; Guetta et al. 2004). Based on this model, core wandering can be naturally explained because the model predicts some scattering of the shock locations caused by the randomness of the ejecta speed. Therefore, we assume that the distances of the shock locations from the black hole immediately after the flare,

, are proportional to the product of the square of the bulk Lorentz factor (

) of the ejecta and the separation length (Δ) of the colliding ejecta. Assuming that a typical separation length is a scale of about 10 times the innermost stable circular orbit for non-rotating black holes (

), in light of numerical simulations of relativistic outflows around black holes (McKinney et al. 2013), very fast ejecta with a Lorentz factor of approximately

 are required to explain the observed magnitude of the core wandering. The

 is comparable to previously reported maximum values (Γ of 40 ∼ 50; Lister et al. 2009, 2013) based on statistical studies by a long-term monitor using VLBI. Moreover, the radio core returned to the reference stationary position after 2012 March 12 (the 10th epoch). This can be explained if the emission from the reference position is identical to the radio core that is in a quiescent state. The radio-core emission in a quiescent state is expected to be persistent. As one of the possibilities for reproducing the observed core wandering, this persistent radio core was obscured by the flare-associated radio core, which therefore must be optically thick against SSA and short lived (a lifetime of approximately 2 weeks), for several epochs. Such a flare-associated radio core must be located at least

 downstream from the persistent radio core. In addition, Koyama et al. (2015) recently conducted multi-epoch astrometric observations of Markarian 501, which is also one of the most nearby TeV blazars by using VERA. However, they detected no significant positional changes of the radio core during its quiescent state. This fact, therefore, seems to support the radio core wandering seen after the large X-ray flare.


In addition to the processes that release SiO into the gas phase, it is also important to
        discuss the properties of the responsible shock. Shocks are divided into three types: jump
        shocks (J-type, Hollenbach & McKee 1979),
        continuous shocks (C-type, Draine 1980), and a
        mixture of both, which is a C-type shock with an introduced discontinuity (CJ-type, Chieze et al. 1998). The type of shock depends mainly on
        the presence of a magnetic field, since a magnetic field is necessary for the shock
        condition to become continuous, the ionization of the preshock gas, since only charged
        particles couple to the magnetic field, and on the velocity of the shock, since J-type
        shocks can have higher velocities than C-type shocks (Flower
          & Pineau des Forêts 2003; Tielens 2005;
          Anderl et al. 2013). A main difference between the
        types is that J shocks lead to partial or complete dissociation of molecules, such as
        molecular hydrogen. Because we observed a lot of H2 emission (see Fig. 3), pure J shocks are fairly improbable in this case, since they would dissociate
        the molecular hydrogen. Studies by Gusdorf et al.
          (2008b) have shown that even CJ-type shocks at a velocity of 25 km s-1 are energetic enough to
        dissociate the ambient hydrogen. However, in a more recent paper, Gusdorf et al. (2015) have found that CJ-type shocks reproduce
          H2 observations
        even better. They found that C-type shocks are not able to reproduce their H2 excitation temperatures. In
        conclusion, the strong observed H2 emission suggests that we are not observing J-type shocks;
        however, we cannot differentiate further between C-type or CJ-type shocks with the present
        data. Another important parameter of the shocks is the velocity. However, it is very
        difficult to estimate the shock velocity in the current case. The SiO signal in the line
        wings is present until 15 km s-1 apart from the rest velocity. This is most likely not the
        maximum shock velocity, as the strong SiO signal at ambient velocity indicates jets or
        outflows with a large velocity component in the plane of the sky. In conclusion, this means
        that SiO emission in this case can be the effect of shocks with comparably high velocities
          (vshock>
          25 km s-1), because the expected C-type or CJ-type shocks can reach
        very high velocities, depending on the preshock density (Le
          Bourlot et al. 2002). These shocks would most likely be a result of the ongoing
        star formation. However, low-velocity shocks are also able to release the SiO if it is
        present in the core mantles.