adsabs/FOCAL huggingface dataset:
Recent MIR studies have provided us with a much more realistic view of the central part of the AGNs. Spitzer studies of nearby Compton-thick AGNs have shown that even Compton-thick AGNs, especially low-luminosity ones, often show only modest to moderate silicate absorption at 





 μm (e.g., Hao et al. 2007; Goulding et al. 2012). A classical smooth torus model, such as that of Pier & Krolik (1992), predicts deeper absorption in proportion to the X-ray absorption column density. On the other hand, if the torus is made of a collection of clouds, each cloud is heated to ∼300 K to emit MIR emission while absorbing the background light when the foreground cloud is cooler than the one behind. The radiation transfer effect among the clouds significantly reduces the net silicate absorption even when the torus is seen edge-on (Nenkova et al. 2002, 2008a, 2008b; Hönig et al. 2006; Hönig & Kishimoto 2010; Stalevski et al. 2012, 2016). Meanwhile, recent MIR interferometric studies of nearby AGNs have started to directly reveal the dust distribution in the vicinity of the AGNs at parsec scales. In some best-studied AGNs, extended optically thin dust emission elongated toward the system’s polar direction (e.g., direction of the extended narrow-line region or outflow) is typically found in addition to the compact disk-like component (e.g., Raban et al. 2009; Hönig et al. 2012, 2013; Tristram et al. 2012, 2014; López-Gonzaga et al. 2016; see also Asmus et al. 2016 for the single-dish study; see Netzer 2015 for a review). Such extended polar emission is clearly inconsistent with the classical idea of the dusty torus in the unification theory, and its nature is under debate. Some proposed ideas are that it originates from the inner funnel of an extended dust distribution above and below the torus and/or the dusty outflow within the ionizing cone that is radiatively driven from the inner wall of the compact dusty torus (e.g., Hönig et al. 2012, 2013; Keating et al. 2012; Roth et al. 2012; Tristram et al. 2014).
Citation: Stalevski et al. 2012
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Citation: Hao et al. 2007
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Citation: Pier & Krolik (1992)
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Citation: Hönig et al. 2012
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Citation: Hönig et al. 2012
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The EPS model developed by Bond et al. (1991) is based on the excursion set formalism. For each collapsed region one constructs random ‘trajectories’ of the linear density contrast δ(M) as a function of the variance σ2(M). Defining

(3)

\begin{equation}
\omega \equiv \delta _{\rm c}(z)\quad {\rm {and}}\quad S\equiv \sigma ^{2}(M),
\end{equation}

we use ω and S to label redshift and mass, respectively. If the initial density field is a Gaussian random field smoothed under a sharp k-space filter, increasing S (corresponding to a decreased in the filter mass M) results in δ(M) starting to wander away from zero, executing a random walk. The fraction of matter in collapsed objects in the mass interval M, M + dM at redshift z is associated with the fraction of trajectories that have their first upcrossing through the barrier ω in the interval S, S + dS, which is given by (Bond et al. 1991; Bower 1991; Lacey & Cole 1993)

(4)

\begin{equation}
f(S,\omega ){\rm d}S=\frac{1}{\sqrt{2\pi }}\frac{\omega }{S^{3/2}}\rm {exp}\left[-\frac{\omega ^{2}}{2S}\right]dS,
\end{equation}

where S is defined as

(5)

\begin{equation}
S(M) = \frac{1}{2\pi ^{2}}\int _{0}^{\infty }P(k)\hat{W}^{2}(k;R)k^{2}{\rm d}k.
\end{equation}

Here P(k) is the linear power spectrum and $\hat{W}(k;R)$ is the Fourier transform of a top hat window function. The probability function in equation (4) yields the PS mass function and gives the probability for a change ΔS in a time-step Δω, since for random walks the upcrossing probabilities are a Markov process (i.e. are independent of the path taken). The analytic function given by equation (4) provides the basis for the construction of merger trees. Neistein et al. (2006) derived a differential equation for the average halo mass history over an ensemble of merger trees from the EPS formalism. Defining MEPS(z) to be the mass of the most massive halo (main progenitor), along the main branch of the merger tree, as a function of redshift, they obtained the differential equation (see derivation in Appendix A)

(6)

\begin{eqnarray}
\frac{{\rm d}M_{\rm {EPS}}}{{\rm d}z}&amp;=&amp; \sqrt{\frac{2}{\pi }}\frac{M_{\rm {EPS}}}{\sqrt{S_{q}-S}}\frac{1.686}{D(z)^{2}}\frac{{\rm d}D(z)}{{\rm d}z},
\end{eqnarray}

where Sq = S(MEPS(z)/q) and S = S(MEPS(z)). The value of q needs to be obtained empirically so that MEPS reproduces halo mass histories from cosmological simulations. Neistein et al. (2006) showed that the uncertainty of q is an intrinsic property of EPS theory, where different algorithms for constructing merger trees may correspond to different values of q.
Citation: Bond et al. (1991)
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Citation: Bond et al. 1991
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Finally, putting everything together, and using dΩu = dϕvdθusin θu, the cross-correlation $\rho _{\ell \ell ^{\prime }ij}^{uv}(\beta , b, \bar{n}_{g})$ can be written as
(28)$$\begin{eqnarray*}
\rho _{\ell \ell ^{\prime }ij}^{uv}(\beta , b, \bar{n}_{g}) = \delta _{ij}^{K} \frac{\kappa _{\ell \ell ^{\prime }}^{uv}(k_{i},\beta ,b,\bar{n}_{g})}{\kappa _{\ell \ell ^{\prime }}(k_{i},\beta ,b,\bar{n}_{g})},
\end{eqnarray*}$$with, at leading order in $(\bar{n}_{g}P_m^\mathrm{lin}(k))^{-1}$ (e.g. Meiksin & White 1999; Howlett & Percival 2017),
(29)$$\begin{eqnarray*}
\kappa _{\ell \ell ^{\prime }}^{uv}(k,\beta ,b,\bar{n}_{g}) &amp;=&amp; \int _{0}^{2\pi } \mathrm{ d}\phi _{v} \int _{0}^{\pi } \mathrm{ d}\theta _{u}\sin {\theta _{u}} \nonumber \\
&amp;&amp;\times \, \bigg[ b^{2}\left(1 + \beta \cos ^{2}{\theta _{u}}\right) \left(1 + \beta \cos ^{2}{\theta _{v}}\right) P_m^\mathrm{lin}(k) \nonumber \\
&amp;&amp; +\, \frac{1}{\bar{n}_{g}} e^{-k^{2}\left(\cos ^{2}{\theta _{u}} + \cos ^{2}{\theta _{v}} - 2 \cos {\theta _{u}}\cos {\theta _{v}} \cos \theta _{uv} \right) f^{2} \sigma _{d}^{2}/2} \bigg]^{2} \nonumber \\
&amp;&amp;\times \, \mathcal {L}_{\ell }(\cos {\theta _{u}})\mathcal {L}_{\ell ^{\prime }}(\cos \theta _{v}),
\end{eqnarray*}$$
 (30)$$\begin{eqnarray*}
&amp;&amp;\kappa _{\ell \ell ^{\prime }}(k,\beta ,b,\bar{n}_{g}) \nonumber \\
&amp;&amp;\quad = 2\pi \int _{0}^{\pi } \mathrm{ d}\theta _{u}\sin {\theta _{u}} \left[ b^{2} \left(1 + \beta \cos ^{2}{\theta _{u}}\right)^{2} P_m^\mathrm{lin}(k) + \frac{1}{\bar{n}_{g}} \right]^{2} \nonumber \\
&amp;&amp;\qquad\times \, \mathcal {L}_{\ell }(\cos {\theta _{u}})\mathcal {L}_{\ell ^{\prime }}(\cos {\theta _{u}}).
\end{eqnarray*}$$In the limit that there is no shot noise, $1/\bar{n}_{g} \rightarrow 0$, and the $P_m^\mathrm{lin}(k)$ in equation (29) cancels with the $P_m^\mathrm{lin}(k)$ in equation (30), removing any k-dependence on the cross-correlation. If the LOS u and v are orthogonal, then we arrive at the same expression as equations (18) and (19).
Citation: Meiksin & White 1999
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In addition, star formation in the halo is modeled by assuming a conversion efficiency from gas into stars ϵ
⋆. In our fiducial case, we adopt ϵ
⋆ = 0.05 (e.g., Visbal et al. 2015), which is motivated by abundance matching and the observed UV luminosity function of galaxies at z ≃ 6 (Bouwens et al. 2015). Note that the efficiency is calculated as the average value over time and scales in galaxies. Alternatively, we suppose that a star formation episode with a high value of ϵ
⋆ lasts within a few megayears in the nuclear region before SN explosions of massive stars begin to occur and regulate the star formation efficiency (SFE) in the bulge. According to numerical simulations that study star cluster formation from a giant molecular cloud with a size of 10–100 pc, the SFE becomes as high as ϵ
⋆ ≳ 0.2–0.3 when the initial gas surface density is higher than ∼103
M
⊙ pc−2 (Fukushima et al. 2020; Fukushima & Yajima 2021). Referring to those observational and theoretical studies, we assume f

n
 = f
0(1 − ϵ
⋆), where f
0 = 1 and ϵ
⋆ = 0.05 (fiducial case) and f
0 = 4 and ϵ
⋆ = 0.5 (high SFE case). Following the definition of the SFE, ϵ
⋆, the SFR is approximated as
32



SFR=4πϵ⋆1−ϵ⋆ρ(r)r2Vc,≃0.11ϵ⋆f0Tvir,43/2M⊙yr−1,

where V
c is the halo circular velocity. This SFR is used to estimate the emissivity of stellar irradiation (LW and X-rays) and to calculate the bulge growth in mass. Note that in most cases, the gas mass within r ≃ r
c for the given initial condition is lower than the total mass of newly forming stars.
10


10
Although we do not consider the self-gravity of gas in our simulations, it would dominate the bulge gravity at the intermediate scale of ∼O(10 pc) only in the early stage of the bulge formation where M
⋆ ≲ 106
M
⊙. In this case, however, radiative feedback associated with BH accretion blows the gas outward, and then the gas self-gravity eventually becomes less important (see Section 3.2.2). Therefore, our star formation model implicitly assumes that the bulge growth is not led by in situ star formation but by efficient migration of stars formed at larger radii with morphological evolution owing to stellar relaxation (see also Appendix A).
Citation: Fukushima & Yajima 2021
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The bolometric luminosity of 3C 84 is about 0.4% of the Eddington luminosity. Thus, the accretion flow of 3C 84 is likely to be a radiatively inefficient accretion flow (RIAF: Narayan & Yi 1995) rather than a standard disk (Shakura & Sunyaev 1973). However, we note that 3C 84 has a cold (






T


e


∼


10


4




 K) disk-like accretion flow, as identified by FFA of the emission from the counter jet in the parsec scale (Walker et al. 2000) and inhomogeneous gas distribution around the black hole (Fujita et al. 2016). A number of theoretical studies predicted that the accretion flow components of hot geometrically thick (RIAF-like) and cold geometrically thin can coexist in either horizontal or vertical stratification (e.g., Miller & Stone 2000; Merloni & Fabian 2002; Liu et al. 2007; Ho 2008; Liu & Taam 2013). The measured Faraday rotation can be caused by such an RIAF-like component. We thus estimate the accretion rate of the RIAF-like component using the measured RM. For a simplicity, we assume that the RIAF-like component is a quasi-spherical Bondi accretion flow with a power-law density profile. We can calculate the accretion rate, following the formulation as follows (Quataert & Gruzinov 2000; Marrone et al. 2006; Kuo et al. 2014).









M


˙




=


1.3
×


10


−
10





[

1
−



(



r


out



/



r


in



)



−
(
3
β
−
1
)

/

2



]



−
2

/

3








×









M


BH




8.0
×


10


8




M


⊙









4

/

3









2


3
β
−
1







−
2

/

3




r


in


7

/

6









RM


rad



m


−
2









2

/

3


.





For an inner effective radius 






r


in




 of 1 pc (




1.3
×


10


4




R


s




), where the hotspot is located, the observed RM implies an accretion rate of 




∼
4.3
×


10


−
2




M


⊙




 yr−1 and 




∼
8.6
×


10


−
2




M


⊙




 yr−1 for 




β
=
0.5


 and 




β
=
1.5


, which are corresponding to convection-dominated accretion flow (CDAF: Narayan et al. 2000; Quataert & Gruzinov 2000) and advection-dominated accretion flow (ADAF: Ichimaru 1977; Narayan & Yi 1995), respectively. Here we assumed the outer effective radius 






r


out




 of 






10


5




R


s




 (∼8 pc), which is approximately the same with the Bondi radius of 8.6 pc (Fujita et al. 2016). The derived accretion rate is roughly consistent with that estimated from the bolometric luminosity with a black hole mass of 




8
×


10


8




M


⊙




 and a radiative efficiency of 10% (






M


˙


∼


L


bol



/

(
0.1


c


2


)
≃
7.1

×


10


−
2




M


⊙




 yr−1).
Citation: Quataert & Gruzinov 2000
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Citation: Quataert & Gruzinov 2000
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We tested the optimization of the physical model for each of these candidates. For each candidate, we constructed a grid of parameters (λL, βL, ϕ0, ψ0, Ia, Ib). The grid for the orientation of the angular momentum vector was constructed by distributing ten different positions evenly on the celestial sphere. Standard Euler angles at t0 were arranged at 60° intervals. In addition, the moments of inertia were sequenced at 0.01 intervals from 0.01 to 0.99 in the case of SAM, and intervals of 0.1 from 1.1 to 10 in the case of LAM. Optimization was performed using the grid as the initial parameter set. The photometric model of the surface properties of airless body was considered as the Hapke model (Hapke 1993). The Hapke model parameters were optimized using initial values of a typical S-type asteroid: ϖ = 0.23, g = −0.27, h = 0.08, B0 = 1.6, and 

$\bar{\theta} = 20^{\circ}$



θ
¯

=

20
°



 (Li et al. 2015), where ϖ denotes the single scattering albedo, g denotes the particle phase function parameter, h and B0 respectively denote the width and amplitude of the opposition surge, and 

$\bar{\theta}$


θ
¯


 denotes the macroscopic roughness angle. Additionally, because the light curves used in this study covered only phases angles from 14.0° to 28.5°, the parameters for opposition surge (h and B0) were fixed during the optimization process. The 

$\bar{\theta}$


θ
¯


 was also fixed because it cannot be reliably obtained from our data. Thus, only two parameters, ϖ and g, were optimized. We found that the physical model is not sensitive to the Hapke model parameters. Solutions corresponding to the 2016 and 2017 data converged at one or two global minima for each frequency combination. However, we found that the values between the moment of inertia obtained from the shape model (assuming constant density) and the dynamical moments of inertia were different in all solutions except for SAM1. Because we preferred the physically self-consistent model, we excluded the combination of LAM and SAM2. In addition, solutions corresponding to the 2016 and 2017 data were similar to SAM1. Therefore, we accepted values for Pψ and Pϕ based on SAM1.
Citation: Li et al. 2015
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We conclude by displaying in Figure 9 the NS moment of inertia calculated from the EoSs without Δ's and with Δ's (with couplings xσΔ = xωΔ = 1.15 and xρΔ = 0). The results have been obtained by solving Hartle’s slow-rotation differential equation for the moment of inertia in general relativity coupled to the TOV equations (Hartle 1967). Astronomical observations of binary pulsars may provide information on the moment of inertia of NSs, ultimately offering possible limits on the underlying EoS (Lattimer & Schutz 2005). The only double-pulsar system known to date is PSR J0737-3039. The mass of its primary component PSR J0737-3039A, or pulsar A, is of 1.338 M⊙. It is expected that a precise measurement regarding the moment of inertia of this slowly rotating pulsar will be obtained in the near future from radio observations of PSR J0737-3039 (Burgay et al. 2003; Lyne et al. 2004). In a recent work, Landry & Kumar (2018) (also see Kumar & Landry 2019) use approximately universal relations among NS observables (Yagi & Yunes 2013a, 2013b), known as the binary-Love and I-Love relations (recall that the tidal deformability is related to the Love number), to determine a range of 





 g cm2 for I of pulsar A from the 90% credible limits on the tidal deformability of a 1.4 M⊙ NS reported by LIGO-Virgo from the GW170817 event (Abbott et al. 2019). Landry & Kumar (2018) also facilitate a wider range I ≤ 1.67 × 1045 g cm2 for I of pulsar A from the less restrictive upper limit on the tidal deformability obtained by the LIGO-Virgo collaboration in their initial data analysis of GW170817 in Abbott et al. (2017). We have plotted in Figure 9 these two constraints reported in Landry & Kumar (2018) for I of pulsar A (we show both of the constraints because there may be a certain dependence on the analysis and on the assumed boundaries for Λ of a 1.4 M⊙ star). We can see in Figure 9 that the moment of inertia is an observable highly sensitive to the existence of Δ isobars in the composition of the core of the star. The presence of these particles, in particular for smaller values of the coupling of the Δ to the ρ-meson, improves the agreement with the constraints on the moment of inertia of pulsar A, whose measurement is anticipated within the next few years.
Citation: Yagi & Yunes; 2013b
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Instabilities, driven by departures from local thermodynamic equilibrium (LTE), are frequently credited with affecting the behavior of rapidly evolving plasma systems, e.g., the expanding solar wind (Matthaeus et al. 2012). To quantify these departures, the underlying charged particle velocity distribution functions (VDFs) are typically modeled as bi-Maxwellians, having anisotropic temperatures T
⊥,j
 and T
∥,j
 with respect to the local magnetic field 
B
; relative field-aligned drifts between each pair of constituent VDF components i and j being Δv

i,j
=(
V


i
 − 
V


j
) · 
B
/∣
B
∣; and temperature disequilibrium between species T

i
 ≠ T

j
 (Marsch et al. 1982). These anisotropies, drifts, and disequilibrium serve as distinct sources of free energy capable of driving the growth of a number of distinct unstable solutions (see, e.g., Section 5 of Verscharen et al. 2019). The presence of multiple free-energy sources makes it difficult to determine which subset of sources drives a given instability; parametric models accounting for a single source of free energy—e.g., the temperature anisotropy of a single population (Gary et al. 1997; Yoon 2017)—do not account for the diminishment or enhancement of predicted linear growth rates associated with the introduction of other departures from LTE, e.g., relative drifts of proton beams (Daughton & Gary 1998; Woodham et al. 2019; Liu et al. 2021), helium (Podesta & Gary 2011; Bourouaine et al. 2013; Verscharen et al. 2013), or their combined effects (Chen et al. 2016). To account for these effects, previous studies implemented Nyquist’s instability criterion (Nyquist 1932; Klein et al. 2017) on limited sets of in situ measurements from the Wind (Klein et al. 2018), Parker Solar Probe (Verniero et al. 2020; Klein et al. 2021), and Helios (Klein et al. 2019) missions, finding that a majority of intervals were unstable, that the kinds of waves driven unstable were very sensitive to the model used to describe the VDF, and that inclusion of multiple ion populations could both enhance or diminish the predicted growth rates.
Citation: Marsch et al. 1982
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None of the galaxies in this paper would be classified as an AGN on the basis of WISE mid-IR colors; they do not meet the 





 (Vega) threshold from Stern et al. (2012) or the reliable AGN criteria from Assef et al. (2013). There are two galaxies with weak X-ray detections (J1506+5402 and J1613+2834, four X-ray counts each) from Sell et al. (2014) that indicate 





 erg s−1 and four galaxies with X-ray upper limits (J0826+4305, J0944+0930, J1558+3957, J2140+1209) that imply 





 erg s−1. All of these galaxies are consistent with the relationship between X-ray luminosity and mid-IR luminosity for starburst galaxies (Asmus et al. 2011; Mineo et al. 2014; Sell et al. 2014). One of the galaxies with a weak X-ray detection (J1506+5402) also has a clear detection of [Ne v] 





 and an emission-line ratio 





, which is the highest ratio in the sample and consistent with a composite Baldwin, Phillips, and Terlevich (BPT) classification (Baldwin et al. 1981; Kewley et al. 2001; Kauffmann et al. 2003; Sell et al. 2014). These [Ne v] and [O iii] emission lines could be produced either by an extreme (





 Myr) starburst or an AGN that contributes 





% of the mid-IR continuum (Diamond-Stanic et al. 2012; Geach et al. 2013; Sell et al. 2014). The galaxy with the slowest outflow velocity in the sample (J2140+1209) has a weak broad Mg ii line, which is a clear indication of a type 1 AGN component, and spectral modeling suggests a 





% AGN continuum contribution at 





 (Sell et al. 2014); the other 11/12 galaxies show no evidence for any AGN continuum contributions at near-UV or optical wavelengths on the basis of high signal-to-noise spectroscopy (as described above and shown in Figure 1, which we describe below). In summary, there is some evidence for AGN activity in several of these 12 galaxies, but in all cases, the upper limits on the AGN emission indicate that it contributes a small fraction of the galaxy’s bolometric luminosity.
Citation: Sell et al. 2014
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Citation: Sell et al. (2014)
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Citation: Sell et al. 2014
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Equation (25) shows that entropy advection can easily result in tens of per cent increase in the outer boundary temperature, and possibly substantially more depending on the depth to which the flow penetrates and whether the Bondi radius is larger than the Hill radius. How will this impact the cooling luminosity? We can estimate the effect on the luminosity if we assume that the radiative zone is isothermal (which applies only to low-metallicity envelopes), so that the temperature at the radiative–convective boundary (RCB) is the same as the outer boundary temperature, TRCB = Tadv. The luminosity, set at the RCB, is
(26)$$\begin{eqnarray*}
L\approx {64\pi GM_\mathrm{ p}\sigma T_{\rm RCB}^4 \nabla _{\rm ad}\over 3\kappa P_{\rm RCB}}\propto {T_{\rm RCB}^4\over \kappa P_{\rm RCB}}
\end{eqnarray*}$$(Arras & Bildsten 2006; Piso & Youdin 2014) (again we will neglect the self-gravity of the envelope). For a power-law dependence of opacity κ ∝ ρaTb ∝ PaTb − a, we find that for a fixed internal entropy so that $P_{\rm RCB}\propto T_{\rm RCB}^{\gamma /(\gamma -1)}$, the luminosity varies with RCB temperature as
(27)$$\begin{eqnarray*}
{\mathrm{ d}\ln L\over \mathrm{ d}\ln T_{\rm RCB}} = 4 - b+a - (1+a){\gamma \over \gamma -1}.
\end{eqnarray*}$$Taking the values a = 2/3 and b = 3 for molecular opacity from Bell & Lin (1994), we find that a change in RCB temperature ΔTRCB leads to a change in luminosity
(28)$$\begin{eqnarray*}
{\Delta L\over L} &amp;\approx &amp; -4 {\Delta T_\mathrm{RCB}\over T_\mathrm{RCB}}\approx -4{T_\mathrm{adv}-T_\mathrm{ d}\over T_\mathrm{ d}}\nonumber \\
&amp;=&amp; -{8\over 5} \left({R_\mathrm{ B}\over R_{\rm out}}\right) \left[{R_{\rm out}\over R_{\rm adv}}-1\right].
\end{eqnarray*}$$A hotter outer boundary leads to a lower luminosity. For Radv/Rout = 0.3 (0.1) and assuming Rout = RB, the predicted decrease in luminosity is a factor of ≈4 (≈14). For dust opacity, Bell & Lin (1994) give a = 0 and b = 1/2 (metal grains) or b = 2 (ice grains). In this case, dln L/dln TRCB = (1/2) − b, so the change in luminosity will be smaller than for molecular opacity.
Citation: Piso & Youdin 2014
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