adsabs/FOCAL huggingface dataset:
In order to examine how our qcr(M1) would affect the brightness distribution of the violent merger scenario, we adopt the same assumptions as in Ruiter et al. (2013) except for qcr(M1). For the primary at the time of merging, we use the same WD mass distribution as Ruiter et al. (2013; see also Ruiter et al. 2011), although it is highly uncertain whether the WD can increase its mass by avoiding the formation of a common envelope during the very rapid accretion from the He star companion. We also assume the same 






m


WD


–


M


bol




 relation of SNe Ia as Ruiter et al. (2013; see Figure 4 in Ruiter et al. 2013; Sim et al. 2010) and a flat mass ratio distribution of DD systems for simplicity. Using either our critical mass ratio or theirs, we calculated the brightness distribution and compared them with each other (Figure 11). We find that there is no significant difference between them qualitatively. This result implies that the qcr of the violent merger-induced explosion is not so crucial for the brightness distribution of SNe Ia, as mentioned in Ruiter et al. (2013). Our results are closest to the η = 1.5 case among Ruiter et al.'s three cases. In the cases of our qcr and Ruiter et al.'s η = 1.5, the brightness distribution concentrates around −19.0 mag. In Figure 11, we add the observational volume-limited brightness distributions of SNe Ia. One in panel (a) is derived by the Lick Observatory Supernova Search (LOSS; Li et al. 2011), and the other in panel (b) is obtained by ROTSE-IIIb (see Table 1 in Quimby et al. 2012). The fraction of faint events in our models is lower than the observation of LOSS. This discrepancy might decrease if we consider the viewing angle effects (see also the discussion in Ruiter et al. 2013), which might be increasingly important especially for a large value of qcr. On the other hand, the results of ROTSE-IIIb are consistent with ours, except most luminous (≲−19.5 mag) events. It should be noted, however, that there are large uncertainties for the observational brightness distribution (e.g., Quimby et al. 2012) and our models are too simple to be compared with the observational results. More detailed studies are required to reach a definitive conclusion.
Citation: Ruiter et al. (2013)
Citation function: Differences; Differences
Citation: Ruiter et al. (2013
Citation function: Similarities; Compare/Contrast
Citation: Ruiter et al. 2013
Citation function: Background
Citation: Ruiter et al. (2013
Citation function: Similarities
Citation: Ruiter et al. (2013)
Citation function: Compare/Contrast; Compare/Contrast; Similarities
Citation: Ruiter et al. 2013
Citation function: Compare/Contrast; Compare/Contrast
Since its discovery in 1983, Phaethon has remained a well-studied yet poorly understood object, known to exhibit both cometary and asteroidal characteristics, and widely presumed to be the parent to the Earth-crossing Geminid meteor shower (Green & Kowal 1983; Gustafson 1989; Williams & Wu 1993). Significant efforts have been made to study the physical properties of the asteroid such as size (6 km in diameter, Taylor et al. 2019), spectral shape (B type, e.g., Licandro et al. 2007), and albedo (0.11, Green et al. 1985), as well as the Geminids (e.g., Hughes & McBride 1989; Jenniskens 1994; Arlt & Rendtel 2006; Blaauw 2017), their relationship to one another (e.g., Gustafson 1989; de León et al. 2010), and the proposed relationship to asteroids 2005 UD and 1999 YC (e.g., Ohtsuka et al. 2006, 2008; Kareta et al. 2021). Several Earth-based studies of Phaethon have sought to investigate the perihelion activity of the asteroid, attempting—but failing—to detect small fragments (Jewitt et al. 2018; Ye et al. 2018) or nearby dust grains (Jewitt et al. 2019) released during its close (0.14 au) passage by the Sun. Despite this, spacecraft observations of Phaethon’s activity at perihelion obtained by the Sun-Earth Connection Coronal and Heliospheric Investigation (Howard et al. 2008) on NASA’s Solar Terrestrial Relations Observatory (Kaiser et al. 2008) during the asteroid’s perihelion passages in 2009, 2012, 2016, and 2022, have shown that the asteroid is clearly active at perihelion, displaying a short tail and reported to be releasing mass on the order ∼2.5 × 108
a
1 kg (where a
1 is the grain radius in millimeters, and noting that the size of dust released at perihelion remains unknown; Jewitt & Li 2010; Jewitt et al. 2013; Hui & Li 2017). This is insufficient by orders of magnitude to support the best estimates for the mass of the Geminids. Shortly before submission of this manuscript, Phaethon was also observed by the Solar and Heliospheric Observatory Large Angle Spectrometric Coronagraph (Brueckner et al. 1995) C2 coronagraph during its 2022 May 15 perihelion passage, constituting the first known detection of Phaethon by this instrument.
Citation: Ye et al. 2018
Citation function: Background; Background
Citation: Green & Kowal 1983
Citation function: Motivation
Citation: Ohtsuka et al. 2006
Citation function: Background; Background
We consider a radio galaxy of SMBH mass M = 109
M
9
M
⊙ with a mass accretion rate of 



Ṁ=ṁLEdd/c2≃1.4×1022M9ṁ−4gcm−2

, where c is the speed of light and L
Edd is the Eddington luminosity. The gravitational radius of the BH is r

g
 = GM/c
2 ≃ 1.5 × 1014
M
9 cm. We consider that the accretion flow is in the MAD state, and then the magnetic field strength around the SMBH is estimated to be 



Bmad=ṀcΦmad2/(4π2rg2)≃1.1×103M9−1/2ṁ−41/2Φmad,1.7G

 (e.g., Yuan & Narayan 2014), where Φmad ≈ 50Φmad,1.7 is the saturated magnetic flux (Tchekhovskoy et al. 2011; Narayan et al. 2012; McKinney et al. 2012; White et al. 2019). The high-resolution GRMHD simulation with a BH spin parameter a = 0.9375 suggests that magnetic reconnection occurs at a distance of r
rec ∼ 2r

g
 (Ripperda et al. 2022). The value of r
rec could depend on a or other parameters, but we fix r
rec = 2r

g
 throughout this paper for simplicity. We estimate the reconnecting magnetic field strength to be (see Appendix A)
1



Brec≈2Bmadrrecrg−2≃3.9×102M9−1/2ṁ−41/2Φrec,1.2G,

where 



Φrec=2Φmad(rrec/rg)−2

 is the effective magnetic flux at the reconnection region. The magnetosphere will be formed around the SMBH. The minimum number density of the magnetosphere that can maintain the electric current for the BZ process is (Goldreich & Julian 1969; Levinson & Cerutti 2018)
2



nGJ=BrecΩF2πec≈Brec8πerg≃2.2×10−4M9−3/2ṁ−41/2Φrec,1.2cm−3,

where Ω
F
 ≈ ac/(4r

g
) is the field line angular velocity (Tchekhovskoy et al. 2010; Nathanail & Contopoulos 2014; Ogihara et al. 2021; Camilloni et al. 2022) and we assume the BH spin parameter as a ∼ 1. For the magnetosphere, which consists of e
+
e
− pair plasma with the density n
GJ, the magnetization parameter is
3



σB,GJ=Brec24πnGJmec2≈6.8×1013M91/2ṁ−41/2Φrec,1.2.

This value should be regarded as an upper limit, because the number density of the magnetosphere can be higher than n
GJ. Various mechanisms of particle injection into the BH magnetosphere have been proposed (see Appendix B), which can lead to multiplicity of κ
± ≡ n/n
GJ ∼ 1 − 103. This results in the magnetization parameter of σ

B
 ≳ 1010.
Citation: McKinney et al. 2012
Citation function: Uses; Uses
Hosler et al. (1957) measured pull-off forces of spherical water-ice particles with radius r0 = 7.366 mm in either air or nitrogen vapour. Prior to their measurements, the two spheres suspended by cotton threads were brought into contact at the position of just touching, resembling the experimental setup of Nakaya & Matsumoto (1954). Therefore, we assume zero indentation indicating that equation (21) applies to their pull-off force measurements, although Hosler et al. (1957) did not report whether or not the particles rotate prior to separation. Since their experiments were carried out in a wide range of temperatures from T = 193 to 273 K and the saturated vapour pressure exponentially decreases with the inverse of the temperature, we may need to consider a variation of relative humidity with the temperature. The saturated vapour pressure psat of water molecules is given by (Kimura, Ishimoto & Mukai 1997)
(22)$$\begin{eqnarray*}
p_\mathrm{sat}(T) &amp;=&amp; p_\infty \exp \left({-\frac{\Delta H_\mathrm{s}}{k_\mathrm{B} T}}\right) ,
\end{eqnarray*}$$where $p_\infty = \displaystyle \lim _{T \rightarrow \infty } p_\mathrm{sat}(T)$ and ΔHs denotes the enthalpy of sublimation. According to Prialnik (1992), we assume the following form:
(23)$$\begin{eqnarray*}
p_\mathrm{sat}(T) &amp;=&amp; 3.56 \times {10}^{12}~\mathrm{Pa} \, \exp \left[{-\left({\frac{T}{6141.667~\mathrm{K}}}\right)^{-1}}\right] .
\end{eqnarray*}$$Fig. 10 depicts the experimental data of Hosler et al. (1957) with open circles for their measurements in air and open squares for those in nitrogen vapour. Also plotted are the temperature variations of equation (21) with the vapour pressure pv = 63.2 in air and 468 Pa in nitrogen vapour. Although the assumption of a constant pv value may be too crude to reproduce the experimental data, equation (21) approximates the experimental data of Hosler et al. (1957) in air and nitrogen vapour within a factor of 2.
Citation: Kimura, Ishimoto & Mukai 1997
Citation function: Uses; Uses
NR simulations of BH–NS mergers are computationally intensive and typically conclude a few ms after the merger. To follow the post-merger dynamics, the unbound ejecta must be transferred to a hydrodynamics simulation that can accommodate the rapid expansion of the distance scale. Few studies have explored the long-term evolution of the unbound component while incorporating the effect of r-process radioactive heating, which can affect the evolution; as an estimate, the total radioactive energy deposited over the first ∼10−4 d is Erad ∼ 1049 erg (Metzger et al. 2010), which is nontrivial compared to the total kinetic energy 






E


kin


∼


M


d




v


d


2



/

2
∼
few
×


10


50




 erg. Fernández et al. (2015) studied the long-term behavior using Newtonian hydrodynamics with a prescription for r-process heating; they found that heating enlarges the ejecta and smooths small-scale irregularities. This corroborated earlier work in the NS–NS merger context by Rosswog et al. (2014), who used a Newtonian smoothed particle hydrodynamics (SPH) code with heating and a nuclear network and additionally found that the ejecta reaches homology at the ≲1% level by ∼102 s and the abundance of nucleosynthesis products remains roughly unaffected by heating. These two studies used Newtonian merger simulations to initialize the unbound ejecta. Roberts et al. (2017) simulated the hydrodynamic evolution of the BH–NS merger unbound component to generate thermodynamic trajectories as inputs for a nuclear reaction network; since their main aim was to study r-process abundances, they did not study the back-reaction of the nuclear heating on the ejecta structure. Kawaguchi et al. (2021) recently examined the NS–NS post-merger evolution using 2D axisymmetric hydrodynamics with radioactive heating. They found that heating only modestly affects the ejecta structure and hydrodynamics minimally impacts the nucleosynthesis, results that are dependent on the details of the NR handoff. The overall ejecta remains mildly prolate with a lanthanide-present torus and some matter falls back to the BH-disk system.
Citation: Metzger et al. 2010
Citation function: Motivation; Motivation
From our MUSE 





 and quasar spectra, we can estimate how many of our nebulae would have been missed by NB filter observations because of filter losses. For this thought experiment, we will assume that quasars would have been selected for NB observations if their estimated systemic redshift from corrected broad-line emission (C iv in our case, but typically Mg ii at 





) would have placed the expected 





 emission at the peak of the NB filter transmission. In reality, the selection is made on a range of systemic redshifts (typically within 500 km s−1 from the filter center), but we will assume that this range is absorbed by the intrinsic scatter in the C iv-corrected redshift estimation (





 km s−1 at 1σ, Shen et al. 2016). Assuming a typical NB filter width of 3000 km s−1 (FWHM), we can notice from Figure 2 that two nebulae would have been totally missed by NB observations (#2, #6) while for the other five (#1, #10, #11, #12, #16) the displacement between the 





 emission and the filter transmission peak would have resulted in a substantial flux loss that would likely have compromised the detectability of the nebulae, especially in the faintest but most extended regions. However, at least nine nebulae (#3, #4, #5, #7, #8, #9, #13, #14, #15, #17), which is at least 50% of the sample, have 





 emission so close to the estimated systemic redshift that they would not have been missed by NB observations, including also the systemic redshift errors from C iv or Mg ii. This factor is much larger than the 10% detection rate estimated from NB imaging. Therefore, we conclude that filter losses cannot completely explain the discrepancy between MUSE detection rates and those of NB surveys, though they can certainly reduce the NB detection rate significantly. We note that radio-loud quasars typically have much broader 





 emission and therefore filter losses would be even less important for these systems. This may partially explain the higher detection rate of radio-loud nebulae versus radio-quiet ones.
Citation: Shen et al. 2016
Citation function: Uses
The fireball model remains the most popular scenario for the gamma-ray burst (GRB) phenomenon (Cavallo & Rees 1978; Goodman 1986; Paczynski 1986; Shemi & Piran 1990; Rees & Mészáros 1992, 1994; Mészáros & Rees 1993). In this model, the GRB central engine is a stellar-mass black hole or a rapidly spinning and highly magnetized neutron star formed by either the collapse of a supermassive star (collapsar; Woosley 1993; MacFadyen & Woosley 1999; Woosley & Heger 2006) or the merger of two compact objects (Paczynski 1986; Fryer et al. 1999; Rosswog 2003). In both cases, the original explosion creates a bipolar collimated jet composed mainly of photons, electrons, positrons, and a small fraction of baryons. The relativistic explosion ejecta within the jet are not homogeneous—they form multiple high density layers, which propagate at various velocities. When the fastest layers catch up with the slowest, the charged particles contained in the layers are accelerated through mildly relativistic collisionless shocks (internal shocks; Rees & Mészáros 1994; Kobayashi et al. 1997; Daigne & Mochkovitch 1998). The particles subsequently cool via emission processes such as synchrotron, Synchrotron Self Compton (SSC), and Inverse Compton (IC). The internal shock phase is usually associated with the so-called GRB prompt emission,17

17
See Pe’er (2015) for a recent review of GRB prompt emission.
 mainly observed in the keV−MeV energy range (see, e.g., the spectral catalogs by Gruber et al. 2014; von Kienlin et al. 2014) and usually lasting from a few ms up to several tens to hundreds of seconds. As the ejecta interact with the interstellar medium they slow down via relativistic collisionless shocks (external shocks; Rees & Mészáros 1992; Mészáros & Rees 1993), accelerating charged particles, which then emit non-thermal synchrotron photons. This external shock phase is usually associated with the so-called GRB afterglow emission observed at radio wavelengths up to X-rays and in some cases even up to the GeV regime hours after the prompt phase, and days and even years for the lowest frequencies. The detailed origin of the gamma-ray emission, however, is not fully understood and many theoretical difficulties remain, such as the composition of the jet, the energy dissipation mechanisms, as well as the radiation mechanisms (e.g., Zhang 2011).
Citation: Daigne & Mochkovitch 1998
Citation function: Background
Citation: Cavallo & Rees 1978
Citation function: Background
Citation: MacFadyen & Woosley 1999
Citation function: Background
Citation: Pe’er (2015)
Citation function: Background; Background
Citation: Zhang 2011
Citation function: Motivation
Once relatively high-resolution cross sections have been computed, it is reasonably simple to produce k-tables using what is known as the correlated k-distribution method; this method is well described in the literature (see, e.g. Lacis & Oinas 1991; Pierrehumbert 2010), and is extensively used for radiative transfer calculations in the context of planetary and substellar atmospheres (see, e.g. Irwin et al. 2008; Showman et al. 2009; Freedman et al. 2008, 2014; Lee et al. 2019; Mollière et al. 2015; Amundsen et al. 2014; Sharp & Burrows 2007; Malik et al. 2017; Drummond et al. 2016; Phillips et al. 2020). K-tables are generally considered faster (and more accurate for the same 



R

=


λ

Δ
λ




$ R~=~\frac{\lambda}{\Delta \lambda} $


) than cross sections, but they also come with their own assumptions and therefore limitations (see, e.g. Rocchetto 2017). However, these can be assumed to be negligible when compared to other unknowns. The general principle is to order spectral lines within a given spectral bin, producing a smooth cumulative distribution function to represent opacity, which can be more efficiently sampled. The number of points used for sampling within a given spectral bin is determined by a set of Gaussian quadrature points, which are assigned corresponding weights. These are often chosen so as to sample the extremes of the bin more finely so as not to miss the weakest and strongest lines (i.e. the distance between sampling points within a bin is not constant). One of the methods used in this work, for example, is based on the use of Gauss Legendre polynomials (see Sect. 4 for details of the opacities produced for individual retrieval codes). K-tables are produced using a method of opacity sampling which enables low-resolution computations while still taking strong opacity fluctuations at high resolution into account; see, for example, Min (2017). The assumption made for the k-distribution method that the k-coefficients at each Guassian quadrature point are correlated, breaks down for inhomogeneous atmospheres (Lee et al. 2019)
Citation: Rocchetto 2017
Citation function: Background; Background
Our starting point of modelling the different two-point functions in the 3×2pt data vector is the three-dimensional (3D) non-linear matter power spectrum P(k, z) at a given wavenumber k and redshift z. We obtain it by using either of the Boltzmann solvers CLASS11 or CAMB12 to calculate the linear power spectrum and the HALOFIT fitting formula (Smith et al. 2003) in its updated version (Takahashi et al. 2012) to turn this into the late-time non-linear power spectrum. From this 3D power spectrum, the angular power spectra required for our three two-point functions [cosmic shear (κκ), galaxy–galaxy lensing (δgκ), and galaxy–galaxy clustering (δgδg)] in the Limber approximation are given by (e.g. Limber 1953; Krause et al. 2017):
(4)$$\begin{eqnarray*}
C^{ij}_{\kappa \kappa }(\ell) = \int \mathrm{ d}\chi \frac{q^i_\kappa (\chi) q^j_\kappa (\chi)}{\chi ^2} P\left(\frac{\ell +\frac{1}{2}}{\chi }, z(\chi)\right),
\end{eqnarray*}$$(5)$$\begin{eqnarray*}
C^{ij}_{\delta _\mathrm{ g} \kappa }(\ell) = \int \mathrm{ d}\chi \frac{q^i_\delta \left(\frac{\ell +\frac{1}{2}}{\chi },\chi \right) q^j_\kappa (\chi)}{\chi ^2} P\left(\frac{\ell +\frac{1}{2}}{\chi }, z(\chi)\right),
\end{eqnarray*}$$(6)$$\begin{eqnarray*}
C^{ij}_{\delta _\mathrm{ g} \delta _\mathrm{ g}}(\ell) = \int \mathrm{ d}\chi \frac{q^i_\delta \left(\frac{\ell +\frac{1}{2}}{\chi },\chi \right) q^j_\delta \left(\frac{\ell +\frac{1}{2}}{\chi },\chi \right)}{\chi ^2} P\left(\frac{\ell +\frac{1}{2}}{\chi }, z(\chi)\right)\ ,
\end{eqnarray*}$$where χ is the comoving radial distance, i and j denote different combinations of pairs of redshift bins, and the lensing efficiency $q^i_\kappa$ and the radial weight function for clustering $q^i_\delta$ are, respectively, given by
(7)$$\begin{eqnarray*}
q^i_\kappa (\chi) &amp;=&amp; \frac{3H_0^2 \Omega _\mathrm{ m}\chi }{2a(\chi)} \int _{\chi }^{\chi _\mathrm{ h}} \mathrm{ d}\chi ^\prime \left(\frac{\chi ^\prime - \chi }{\chi }\right) n^i_\kappa (z(\chi ^\prime)) \frac{\mathrm{ d} z}{\mathrm{ d}\chi ^\prime } , \nonumber \\
q^i_\delta (k,\chi) &amp;=&amp; b^i(k, z(\chi))\ n^i_\delta (z(\chi)) \frac{\mathrm{ d} z}{\mathrm{ d}\chi }\ .
\end{eqnarray*}$$Here, H0 is the Hubble parameter today, Ωm is the ratio of today’s matter density to today’s critical density of the Universe, a(χ) is the Universe’s scale factor at comoving distance χ, and bi(k, z) is a scale- and redshift-dependent galaxy bias. Furthermore, $n^i_{\kappa , \mathrm{ g}}(z)$ denote the redshift distributions of the different DES-Y3 redshift bins of source and lens galaxies, respectively, normalized such that
(8)$$\begin{eqnarray*}
\int \mathrm{ d}z \,\, n^i_{\kappa , \mathrm{ g}}(z) = 1\ .
\end{eqnarray*}$$Note that on large angular scales the DES-Y3 analysis does not make use of the Limber approximation for galaxy clustering but instead employs the method derived in Fang, Eifler & Krause (2020a).
Citation: Krause et al. 2017
Citation function: Uses; Uses
For the five He ii sightlines recorded at sufficiently high spectral resolution (





), coeval spectra of the optically thin H i Lyα forest provide estimates of the number density ratio 





. In a fully reionized IGM 





 probes the spectral shape of the UV background and its source population (e.g., Miralda-Escudé & Ostriker 1990; Madau & Meiksin 1994; Fardal et al. 1998; Haardt & Madau 2012), so observational constraints are of great astrophysical interest. The patches of strong quasi-continuous He ii absorption at 





 typically require 





 (Reimers et al. 1997, 2005; Heap et al. 2000; Smette et al. 2002; Shull et al. 2010; Syphers & Shull 2014), whereas the 





 He ii Lyα forest revealed order-of-magnitude fluctuations around 





 on scales down to ∼1 Mpc (Kriss et al. 2001; Shull et al. 2004; Zheng et al. 2004b; Fechner et al. 2006; Fechner & Reimers 2007). However, these studies were affected by various systematics, most importantly by uncertainty in the zero level of the FUSE data (Fechner & Reimers 2007) and H i continuum uncertainty (e.g., Heap et al. 2000). We recently showed that by accounting for H i continuum systematics with realistic mock spectra from numerical simulations, the higher-quality COS spectra from the two sightlines sampling 





 are consistent with 





 without the need for fluctuations exceeding a factor of two (McQuinn & Worseck 2014). This implies that in the post-reionization IGM, radiative transfer effects (Maselli & Ferrara 2005; Tittley & Meiksin 2007; Meiksin & Tittley 2012) or Poisson fluctuations in the number density of quasars (Bolton et al. 2006) generate only modest UV background fluctuations. However, all existing inferences on the epoch of He ii reionization have been tempered by the very small sample of sightlines available to study He ii Lyα absorption. Indeed, expanding the data set has been the most pressing need to advance our understanding of He ii reionization.
Citation: Fechner & Reimers 2007
Citation function: Uses
Citation: Fechner & Reimers 2007
Citation function: Uses