adsabs/FOCAL huggingface dataset:
H α velocity dispersion. for Hα, the mass of ionized hydrogen is not a good estimate of the Hα intensity, since the emission decreases with increasing temperature. Here, we compute the Hα flux from two contributions, namely the recombination of ionized hydrogen and collisional excitation from the ground state to level n = 3. We have to neglect the contribution from H ii regions around young massive stars since these are not treated in the simulations. Collisional excitations to n > 3 represent a negligible contribution to the total Hα emission since transitions to these levels are significantly less likely (Anderson et al. 2000, 2002, but see also Péquignot & Tsamis 2005 and references therein). We compute mHα (dLHα) and Mtot,Hα (Ltot,Hα), required in equation (9), following the emissivity calculations for recombination and collisional excitation of Draine (2011), Dong & Draine (2011), and Kim et al. (2013b) (but see also Aggarwal 1983):

(11)

\begin{equation}
{\rm d}L_{\mathrm{H}\alpha ,\mathrm{R}}\propto T_4^{-0.942-0.031\ln (T_4)}n_\mathrm{e} n_{\mathrm{H\small {II}}} {\rm d}V\,,
\end{equation}


(12)

\begin{equation}
{\rm d}L_{\mathrm{H}\alpha ,\mathrm{C}}\propto \frac{\Gamma _{13}(T_\mathrm{e})}{\sqrt{T_\mathrm{e}}}{\rm e}^{\frac{-12.1 \mathrm{eV}}{k_\mathrm{B} T_\mathrm{e}}} n_\mathrm{e} n_{\mathrm{H\small {I}}} {\rm d}V\,,
\end{equation}

where T4 = T/104 K, Te is the electron temperature, nj is the number density of species j in cm−3, dV is the zone volume, and

(13)

\begin{eqnarray}
\Gamma _{13}(T_\mathrm{e})&amp;=&amp;0.35-2.62\times 10^{-7}T_\mathrm{e}-8.15\times 10^{-11}T_\mathrm{e}^2\nonumber\\
&amp;&amp;+\;6.19\times 10^{-15}T_\mathrm{e}^3.
\end{eqnarray}

We apply equation (12) only for cells with temperatures 4000  T  25 000 K assuming Te = T. We only consider this temperature range because emission at T  4000 K will be negligible, while we expect to find very little atomic hydrogen at T > 25 000 K. We also assume $n_\mathrm{e}=n_{\mathrm{H\,\small {II}}}$, which results in an ∼10 per cent error at most in regions where helium is ionized.
Citation: Aggarwal 1983
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There are many types of nonstationarity for a shock front, e.g., self-reformation (Lembège & Dawson 1987; Hada et al. 2003; Chapman et al. 2005; Matsukiyo & Scholer 2014), self-excited ripples (Winske & Quest 1988; Savoini & Lembège 1994; Lembège et al. 2004; Burgess & Scholer 2007), and pre-existing waves or turbulence (Giacalone 2005; Guo & Giacalone 2010), some of which likely cause the unexpected motions of the TS. These nonstationarities are predicted and observed by numerical simulations and satellite observations, respectively. The term “self-reformation” describes a process wherein the particles reflected by the shock ramp accumulate ahead of the shock and form a shock foot, which then grows and becomes the new ramp. The new ramp starts to reflect incident particles, and the process repeats. Self-reformation of the shock front was predicted by both hybrid simulations (Tiu et al. 2011; Hellinger & Trávnícek 2002; Lembège et al. 2009; Yuan et al. 2009; Su et al. 2012) and particle-in-cell (PIC) simulations (Lembège & Dawson 1987; Hada et al. 2003; Nishimura et al. 2003; Scholer et al. 2003; Lee et al. 2005a; Yang et al. 2009, 2013) for large Mach number and low 





 shocks, where 





 is the ratio of the thermal pressure of ions to the magnetic pressure. Even in the presence of PUIs, self-reformation occurs under some conditions (Chapman et al. 2005; Lee et al. 2005b; Oka et al. 2011; Yang et al. 2012a; Matsukiyo & Scholer 2014). For the heliospheric TS, the values of 





 and the Mach number are relatively low and high, respectively. The TS is generally believed to be in the supercritical regime and probably undergoes self-reformation (Burlaga et al. 2008). Self-excited ripples are usually found in two-dimensional (2D) hybrid simulations (Thomas 1989; Burgess & Scholer 2007) and PIC simulations (Savoini & Lembège 1994; Lembège et al. 2009; Yang et al. 2012b). Shock front ripples are robust in three-dimensional (3D) hybrid simulations (Thomas 1989; Hellinger et al. 1996). The filament instability of the shock front found in high-dimensional simulations can also contribute to the shock front nonstationarity (Spitkovsky 2005; Guo & Giacalone 2013; Caprioli & Spitkovsky 2014). Not all of the simulations above include PUIs. By using the 2D Los Alamos hybrid simulation code with PUIs, Liu et al. (2010) studied the Alfvén-cyclotron and mirror modes excited in the near-TS heliosheath. The impact of the PUIs on the shock front ripples and self-reformation is not mentioned. It is expected that the density of PUIs at the TS is of the order of 20%–30% of the solar wind density (Richardson et al. 2008; Wu et al. 2009; Matsukiyo & Scholer 2014). The impact of such a high percentage of PUIs on the shock front ripples has not been studied yet. The relevance of the shock front ripples to the multiple TS crossings still remains unclear. A precise description of this influence would require at least a 2D full particle model.
Citation: Yang et al.; 2013
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However, in the case of stationary collisionless stellar systems with gravitomagnetic forces, the situation is not so simple, because while E is still an integral of motion, J

z
 is not conserved along orbits and so it cannot be used as an isolating integral in the DF. Fortunately, the problem is solved as follows. As is well known, the Lagrangian (per unit mass) associated with Equation (30) is
34



=∥v∥22−(ϕ+A·v),

where, at variance with the EM case (e.g., see Landau & Lifshitz 1971), the + sign in the generalized potential derives from the – sign in the gravitomagnetic Lorentz force. Suppose now that 
v
 = v

φ
(R, z)
e


φ
, so that 
A
 = A

φ
(R, z)
e


φ
 from the results in Section 2.1. The Euler–Lagrange equations show immediately that J

z
 is not conserved, but a second integral of motion exists, I
2 = J

z
 − RA

φ
. The Jeans theorem then in principle allows for a two-integral DF, f(E, I
2), and an interesting question arises whether such a DF is consistent with the assumption of streaming motions with 
v
 = v

φ
(R, z)
e


φ
 used to prove the existence of I
2. The answer is in the affirmative, and it is easy to prove that properties (1) and (2) mentioned above for systems supported by a f(E, J

z
) are preserved by the generalized f(E, I
2), in particular the fact that v

R
 = v

z
 = 0. Therefore, the vertical and radial Jeans Equations (B2) for a stationary, axisymmetric two-integral system with gravitomagnetic forces, supported by a DF of the family f(E, I
2), become
35



∂ρσ2∂z=−ρ∂ϕ∂z+jBR[j],j=ρvφ,∂ρσ2∂R−ρΔR=−ρ∂ϕ∂R−jBz[j],

where 



Δ=vφ2¯−σ2

, and in the isotropic rotator case 



Δ=vφ2

. Finally, the azimuthal Jeans equation vanishes identically also in the gravitomagnetic case, as obvious from the last of Equations (B2). Notice how, at variance with the classical Newtonian case, now the vertical and radial velocity dispersions depend on the ordered rotational field v

φ
(R, z), yet to be determined.
Citation: Landau & Lifshitz 1971
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We performed an accurate estimation of the physical properties derived from SED fitting (e.g., absolute magnitude, stellar mass, and star formation rate) and characterized each sample as a whole with the median of each of these properties. Figure 6 shows the median of the probability distribution of stellar mass, absolute magnitude, and star formation rate for the BJGKn 6 (red squares) samples as a function of redshift. In the stellar mass panel, the dashed line shows the evolution of the stellar mass for galaxies with present-day stellar masses of log (M∗) ≈ 10.7, such as our Milky Way galaxy. The data are taken from the analysis of the CANDELS survey by van Dokkum et al. (2013). The observed mass growth determined by van Dokkum et al. (2013), which slightly increase by a factor of 0.1 dex from z = 1 to z = 0.5,  agrees well with the flat behavior found in this work. In the star formation rate panel, the dashed line shows the evolution of the implied star formation rate that is caused by the evolution of the stellar mass of galaxies with present-day stellar masses of log (M∗) ≈ 10.7, such as our Milky Way, also taken from van Dokkum et al. (2013). Our results are slightly lower, suggesting that the SFR is sufficient to account for the increment in stellar mass between z = 1 and z = 0.5  and that major mergers play a minor role in this redshift range. The evolution of the SFR and sSFR resembles the expected main-sequence behavior of star-forming galaxies (Rodighiero et al. 2011). The BJGK evolution from z ~ 1 to z = 0 of the B-band absolute luminosity agrees with the evolution measured by Tasca et al. (2014). They found that the contribution of disks to the total B-band luminosity decreases by 30%  from z ~ 1 to z = 0, while for the BJGs the median B-band luminosity decreases by a factor of 0.5 dex. The distribution of galaxy ages obtained by iSEDfit has a large dispersion, but even so, its increment between two epochs corresponds to the Universe age increment indicated by the redshift. According to the models of Lagos et al. (2014), galaxies of properties similar to the BJGs host most of the neutral gas at 0.5 z 1.5. Hence the BJG samples contain tentative targets to sample the neutral gas with submillimeter surveys.
Citation: van Dokkum et al. (2013)
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We revisit the total (star + circumstellar) mass estimate for the M1701117 system, and the likelihood of it evolving into a brown dwarf. From ALMA continuum observations, the total (dust+gas) mass arising from the circumstellar material in the M1701117 system is 20.98 ± 1.24 MJup. To estimate the intrinsic stellar mass for M1701117, we have used the infrared photometry for this object and the evolutionary models by Baraffe et al. (2003). The J band, in particular, is considered to be least affected by the potential effects of veiling at bluer wavelengths, and circumstellar disc emission further into the infrared (e.g. Hartigan et al. 1995; White & Hillenbrand 2004; Cieza et al. 2005). Fig. 10 shows the UKIDSS (J − K, J) colour–magnitude diagram (cmd). The filled circles represent known members from previous studies in the σ Orionis cluster (Béjar et al. 1999, 2001; Zapatero et al. 2000; Caballero et al. 2007; Caballero 2008). The cluster suffers from negligible reddening (AV ≤ 1 mag; Béjar et al. 1999) and the photometric data has been corrected for the interstellar reddening. M1701117 appears much redder than the main cluster member sequence, which is due to the large K-band excess emission from the circumstellar material. We have overplotted in Fig. 10 the 1, 3, 5, and 8 Myr isochrones from the Baraffe et al. (2003) models. The isochrones at ages of 1 Myr are not provided in these models. The mass scale shown on the right-hand side in Fig. 10 is from the 1 Myr model isochrone at a distance of 410 pc for the cluster. Assuming an age of 1 Myr, we can estimate a stellar mass of ∼40 MJup and a stellar luminosity of 0.012 L$\odot$ for M1701117. The location of M1701117 to the red of the 1 Myr isochrone in the cmd indicates an age younger than 1 Myr. The typical age of the embedded phase or the age of the protostar formation is considered to be ∼0.01–0.05 Myr, based on the statistics of embedded-to-Class II sources (e.g. Evans et al. 2009). On the other hand, the embedded phase may be shorter for very low-mass protostars and brown dwarfs, as indicated by numerical simulations. The estimates on the stellar mass and luminosity for M1701117 will be lower if the object is younger than 1 Myr.
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Citation: Baraffe et al. (2003); Baraffe et al. (2003)
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Citation: Evans et al. 2009
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For MS high-velocity stars seemingly ejected from the Galactic disc, on the other hand, two main processes are typically blamed. In the dynamical ejection scenario (DES; e.g. Poveda, Ruiz & Allen 1967; Leonard & Duncan 1990; Leonard 1991; Perets & Šubr 2012; Oh & Kroupa 2016), exchange encounters in dense stellar systems (Aarseth 1974) may eject stars at high velocities. In the binary supernova scenario (BSS; e.g. Blaauw 1961; Boersma 1961; Tauris & Takens 1998; Portegies Zwart 2000; Tauris 2015; Renzo et al. 2019b), the massive primary in a binary system explodes in a core-collapse (CC) supernova, disrupting the binary and ejecting its MS companion with a velocity comparable to its pre-CC orbital velocity. Both processes are known to occur in the Milky Way (Hoogerwerf, de Bruijne & de Zeeuw 2001; Jilinski et al. 2010) and are generally thought to be responsible for the known sample of ‘runaway stars’ with ejection velocities of ${\ge}30\!-\!40\, \mathrm{km\ s^{-1}}$ (Blaauw 1961), though their relative contribution is not yet well constrained (see Hoogerwerf et al. 2001; Renzo et al. 2019b). With characteristic ejection speeds of the order of a few tens of km s−1, it is not yet known whether these mechanisms can eject stars of the order of hundreds of km s−1 with sufficient frequency to explain the current known sample of ‘hyper-runaway stars’ (HRSs) – runaway stars ejected near to or above the Galactic escape velocity at their location. While ejection velocities in the neighbourhood of ∼1000 km s−1 are possible in both the DES (Leonard 1991) and BSS (e.g. Tauris & Takens 1998; Tauris 2015) scenarios, these situations are thought to be rare. Recent N-body simulations of young star clusters have found that ejections in excess of 200 km s−1 are very rare (Perets & Šubr 2012; Oh & Kroupa 2016). Binary population synthesis models simulating a large number of binary systems show that ejections above 200 km s−1 are vastly outnumbered by ejections of the order of ∼10 km s−1 (Portegies Zwart 2000; Eldridge, Langer & Tout 2011; Renzo et al. 2019b).
Citation: Renzo et al. 2019b
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CCSNe are also of interest for GW astronomy as targets in their own right. As the sensitivity of GW detectors increases, they will begin to detect not only binary mergers but also other lower amplitude sources of GWs such as CCSNe. Accurate knowledge of the GW emission from CCSNe will be essential for detection and parameter estimation. The GW signal from rotational core bounce has already been well covered in the literature (e.g. Dimmelmeier et al. 2008; Abdikamalov et al. 2014; Fuller et al. 2015; Richers et al. 2017). In the non-rotating case, the GW emission from the post-bounce phase has been studied using self-consistent 3D simulations by many groups (Kuroda, Kotake & Takiwaki 2016; Andresen et al. 2017, 2019; Kuroda et al. 2017, 2018; Powell & Müller 2019, 2020; Radice et al. 2019; Andresen, Glas & Janka 2020; Mezzacappa et al. 2020; Pan et al. 2020). The structure of the GW emission has shown common features in different simulations from recent years. The dominant emission feature in the GW emission is due to the quadrupolar surface f/g mode 1 of the proto-neutron star (PNS), which produces GW frequencies rising in time from a few hundred Hz up to a few kHz (Müller, Janka & Wongwathanarat 2012; Sotani et al. 2017; Kuroda et al. 2018; Morozova et al. 2018; Torres-Forné et al. 2018, 2019). In addition, some models (Kuroda et al. 2016, 2017; Andresen et al. 2017; Mezzacappa et al. 2020; Powell & Müller 2020) exhibit low-frequency GW emission due to the standing accretion shock instability (SASI; Blondin, Mezzacappa & DeMarino 2003; Blondin & Mezzacappa 2006; Foglizzo et al. 2007). In rapidly rotating models, very strong GW emission can also occur during the post-bounce phase due to a corotation instability (Takiwaki & Kotake 2018). The emerging understanding of the GW emission features has led to the formulation of universal relations for the GW emission (Torres-Forné et al. 2019) and paved the way for phenomenological modelling for CCSN signals (Astone et al. 2018). Further work is still needed, however, to extend these models to fully explore CCSN GW signals from across the progenitor parameter space. The majority of 3D simulations that include GW emission are for progenitor stars below $30\, \mathrm{M}_{\odot }$. In this paper, we perform simulations of high-mass Population III (Pop-III) stars in the pulsational pair instability regime to expand the parameter space coverage of 3D simulations and to provide further insights into the massive and very massive star remnant BH population.
Citation: Pan et al. 2020
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Citation: Astone et al. 2018
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The total energy at each point is defined as a sum of four separate components; the CCSD(T) energy extrapolated to the complete basis set (CBS) limit and three energy increments. Each increment represents a source of electron correlation omitted from the above CBS energy: core-correlation, scalar-relativistic correlation, and higher order dynamic correlation. A nomenclature has been used in the past to describe this composite theory by its components, where C represents CBS-extrapolation, cC represents core-correlation, R represents scalar-relativity, and E represents higher order correlation (Fortenberry et al. 2011). For example, the CcCRE potential surface (equation 2) includes all of the corrections, but the CcCR omits the higher order correlation correction. 
(2)
\begin{equation*}
E_\text{CcCRE} = E_\text{CBS} + \Delta E_\text{core} + \Delta E_\text{rel} + \Delta E_\text{hlc}
\end{equation*}
Two different procedures are used to extrapolate the CCSD(T) energy to the CBS limit. The first scheme used is the three-point total energy extrapolation shown in equation (3, Martin & Lee 1996). 
(3)
\begin{equation*}
E(X) = E_\text{CBS}+ A(X+1/2)^{-4} + B(X+1/2)^{-6}
\end{equation*}
The second scheme extrapolates the Hartree–Fock energy and the correlation energy, represented here as ε, separately using equations (4) and (5), respectively (Feller 1993; Helgaker et al. 1997). 
(4)
\begin{equation*}
E^\text{HF}(X) = E^\text{HF}_\text{CBS} + A e^{BX}
\end{equation*}
(5)
\begin{equation*}
\varepsilon ^\text{(T)}(X) = \varepsilon ^\text{(T)}_\text{CBS} + A X^{-3}
\end{equation*}
The resulting CCSD(T)/CBS energy in this latter scheme is $E^{\prime }_\text{CBS} = E^\text{HF}_\text{CBS} + \varepsilon ^\text{(T)}_\text{CBS}$, where the prime is simply used to distinguish the two CBS extrapolations. Each energy correction (increment) is defined as the difference between the energy with the correlation effect considered and the energy without it when using the same basis set. The core-correlation correction, ΔEcore, is EMTc − EMT as defined with the geometry correction. Scalar relativity is incorporated through ΔErel, which is taken as the difference in the all-electron CCSD(T)/cc-pCV(T+d)Z-DK energy with and without the Douglas–Kroll–Hess (DKH) corrections to second-order (Reiher & Wolf 2004). The energy contribution from non-iterative quadruple excitations in the coupled cluster wavefunction, ΔEhlc, is defined as the difference between CCSDT(Q)/cc-pV(T+d)Z and CCSD(T)/cc-pV(T+d)Z at each point.
Citation: Martin & Lee 1996
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However, in our model, the interactions between strangeons are dominated by strong force. The detailed calculations of the shear modulus is still not performed, but it should be much larger than that of the NS’s crust. If the burst oscillation frequencies observed in low-mass X-ray binaries correspond to the first few torsional modes of SSs, the shear modulus should be about one thousand times of the NS’s crust, say $\mu \simeq 4\times 10^{32}\, \rm erg\, cm^{-3}$ (Xu 2003; Owen 2005). We do not know how large the tidal deformability will deviate from the fluid case for SSs, but we can obtain some key insights of this problem from the calculations of tidal deformabilities for crystalline colour superconducting phase (Lau, Leung & Lin 2017, 2019). QSs composed of crystalline colour superconducting phase are rigid with extremely high shear modulus (Alford, Bowers & Rajagopal 2001; Mannarelli, Rajagopal & Sharma 2007). The shear modulus is approximately given by (Mannarelli et al. 2007)
(77)$$\begin{eqnarray*}
\mu =2.47 \, \mathrm{MeV} / \mathrm{fm}^{3}\left(\frac{\Delta }{10 \, \mathrm{MeV}}\right)^{2}\left(\frac{\mu _{\rm q}}{400 \, \mathrm{MeV}}\right)^{2}\, ,
\end{eqnarray*}$$where μq is the average quark chemical potential and Δ is the gap parameter which is in the range of 5–$25\, \rm MeV$. If the shear modulus is taken to be $\mu =4\times 10^{32}\, \rm erg\, cm^{-3}$ ($\Delta \simeq 5\, \rm MeV$), according to the results in Lau et al. (2017, 2019), the deviations of the tidal deformabilities from the fluid case are in the order of $1{{\ \rm per\ cent}}$. For larger gap parameters, the deviations can be very large and more interestingly, they found that the universal relations between the moment of inertia and tidal deformability will deviate from the ones for fluid stars. If we take the shear modulus to be about $\mu \simeq 4\times 10^{32}\, \rm erg\, cm^{-3}$, the corrections may not be very large and the results discussed in our work is a good approximation. But if the shear modulus is actually larger, then we need to consider the corrections due to the elasticity.
Citation: Mannarelli et al. 2007
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We derive leftover planetesimal populations directly from our simulations sets that incorporate planetesimals (see Table 1 and the left panel of Figure 1), and perform an additional batch of ∼105 simulations of the final few giant impacts in our systems to derive collisional fragment distributions. This additional suite of computations utilizes a modified version of the Mercury integration package described in Chambers (2013) that incorporates collisional parameter space mapped in Stewart & Leinhardt (2012) to track hit-and-run and fragmenting impacts. Aside from the fragmentation algorithm, the integration parameters (i.e., time step, ejection radius, etc.) are identical to those utilized in Section 2.1. To prevent the calculation from becoming intractable, the user must establish a minimum fragment mass (MFM; 0.005 M
⊕ in our simulations based on previous experience with the code; Quintana et al. 2016; Clement et al. 2019b). When the algorithm detects a fragmenting collision, the total remnant mass is divided into a number of equal-mass fragments with M > M
MFM that are ejected in uniformly spaced directions in the collisional plane at v ≃ 1.05v
esc. If the total eroded mass is less than the MFM, the collision is considered totally accretionary. While this treatment of fragmentation is obviously somewhat contrived (see Section 4 for a discussion of some of these caveats), a first-order dissection of the distinctive populations of collisionally generated debris and unaltered planetesimals is important for our study as the fragment material might posses enhanced volatile and light element inventories if it is ejected from near the surface of partially or fully differentiated proto-planets. Moreover, since we utilize these simulations to infer the orbital distribution of debris given a supposed size frequency distribution (SFD), our particular selection of MFM is not carried forward into our study of late bombardment, and is therefore only important for keeping our experiments computationally feasible.
Citation: Quintana et al. 2016
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