arXiv subjects

Shing-Chi Leung

Publications and source records attributed to Shing-Chi Leung.

At least 37 records · Page 2Linked to original sources

arXiv2021

Type Ia Supernovae and their Explosive Nucleosynthesis: Constraints on Progenitors

What the progenitors of Type Ia supernovae (SNe Ia) are, whether they are near-Chandrasekhar mass or sub-Chandrasekhar mass white dwarfs, has been the matter of debate for decades. Various observational hints are supporting both models as the main progenitors. In this paper, we review the explosion physics and the chemical abundance patterns of SNe Ia from these two classes of progenitors. We will discuss how the observational data of SNe Ia, their remnants, the Milky Way Galaxy, and galactic clusters can help us to determine the essential features where numerical models of SNe Ia need to match.

astro-ph.HE↗

arXiv2021

Spatially Resolved X-ray Study of Supernova Remnant G306.3$-$0.9 with Unusually High Calcium Abundance

G306.3$-$0.9 is an asymmetric Galactic supernova remnant (SNR), whose progenitor has been thought to be a Type Ia supernova (SN), but its high Ca abundance appears inconsistent with the Type Ia origin. Hoping to uncover the reason for its asymmetry and the origin of this SNR, we performed a spatially resolved X-ray spectroscopic analysis of XMM-Newton and Chandra observation data. We divided the SNR into 13 regions and analyzed the spectra using two-temperature models (0.2 keV + 1 keV). Compared to the southwestern regions, the northeastern regions have higher metal abundances and a lower gas density. This suggests that the asymmetric morphology results from the non-uniform ambient environment. We found that neither Type Ia nor core-collapse SN models can account for the abnormally high abundance ratios of Ar/Si, Ca/Si, or the shape of the abundance curve. A comparison with the Ca-rich transient models shows that G306.3$-$0.9 is likely to be the first identified Galactic "Ca-rich transient" remnant, although the theoretical production of element S is lower. We also note that the conclusion for the SNR's origin relies on the measured abundance ratios and existing nucleosynthesis models. Between two groups of Ca-rich transient explosion models, we prefer the He shell detonation for an accreting WD, rather than the merger of a white dwarf and a neutron star.

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arXiv2021

Origin of metals in old Milky Way halo stars based on GALAH and Gaia

Stellar and supernova nucleosynthesis in the first few billion years of the cosmic history have set the scene for early structure formation in the Universe, while little is known about their nature. Making use of stellar physical parameters measured by GALAH Data Release 3 with accurate astrometry from the Gaia EDR3, we have selected $\sim 100$ old main-sequence turn-off stars (ages $\gtrsim 12$ Gyrs) with kinematics compatible with the Milky Way stellar halo population in the Solar neighborhood. Detailed homogeneous elemental abundance estimates by GALAH DR3 are compared with supernova yield models of Pop~III (zero-metal) core-collapse supernovae (CCSNe), normal (non-zero-metal) CCSNe, and Type Ia supernovae (SN Ia) to examine which of the individual yields or their combinations best reproduce the observed elemental abundance patterns for each of the old halo stars ("OHS"). We find that the observed abundances in the OHS with [Fe/H]$>-1.5$ are best explained by contributions from both CCSNe and SN~Ia, where the fraction of SN~Ia among all the metal-enriching SNe is up to 10-20 % for stars with high [Mg/Fe] ratios and up to 20-27 % for stars with low [Mg/Fe] ratios, depending on the assumption about the relative fraction of near-Chandrasekhar-mass SNe Ia progenitors. The results suggest that, in the progenitor systems of the OHS with [Fe/H]$>-1.5$, $\sim$ 50-60% of Fe mass originated from normal CCSNe at the earliest phases of the Milky Way formation. These results provide an insight into the birth environments of the oldest stars in the Galactic halo.

astro-ph.GA↗

arXiv2021

Discovery of the Highly-Neutronized Ejecta Clump with Enhanced Abundances of Titanium and Chromium in the Type Ia Supernova Remnant 3C 397

The supernova remnant (SNR) 3C 397 is thought to originate from a Type Ia supernova (SN Ia) explosion of a near-Chandrasekhar-mass ($M_{\rm Ch}$) progenitor, based on the enhanced abundances of Mn and Ni revealed by previous X-ray study with Suzaku. Here we report follow-up XMM-Newton observations of this SNR, conducted with the aim of investigating the detailed spatial distribution of the Fe-peak elements. We have discovered an ejecta clump with extremely high abundances of Ti and Cr, in addition to Mn, Fe, and Ni, in the southern part of the SNR. The Fe mass of this ejecta clump is estimated to be $\sim$ 0.06 $M_{\odot}$, under the assumption of a typical Fe yield for SNe Ia (i.e., $\sim$ 0.8 $M_{\odot}$). The observed mass ratios among the Fe-peak elements and Ti require substantial neutronization that is achieved only in the innermost regions of a near-$M_{\rm Ch}$ SN Ia with a central density of $ρ_c \sim 5 \times 10^9$ g cm$^{-3}$, significantly higher than typically assumed for standard near-$M_{\rm Ch}$ SNe Ia ($ρ_c \sim 2 \times 10^9$ g cm$^{-3}$). The overproduction of the neutron-rich isotopes (e.g., $^{50}$Ti and $^{54}$Cr) is significant in such high-$ρ_c$ SNe Ia, with respect to the solar composition. Therefore, if 3C 397 is a typical high-$ρ_c$ near-$M_{\rm Ch}$ SN Ia remnant, the solar abundances of these isotopes could be reproduced by the mixture of the high- and low-$ρ_c$ near-$M_{\rm Ch}$ and sub-$M_{\rm Ch}$ Type Ia events, with $\lesssim$ 20 % being high-$ρ_c$ near-$M_{\rm Ch}$.

astro-ph.HE↗

arXiv2021

Fast Blue Optical Transients due to Circumstellar Interaction and the Mysterious Supernova SN 2018gep

The discovery of SN 2018gep (ZTF18abukavn) challenged our understanding of the late-phase evolution of massive stars and their supernovae (SNe). The fast rise in luminosity of this SN (spectroscopically classified as a broad-lined Type Ic SN), indicates that the ejecta interacts with a dense circumstellar medium (CSM), while an additional energy source such as $^{56}$Ni-decay is required to explain the late-time light curve. These features hint at the explosion of a massive star with pre-supernova mass-loss. In this work, we examine the physical origins of rapidly evolving astrophysical transients like SN 2018gep. We investigate the wave-driven mass-loss mechanism and how it depends on model parameters such as progenitor mass and deposition energy, searching for stellar progenitor models that can reproduce the observational data. A model with an ejecta mass $\sim \! 2 \, M_{\odot}$, explosion energy $\sim \! 10^{52}$ erg, a circumstellar medium of mass $\sim \! 0.3 \, M_{\odot}$ and radius $\sim \! 1000 \, R_{\odot}$, and a $^{56}$Ni mass of $\sim \! 0.3 \, M_{\odot}$ provides a good fit to the bolometric light curve. We also examine how interaction-powered light curves depend more generally on these parameters, and how ejecta velocities can help break degeneracies. We find both wave-driven mass-loss and mass ejection via pulsational pair-instability can plausibly create the dense CSM in SN 2018gep, but we favor the latter possibility.

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arXiv2021

A Model for Fast Blue Optical Transient AT2018Cow: Circumstellar Interaction of a Pulsational Pair-instability Supernova

The Fast Blue Optical Transient (FBOT) ATLAS18qqn (AT2018cow) has a light curve as bright as superluminous supernovae but rises and falls much faster. We model this light curve by circumstellar interaction of a pulsational pair-instability (PPI) supernova (SN) model based on our PPISN models studied in previous work. We focus on the 42 $M_\odot$ He star (core of a 80 $M_{\odot}$ star) which has circumstellar matter of mass 0.50 $M_\odot$. With the parameterized mass cut and the kinetic energy of explosion $E$, we perform hydrodynamical calculations of nucleosynthesis and optical light curves of PPISN models. The optical light curve of the first $\sim$ 20 days of AT2018cow is well-reproduced by the shock heating of circumstellar matter for the $42 ~M_{\odot}$ He star with $E = 5 \times 10^{51}$ erg. After day 20, the light curve is reproduced by the radioactive decay of 0.6 $M_\odot$ $^{56}$Co, which is a decay product of $^{56}$Ni in the explosion. We also examine how the light curve shape depends on the various model parameters, such as CSM structure and composition. We also discuss (1) other possible energy sources and their constraints, (2) origin of observed high-energy radiation, and (3) how our result depends on the radiative transfer codes. Based on our successful model for AT2018cow and the model for SLSN with the CSM mass as large as $20 ~M_\odot)$, we propose the working hypothesis that PPISN produces SLSNe if CSM is massive enough and FBOTs if CSM is less than $\sim 1 ~M_\odot$.

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arXiv2021

Exploration of Aspherical Ejecta Properties in Type Ia Supernova: Progenitor Dependence and Applications to Progenitor Classification

Several explosions of thermonuclear supernovae (SNe Ia) have been found to exhibit deviations from spherical symmetry upon closer inspection. Examples are the gamma-ray lines from SN 2014J as measured by INTEGRAL/SPI, and morphology information from radioactive isotopes in older remnants such as Tycho. A systematic study on the effects of parameters such as ignition geometry and burning morphology in SNe Ia is still missing. We use a 2D hydrodynamics code with post-processing nucleosynthesis and simulate the double detonations in a sub-Chandrasekhar mass carbon-oxygen white dwarf starting from the nuclear runaway in the accumulated He envelope towards disruption of the white dwarf. We explore potential variety through four triggering scenarios that sample main asymmetry drivers. We further investigate their global effects on the aspherical structure of the ejecta based on individual elements. We apply the results to the well observed SN 2014J and other recently observed SN remnants in order to illustrate how these new observational data together with other observed quantities help to constrain the explosion and the progenitors of SNe Ia.

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arXiv2020

Chemical abundances in Sgr A East: evidence for a Type Iax supernova remnant

Recent observations have shown a remarkable diversity of observational behaviors and explosion mechanisms in thermonuclear supernovae (SNe). An emerging class of peculiar thermonuclear SNe, called Type Iax, show photometric and spectroscopic behaviors distinct from normal Type Ia. Their origin remains highly controversial, but pure turbulent deflagration of white dwarfs (WDs) has been regarded as the leading formation theory. The large population of Type Iax indicates the existence of unidentified Galactic Type Iax supernova remnants (SNRs). We report evidence that SNR Sgr A East in the Galactic center resulted from a pure turbulent deflagration of a Chandrasekhar-mass carbon-oxygen WD, an explosion mechanism used for Type Iax SNe. Our X-ray spectroscopic study of Sgr A East using 3 Ms of Chandra data shows a low ratio of intermediate-mass elements to Fe and large Mn/Fe and Ni/Fe ratios. This abundance pattern does not accord with the core-collapse or normal Type Ia models. Sgr A East is thus the first Galactic SNR for which a likely Type Iax origin has been proposed and the nearest target for studying this peculiar class. We compared Sgr A East with the Fe-rich SNRs 3C 397 and W49B, which also have high Mn and Cr abundances and were claimed to result from deflagration-to-detonation explosions of Chandrasekhar-mass WDs (although with disputes). Our study shows that they have distinct abundance patterns. The X-ray spectroscopic studies of thermonuclear SNRs provide observational evidence for the theories that there are diverse explosion channels and various metal outputs for Chandrasekhar-mass WDs.

astro-ph.HE↗

arXiv2020

Standing on the shoulders of giants: New mass and distance estimates for Betelgeuse through combined evolutionary, asteroseismic, and hydrodynamical simulations with MESA

We conduct a rigorous examination of the nearby red supergiant Betelgeuse by drawing on the synthesis of new observational data and three different modeling techniques. Our observational results include the release of new, processed photometric measurements collected with the space-based SMEI instrument prior to Betelgeuse's recent, unprecedented dimming event. We detect the first radial overtone in the photometric data and report a period of $185\pm13.5$ d. Our theoretical predictions include self-consistent results from multi-timescale evolutionary, oscillatory, and hydrodynamic simulations conducted with the Modules for Experiments in Stellar Astrophysics (MESA) software suite. Significant outcomes of our modeling efforts include a precise prediction for the star's radius: $764^{+116}_{-62} R_{\odot}$. In concert with additional constraints, this allows us to derive a new, independent distance estimate of $168^ {+27}_{-15}$ pc and a parallax of $π=5.95^{+0.58}_{-0.85}$ mas, in good agreement with Hipparcos but less so with recent radio measurements. Seismic results from both perturbed hydrostatic and evolving hydrodynamic simulations constrain the period and driving mechanisms of Betelgeuse's dominant periodicities in new ways. Our analyses converge to the conclusion that Betelgeuse's $\approx 400$ day period is the result of pulsation in the fundamental mode, driven by the $κ$-mechanism. Grid-based hydrodynamic modeling reveals that the behavior of the oscillating envelope is mass-dependent, and likewise suggests that the non-linear pulsation excitation time could serve as a mass constraint. Our results place $α$ Ori definitively in the core helium-burning phase near the base of the red supergiant branch. We report a present-day mass of $16.5$--$19 ~M_{\odot}$---slightly lower than typical literature values.

astro-ph.SR↗

arXiv2020

Hydrodynamic Simulations of Pre-Supernova Outbursts in Red Supergiants: Asphericity and Mass Loss

The activity of massive stars approaching core-collapse can strongly affect the appearance of the star and its subsequent supernova. Late-phase convective nuclear burning generates waves that propagate toward the stellar surface, heating the envelope and potentially triggering mass loss. In this work, we improve on previous one-dimensional models by performing two-dimensional simulations of the pre-supernova mass ejection phase due wave heat deposition. Beginning with stellar evolutionary models of a 15 $M_{\odot}$ red supergiant star during core O-burning, we treat the energy deposition rate and duration as model parameters and examine the mass-loss dependence and the pre-explosion morphology accordingly. Unlike one-dimensional models, density inversions due to wave heating are smoothed by Rayleigh-Taylor instabilities, and the primary effect of wave heating is to radially expand the star's hydrogen envelope. For low heating rates with long durations, the expansion is nearly homologous, whereas high but short-lived heating can generate a shock that drives envelope expansion and results in a qualitatively different density profile at the time of core-collapse. Asymmetries are fairly small, and large amounts of mass loss are unlikely unless the wave heating exceeds expectations. We discuss implications for pre-supernova stellar variability and supernovae light curves.

astro-ph.HE↗

arXiv2020

Explosive Nucleosynthesis in Near-Chandrasekhar-mass White Dwarf Models for Type Iax Supernovae: Dependence on Model Parameters

The recently observed diversity of Type Ia supernovae (SNe Ia) has motivated us to conduct the theoretical modeling of SNe Ia for a wide parameter range. In particular, the origin of Type Iax supernovae (SNe Iax) has been obscure. Following our earlier work on the parameter dependence of SN Ia models, we focus on SNe Iax in the present study. For a model of SNe Iax, we adopt the currently leading model of pure turbulent deflagration (PTD) of near-Chandrasekhar mass C+O white dwarfs (WDs). We carry out 2-dimensional hydrodynamical simulations of the propagation of deflagration wave, which leaves a small WD remnant behind and eject nucleosynthesis materials. We show how the explosion properties, such as nucleosynthesis and explosion energy, depend on the model parameters such as central densities and compositions of the WDs (including the hybrid WDs), and turbulent flame prescription and initial flame geometry. We extract the associated observables in our models, and compare with the recently discovered low-mass WDs with unusual surface abundance patterns and the abundance patterns of some SN remnants. We provide the nucleosynthesis yield tables for applications to stellar archaeology and galactic chemical evolution. Our results are compared with the representative models in the literature.

astro-ph.HE↗

arXiv2020

Pulsational Pair-instability Supernovae. II. Neutrino Signals from Pulsations and their Detection by Terrestrial Neutrino Detectors

A Pulsational Pair-instability supernova (PPISN) evolves from a massive star with a mass $\sim 80$ -- 140 $M_{\odot}$ which develops the electron-positron pair-instability after the hydrostatic He-burning in the core has finished. In [Leung et al., ApJ 887, 72 (2019)] (Paper I) we examined the evolutionary tracks and the pulsational mass loss history of this class of stars. In this paper, we analyze the thermodynamical history to explore the neutrino observables of PPISNe. We compute the neutrino light curves and spectra during pulsation. We study the detailed neutrino emission profiles of these stars. Then, we estimate the expected neutrino detection count for different terrestrial neutrino detectors including, e.g., KamLAND and Super-Kamiokande. Finally, we compare the neutrino pattern of PPISN with other types of supernovae based on a canonical 10 kt detector. The predicted neutrino signals can provide the early warning for the telescopes to trace for the early time optical signals. Implications of neutrino physics on the expected detection are discussed.

astro-ph.HE↗

arXiv2020

Explosive Nucleosynthesis in Sub-Chandrasekhar Mass White Dwarf Models for Type Ia Supernovae: Dependence on Model Parameters

Recent observations of Type Ia supernovae (SNe Ia) have shown diversified properties of the explosion strength, light curves and chemical composition. To investigate possible origins of such diversities in SNe Ia, we have presented multi-dimensional hydrodynamical study of explosions and associated nucleosynthesis in the near Chandrasekhar mass carbon-oxygen (CO) white dwarfs (WDs) for a wide range of parameters (Leung and Nomoto 2018 ApJ). In the present paper, we extend our wide parameter survey of models to the explosions of sub-Chandrasekhar mass CO WDs. We take the double detonation model for the explosion mechanism. The model parameters of the survey include the metallicity of $Z = 0 - 5~Z_\odot$, the CO WD mass of $M = 0.90 - 1.20~M_\odot$, and the He envelope mass of $M_{\rm He} = 0.05 - 0.20~M_\odot$. We also study how the initial He detonation configuration, such as spherical, bubble, and ring shapes, triggers the C detonation. For these parameters, we derive the minimum He envelope mass necessary to trigger the C detonation. We then examine how the explosion dynamics and associated nucleosynthesis depend on these parameters, and compare our results with the previous representative models. We compare our nucleosynthesis yields with the unusual abundance patterns of Fe-peak elements and isotopes observed in SNe Ia 2011fe, 2012cg and 2014J, as well as SN Ia remnant 3C 397 to provide constraints on their progenitors and environments. We provide the nucleosynthesis yields table of the sub-Chandrasekhar mass explosions, to discuss their roles in the galactic chemical evolution and archaeology.

astro-ph.HE↗

arXiv2020

Electron Capture Supernovae of Super-AGB Stars: Sensitivity on Input Physics

Stars of $\sim$ 8 - 10 $M_{\odot}$ on the main-sequence form strongly electron-degenerate O+Ne+Mg core and become super-AGB stars. If such an O+Ne+Mg core grows to 1.38 $M_\odot$, electron captures on $^{20}$Ne$(e,ν_e)^{20}$F$(e,ν_e)^{20}$O take place and ignite O-Ne deflagration around the center. In this paper, we perform two-dimensional hydrodynamics simulations of the propagation of the O-Ne flame to see whether such a flame induces a collapse of the O+Ne+Mg core due to subsequent electron capture behind the flame or triggers a thermonuclear explosion. We present a series of models to explore how the outcome depends on model parameters for the central density in the range from $10^{9.80}$ to $10^{10.20}$ g cm$^{-3}$, flame structure of both centered and off-centered ignition kernels, special and general relativistic effects, turbulent flame speed formula and the treatments of laminar burning phase. We find that the O+Ne+Mg core obtained from stellar evolutionary models has a high tendency to collapse into a neutron star. We obtain the bifurcation between the electron-capture collapse and thermonuclear explosion. We discuss the implication in nucleosynthesis and the possible observational signals of this class of supernovae.

astro-ph.HE↗

arXiv2020

New Type Ia supernova Yields and the Manganese and Nickel Problems in the Milky Way and Dwarf Spheroidal Galaxies

In our quest to identify the progenitors of Type Ia supernovae (SNe Ia), we first update the nucleosynthesis yields both for near-Chandrasekhar (Ch) and sub-Ch mass white dwarfs (WDs), for a wide range of metallicity, with our two-dimensional hydrodynamical code and the latest nuclear reaction rates. We then include the yields in our galactic chemical evolution code to predict the evolution of elemental abundances in the solar neighborhood and dwarf spheroidal (dSph) galaxies: Fornax, Sculptor, Sextans, and Carina. In the observations of the solar neighborhood stars, Mn shows an opposite trend to $α$ elements, showing an increase toward higher metallicities, which is very well reproduced by deflagration-detonation transition of Ch-mass WDs, but never by double detonations of sub-Ch-mass WDs alone. The problem of Ch-mass SNe Ia was the Ni over-production at high metallicities. However, we found that Ni yields of Ch-mass SNe Ia are much lower with the solar-scaled initial composition than in previous works, which keeps the predicted Ni abundance within the observational scatter. From the evolutionary trends of elemental abundances in the solar neighborhood, we conclude that the contribution of sub-Ch-mass SNe Ia in chemical enrichment is up to 25\%. In dSph galaxies, however, larger enrichment from sub-Ch-mass SNe Ia than in the solar neighborhood may be required, which causes a decrease in [(Mg, Cr, Mn, Ni)/Fe] at lower metallicities. The observed high [Mn/Fe] ratios in Sculptor and Carina may also require additional enrichment from pure deflagrations, possibly as Type Iax supernovae. Future observations of dSph stars will provide more stringent constraints on the progenitor systems and explosion mechanism of SNe Ia.

astro-ph.HE↗

arXiv2019

Dark Matter Admixed Type Ia Supernovae

We perform two-dimensional hydrodynamic simulations for the thermonuclear explosion of Chandrasekhar-mass white dwarfs with dark matter (DM) cores in Newtonian gravity. We include a 19-isotope nuclear reaction network and make use of the pure turbulent deflagration model as the explosion mechanism in our simulations. Our numerical results show that the general properties of the explosion depend quite sensitively on the mass of the DM core M$_{\rm DM}$: a larger M$_{\rm DM}$ generally leads to a weaker explosion and a lower mass of synthesized iron-peaked elements. In particular, the total mass of $^{56}$Ni produced can drop from about 0.3 to 0.03 $M_{\odot}$ as M$_{\rm DM}$ increases from 0.01 to 0.03 $M_{\odot}$. We have also constructed the bolometric light curves obtained from our simulations and found that our results match well with the observational data of sub-luminous Type-Ia supernovae.

astro-ph.CO↗

arXiv2019

Accretion-Induced Collapse of Dark Matter Admixed White Dwarfs -- I: Formation of Low-mass Neutron Stars

Recently observed pulsars with masses $\sim 1.1 ~M_{\odot}$ challenge the conventional neutron star (NS) formation path by core-collapse supernova (CCSN). Using spherically symmetric hydrodynamics simulations, we follow the collapse of a massive white dwarf (WD) core triggered by electron capture, until the formation of a proto-NS (PNS). For initial WD models with the same central density, we study the effects of a static, compact dark matter (DM) admixed core on the collapse and bounce dynamics and mass of the PNS, with DM mass $\sim 0.01 ~M_{\odot}$. We show that increasing the admixed DM mass generally leads to slower collapse and smaller PNS mass, down to about 1.0 $M_{\odot}$. Our results suggest that the accretion-induced collapse of dark matter admixed white dwarfs can produce low-mass neutron stars, such as the observed low-mass pulsar J0453+1559, which cannot be obtained by conventional NS formation path by CCSN.

astro-ph.HE↗

arXiv2019

Pulsational Pair-instability Supernovae. I. Pre-collapse Evolution and Pulsational Mass Ejection

We calculate the evolution of massive stars, which undergo pulsational pair-instability (PPI) when the O-rich core is formed. The evolution from the main-sequence through the onset of PPI is calculated for stars with the initial masses of $80 - 140$ $M_{\odot}$ and metallicities of $Z = 10^{-3} - 1.0$ $Z_\odot$. Because of mass loss, $Z \leq 0.5$ $Z_\odot$ is necessary for stars to form He cores massive enough (i.e., mass $>40 ~M_\odot$) to undergo PPI. The hydrodynamical phase of evolution from PPI through the beginning of Fe core collapse is calculated for the He cores with masses of $40 - 62 ~M_\odot$ and $Z = 0$. During PPI, electron-positron pair production causes a rapid contraction of the O-rich core which triggers explosive O-burning and a pulsation of the core. We study the mass dependence of the pulsation dynamics, thermodynamics, and nucleosynthesis. The pulsations are stronger for more massive He cores and result in such a large amount of mass ejection such as $3 - 13$ $M_\odot$ for $40 - 62 ~M_\odot$ He cores. These He cores eventually undergo Fe-core collapse. The $64 ~M_\odot$ He core undergoes complete disruption and becomes a pair-instability supernova. The H-free circumstellar matter ejected around these He cores is massive enough for to explain the observed light curve of Type I (H-free) superluminous supernovae with circumstellar interaction. We also note that the mass ejection sets the maximum mass of black holes (BHs) to be $\sim 50$ $M_{\odot}$, which is consistent with the masses of BHs recently detected by VIRGO and aLIGO.

astro-ph.HE↗