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Register a new userThe Pair-Instability Mass Gap for Black Holes
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Stellar evolution theory predicts a gap in the black hole birth function caused by the pair instability. Presupernova stars that have a core mass below some limiting value, Mlo, after all pulsational activity is finished, collapse to black holes, whereas more massive ones, up to some limiting value, Mhi, explode, promptly and completely, as pair-instability supernovae. Previous work has suggested Mlo is approximately 50 solar masses and Mhi is approximately 130 solar masses. These calculations have been challenged by recent LIGO observations that show many black holes merging with individual masses, Mlo is least some 65 solar masses. Here we explore four factors affecting the theoretical estimates for the boundaries of this mass gap: nuclear reaction rates, evolution in detached binaries, rotation, and hyper-Eddington accretion after black hole birth. Current uncertainties in reaction rates by themselves allow Mlo to rise to 64 solar masses and Mhi as large as 161 solar masses. Rapid rotation could further increase Mlo to about 70 solar masses, depending on the treatment of magnetic torques. Evolution in detached binaries and super-Eddington accretion can, with great uncertainty, increase Mlo still further. Dimensionless Kerr parameters close to unity are allowed for the more massive black holes produced in close binaries, though they are generally smaller.
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The recent detection of GW190521 stimulated ideas on how to populate the predicted black hole pair-instability mass gap. One proposed scenario is the dynamical merger of two stars below the pair instability regime forming a star with a small core and an over-sized envelope. We explore this scenario with detailed stellar evolution calculations, starting with ad-hoc initial conditions enforcing no core growth during the merger. We outline the main challenges this scenario has to overcome, in particular the requirement to retain enough of its mass at merger time, in the subsequent evolution, and at core-collapse. We found that these massive merger products are likely helium-rich, and spend most of their remaining lifetime within regions of the Herzsprung-Russell diagram where envelope instabilities akin to luminous blue variable (LBV) eruptions are expected. An energetic estimate of the amount of mass loss neglecting the back-reaction of the star suggests that the total amount of mass that can be removed at low metallicity is . 1 M . This is small enough that at core-collapse our models are retaining sufficient mass to form black holes in the pair-instability gap similar to the recent ones detected by LIGO/Virgo. However, mass loss at the time of merger and the neutrino-driven mass loss at core collapse still need to be quantified for these models in order to confirm the viability of this scenario.
By probing the population of binary black hole (BBH) mergers detected by LIGO-Virgo, we can infer properties about the underlying black hole formation channels. A mechanism known as pair-instability (PI) supernova is expected to prevent the formation of black holes from stellar collapse with mass greater than $sim 40-65,M_odot$ and less than $sim 120,M_odot$. Any BBH merger detected by LIGO-Virgo with a component black hole in this gap, known as the PI mass gap, likely originated from an alternative formation channel. Here, we firmly establish GW190521 as an outlier to the stellar-mass BBH population if the PI mass gap begins at or below $65, M_{odot}$. In addition, for a PI lower boundary of $40-50, M_{odot}$, we find it unlikely that the remaining distribution of detected BBH events, excluding GW190521, is consistent with the stellar-mass population.
Gravitational-wave detections are now starting to probe the mass distribution of stellar-mass black holes (BHs). Robust predictions from stellar models are needed to interpret these. Theory predicts the existence of a gap in the BH mass distribution because of pair-instability supernova. The maximum BH mass below the gap is the result of pulsational mass loss. We evolve massive helium stars through their late hydrodynamical phases of evolution using the open-source MESA stellar evolution code. We find that the location of the lower edge of the mass gap at 45$M_odot$ is remarkably robust against variations in the metallicity ($approx 3M_odot$), the treatment of internal mixing ($approx 1M_odot$), stellar wind mass loss ($approx 4M_odot$), making it the most robust predictions for the final stages of massive star evolution. The reason is that the onset of the instability is dictated by the near-final core mass, which in turn sets the resulting BH mass. However, varying $^{12}Cleft(alpha,gammaright)^{16}O$ reaction rate within its $1sigma$ uncertainties shifts the location of the gap between $40M_odot$ and $56M_odot$. We provide updated analytic fits for population synthesis simulations. Our results imply that the detection of merging BHs can provide constraints on nuclear astrophysics. Furthermore, the robustness against metallicity suggests that there is a universal maximum for the location of the lower edge of the gap, which is insensitive to the formation environment and redshift for first-generation BHs. This is promising for the possibility to use the location of the gap as a standard siren across the Universe.
Gravitational-wave detections are now probing the black hole (BH) mass distribution, including the predicted pair-instability mass gap. These data require robust quantitative predictions, which are challenging to obtain. The most massive BH progenitors experience episodic mass ejections on timescales shorter than the convective turn-over timescale. This invalidates the steady-state assumption on which the classic mixing-length theory relies. We compare the final BH masses computed with two differe
The theory for single stellar evolution predicts a gap in the mass distribution of black holes (BHs) between approximately 45-130M$_{odot}$, the so-called pair-instability mass gap. We examine whether BHs can pollute the gap after accreting from a stellar companion. To this end, we simulate the evolution of isolated binaries using a population synthesis code, where we allow for super-Eddington accretion. Under our most extreme assumptions, we find that at most about 2% of all merging binary BH systems contains a BH with a mass in the pair-instability mass gap, and we find that less than 0.5% of the merging systems has a total mass larger than 90M$_{odot}$. We find no merging binary BH systems with a total mass exceeding 100M$_{odot}$. We compare our results to predictions from several dynamical pathways to pair-instability mass gap events and discuss the distinguishable features. We conclude that the classical isolated binary formation scenario will not significantly contribute to the pollution of the pair-instability mass gap. The robustness of the predicted mass gap for the isolated binary channel is promising for the prospective of placing constraints on (i) the relative contribution of different formation channels, (ii) the physics of the progenitors including nuclear reaction rates, and (iii), tentatively, the Hubble parameter.
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