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Register a new userMind the gap: The location of the lower edge of the pair instability supernovae black hole mass gap
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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.
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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
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.
Models of pair-instability supernovae (PISNe) predict a gap in black hole (BH) masses between $sim 45M_odot-120M_odot$, which is referred to as the upper BH mass-gap. With the advent of gravitational-wave astrophysics it has become possible to test this prediction, and there is an important associated effort to understand what theoretical uncertainties modify the boundaries of this gap. In this work we study the impact of rotation on the hydrodynamics of PISNe, which leave no compact remnant, as well as the evolution of pulsational-PISNe (PPISNe), which undergo thermonuclear eruptions before forming a compact object. We perform simulations of non-rotating and rapidly-rotating stripped helium stars in a metal poor environment $(Z_odot/50)$ in order to resolve the lower edge of the upper mass-gap. We find that the outcome of our simulations is dependent on the efficiency of angular momentum transport, with models that include efficient coupling through the Spruit-Tayler dynamo shifting the lower edge of the mass-gap upwards by $sim 4%$, while simulations that do not include this effect shift it upwards by $sim 15%$. From this, we expect the lower edge of the upper mass-gap to be dependent on BH spin, which can be tested as the number of observed BH mergers increases. Moreover, we show that stars undergoing PPISNe have extended envelopes ($Rsim 10-1000~R_odot$) at iron-core collapse, making them promising progenitors for ultra-long gamma-ray bursts.
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.
We perform a binary population synthesis calculation incorporating very massive population (Pop.) III stars up to 1500 $M_odot$, and investigate the nature of binary black hole (BBH) mergers. Above the pair-instability mass gap, we find that the typical primary black hole (BH) mass is 135-340 $M_odot$. The maximum primary BH mass is as massive as 686 $M_odot$. The BBHs with both of their components above the mass gap have low effective inspiral spin $sim$ 0. So far, no conclusive BBH merger beyond the mass gap has been detected, and the upper limit on the merger rate density is obtained. If the initial mass function (IMF) of Pop. III stars is simply expressed as $xi_m(m) propto m^{-alpha}$ (single power law), we find that $alpha gtrsim 2.8$ is needed in order for the merger rate density not to exceed the upper limit. In the future, the gravitational wave detectors such as Einstein telescope and Pre-DECIGO will observe BBH mergers at high redshift. We suggest that we may be able to impose a stringent limit on the Pop. III IMF by comparing the merger rate density obtained from future observations with that derived theoretically.
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