Detections of gravitational waves 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 supernovae. 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 is remarkably robust against variations in the metallicity ( 3 ), the treatment of internal mixing ( 1 ), and stellar wind mass loss ( 4 ), making it the most robust predictor for the final stages of the evolution of massive stars. 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 the reaction rate within its 1 uncertainties shifts the location of the gap between 40 and 56 . 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.
The energy budget in common-envelope events (CEEs) is not well understood, with substantial uncertainty even over to what extent the recombination energy stored in ionized hydrogen and helium might ...be used to help envelope ejection. We investigate the reaction of a red giant envelope to heating which mimics limiting cases of energy input provided by the orbital decay of a binary during a CEE, specifically during the post-plunge-in phase during which the spiral-in has been argued to occur on a time-scale longer than dynamical. We show that the outcome of such a CEE depends less on the total amount of energy by which the envelope is heated than on how rapidly the energy was transferred to the envelope and on where the envelope was heated. The envelope always becomes dynamically unstable before receiving net heat energy equal to the envelope's initial binding energy. We find two types of outcome, both of which likely lead to at least partial envelope ejection: 'runaway' solutions in which the expansion of the radius becomes undeniably dynamical, and superficially 'self-regulated' solutions, in which the expansion of the stellar radius stops but a significant fraction of the envelope becomes formally dynamically unstable. Almost the entire reservoir of initial helium recombination energy is used for envelope expansion. Hydrogen recombination is less energetically useful, but is nonetheless important for the development of the dynamical instabilities. However, this result requires the companion to have already plunged deep into the envelope; therefore this release of recombination energy does not help to explain wide post-common-envelope orbits.
Gravitational-wave detections are starting to allow us to probe the physical processes in the evolution of very massive stars through the imprints they leave on their final remnants. Stellar ...evolution theory predicts the existence of a gap in the black hole mass distribution at high mass due to the effects of pair instability. Previously, we showed that the location of the gap is robust against model uncertainties, but it does depend sensitively on the uncertain rate. This rate is of great astrophysical significance and governs the production of oxygen at the expense of carbon. We use the open-source MESA stellar evolution code to evolve massive helium stars to probe the location of the mass gap. We find that the maximum black hole mass below the gap varies between and , depending on the strength of the uncertain reaction rate. With the first 10 gravitational-wave detections of black holes, we constrain the astrophysical S-factor for , at , to at 68% confidence. With detected binary black hole mergers, we expect to constrain the S-factor to within 10-30 . We also highlight a role for independent constraints from electromagnetic transient surveys. The unambiguous detection of pulsational pair-instability supernovae would imply that . Degeneracies with other model uncertainties need to be investigated further, but probing nuclear stellar astrophysics poses a promising science case for the future gravitational-wave detectors.
The majority of massive stars live in binary or multiple systems and will interact with a companion during their lifetimes, which helps to explain the observed diversity of core-collapse supernovae. ...Donor stars in binary systems can lose most of their hydrogen-rich envelopes through mass transfer. As a result, not only are the surface properties affected, but so is the core structure. However, most calculations of the core-collapse properties of massive stars rely on single-star models. We present a systematic study of the difference between the pre-supernova structures of single stars and stars of the same initial mass (11–21
M
⊙
) that have been stripped due to stable post-main-sequence mass transfer at solar metallicity. We present the pre-supernova core composition with novel diagrams that give an intuitive representation of the isotope distribution. As shown in previous studies, at the edge of the carbon-oxygen core, the binary-stripped star models contain an extended gradient of carbon, oxygen, and neon. This layer remains until core collapse and is more extended in mass for higher initial stellar masses. It originates from the receding of the convective helium core during core helium burning in binary-stripped stars, which does not occur in single-star models. We find that this same evolutionary phase leads to systematic differences in the final density and nuclear energy generation profiles. Binary-stripped star models have systematically higher total masses of carbon at the moment of core collapse compared to single-star models, which likely results in systematically different supernova yields. In about half of our models, the silicon-burning and oxygen-rich layers merge after core silicon burning. We discuss the implications of our findings for the “explodability”, supernova observations, and nucleosynthesis of these stars. Our models are publicly available and can be readily used as input for detailed supernova simulations.
Abstract
Gravitational-wave detectors are starting to reveal the redshift evolution of the binary black hole (BBH) merger rate,
R
BBH
(
z
). We make predictions for
R
BBH
(
z
) as a function of black ...hole mass for systems originating from isolated binaries. To this end, we investigate correlations between the delay time and black hole mass by means of the suite of binary population synthesis simulations,
COMPAS
. We distinguish two channels: the common envelope (CE), and the stable Roche-lobe overflow (RLOF) channel, characterized by whether the system has experienced a common envelope or not. We find that the CE channel preferentially produces BHs with masses below about 30
M
⊙
and short delay times (
t
delay
≲ 1 Gyr), while the stable RLOF channel primarily forms systems with BH masses above 30
M
⊙
and long delay times (
t
delay
≳ 1 Gyr). We provide a new fit for the metallicity-dependent specific star formation rate density based on the Illustris TNG simulations, and use this to convert the delay time distributions into a prediction of
R
BBH
(
z
). This leads to a distinct redshift evolution of
R
BBH
(
z
) for high and low primary BH masses. We furthermore find that, at high redshift,
R
BBH
(
z
) is dominated by the CE channel, while at low redshift, it contains a large contribution (∼40%) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above 30
M
⊙
will become increasingly scarce relative to less massive BBH systems. Evidence of this distinct evolution of
R
BBH
(
z
) for different BH masses can be tested with future detectors.
Massive binaries that merge as compact objects are the progenitors of gravitational-wave sources. Most of these binaries experience one or more phases of mass transfer, during which one of the stars ...loses all or part of its outer envelope and becomes a stripped-envelope star. The evolution of the size of these stripped stars is crucial in determining whether they experience further interactions and understanding their ultimate fate. We present new calculations of stripped-envelope stars based on binary evolution models computed with MESA. We use these to investigate their radius evolution as a function of mass and metallicity. We further discuss their pre-supernova observable characteristics and potential consequences of their evolution on the properties of supernovae from stripped stars. At high metallicity, we find that practically all of the hydrogen-rich envelope is removed, which is in agreement with earlier findings. Only progenitors with initial masses below 10
M
⊙
expand to large radii (up to 100
R
⊙
), while more massive progenitors remain compact. At low metallicity, a substantial amount of hydrogen remains and the progenitors can, in principle, expand to giant sizes (> 400
R
⊙
) for all masses we consider. This implies that they can fill their Roche lobe anew. We show that the prescriptions commonly used in population synthesis models underestimate the stellar radii by up to two orders of magnitude. We expect that this has consequences for the predictions for gravitational-wave sources from double neutron star mergers, particularly with regard to their metallicity dependence.
ABSTRACT
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 time-scales shorter than the convective turnover time-scale. This invalidates the steady-state assumption on which the classic mixing length theory relies. We compare the final BH masses computed with two different versions of the stellar evolutionary code $\tt{MESA}$: (i) using the default implementation of Paxton et al. (2018) and (ii) solving an additional equation accounting for the time-scale for convective deceleration. In the second grid, where stronger convection develops during the pulses and carries part of the energy, we find weaker pulses. This leads to lower amounts of mass being ejected and thus higher final BH masses of up to ∼$5\, \mathrm{M}_\odot$. The differences are much smaller for the progenitors that determine the maximum mass of BHs below the gap. This prediction is robust at $M_{\rm BH, max}\simeq 48\, \mathrm{M}_\odot$, at least within the idealized context of this study. This is an encouraging indication that current models are robust enough for comparison with the present-day gravitational-wave detections. However, the large differences between individual models emphasize the importance of improving the treatment of convection in stellar models, especially in the light of the data anticipated from the third generation of gravitational-wave detectors.
Present and upcoming time-domain astronomy efforts, in part driven by gravitational-wave follow-up campaigns, will unveil a variety of rare explosive transients in the sky. Here, we focus on ...pulsational pair-instability evolution, which can result in signatures that are observable with electromagnetic and gravitational waves. We simulated grids of bare helium stars to characterize the resulting black hole (BH) masses together with the ejecta composition, velocity, and thermal state. We find that the stars do not react “elastically” to the thermonuclear ignition in the core: there is not a one-to-one correspondence between pair-instability driven ignition and mass ejections, which causes ambiguity as to what is an observable pulse. In agreement with previous studies, we find that for initial helium core masses of 37.5
M
⊙
≲
M
He, init
≲ 41
M
⊙
, corresponding to carbon-oxygen core masses 27.5
M
⊙
≲
M
CO
≲ 30.1
M
⊙
, the explosions are not strong enough to affect the surface. With increasing initial helium core mass, they become progressively stronger causing first large radial expansion (41
M
⊙
≲
M
He, init
≲ 42
M
⊙
, corresponding to 30.1
M
⊙
≲
M
CO
≲ 30.8
M
⊙
) and, finally, also mass ejection episodes (for
M
He, init
≳ 42
M
⊙
, or
M
CO
≳ 30.8
M
⊙
). The lowest mass helium core to be fully disrupted in a pair-instability supernova is
M
He, init
≃ 80
M
⊙
, corresponding to
M
CO
≃ 55
M
⊙
. Models with
M
He, init
≳ 200
M
⊙
(
M
CO
≳ 114
M
⊙
) reach the photodisintegration regime, resulting in BHs with masses of
M
BH
≳ 125
M
⊙
. Although this is currently considered unlikely, if BHs from these models form via (weak) explosions, the previously-ejected material might be hit by the blast wave and convert kinetic energy into observable electromagnetic radiation. We characterize the hydrogen-free circumstellar material from the pulsational pair-instability of helium cores by simply assuming that the ejecta maintain a constant velocity after ejection. We find that our models produce helium-rich ejecta with mass of 10
−3
M
⊙
≲
M
CSM
≲ 40
M
⊙
, the larger values corresponding to the more massive progenitor stars. These ejecta are typically launched at a few thousand km s
−1
and reach distances of ∼10
12
− 10
15
cm before the core-collapse of the star. The delays between mass ejection events and the final collapse span a wide and mass-dependent range (from subhour to 10
4
years), and the shells ejected can also collide with each other, powering supernova impostor events before the final core-collapse. The range of properties we find suggests a possible connection with (some) type Ibn supernovae.
The theory for single stellar evolution predicts a gap in the mass distribution of black holes (BHs) between approximately 45 and 130 , 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 90 . We find no merging binary BH systems with a total mass exceeding 100 . 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, tentatively, (iii) the Hubble parameter.
The majority of massive stars, which are the progenitors of core-collapse supernovae (SNe), are found in close binary systems. In a previous work, we modeled the fraction of hydrogen-rich, Type II SN ...progenitors whose evolution is affected by mass exchange with their companion, finding this to be between ≈1/3 and 1/2 for most assumptions. Here we study in more depth the impact of this binary history of Type II SN progenitors on their final pre-SN core mass distribution, using population synthesis simulations. We find that binary star progenitors of Type II SNe typically end their life with a larger core mass than they would have had if they had lived in isolation because they gained mass or merged with a companion before their explosion. The combination of the diverse binary evolutionary paths typically leads to a marginally shallower final core mass distribution. In discussing our results in the context of the red supergiant problem, that is, the reported lack of detected high luminosity progenitors, we conclude that binary evolution does not seem to significantly affect the issue. This conclusion is quite robust against our variations in the assumptions of binary physics. We also predict that inferring the initial masses of Type II SN progenitors by “age-dating” their surrounding environment systematically yields lower masses compared to methods that probe the pre-SN core mass or luminosity. A robust discrepancy between the inferred initial masses of a SN progenitor from those different techniques could indicate an evolutionary history of binary mass accretion or merging.
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