Pair-instability Mass Gap Research Articles

Evolutionary tracks, ejecta, and ionizing photons from intermediate-mass to very massive stars with PARSEC

Recent advancements in stellar evolution modeling offer unprecedented accuracy in predicting the evolution and deaths of stars. We present new stellar evolutionary models computed with the updated V2.0 code for a comprehensive and homogeneous grid of metallicities and initial masses. Nuclear reaction networks, mass loss prescriptions, and the treatment of elemental mixing have all been updated in V2.0. We computed models for thirteen initial metallicities spanning Z = to Z = 0.03, with masses ranging from 2.0 to 2000 consisting of a library of over 1,100 (∼ 2100 tracks including pure-He models) full stellar evolution tracks. For each track, the evolution is followed from the pre-main-sequence to the most advanced early-asymptotic-giant-branch or the pre-supernova phases (depending on the stellar mass). Here, we describe the properties of the tracks and their chemical and structural evolution. We computed the final fates and the remnant masses and built the mass spectrum for each metallicity, finding that the combined black hole (BH) pair-instability mass gap spans just between 100 and 130 Moreover, the remnant masses provide models consistent with observed BH masses, such as those from the primaries of GW190521, Cygnus X-1, and Gaia BH3 binary systems. We computed and provided the chemical ejecta from stellar winds and explosive final fates, along with the ionizing photon rates. We show how metallicity affects the evolution, fates, ejecta, and ionizing photon counts from these stars. Our results show strong overall consistency with other tracks computed with different codes, and the most significant discrepancies arise for very massive stars (Mz > 120 due to the different treatment of mixing and mass loss. A comparison with a large sample of observed massive stars in the Tarantula Nebula of the Large Magellanic Cloud shows that our tracks nicely reproduce the majority of stars that lie on the main sequence. All the models are publicly available and can be retrieved in the parsec database.

Star Cluster Population of High Mass Black Hole Mergers in Gravitational Wave Data

Stellar evolution theories predict a gap in the black hole birth mass spectrum as the result of pair instability processes in the cores of massive stars. This gap, however, is not seen in the binary black hole masses inferred from gravitational wave data. One explanation is that black holes form dynamically in dense star clusters where smaller black holes merge to form more massive black holes, populating the mass gap. We show that this model predicts a distribution of the effective and precessing spin parameters, χeff and χp, within the mass gap that is insensitive to assumptions about black hole natal spins and other astrophysical parameters. We analyze the distribution of χeff as a function of primary mass for the black hole binaries in the third gravitational wave transient catalog. We infer the presence of a high mass and isotropically spinning population of black holes that is consistent with hierarchical formation in dense star clusters and a pair-instability mass gap with a lower edge at 44−4+6M⊙. We compute a Bayes factor B>104 relative to models that do not allow for a high mass population with a distinct χeff distribution. Upcoming data will enable us to tightly constrain the hierarchical formation hypothesis and refine our understanding of binary black hole formation. Published by the American Physical Society 2025

Are all models wrong? Falsifying binary formation models in gravitational-wave astronomy using exceptional events

Abstract As the catalogue of gravitational-wave transients grows, several entries appear ‘exceptional’ within the population. Tipping the scales with a total mass of ∼150M⊙, GW190521 likely contained black holes in the pair-instability mass gap. The event GW190814, meanwhile, is unusual for its extreme mass ratio and the mass of its secondary component. A growing model-building industry has emerged to provide explanations for such exceptional events, and Bayesian model selection is frequently used to determine the most informative model. However, Bayesian methods can only take us so far. They provide no answer to the question: does our model provide an adequate explanation for exceptional events in the data? If none of the models we are testing provide an adequate explanation, then it is not enough to simply rank our existing models—we need new ones. In this paper, we introduce a method to answer this question with a frequentist p-value. We apply the method to different models that have been suggested to explain the unusually massive event GW190521: hierarchical mergers in active galactic nuclei and globular clusters. We show that some (but not all) of these models provide adequate explanations for exceptionally massive events like GW190521.

Reconstructing the Genealogy of LIGO-Virgo Black Holes

We propose a Bayesian inference framework to predict the merger history of LIGO-Virgo binary black holes (BHs), whose binary components may have undergone hierarchical mergers in the past. The framework relies on numerical relativity predictions for the mass, spin, and kick velocity of the remnant BHs. This proposed framework computes the masses, spins, and kicks imparted to the remnant of the parent binaries, given the initial masses and spin magnitudes of the binary constituents. We validate our approach by performing an “injection study” based on a constructed sequence of hierarchically formed binaries. Noise is added to the final binary in the sequence, and the parameters of the “parent” and “grandparent” binaries in the merger chain are then reconstructed. This method is then applied to three GWTC-3 events: GW190521, GW200220_061928, and GW190426_190642. These events were selected because at least one of the binary companions lies in the putative pair-instability supernova mass gap, in which stellar processes alone cannot produce BHs. Hierarchical mergers offer a natural explanation for the formation of BHs in the pair-instability mass gap. We use the backward evolution framework to predict the parameters of the parents of the primary companion of these three binaries. For instance, the parent binary of GW190521 has masses 72−22+32M⊙ and 31−23+24M⊙ within the 90% credible interval. Astrophysical environments with escape speeds ≥100 km s−1 are preferred sites to host these events. Our approach can be readily applied to future high-mass gravitational wave events to predict their formation history under the hierarchical merger assumption.

Binary black hole mergers from Population III star clusters

Binary black holes (BBHs) that are born from the evolution of Population III (Pop. III) stars are one of the main high-redshift targets for next-generation ground-based gravitational-wave (GW) detectors. Their predicted initial mass function and lack of metals make them the ideal progenitors of black holes above the upper edge of the pair-instability mass gap, that is, with a mass higher than ~134 (241) M⊙ for stars that become (or do not become) chemically homogeneous during their evolution. We investigate the effects of cluster dynamics on the mass function of BBHs that are born from Pop. III stars by considering the main uncertainties on the mass function of Pop. III stars, the orbital properties of the binary systems, the star cluster mass, and the disruption time. In our dynamical models, at least ~5% and up to 100% BBH mergers in Pop. III star clusters have a primary mass m1 above the upper edge of the pair-instability mass gap. In contrast, only ≲3% isolated BBH mergers have a primary mass above the gap, unless their progenitors evolved as chemically homogeneous stars. The lack of systems with a primary and/or secondary mass inside the gap defines a zone of avoidance with sharp boundaries in the plane of the primary mass-mass ratio. Finally, we estimate the merger rate density of BBHs. In the most optimistic case, we find a maximum of ℛ ~ 200 Gpc-3 yr-1 at ɀ ~ 15 for BBHs that formed via dynamical capture. For comparison, the merger rate density of isolated Pop. III BBHs is ℛ ≤ 10 Gpc−3 yr−1 for the same model of Pop. III star formation history.

Hierarchical binary black hole mergers in globular clusters: Mass function and evolution with redshift

Hierarchical black hole (BH) mergers are one of the most straightforward mechanisms producing BHs inside and above the pair-instability mass gap. We investigated the impact of globular cluster (GC) evolution on hierarchical mergers, accounting for the uncertainties related to BH mass pairing functions on the predicted primary BH mass, mass ratio, and spin distribution. We find that the evolution of the host GC quenches the hierarchical BH assembly at the third generation, mainly due to cluster expansion powered by a central BH subsystem. Hierarchical mergers match the primary BH mass distribution from GW events for m1 > 50 M⊙ regardless of the assumed BH pairing function. At lower masses, however, different pairing functions lead to dramatically different predictions on the primary BH mass merger-rate density. We find that the primary BH mass distribution evolves with redshift, with a larger contribution from mergers with m1 ≥ 30 M⊙ for z ≥ 2. Finally, we calculate the mixing fraction of binary black holes (BBHs) from GCs and isolated binary systems. Our predictions are very sensitive to the spins, which favor a large fraction (> 0.6) of BBHs born in GCs in order to reproduce misaligned spin observations.

Observing black hole mergers beyond the pair-instability mass gap with next-generation gravitational wave detectors

Stellar evolution predicts the existence of a mass gap for black hole remnants produced by pair-instability supernova dynamics, whose lower and upper edges are very uncertain. We study the possibility of constraining the location of the upper end of the pair-instability mass gap, which is believed to appear around mmin∼130M⊙, using gravitational wave observations of compact binary mergers with next-generation ground-based detectors. While high metallicity may not allow for the formation of first-generation black holes on the “far side” beyond the gap, metal-poor environments containing population III stars could lead to such heavy black hole mergers. We show that, even in the presence of contamination from other merger channels, next-generation detectors will measure the location of the upper end of the mass gap with a relative precision close to Δmmin/mmin≃4%(Ndet/100)−1/2 at 90% CL, where Ndet is the number of detected mergers with both members beyond the gap. These future observations could reduce current uncertainties in nuclear and astrophysical processes controlling the location of the gap. Published by the American Physical Society 2024

The Evolution of Inclined Binary Black Holes in the Disks of Active Galactic Nuclei

The accretion disks that fuel active galactic nuclei (AGNs) may house numerous stars and compact objects, formed in situ or captured from nearby star clusters. Embedded neutron stars and black holes may form binaries and eventually merge, emitting gravitational waves detectable by LIGO/VIRGO. AGN disks are a particularly promising environment for the production of high-mass gravitational-wave events involving black holes in the pair-instability mass gap, and may facilitate electromagnetic counterparts to black hole binary mergers. However, many orders of magnitude separate the typical length scales of binary formation and those on which gravitational waves can drive binary inspirals, making binary mergers inside the disk uncertain. Previous hydrodynamical simulations of binaries have either been restricted to two dimensions entirely, or focused on binaries aligned with the midplane of the disk. Herein we present the first three-dimensional, high-resolution, local-shearing-box, inviscid hydrodynamical simulations of disk-embedded binaries over a range of orbital inclinations. We find that retrograde binaries can shrink up to 4 times as quickly as prograde binaries, and that all binaries not perfectly aligned (or anti-aligned) with the AGN disk are driven into alignment. An important consequence of this is that initially retrograde binaries will traverse the inclinations where von Zeipel–Lidov–Kozai oscillations can drive binary eccentricities to large values, potentially facilitating mergers. We also find that interactions with the AGN disk may excite eccentricities in retrograde binaries and cause the orbits of embedded binaries to precess.

Identifying heavy stellar black holes at cosmological distances with next-generation gravitational-wave observatories

ABSTRACT We investigate the detectability of single-event coalescing black hole binaries with total mass of $100\!-\!600{\, {\rm {M}}_{\odot }}$ at cosmological distances (5 ≲ z ≲ 20) with the next generation of terrestrial gravitational wave observatories, specifically Einstein Telescope and Cosmic Explorer. Our ability to observe these binaries is limited by the low-frequency performance of the detectors. Higher order multipoles of the gravitational wave signal are observable in these systems, and detection of such multipoles serves to both extend the mass range over which black hole binaries are observable and improve the recovery of their individual masses and redshift. For high-redshift systems of $\sim 200 {\, {\rm {M}}_{\odot }}$ we will be able to confidently infer that the redshift is at least z = 12, and for systems of $\sim 400 {\, {\rm {M}}_{\odot }}$ we can infer a minimum redshift of at least z = 8. We discuss the impact that these observations will have in narrowing uncertainties on the existence of the pair-instability mass gap, and their implications on the formation of the first stellar black holes that could be seeds for the growth of supermassive black holes powering high-z quasars.

On the Likely Dynamical Origin of GW191109 and Binary Black Hole Mergers with Negative Effective Spin

With the growing number of binary black hole (BBH) mergers detected by LIGO/Virgo/KAGRA, several systems have become difficult to explain via isolated binary evolution, having components in the pair-instability mass gap, high orbital eccentricities, and/or spin–orbit misalignment. Here we focus on GW191109_010717, a BBH merger with component masses of and M ⊙ and an effective spin of , which could imply a spin–orbit misalignment of more than π/2 rad for at least one of its components. Besides its component masses being in the pair-instability mass gap, we show that isolated binary evolution is unlikely to reproduce the proposed spin–orbit misalignment of GW191109 with high confidence. On the other hand, we demonstrate that BBHs dynamically assembled in dense star clusters would naturally reproduce the spin–orbit misalignment and masses of GW191109 and the rates of GW191109-like events if at least one of the components were to be a second-generation BH. Finally, we generalize our results to all events with a measured negative effective spin, arguing that GW200225 also has a likely dynamical origin.

Massive binary black holes from Population II and III stars

ABSTRACT Population III stars, born from the primordial gas in the Universe, lose a negligible fraction of their mass via stellar winds and possibly follow a top-heavy mass function. Hence, they have often been regarded as the ideal progenitors of massive black holes (BHs), even above the pair instability mass gap. Here, we evolve a large set of Population III binary stars (metallicity Z = 10−11) with our population-synthesis code sevn, and compare them with Population II binary stars (Z = 10−4). In our models, the lower edge of the pair-instability mass gap corresponds to a BH mass of ≈86 (≈91) M⊙ for single Population III (II) stars. Overall, we find only mild differences between the properties of binary BHs (BBHs) born from Population III and II stars, especially if we adopt the same initial mass function and initial orbital properties. Most BBH mergers born from Population III and II stars have primary BH mass below the pair-instability gap, and the maximum secondary BH mass is <50 M⊙. Only up to ≈3.3 per cent (≈0.09 per cent) BBH mergers from Population III (II) progenitors have primary mass above the gap. Unlike metal-rich binary stars, the main formation channel of BBH mergers from Population III and II stars involves only stable mass transfer episodes in our fiducial model.

Simulations of PBH formation at the QCD epoch and comparison with the GWTC-3 catalog

The probability of primordial black hole (PBH) formation is known to be boosted during the Quantum Chromodynamics (QCD) crossover due to a slight reduction of the equation of state. This induces a high peak and other features in the PBH mass distribution. But the impact of this variation during theprocess of PBH formation has so farnot been considered in numerical simulations.In this work we simulatethe formation of PBHs by taking into account the varying equation of state at the QCD epoch, compute the over-density threshold using different curvature profilesand find that the resulting PBH mass distributions are significantly impacted. The expected merger rate distributions of early and late PBH binaries is comparable to the ones inferred from the GWTC-3 catalog for dark matter fractions in PBHs within 0.1 < f PBH < 1. The distribution of gravitational-wave events estimated from the volume sensitivity could explain mergers around 30–50 M ⊙, with asymmetric masses like GW190814, or in the pair-instability mass gap like GW190521. However, none of the considered cases leads to a multi-modal distribution with a secondary peak around 8–15 M ⊙, as suggested by the GWTC-3 catalog, possibly pointing to a mixed population of astrophysical and primordial black holes.

New Determination of the 12C(α, γ)16O Reaction Rate and Its Impact on the Black-hole Mass Gap

We present a precise measurement of the asymptotic normalization coefficient (ANC) for the 16O ground state (GS) through the 12C(11B, 7Li)16O transfer reaction using the Quadrupole‐3‐Dipole (Q3D) magnetic spectrograph. The present work sheds light on the existing discrepancy of more than 2 orders of magnitude between the previously reported GS ANC values. This ANC is believed to have a strong effect on the 12C(α, γ)16O reaction rate by constraining the external capture to the 16O ground state, which can interfere with the high-energy tail of the 2+ subthreshold state. Based on the new ANC, we determine the astrophysical S-factor and the stellar rate of the 12C(α, γ)16O reaction. An increase of up to 21% in the total reaction rate is found within the temperature range of astrophysical relevance compared with the previous recommendation of a recent review. Finally, we evaluate the impact of our new rate on the pair-instability mass gap for black holes (BH) by evolving massive helium core stars using the MESA stellar evolution code. The updated 12C(α, γ)16O reaction rate decreases the lower and upper edges of the BH gap about 12% and 5%, respectively.

Formation of black holes in the pair-instability mass gap: hydrodynamical simulations of a head-on massive star collision

ABSTRACT The detection of the binary black hole merger GW190521, with primary black hole mass $85^{+21}_{-14} {\rm M}_{\odot }$, proved the existence of black holes in the theoretically predicted pair-instability gap ($\sim 60-120 \, {\rm M}_{\odot }$) of their mass spectrum. Some recent studies suggest that such massive black holes could be produced by the collision of an evolved star with a carbon–oxygen core and a main sequence star. Such a post-coalescence star could end its life avoiding the pair-instability regime and with a direct collapse of its very massive envelope. It is still not clear, however, how the collision shapes the structure of the newly produced star and how much mass is actually lost in the impact. We investigated this issue by means of hydrodynamical simulations with the smoothed particle hydrodynamics code StarSmasher, finding that a head-on collision can remove up to 12 per cent of the initial mass of the colliding stars. This is a non-negligible percentage of the initial mass and could affect the further evolution of the stellar remnant, particularly in terms of the final mass of a possibly forming black hole. We also found that the main sequence star can plunge down to the outer boundary of the core of the primary, changing the inner chemical composition of the remnant. The collision expels the outer layers of the primary, leaving a remnant with an helium-enriched envelope (reaching He fractions of about 0.4 at the surface). These more complex abundance profiles can be directly used in stellar evolution simulations of the collision product.

“Super-kilonovae” from Massive Collapsars as Signatures of Black Hole Birth in the Pair-instability Mass Gap

The core collapse of rapidly rotating massive ∼ 10M ⊙ stars (“collapsars”), and the resulting formation of hyperaccreting black holes, comprise a leading model for the central engines of long-duration gamma-ray bursts (GRBs) and promising sources of r-process nucleosynthesis. Here, we explore the signatures of collapsars from progenitors with helium cores ≳ 130M ⊙ above the pair-instability mass gap. While the rapid collapse to a black hole likely precludes prompt explosions in these systems, we demonstrate that disk outflows can generate a large quantity (up to ≳ 50M ⊙) of ejecta, comprised of ≳ 5–10M ⊙ in r-process elements and ∼ 0.1–1M ⊙ of 56Ni, expanding at velocities ∼0.1 c. Radioactive heating of the disk wind ejecta powers an optical/IR transient, with a characteristic luminosity ∼ 1042 erg s−1 and a spectral peak in the near-IR (due to the high optical/UV opacities of lanthanide elements), similar to kilonovae from neutron star mergers, but with longer durations ≳1 month. These “super-kilonovae” (superKNe) herald the birth of massive black holes ≳ 60M ⊙, which—as a result of disk wind mass loss—can populate the pair-instability mass gap “from above,” and could potentially create the binary components of GW190521. SuperKNe could be discovered via wide-field surveys, such as those planned with the Roman Space Telescope, or via late-time IR follow-up observations of extremely energetic GRBs. Multiband gravitational waves of ∼ 0.1–50 Hz from nonaxisymmetric instabilities in self-gravitating massive collapsar disks are potentially detectable by proposed observatories out to hundreds of Mpc; in contrast to the “chirp” from binary mergers, the collapsar gravitational-wave signal decreases in frequency as the disk radius grows (“sad trombone”).

GW190425, GW190521 and GW190814: Three candidate mergers of primordial black holes from the QCD epoch

The two recent gravitational-wave events GW190425 and GW190814 from the third observing run of LIGO/Virgo have both a companion which is unexpected if originated from a neutron star or a stellar black hole, with masses [ 1 . 6 − 2 . 5 ] M ⊙ and [ 2 . 5 − 2 . 7 ] M ⊙ and merging rates 46 0 − 360 + 1050 and 7 − 6 + 16 events/yr/Gpc 3 respectively, at 90% confidence level. Moreover, the recent event GW190521 has black hole components with masses 67 and 91 M ⊙ , and therefore lies in the so-called pair-instability mass gap, where there should not be direct formation of stellar black holes. The possibility that all of these compact objects are Primordial Black Holes (PBHs) is investigated. The known thermal history of the Universe predicts that PBH formation is boosted at the time of the QCD transition, inducing a peak in their distribution at this particular mass scale, and a bump around 30 − 50 M ⊙ . We find that the merging rates inferred from GW190425, GW190521 and GW190814 are consistent with PBH binaries formed by capture in dense halos in the matter era or in the early universe. At the same time, the rate of black hole mergers around 30 M ⊙ and of sub-solar PBH mergers do not exceed the LIGO/Virgo limits. Such PBHs could explain a significant fraction, or even the totality of the Dark Matter, but they must be sufficiently strongly clustered in order to be consistent with current astrophysical limits.

Dynamics of binary black holes in young star clusters: the impact of cluster mass and long-term evolution

ABSTRACT Dynamical interactions in dense star clusters are considered one of the most effective formation channels of binary black holes (BBHs). Here, we present direct N-body simulations of two different star cluster families: low-mass (∼500–800 M⊙) and relatively high-mass star clusters (≥5000 M⊙). We show that the formation channels of BBHs in low- and high-mass star clusters are extremely different and lead to two completely distinct populations of BBH mergers. Low-mass clusters host mainly low-mass BBHs born from binary evolution, while BBHs in high-mass clusters are relatively massive (chirp mass up to ∼100 M⊙) and driven by dynamical exchanges. Tidal disruption dramatically quenches the formation and dynamical evolution of BBHs in low-mass clusters on a very short time-scale (≲100 Myr), while BBHs in high-mass clusters undergo effective dynamical hardening until the end of our simulations (1.5 Gyr). In high-mass clusters, we find that 8 per cent of BBHs have primary mass in the pair-instability mass gap at metallicity Z = 0.002, all of them born via stellar collisions, while only one BBH with primary mass in the mass gap forms in low-mass clusters. These differences are crucial for the interpretation of the formation channels of gravitational-wave sources.

"Super-Kilonovae" from Massive Collapsars as Signatures of Black Bole Birth in the Pair-instability Mass Gap

"Super-Kilonovae" from Massive Collapsars as Signatures of Black Bole Birth in the Pair-instability Mass Gap

"Super-Kilonovae" from Massive Collapsars as Signatures of Black Bole Birth in the Pair-instability Mass Gap

"Super-Kilonovae" from Massive Collapsars as Signatures of Black Bole Birth in the Pair-instability Mass Gap

Formation of black holes in the pair-instability mass gap: Evolution of a post-collision star

ABSTRACT The detection of GW190521 by the LIGO–Virgo collaboration has revealed the existence of black holes (BHs) in the pair-instability (PI) mass gap. Here, we investigate the formation of BHs in the PI mass gap via star–star collisions in young stellar clusters. To avoid PI, the stellar-collision product must have a relatively small core and a massive envelope. We generate our initial conditions from the outputs of a hydrodynamical simulation of the collision between a core helium burning star (∼58 M⊙) and a main-sequence star (∼42 M⊙). The hydrodynamical simulation allows us to take into account the mass lost during the collision (∼12 M⊙) and to build the chemical composition profile of the post-collision star. We then evolve the collision product with the stellar evolution codes parsec and mesa. We find that the post-collision star evolves through all the stellar burning phases until core collapse, avoiding PI. At the onset of core collapse, the post-collision product is a blue supergiant star. We estimate a total mass-loss of about 1 M⊙ during the post-collision evolution, due to stellar winds and shocks induced by neutrino emission in a failed supernova. The final BH mass is ≈87 M⊙. Therefore, we confirm that the collision scenario is a suitable formation channel to populate the PI mass gap.