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The production of black holes with masses between ∼50𝑀⊙−130𝑀⊙ is believed to be prohibited by stellar processes due to (pulsational) pair-instability supernovae. Hierarchical mergers of black holes in dense star clusters are proposed as a mechanism to explain the observations of binary black holes with component masses in this range by LIGO/Virgo. We study the efficiency with which hierarchical mergers can produce higher and higher masses using a simple model of the forward evolution of binary black hole populations in gravitationally bound systems like stellar clusters. The model relies on pairing probability and initial mass functions for the black hole population, along with numerical relativity fitting formulas for the mass, spin, and kick speed of the merger remnant. We carry out an extensive comparison of the predictions of our model with clusterBHBdynamics (cBHBD) model, a fast method for the evolution of star clusters and black holes therein. For this comparison, we consider three different pairing functions of black holes and consider simulations from high- and low-metallicity cluster environments from cBHBD. We find good agreements between our model and the cBHBD results when the pairing probability of binaries depends on both total mass and mass ratio. We also assess the efficiency of hierarchical mergers as a function of merger generation and derive the mass distribution of black holes using our model. We find that the multimodal features in the observed binary black hole mass spectrum—revealed by the nonparametric population models—can be interpreted by invoking the hierarchical merger scenario in dense, metal-rich, stellar environments. Further, the two subdominant peaks in the GWTC-3 component mass spectrum are consistent with second and third-generation mergers in metal-rich, dense environments. With more binary black hole detections, our model could be used to infer the black hole initial mass function and pairing probability exponents.
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On the mass distribution of the LIGO-Virgo-KAGRA events
The merging black hole binaries detected by the LIGO-Virgo-KAGRA (LVK) gravitational-wave observatories may help us shed light on how such binaries form. In addition, these detections can help us probe the hypothesized primordial black holes, a candidate for the observed abundance of dark matter. In this work, we study the black-hole mass distribution obtained from the LVK binary black hole merger events. In particular, we study the primary mass 𝑚1-distribution of the observed black hole binaries, and also the secondary to primary mass ratio 𝑞 =𝑚2/𝑚1 distribution. We obtain those distributions by first associating a skewed normal distribution to each event detected with a signal to noise ratio (SNR)>8 and then summing all such distributions. We also sample black hole binaries from two separate populations of merging binaries to which we associate a redshift from the redshift distribution. One of these is a stellar-origin population that follows a mass-distribution similar to the zero-age mass function of stars. The second population of black holes follows a Gaussian mass-distribution. Such a distribution could approximate a population of black hole binaries formed from earlier black hole mergers in dense stellar environments, or binaries of primordial black holes among other astrophysical processes. For those populations, we evaluate the number of detectable events and fit their combination to the LVK observations. In our work, we assume that stellar-origin binary black holes follow a similar mass-distribution to that of the initial mass-function of stars. We simulate a wide range of stellar-origin black-hole mass distributions. In agreement with the binary black hole merger rates-analysis of the LVK collaboration, we find that studying the observed LVK events can be fitted better by the combination of such a stellar-origin mass distribution and a Gaussian distribution, than by the stellar-origin mass distribution alone. As we demonstrate with some simple examples, our methodology allows for rapid testing of potential theoretical models for the binary black hole mergers to the observed events by LVK.
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- Award ID(s):
- 2207912
- PAR ID:
- 10654152
- Publisher / Repository:
- Physical Review D
- Date Published:
- Journal Name:
- Physical Review D
- Volume:
- 111
- Issue:
- 4
- ISSN:
- 2470-0010
- Subject(s) / Keyword(s):
- LIGO, gravitational waves, black holes, primordial black holes, dark matter
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The possible existence of primordial black holes in the stellar-mass window has received considerable attention because their mergers may contribute to current and future gravitational-wave detections. Primordial black hole mergers, together with mergers of black holes originating from Population III stars, are expected to dominate at high redshifts ( z ≳ 10). However, the primordial black hole merger rate density is expected to rise monotonically with redshift, while Population III mergers can only occur after the birth of the first stars. Next-generation gravitational-wave detectors such as the Cosmic Explorer (CE) and Einstein Telescope (ET) can access this distinctive feature in the merger rates as functions of redshift, allowing for direct measurement of the abundance of the two populations and hence for robust constraints on the abundance of primordial black holes. We simulate four months’ worth of data observed by a CE-ET detector network and perform hierarchical Bayesian analysis to recover the merger rate densities. We find that if the universe has no primordial black holes with masses of ( 10 M ⊙ ) , the projected upper limit on their abundance f PBH as a fraction of dark matter energy density may be as low as f PBH ∼ ( 10 − 5 ) , about two orders of magnitude lower than the current upper limits in this mass range. If instead f PBH ≳ 10 −4 , future gravitational-wave observations would exclude f PBH = 0 at the 95% credible interval.more » « less
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Abstract The population of binary black hole mergers identified through gravitational waves has uncovered unexpected features in the intrinsic properties of black holes in the universe. One particularly surprising and exciting result is the possible existence of black holes in the pair-instability mass gap, ∼50–120 M ⊙ . Dense stellar environments can populate this region of mass space through hierarchical mergers, with the retention efficiency of black hole merger products strongly dependent on the escape velocity of the host environment. We use simple toy models to represent hierarchical merger scenarios in various dynamical environments. We find that hierarchical mergers in environments with high escape velocities (≳300 km s −1 ) are efficiently retained. If such environments dominate the binary black hole merger rate, this would lead to an abundance of high-mass mergers that is potentially incompatible with the empirical mass spectrum from the current catalog of binary black hole mergers. Models that efficiently generate hierarchical mergers, and contribute significantly to the observed population, must therefore be tuned to avoid a “cluster catastrophe” of overproducing binary black hole mergers within and above the pair-instability mass gap.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/PhysRevD.111.043020
