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Abstract 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 ${72}_{-22}^{+32}{M}_{\odot }$and ${31}_{-23}^{+24}{M}_{\odot }$within the 90% credible interval. Astrophysical environments with escape speeds ≥100 km s⁻¹are 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. 

Abstract We report the observation of a coalescing compact binary with component masses 2.5–4.5M_⊙and 1.2–2.0M_⊙(all measurements quoted at the 90% credible level). The gravitational-wave signal GW230529_181500 was observed during the fourth observing run of the LIGO–Virgo–KAGRA detector network on 2023 May 29 by the LIGO Livingston observatory. The primary component of the source has a mass less than 5M_⊙at 99% credibility. We cannot definitively determine from gravitational-wave data alone whether either component of the source is a neutron star or a black hole. However, given existing estimates of the maximum neutron star mass, we find the most probable interpretation of the source to be the coalescence of a neutron star with a black hole that has a mass between the most massive neutron stars and the least massive black holes observed in the Galaxy. We provisionally estimate a merger rate density of ${55}_{-47}^{+127}{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$for compact binary coalescences with properties similar to the source of GW230529_181500; assuming that the source is a neutron star–black hole merger, GW230529_181500-like sources may make up the majority of neutron star–black hole coalescences. The discovery of this system implies an increase in the expected rate of neutron star–black hole mergers with electromagnetic counterparts and provides further evidence for compact objects existing within the purported lower mass gap. 

The production of black holes with masses between ∼50⁢𝑀⊙−130⁢𝑀⊙ 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. 

The inspiral-merger-ringdown (IMR) consistency test checks the consistency of the final mass and final spin of a binary black hole merger remnant, independently inferred via the inspiral and merger-ringdown parts of the waveform. As binaries are expected to be nearly circularized when entering the frequency band of ground-based detectors, tests of general relativity (GR) currently employ quasicircular waveforms. We quantify the effect of residual orbital eccentricity on the IMR consistency test. We find that eccentricity causes a significant systematic bias in the inferred final mass and spin of the remnant black hole at an orbital eccentricity (defined at 10 Hz) of e0≳0.1 in the LIGO band (for a total binary mass in the range 65-200M⊙). For binary black holes observed by Cosmic Explorer (CE), the systematic bias becomes significant for e0≳0.015 (for 200-600M⊙ systems). This eccentricity-induced bias on the final mass and spin leads to an apparent inconsistency in the IMR consistency test, manifesting as a false violation of GR. Hence, eccentric corrections to waveform models are important for constructing a robust test of GR, especially for third-generation detectors. We also estimate the eccentric corrections to the relationship between the inspiral parameters and the final mass and final spin; they are shown to be quite small.