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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. 

General relativity (GR) has proven to be a highly successful theory of gravity since its inception. The theory has thrivingly passed numerous experimental tests, predominantly in weak gravity, low relative speeds, and linear regimes, but also in the strong-field and very low-speed regimes with binary pulsars. Observable gravitational waves (GWs) originate from regions of spacetime where gravity is extremely strong, making them a unique tool for testing GR, in previously inaccessible regions of large curvature, relativistic speeds, and strong gravity. Since their first detection, GWs have been extensively used to test GR, but no deviations have been found so far. Given GR’s tremendous success in explaining current astronomical observations and laboratory experiments, accepting any deviation from it requires a very high level of statistical confidence and consistency of the deviation across GW sources. In this paper, we compile a comprehensive list of potential causes that can lead to a false identification of a GR violation in standard tests of GR on data from current and future ground-based GW detectors. These causes include detector noise, signal overlaps, gaps in the data, detector calibration, source model inaccuracy, missing physics in the source and in the underlying environment model, source misidentification, and mismodeling of the astrophysical population. We also provide a rough estimate of when each of these causes will become important for tests of GR for different detector sensitivities. We argue that each of these causes should be thoroughly investigated, quantified, and ruled out before claiming a GR violation in GW observations. 

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. 

Detections of gravitational waves emitted from binary black hole coalescences allow us to probe the strong-field dynamics of general relativity (GR). One can compare the observed gravitational-wave signals with theoretical waveform models to constrain possible deviations from GR. Any physics that is not included in these waveform models might show up as apparent GR deviations. The waveform models used in current tests of GR describe binaries on quasicircular orbits, since most of the binaries detected by ground-based gravitational-wave detectors are expected to have negligible eccentricities. Thus, a signal from an eccentric binary in GR is likely to show up as a deviation from GR in the current implementation of these tests. We study the response of four standard tests of GR to eccentric binary black hole signals with the forecast O4 sensitivity of the LIGO-Virgo network. Specifically, we consider two parametrized tests (TIGER and FTI), the modified dispersion relation test, and the inspiral-merger-ringdown consistency test. To model eccentric signals, we use nonspinning numerical relativity simulations from the SXS catalog with three mass ratios (1, 2, 3), which we scale to a redshifted total mass of 80M⊙ and luminosity distance of 400 Mpc. For each of these mass ratios, we consider signals with eccentricities of ∼0.05 and ∼0.1 at 17 Hz. We find that signals with larger eccentricity lead to very significant false GR deviations in most tests while signals having smaller eccentricity lead to significant deviations in some tests. For the larger eccentricity cases, one would even get a deviation from GR with TIGER at ∼90% credibility at a distance of ≳1.5 Gpc. Thus, it will be necessary to exclude the possibility of an eccentric binary in order to make any claim about detecting a deviation from GR.