Predictions of a simple parametric model of hierarchical black hole mergers

Abstract

Hierarchical mergers of black holes are proposed as a mechanism to explain the observations of binary black holes with component masses between $\sim 50M_{\odot }–130M_{\odot }$ by LIGO/Virgo, often referred to as "upper mass gap". 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 multi-modal features in the observed binary black hole mass spectrum -- revealed by the non-parametric 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 exponent.

18 pages, 5 figures, 1 table; matches with the published version

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• A Mid-Thirties Crisis: Dissecting the Properties of Gravitational Wave Sources Near the 35 Solar Mass Peak
• The origin channels of hierarchical binary black hole mergers in the LIGO-Virgo-KAGRA O1, O2, and O3 runs
• Identifying intermediate mass binary black hole mergers in AGN disks using LISA
• Gravitational-wave signatures of mirror (a)symmetry in binary black hole mergers: measurability and correlation to gravitational-wave recoil
• The Nature of Gravitational Wave Events with Host Environment Escape Velocities
• Effect of kick velocity on gravitational wave detection of binary black holes with space- and ground-based detectors
• Extending Ground-Based Gravitational-Wave Sensitivity to 5 Hz
• Examining the Gap in the Chirp Mass Distribution of Binary Black Holes
• Characterizing Binary Black Hole Subpopulations in GWTC-4 with Binned Gaussian Processes: On the Origins of the $35M_{\odot }$ Peak