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Coalescence Forensics: Weighing the Hosts of Hierarchical Binary Black Hole Mergers

Avinash Tiwari, Shasvath J. Kapadia

TL;DR

This work introduces a framework to infer the mass of a star cluster hosting a hierarchical BBH merger from a single GW event by enforcing two dynamical requirements: retention of the 2G remnant and a subsequent encounter. It builds analytic scaling relations within a Plummer-cluster model to connect retention, encounter probabilities, and recoil velocity to the host mass, and then performs exact marginalization over nuisance parameters to obtain a posterior on M. Applied to GW241011 and GW241110, the inferred host masses span roughly 10^{5.7}-10^{7.7} M⊙, compatible with heavy globular clusters or nuclear star clusters depending on the recoil-velocity prior, illustrating a viable single-event, dynamics-based host-environment inference. The results highlight the sensitivity to recoil priors and size-mass scaling and demonstrate that even without electromagnetic counterparts, meaningful constraints on BBH environments can be drawn from hierarchical-merger dynamics at the level of individual events.

Abstract

We present a novel framework to infer the mass of clusters that host hierarchical binary black hole (BBH) mergers detected with gravitational-waves (GWs), on a single event basis. We show that the requirement that a second-generation (2G) remnant be retained, and subsequently undergo a dynamical encounter, places strong constraints on the mass of the cluster. Using a Plummer model as a readily interpretable baseline, we derive analytic scaling relations between the peak of the inferred host mass posterior, the GW-driven recoil velocity of the remnant, and the parameters that determine the structure of the host. We then perform exact numerical marginalization over thermal and recoil velocities, angles, and cluster structure parameters, to infer the host-mass posterior. We apply our framework to putative hierarchical mergers GW241011 and GW241110, and infer the masses of their hosts on a single-event basis. We find that these are consistent with either heavy globular clusters or nuclear star clusters, with inferred masses spanning $10^{5.7 - 7.7} M_{\odot}$ at $68\%$ confidence depending on the 2G recoil velocity distribution used.

Coalescence Forensics: Weighing the Hosts of Hierarchical Binary Black Hole Mergers

TL;DR

This work introduces a framework to infer the mass of a star cluster hosting a hierarchical BBH merger from a single GW event by enforcing two dynamical requirements: retention of the 2G remnant and a subsequent encounter. It builds analytic scaling relations within a Plummer-cluster model to connect retention, encounter probabilities, and recoil velocity to the host mass, and then performs exact marginalization over nuisance parameters to obtain a posterior on M. Applied to GW241011 and GW241110, the inferred host masses span roughly 10^{5.7}-10^{7.7} M⊙, compatible with heavy globular clusters or nuclear star clusters depending on the recoil-velocity prior, illustrating a viable single-event, dynamics-based host-environment inference. The results highlight the sensitivity to recoil priors and size-mass scaling and demonstrate that even without electromagnetic counterparts, meaningful constraints on BBH environments can be drawn from hierarchical-merger dynamics at the level of individual events.

Abstract

We present a novel framework to infer the mass of clusters that host hierarchical binary black hole (BBH) mergers detected with gravitational-waves (GWs), on a single event basis. We show that the requirement that a second-generation (2G) remnant be retained, and subsequently undergo a dynamical encounter, places strong constraints on the mass of the cluster. Using a Plummer model as a readily interpretable baseline, we derive analytic scaling relations between the peak of the inferred host mass posterior, the GW-driven recoil velocity of the remnant, and the parameters that determine the structure of the host. We then perform exact numerical marginalization over thermal and recoil velocities, angles, and cluster structure parameters, to infer the host-mass posterior. We apply our framework to putative hierarchical mergers GW241011 and GW241110, and infer the masses of their hosts on a single-event basis. We find that these are consistent with either heavy globular clusters or nuclear star clusters, with inferred masses spanning at confidence depending on the 2G recoil velocity distribution used.
Paper Structure (12 sections, 28 equations, 2 figures, 1 table)

This paper contains 12 sections, 28 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. The Plummer Sphere
  4. Retention Probability
  5. Encounter Probability
  6. Mode of the cluster mass posterior
  7. Results and Discussion
  8. Acknowledgments
  9. The Plummer Velocity Distribution
  10. Isotropic Averaging of the Retention Probability
  11. Mean Square Plummer Velocity
  12. Mass-scaling of Encounter Probability

Figures (2)

  • Figure 1: Schematic illustration of the sequence of events leading to a hierarchical 1G+2G black-hole merger in a dense stellar cluster. Such a merger requires (i) retention of the 2G remnant following the initial 1G+1G merger, and (ii) a subsequent dynamical encounter between the retained remnant and a stellar system containing at least one 1G BH, shown here for illustration as a 1G+main-sequence-star binary. In this encounter, the lighter main-sequence star is ejected and the 2G remnant forms a binary with the 1G black hole, which subsequently merges. The observed GW signal enables direct inference of the masses and spins of the merging components, and hence a posterior on the recoil velocity of the 2G remnant. Combined with the requirements of retention and encounter, this information yields a preferred mass scale for the host cluster in which the hierarchical merger occurred.
  • Figure 2: Posteriors of inferred cluster mass under different assumptions for GW241011 (left) and GW241110 (right). The posteriors correspond to rows 1, 3, and 5 in Table \ref{['tab:cluster_mass_inference']}.