Kick matters: The impact of a new recoil model on the retention of hierarchical black-hole remnants in globular clusters

TL;DR

This paper introduces a new recoil kick model for black-hole mergers in globular clusters, showing it increases retention of merger remnants and alters their mass and spin distributions, impacting hierarchical black hole formation.

Contribution

The study develops and applies a state-of-the-art recoil model based on numerical relativity and data-driven techniques, improving predictions of black hole retention in clusters.

Findings

Increased retention probability of hierarchical-merger remnants.

Altered mass and spin distributions of black holes.

Implications for massive binary events like GW231123.

Abstract

In globular clusters, hierarchical mergers are among the most promising pathways to forming massive black holes such as GW231123. A key factor determining whether a merger-remnant black hole will be retained in these environments and thus participate in subsequent hierarchical mergers is the recoil kick velocity. Analytic models for the recoil velocity are currently employed in nearly all population-synthesis frameworks. We instead use a state-of-the-art recoil-kick model gwModel_flow_prec developed from a combination of numerical-relativity and black-hole perturbation-theory data, together with data-driven techniques such as normalizing flows and the post-Newtonian structure of the kick. Employing both back-of-the-envelope estimates and detailed N-body as well as semi-analytical cluster simulations, we show that gwModel_flow_prec leads to a noticeable increase in the retention probability of hierarchical-merger remnants compared to the previously used analytic model and changes the mass and spin distribution of the black holes formed through hierarchical mergers. Additionally, we discuss the implications of our results in the context of massive binaries such as GW231123.