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

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.

Figures (11)

• Figure 1: We show the Jensen--Shannon divergence (JSD; color-coded) between the kick-velocity distributions predicted by the new gwModel_flow_prec model and the widely-used analytic model HLZ. The kick distributions for each point in the $q, |\chi_1|, |\chi_2|$ space is generated by drawing 5000 spin orientation angles from an isotropic distribution. The symbol size scales with the mass ratio: smaller circles correspond to smaller $q$, while larger circles correspond to larger $q$. There is substantial discrepancies between the two models when one or both spin magnitudes are small and/or when the mass ratio becomes increasingly asymmetric. More details are in Section \ref{['sec:model']}.
• Figure 2: Probability of retaining the merger remnant of a BBH (shown by the colorbar) as a function of the BBH mass ratio and the maximum black-hole spins, shown for different cluster escape speeds: 50$-$500 km s$^{-1}$ (increasing from top to bottom). The left columns show the results obtained using the HLZ recoil-kick model, while the right columns show the results for the gwModel_flow_prec. The black-hole spins are drawn from a uniform distribution in the range $[0, \chi_{\max}]$ and spin angles are chosen isotropically. Details are in Section \ref{['sec:pret']}.
• Figure 3: For creating compact objects in our cluster simulations, we use the updated single-star evolution (SSE) delayed prescription of Refs. Hurley:2000pk2002MNRAS.329..897HBanerjee:2019jjs. Here, we show the masses of remnant black holes formed from stellar collapse as a function of the progenitor star's ZAMS mass, with metallicity indicated in the color bar. More details are in Section \ref{['sec:pimbh']}.
• Figure 4: Probability of forming a black hole mass of at least $250\,M_\odot$ through successive mergers as a function of the BH seed mass, shown for different cluster escape speeds: 200 km s$^{-1}$ (top panels), and 500 km s$^{-1}$ (bottom panels). The left columns show the results obtained using the HLZ recoil-kick model, while the right columns show the results for the gwModel_flow_prec. The black-hole spins are drawn from a uniform distribution in the range $[0, \chi_{\max}]$. We choose metalicity of $Z=0.005$. Details are in Section \ref{['sec:pimbh']}.
• Figure 5: Distribution of retained black-hole masses and spins across five merger generations. For reference, we show the mass and spin inference of BHs in the GW231123 binary in black and blue error bars throughout the paper. In each panel, the upper subplot corresponds to the HLZ model and the middle subplot to the gwModel_flow_prec whereas the lower subplot shows the mass distribution of the retained remnants. The spins of the 1G black-hole population are drawn uniformly from $[0,1]$, and the initial black-hole masses from $[3,60]\,M_\odot$. We vary the initial mass distribution (uniform/power-law) and the pairing function (random/model A/model B, see Eqs. \ref{['eq:model_A']} and \ref{['eq:model_B']}) one at a time: uniform IMF with random pairing (upper left), power-law IMF with random pairing (upper right), uniform IMF with model A pairing (lower left), and uniform IMF with model B pairing (lower right). In all cases, escape velocities are drawn uniformly from $[1,300]$ km s$^{-1}$, typical of globular clusters. Details are in Section \ref{['sec:toy_ng_problem']}.