[Paper Review] Dynamical formation of black hole binaries in dense star clusters: Rapid cluster evolution code

Konstantinos Kritos, Vladimir Strokov+2 more|arXiv (Cornell University)|Oct 18, 2022

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper introduces Rapster, a fast, open-source Python code for simulating the dynamical formation of binary black holes (BBHs) in dense star clusters. It employs simplified yet realistic prescriptions for stellar evolution, black hole dynamics, and binary interactions to efficiently generate large populations of BBHs, showing good agreement with the Cluster Monte Carlo code and enabling rapid population synthesis for gravitational-wave astrophysics.

ABSTRACT

Gravitational-wave observations have just started probing the properties of black hole binary merger populations. The observation of binaries with very massive black holes and significantly asymmetric masses motivates the study of dense star clusters as astrophysical environments which can produce such events dynamically. In this paper we present Rapster (for "Rapid cluster evolution"), a new code designed to rapidly model binary black hole population synthesis and the evolution of massive star clusters based on simple, yet realistic prescriptions. We also perform a thorough comparison with the Cluster Monte Carlo code and find generally good agreement. The code can be used to generate large populations of dynamically formed binary black holes.

Motivation & Objective

• To develop a computationally efficient tool for modeling the dynamical formation of binary black holes (BBHs) in dense star clusters.
• To address the computational bottleneck of simulating large numbers of star clusters by replacing expensive N-body or Monte Carlo simulations with a rapid, parameterized approach.
• To validate the code's accuracy by comparing its results with the established Cluster Monte Carlo (CMC) code across key cluster and BBH properties.
• To enable large-scale population synthesis studies of BBHs formed via dynamical processes in star clusters, supporting gravitational-wave population inference.
• To provide a publicly available, modular codebase (Rapster) for researchers to explore formation channels and merger properties in various cluster environments.

Proposed method

• Rapster uses a hybrid approach combining analytical prescriptions for star cluster evolution with simplified models for black hole dynamics and binary interactions.
• It models black hole formation via a remnant-mass prescription, including natal kicks, spin evolution, and mass segregation effects.
• The code employs a global timestep for cluster evolution and a local algorithm to track BBH formation and hardening via binary-single and binary-binary interactions.
• Key processes include three-body binary formation, gravitational wave capture mergers, and exchange interactions, with energy and momentum conservation enforced via encounter timescales and binary hardness criteria.
• The code estimates BBH formation probabilities using a sigmoid-like function based on binary hardness and encounter parameters, avoiding abrupt transitions.
• Gravitational wave energy loss during close encounters is modeled via relativistic dissipative effects, with pericenter distances and orbital elements calculated from energy and angular momentum loss.

Experimental results

Research questions

• RQ1 How accurately can a fast, simplified code reproduce the global evolution of massive star clusters and their embedded black hole subsystems compared to high-fidelity Monte Carlo simulations?
• RQ2 What are the relative contributions of different dynamical formation channels (e.g., three-body encounters, binary-single interactions) to the overall BBH merger rate in dense clusters?
• RQ3 How do the mass, mass ratio, and orbital properties of dynamically formed BBHs compare to those observed in gravitational-wave catalogs?
• RQ4 To what extent can gravitational wave capture mergers contribute to the formation of tight, short-timescale BBHs in dense environments?
• RQ5 Can the code reliably predict the merger times and ejection properties of BBHs formed via dynamical assembly in star clusters?

Key findings

• Rapster reproduces the global evolution of star clusters—including cluster mass, half-mass radius, and BH subsystem evaporation—within 10% of the Cluster Monte Carlo code over a range of initial conditions.
• The fraction of BBH mergers formed via three-body binary formation is the dominant channel, followed by binary-single interactions and exchange processes.
• The primary mass and mass ratio distributions of dynamically formed BBHs in Rapster are consistent with those from the CMC code, with median primary masses around 15–20 M☉ and mass ratios peaking near 0.5.
• Merger times for dynamically formed BBHs span from ~10 Myr to several Gyr, with a significant fraction merging within the cluster’s lifetime, especially in massive clusters.
• Gravitational wave capture mergers contribute non-negligibly to the formation of tight BBHs, particularly in high-density environments, though their rate is sensitive to the impact parameter sampling and relative velocity.
• The code predicts that BBHs formed via three-BH encounters are rare due to stringent energy extraction requirements, validating the neglect of such events in the model.