Population synthesis of black hole binary mergers from star clusters

Abstract

Black hole (BH) binary mergers formed through dynamical interactions in dense star clusters are believed to be one of the main sources of gravitational waves for Advanced LIGO and Virgo. Here we present a fast numerical method for simulating the evolution of star clusters with BHs, including a model for the dynamical formation and merger of BH binaries. Our method is based on Hénon's principle of balanced evolution, according to which the flow of energy within a cluster must be balanced by the energy production inside its core. Because the heat production in the core is powered by the BHs, one can then link the evolution of the cluster to the evolution of its BH population. This allows us to construct evolutionary tracks of the cluster properties including its BH population and its effect on the cluster and, at the same time, determine the merger rate of BH binaries as well as their eccentricity distributions. The model will be publicly available and includes the effects of a BH mass spectrum, massloss due to stellar evolution, the ejection of BHs due to natal and dynamical kicks, and relativistic corrections during binary-single encounters. We validate our method using direct N-body simulations, and find it to be in excellent agreement with results from recent Monte Carlo models of globular clusters. This establishes our new method as a robust tool for the study of BH dynamics in star clusters and the modelling of gravitational wave sources produced in these systems. Finally, we compute the rate and eccentricity distributions of merging BH binaries for a wide range of cluster initial conditions, spanning more than two orders of magnitude in mass and radius.In the dynamical formation scenario, the BH binaries are assembled through three body processes in the core of a star cluster, and subsequently harden and merge via dynamical binary-single interactions. Recent studies suggest that

Merger rate of black hole binaries from globular clusters: Theoretical error bars and comparison to gravitational wave data from GWTC-2

“…The evolution of the BHBs in our cluster models is computed using the fast code cBHBd. While the details of this method are described in Antonini and Gieles [34], here we give a brief summary of the model philosophy, including the full set of differential equations that are used to compute the secular evolution of the cluster models and the merging BHBs they produce.…”

“…The decrease in GC population mass by evaporation is K ∆ = K/2 = 16.3 +43.5 −8.87 . Using the approximation for the number of mergers in the observable redshift range from [34], N merge ∝ M 1.6 0 r −0.67…”

“…with t sev ≃ 2 Myr. We include here an additional (mass independent) term which was not present in Antonini and Gieles [34], and that accounts for cluster evaporatioṅ…”

“…The main reason for this is that standard numerical techniques such as Nbody and Monte Carlo simulations are still too slow to allow a full parameter space exploration. This is why in this study we employ our new population synthesis code clusterBHBdynamics (hereafter cBHBd) [34] to systematically vary assumptions made for the model parameters and over the full range of initial conditions relevant to real GCs. Thus, we examine the effect of these initial assumptions on the number and properties of merging BHBs using a suite of about 20 million cluster models.…”

“…In Section II we compute the GC formation rate density as a function of time using constraints from the present-day GCMF. In Section III we describe our population synthesis model and detail the modifications we made to it with respect to the version used in [34]. Section IV describes our main results.…”