Evolution of Compact-Binary Populations in Globular Clusters: A Boltzmann Study. I. The Continuous Limit

TL;DR

This paper develops a Boltzmann-based model to study the evolution of compact binary populations in globular clusters, focusing on formation, destruction, and orbital evolution processes, and compares results with observations.

Contribution

It introduces a continuous limit approach to stochastic encounter processes in modeling globular cluster binary evolution, aligning theoretical predictions with observations.

Findings

Model predictions of X-ray source numbers match observed scaling with cluster encounter rates.

The approach successfully reproduces the observed orbital-period distribution of X-ray binaries.

Results support the validity of the continuous limit approximation for stochastic processes.

Abstract

We explore a Boltzmann scheme for studying the evolution of compact binary populations of globular clusters. We include processes of compact-binary formation by tidal capture and exchange encounters, binary destruction by dissociation and other mechanisms, and binary hardening by encounters, gravitational radiation and magnetic braking, as also the orbital evolution during mass transfer, following Roche lobe contact. For the encounter processes which are stochastic in nature, we study the probabilistic, continuous limit in this introductory work, deferring the specific handling of the stochastic terms to the next step. We focus on the evolution of (a) the number of X-ray sources N_{XB} in globular clusters, and (b) the orbital-period distribution of the X-ray binaries, as a result of the above processes. We investigate the dependence of N_{XB} on two essential cluster properties, namely, the star-star and star-binary encounter-rate parameters 'Gamma' and 'gamma', which we call Verbunt parameters. We compare our model results with observation, showing that the model values of N_{XB} and their expected scaling with the Verbunt parameters are in good agreement with results from recent X-ray observations of Galactic globular clusters, encouraging us to build more detailed models.