The mean free path approximation and stellar collisions in star clusters: Numerical exploration of the analytic rates and the role of perturbations on binary star mergers

Abstract

In this paper we compute predictions for the number of stellar collisions derived from analytic models based on the mean free path (MFP) approximation and compare them to the results of $N$-body simulations. Our goal is to identify the cluster conditions under which the MFP approximation remains valid. Adopting a range of particle numbers ($100\le N\le 5000$) and different combinations of particle masses and radii, we explore three different channels leading to stellar collisions, all of which are expected to occur in realistic stellar environments. At high densities, binaries form from isolated three-body interactions of single stars. Hence, we consider collisions between single stars and collisions involving binary stars, after they form in our simulations. For the latter, we consider two channels for mergers, namely direct stellar collisions during chaotic single-binary interactions and perturbation-driven mergers of binaries due to random walks in eccentricity approaching unity. In the densest systems considered here, a very massive object is formed at the cluster centre, causing local stellar orbits to become increasingly Keplerian and the assumptions going into our analytic model to break down. Before reaching this limit, we obtain excellent agreement between our theoretical predictions and the simulations: the analytic rates are typically accurate to within one standard deviation for the entire parameter space considered here, but the agreement is best for short integration times. Our results have direct implications for blue straggler formation in dense star clusters, and stellar mergers in galactic nuclei hosting massive black holes.

13 pages, 7 figures. Accepted by MNRAS

References in corpus (14)

• Formation of the first nuclear clusters and massive black holes at high redshift
• A Binary Origin for Blue Stragglers in Globular Clusters
• Constraining the high redshift formation of black hole seeds in nuclear star clusters with gas inflows
• Dynamical Formation of Close Binaries in Globular Clusters II: Cataclysmic Variables
• Secular Evolution Of Binaries Near Massive Black Holes: Formation of compact binaries, merger/collision products and G2-like objects
• Formation of supermassive black hole seeds in nuclear star clusters via gas accretion and runaway collisions
• The Blue Straggler Star Population in NGC 1261: Evidence for a Post-Core-Collapse Bounce State
• The chaotic four-body problem in Newtonian gravity I: Identical point-particles
• Formation of SMBH seeds in Pop III star clusters through collisions : the importance of mass loss
• The effects of a background potential in star cluster evolution: a delay in the relaxation time-scale and runaway collision processes
• Small-N collisional dynamics III: The battle for the realm of not-so-small-N
• A study of the blue straggler population of the old open cluster Collinder 261
• Small-N collisional dynamics II: Roaming the realm of not-so-small-N
• Small-N Collisional Dynamics V: Beyond the Realm of Not-So-Small-N

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