Stellar collisions in flattened and rotating Pop. III star clusters

TL;DR

This study models dense, rotating, and flattened Pop. III star clusters to understand stellar collision rates, revealing that cluster shape and rotation have minor effects, but influence star retention and collision outcomes.

Contribution

It provides a detailed analysis of how flattening and rotation affect stellar collision rates and star retention in Pop. III clusters using Miyamoto-Nagai models.

Findings

Collision rates depend mainly on star number and initial radii.

Rotation affects collision rates by at most 20%.

Flattening changes collision rates by less than 25%.

Abstract

Fragmentation often occurs in disk-like structures, both in the early Universe and in the context of present-day star formation. Supermassive black holes (SMBHs) are astrophysical objects whose origin is not well understood; they weigh millions of solar masses and reside in the centers of galaxies. An important formation scenario for SMBHs is based on collisions and mergers of stars in a massive cluster, in which the most massive star moves to the center of the cluster due to dynamical friction. This increases the rate of collisions and mergers since massive stars have larger collisional cross sections. This can lead to runaway growth of a very massive star which may collapse to become an intermediate-mass black hole. Here we investigate the dynamical evolution of Miyamoto-Nagai models that allow us to describe dense stellar clusters, including flattening and different degrees of rotation. We find that the collisions in these clusters depend mostly on the number of stars and the initial stellar radii for a given radial size of the cluster. By comparison, rotation seems to affect the collision rate by at most $20\%$. For flatness, we compared spherical models with systems that have a scale height of about $10\%$ of their radial extent, in this case finding a change in the collision rate of less than $25\%$. Overall, we conclude that the parameters only have a minor effect on the number of collisions. Our results also suggest that rotation helps to retain more stars in the system, reducing the number of escapers by a factor of $2-3$ depending on the model and the specific realization. After two million years, a typical lifetime of a very massive star, we find that about $630$ collisions occur in typical models with $N=10^4$, $R=100$ $\rm~R_\odot$ and a half-mass radius of $0.1$ $\rm~pc$, leading to a mass of about $6.3\times10^3$ $\rm~M_\odot$ for the most massive object.