Stellar collisions in flattened and rotating Population III star clusters

¹ Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepcion, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C, Concepcion, Chile
e-mail: marccortes@udec.cl
² Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, UK
³ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
⁴ Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
⁵ Department of Astrophysics, American Museum of Natural History, New York, NY 10024, USA

Received: 7 January 2021
Accepted: 8 March 2021

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 with a high stellar density, 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 a 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 a typical models with N = 10⁴, R = 100 R_⊙ and a half-mass radius of 0.1 pc, leading to a mass of about 6.3 × 10³ M_⊙ for the most massive object. We note that our simulations do not include mass loss during mergers or due to stellar winds. On the other hand, the growth of the most massive object may subsequently continue, depending on the lifetime of the most massive object.