Efficiency of black hole formation via collisions in stellar systems

Data analysis from simulations and observations

¹ Astronomisches Rechen-Institut, Zentrum für Astronomie, University of Heidelberg, Mönchhofstrasse 12-14, 69120 Heidelberg, Germany
² 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: dschleicher@astro-udec.cl
³ Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
e-mail: aescala@das.uchile.cl
⁴ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
⁵ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁶ Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20118 Donostia-San Sebastián, Spain
⁷ National Astronomical Observatories and Key Laboratory of Computational Astrophysics, Chinese Academy of Sciences, 20A Datun Rd., Chaoyang District, Beijing 100012, China
⁸ Kavli Institute for Astronomy and Astrophysics, Peking University, Yiheyuan Lu 5, Haidian Qu, 100871 Beijing, China

Received: 13 March 2024
Accepted: 29 May 2024

Abstract

Context. This paper explores the theoretical relation between star clusters and black holes within them, focusing on the potential role of nuclear star clusters (NSCS), globular clusters (GCS), and ultra-compact dwarf galaxies (UCDS) as environments that allow for black hole formation via stellar collisions.

Aims. This study aims to identify the optimal conditions for stellar collisions across a range of stellar systems, leading to the formation of very massive stars that subsequently collapse into black holes. We analyze data from numerical simulations and observations of diverse stellar systems, encompassing various initial conditions, initial mass functions, and evolution scenarios.

Methods. We computed a critical mass, determined by the interplay of the collision time, system age, and initial properties of the star cluster. The efficiency of black hole formation (ϵ_BH) is defined as the ratio of initial stellar mass divided by the critical mass.

Results. We find that stellar systems with a ratio of initial stellar mass over critical mass above 1 exhibit a high efficiency in terms of black hole formation, ranging from 30 − 100%. While there is some scatter, potentially attributed to complex system histories and the presence of gas, the results highlight the potential for achieving high efficiencies via a purely collisional channel in black hole formation.

Conclusions. In conclusion, this theoretical exploration elucidates the connection between star clusters and black hole formation. The study underscores the significance of UCDS, GCS, and NSCS as environments conducive to the black hole formation scenario via stellar collisions. The defined black hole formation efficiency (ϵ_BH) is shown to be influenced by the ratio of the initial stellar mass to the critical mass.