Introducing a new multi-particle collision method for the evolution of dense stellar systems

II. Core collapse

¹ Dipartimento di Fisica e Astronomia & CSDC, Università di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy
e-mail: pierfrancesco.dicintio@unifi.it, alicia.simonpetit@unifi.it
² INFN – Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy
³ CREF, Via Panisperna 89A, 00184 Rome, Italy
⁴ Center for Astro, Particle and Planetary Physics (CAP 3), New York University, Abu Dhabi, UAE
e-mail: mp5757@nyu.edu
⁵ Department of Astronomy and Center for Galaxy Evolution Research, Yonsei University, Seoul 120-749, Republic of Korea

Received: 3 March 2021
Accepted: 14 June 2021

Abstract

Context. In a previous paper we introduced a new method for simulating collisional gravitational N-body systems with linear time scaling on N, based on the multi-particle collision (MPC) approach. This allows us to easily simulate globular clusters with a realistic number of stellar particles (10⁵ − 10⁶) in a matter of hours on a typical workstation.

Aims. We evolve star clusters containing up to 10⁶ stars to core collapse and beyond. We quantify several aspects of core collapse over multiple realizations and different parameters while always resolving the cluster core with a realistic number of particles.

Methods. We run a large set of N-body simulations with our new code MPCDSS. The cluster mass function is a pure power law with no stellar evolution, allowing us to clearly measure the effects of the mass spectrum on core collapse.

Results. Leading up to core collapse, we find a power-law relation between the size of the core and the time left to core collapse. Our simulations thus confirm the theoretical self-similar contraction picture but with a dependence on the slope of the mass function. The time of core collapse has a non-monotonic dependence on the slope, which is well fitted by a parabola. This also holds for the depth of core collapse and for the dynamical friction timescale of heavy particles. Cluster density profiles at core collapse show a broken-power-law structure, suggesting that central cusps are a genuine feature of collapsed cores. The core bounces back after collapse, with visible fluctuations, and the inner density slope evolves to an asymptotic value. The presence of an intermediate-mass black hole inhibits core collapse, making it much shallower, irrespective of the mass-function slope.

Conclusions. We confirm and expand on several predictions of star cluster evolution before, during, and after core collapse. Such predictions were based on theoretical calculations or small-size direct N-body simulations. Here we put them to the test in MPC simulations with a much larger number of particles, allowing us to resolve the collapsing core.