Dynamics of intermediate mass black holes in globular clusters

Wander radius and anisotropy profiles

¹ Institute of Complex Systems – National Council of Research (ISC-CNR), via della Lastruccia 10, 50019 Sesto Fiorentino, Italy
e-mail: pierfrancesco.dicintio@cnr.it
² Physics and Astronomy Department, University of Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
³ INAF, Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi, 5, 50125 Firenze, Italy
⁴ INFN – Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
⁵ Physics and Astronomy Department Galileo Galilei, University of Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
⁶ Département de Physique, Université de Montréal, Montreal, Quebec H3T 1J4, Canada
⁷ The University of Tokyo, Earth Science and Astronomy Department, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
⁸ Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna-son, Kunigami-gun, 904-0495 Okinawa, Japan
⁹ McWilliams Center for Cosmology and Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Received: 10 February 2023
Accepted: 24 March 2023

Abstract

Context. We recently introduced a new method for simulating collisional gravitational N-body systems with approximately linear time scaling with N. Our method is based on the multi-particle collision (MPC) scheme, previously applied in fluid dynamics and plasma physics. We were able to simulate globular clusters with a realistic number of stellar particles (at least up to several times 10⁶) on a standard workstation.

Aims. We simulated clusters hosting an intermediate mass black hole (IMBH), probing a broad range of BH-cluster and BH–average-star mass ratios, unrestricted by the computational constraints that affect direct N-body codes.

Methods. We set up a grid of hybrid particle-in-cell-MPC N-body simulations using our implementation of the MPC method, MPCDSS. We used either single mass models or models with a Salpeter mass function (a single power law with an exponent of −2.35), with the IMBH initially sitting at the centre. The force exerted by and on the IMBH was evaluated with a direct sum scheme with or without softening. For all simulations we measured the evolution of the Lagrangian radii and core density and velocity dispersion over time. In addition, we also measured the evolution of the velocity anisotropy profiles.

Results. We find that models with an IMBH undergo core collapse at earlier times, the larger the IMBH mass the shallower they are, with an approximately constant central density at core collapse. The presence of an IMBH tends to lower the central velocity dispersion. These results hold independently of the mass function of the model. For the models with Salpeter MF, we observed that equipartition of kinetic energies is never achieved, even long after core collapse. Orbital anisotropy at large radii appears to be driven by energetic escapers on radial orbits, triggered by strong collisions with the IMBH in the core. We measured the wander radius, that is the distance of the IMBH from the centre of mass of the parent system over time, finding that its distribution has positive kurtosis.

Conclusions. Among the results we obtained, which mostly confirm or extend previously known trends that had been established over the range of parameters accessible to direct N-body simulations, we underline that the leptokurtic nature of the IMBH wander radius distribution might lead to IMBHs presenting as off-centre more frequently than expected, with implications on observational IMBH detection.