Dynamics of star clusters with tangentially anisotropic velocity distribution

¹ Astronomical Institute of the Czech Academy of Sciences, Boční II 1401, 141 00 Prague 4, Czech Republic
² Department of Astronomy, Indiana University, Swain Hall West, 727 E 3rd Street, Bloomington, IN 47405, USA
³ Aventinum Publishing House, Tolstého 22, 101 00 Prague 10, Czech Republic
⁴ School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Kings Buildings, Edinburgh EH9 3FD, UK
⁵ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

Received: 5 April 2024
Accepted: 29 May 2024

Abstract

Context. Recent high-precision observations with HST and Gaia enabled new investigations of the internal kinematics of star clusters (SCs) and the dependence of kinematic properties on the stellar mass. These studies raised new questions about the dynamical evolution of self-gravitating stellar systems.

Aims. We aim to develop a more complete theoretical understanding of how the various kinematical properties of stars affect the global dynamical development of their host SCs.

Methods. We perform N-body simulations of globular clusters with isotropic, radially anisotropic, and tangentially anisotropic initial velocity distributions. We also study the effect of an external Galactic tidal field.

Results. We obtain three main results. First, compared to the conventional, isotropic case, the relaxation processes are accelerated in the tangentially anisotropic models and, in agreement with our previous investigations, are slower in the radially anisotropic ones. This leads to, for example, more rapid mass segregation in the central regions of the tangential models or their earlier core collapse. Second, although all SCs become isotropic in the inner regions after several relaxation times, we observe differences in the anisotropy profile evolution in the outer cluster regions – all tidally filling models gain tangential anisotropy there, while the underfilling models become radially anisotropic. Third, we observe different rates of evolution towards energy equipartition (EEP). While all SCs evolve towards EEP in their inner regions (regardless of the filling factor), the outer regions of the tangentially anisotropic and isotropic models are evolving to an ‘inverted’ EEP (i.e. with the high-mass stars having higher velocity dispersion than the low-mass ones). The extent (both spatial and temporal) of this inversion can be attributed to the initial velocity anisotropy – it grows with increasing tangential anisotropy and decreases as the radial anisotropy rises.