Revisiting relaxation in globular clusters

Chris Hamilton (1, 2) , Jean-Baptiste Fouvry (3) , James Binney (1) , Christophe Pichon (4, 5, 6)

1 Rudolf Peierls Centre for Theoretical Physics
2 CAM - University of Cambridge [UK]
3 IAS - Institute for Advanced Study [Princeton]
4 IAP - Institut d'Astrophysique de Paris
5 Edin. - University of Edinburgh
6 KIAS - Korea Institute for Advanced Study

The classical theory of cluster relaxation is unsatisfactory because it involves the Coulomb logarithm. The Balescu-Lenard (BL) equation provides a rigorous alternative that has no ill-defined parameter. Moreover, the BL equation, unlike classical theory, includes the cluster's self-gravity. A heuristic argument is given that indicates that relaxation does not occur predominantly through two-particle scattering and is enhanced by self-gravity. The BL equation is adapted to a spherical system and used to estimate the flux through the action space of isochrone clusters with different velocity anisotropies. A range of fairly different secular behaviours is found depending on the fraction of radial orbits. Classical theory is also used to compute the corresponding classical fluxes. The BL and classical fluxes are very different because (a) the classical theory materially underestimates the impact of large-scale collectively amplified fluctuations and (b) only the leading terms in an infinite sum for the BL flux are computed. A complete theory of cluster relaxation likely requires that the sum in the BL equation be decomposed into a sum over a finite number of small wavenumbers complemented by an integral over large wavenumbers analogous to classical theory.

Domaines: Astrophysique galactique [astro-ph.GA]

Chris Hamilton, Jean-Baptiste Fouvry, James Binney, Christophe Pichon. Revisiting relaxation in globular clusters. Monthly Notices of the Royal Astronomical Society, 2018, 481 (2), pp.2041-2061. ⟨10.1093/mnras/sty2295⟩. ⟨hal-02055691⟩