Diffusion and Mixing in Globular Clusters
Abstract
Collisional relaxation describes the stochastic process with which a selfgravitating system near equilibrium evolves in phasespace due to the fluctuating gravitational field of the system. The characteristic timescale of this process is called the relaxation time. In this paper, we highlight the difference between two measures of the relaxation time in globular clusters: (1) the diffusion time with which the isolating integrals of motion (i.e., energy E and angular momentum magnitude L) of individual stars change stochastically and (2) the asymptotic timescale required for a family of orbits to mix in the cluster. More specifically, the former corresponds to the instantaneous rate of change of a star’s E or L, while the latter corresponds to the timescale for the stars to statistically forget their initial conditions. We show that the diffusion timescales of E and L vary systematically around the commonly used halfmass relaxation time in different regions of the cluster by a factor of ∼10 and ∼100, respectively, for more than 20% of the stars. We define the mixedness of an orbital family at any given time as the correlation coefficient between its E or L probability distribution functions and those of the whole cluster. Using Monte Carlo simulations, we find that mixedness converges asymptotically exponentially with a decay timescale that is ∼10 times the halfmass relaxation time.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 2018
 DOI:
 10.3847/15384357/aaadac
 arXiv:
 arXiv:1801.01123
 Bibcode:
 2018ApJ...855...87M
 Keywords:

 diffusion;
 globular clusters: general;
 stars: kinematics and dynamics;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 Accepted for publication in ApJ