On the mass-radius relation of hot stellar systems

TL;DR

This paper investigates the mass-radius relation of hot stellar systems, revealing a break at ~10^6 solar masses due to stellar evolution and binary interactions, and suggests a common initial formation relation for all such systems.

Contribution

It demonstrates that globular clusters' current properties result from balanced stellar and dynamical evolution, obscuring their initial mass-radius relation.

Findings

Globular clusters have a mass-radius relation independent of initial conditions.

A break in the relation occurs at ~10^6 solar masses due to stellar evolution effects.

All hot stellar systems likely formed with a similar initial mass-radius relation.

Abstract

Most globular clusters have half-mass radii of a few pc with no apparent correlation with their masses. This is different from elliptical galaxies, for which the Faber-Jackson relation suggests a strong positive correlation between mass and radius. Objects that are somewhat in between globular clusters and low-mass galaxies, such as ultra-compact dwarf galaxies, have a mass-radius relation consistent with the extension of the relation for bright ellipticals. Here we show that at an age of 10 Gyr a break in the mass-radius relation at ~10^6 Msun is established because objects below this mass, i.e. globular clusters, have undergone expansion driven by stellar evolution and hard binaries. From numerical simulations we find that the combined energy production of these two effects in the core comes into balance with the flux of energy that is conducted across the half-mass radius by relaxation. An important property of this `balanced' evolution is that the cluster half-mass radius is independent of its initial value and is a function of the number of bound stars and the age only. It is therefore not possible to infer the initial mass-radius relation of globular clusters and we can only conclude that the present day properties are consistent with the hypothesis that all hot stellar systems formed with the same mass-radius relation and that globular clusters have moved away from this relation because of a Hubble time of stellar and dynamical evolution.