The mass-radius relation of hot stellar systems
Mark Gieles (IoA, Cambridge)

There are several internal and external factors that play a role in the evolution of star clusters. Here we focus on two dominant 
effects, namely close encounters between stars, often referred to as 2-body relaxation, and mass-loss of the stars through 
stellar winds and supernovae explosions. Since the former operates on the relaxation time-scale of the cluster and the latter 
on the stellar evolution time-scale of the stars it is often assumed that the combined effect on the evolution of the cluster is 
complicated. In this contribution we show that the interplay between stellar evolution and 2-body relaxation is in fact quite 
simple. The result is an overall expansion of clusters, which is more important for low mass clusters, such that after some 
time the radii of clusters depend very little on their masses, even if all clusters have the same (surface) density initially. 
Several predictions are made for the relation between mass, radius, age and galactocentric radius and good agreement is 
found with properties of globular cluster in different galaxies. Objects more massive than ~10^6 Msun, such as Ultra Compact 
Dwarf galaxies (UCDs), are not affected by this expansion yet and their mass-radius relation is, therefore, close to the initial 
one.