Radial Variation in the Stellar Mass Functions of Star Clusters

TL;DR

This study uses N-body simulations to analyze how the stellar mass function slope varies with radius in star clusters, revealing insights into their dynamical evolution and initial conditions.

Contribution

It introduces a comprehensive analysis of the radial variation of stellar mass functions in clusters, linking it to their dynamical history and initial conditions.

Findings

Clusters follow a predictable track in the $oldsymbol{ ext{α}_G}$-$oldsymbol{d ext{α}(r)/d ext{ln}(r/r_m)}$ plane.

The position in this plane constrains the cluster's dynamical history and initial mass function.

The $oldsymbol{ ext{α}_G}$-$oldsymbol{d ext{α}(r)/d ext{ln}(r/r_m)}$ plane is a key tool for analyzing cluster evolution.

Abstract

A number of recent observational studies of Galactic globular clusters have measured the variation in the slope of a cluster's stellar mass function $\alpha$ with clustercentric distance $r$. In order to gather a deeper understanding of the information contained in such observations, we have explored the evolution of $\alpha(r)$ for star clusters with a variety of initial conditions using a large suite of $N$-body simulations. We have specifically studied how the time evolution of $\alpha(r)$ is affected by initial size, mass, binary fraction, primordial mass segregation, black hole retention, an external tidal field, and the initial mass function itself. Previous studies have shown that the evolution of $\alpha_G$ is closely related to the amount of mass loss suffered by a cluster. Hence for each simulation we have also followed the evolution of the slope of the cluster's global stellar mass function, $\alpha_G$, and have shown that clusters follow a well-defined track in the $\alpha_G$-$d\alpha(r)/d(ln(r/r_m))$ plane. The location of a cluster on the $\alpha_G-d\alpha(r)/d(ln(r/r_m))$ plane can therefore constrain its dynamical history and, in particular, constrain possible variations in the stellar initial mass function. The $\alpha_G$-$d\alpha(r)/d(ln(r/r_m))$ plane thus serves as a key tool for fully exploiting the information contained in wide field studies of cluster stellar mass functions.