Radial variation in the stellar mass functions of star clusters

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 α with clustercentric distance r. In order to gather a deeper understanding of the information contained in such observations, we have explored the evolution of α(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 α(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 α 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, α G , and have shown that clusters follow a well-defined track in the α G -dα(r)/d(ln(r/r m )) plane. The location of a cluster on the α G − dα(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 α G -dα(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.

The global mass functions of 35 Galactic globular clusters: I. Observational data and correlations with cluster parameters

“…So, the shorter the timescale of internal dynamical evolution the more efficient is the depletion of the MF. However, the location of N-body simulations in the log t rh − α plane is highly sensitive to the original slope of the IMF, with clusters starting with a steeper IMF reaching also steeper present-day MFs after a given number of elapsed relaxation times than clusters starting with flatter IMFs (Webb & Vesperini 2016). Thus, a significant spread in this relation would be apparent if cluster-to-cluster variations of the IMF were present at the epoch of their formation.…”

“…Piotto & Zoccali 1999). On the theoretical side, many surveys of N-body simulations have been performed to investigate the evolution of the MF in GC-like objects (Vesperini & Heggie 1997;Baumgardt & Makino 2003;Lamers, Baumgardt & Gieles 2013;Webb & Vesperini 2014, 2016. In particular, Leigh et al (2012) used a set of N-body runs assuming different masses, concentrations, orbital eccentricities and tidal environments to reproduce the MFs of a sample of 27 Galactic GCs and showed that the natural evolution of a universal IMF could actually produce the observed cluster-to-cluster differences.…”

Correlation between mass segregation and structural concentration in relaxed stellar clusters

“…In fact, we do not include primordial mass segregation as its effects on the overall mass function evolution should be lost at later times, when clusters begin losing stars via tidal stripping (see Subsec. 3.5 of Webb & Vesperini 2016). The simulations include tidal forces, computed assuming that the clusters follow circular orbits in a point-mass galactic gravitational field (see Trenti et al 2007a for details), underfilling the tidal radius by a factor of 3.…”

Do star clusters form in a completely mass-segregated way?

“…Primordial mass segregation also affects the dynamical evolution of a cluster through stellar evolutionary mass loss of the massive stars. Initial mass segregation may also lead to a different evolution of the radial dependence of the stellar mass function in the evolving star cluster when compared to a cluster not initially mass segregated (Webb & Vesperini 2016).…”