A novel look at energy equipartition in globular clusters

Abstract

Two-body interactions play a major role in shaping the structural and dynamical properties of globular clusters (GCs) over their long-term evolution. In particular, GCs evolve toward a state of partial energy equipartition that induces a mass-dependence in their kinematics. By using a set of Monte Carlo cluster simulations evolved in quasiisolation, we show that the stellar mass dependence of the velocity dispersion σ(m) can be described by an exponential function σ 2 ∝ exp(−m/m eq ), with the parameter m eq quantifying the degree of partial energy equipartition of the systems. This simple parametrization successfully captures the behaviour of the velocity dispersion at lower as well as higher stellar masses, that is, the regime where the system is expected to approach full equipartition. We find a tight correlation between the degree of equipartition reached by a GC and its dynamical state, indicating that clusters that are more than about 20 core relaxation times old, have reached a maximum degree of equipartition. This equipartition−dynamical state relation can be used as a tool to characterize the relaxation condition of a cluster with a kinematic measure of the m eq parameter. Vice versa, the mass-dependence of the kinematics can be predicted knowing the relaxation time solely on the basis of photometric measurements. Moreover, any deviations from this tight relation could be used as a probe of a peculiar dynamical history of a cluster. Finally, our novel approach is important for the interpretation of state-of-the-art Hubble Space Telescope proper motion data, for which the mass dependence of kinematics can now be measured, and for the application of modeling techniques which take into consideration multi-mass components and mass segregation.

N-body modelling of globular clusters: masses, mass-to-light ratios and intermediate-mass black holes

“…In contrast, for strongly mass segregated clusters the variation of the M/L ratio can reach a factor of 4 between the core region and the cluster outskirts. This agrees with recent results of Monte Carlo simulations by Bianchini et al (2016), who found that the amount of mass segregation tightly correlates with the dynamical state of the cluster. Table 2 presents a summary of our results.…”

“…Hence the assumption of a constant mass-to-light ratio is not valid for globular clusters. In addition, due to energy equipartition, massive stars move more slowly at a given radius compared to average cluster stars (Trenti & van der Marel 2013;Bianchini et al 2016). As a result, the velocity dispersion derived from giant stars will underestimate the true velocity dispersion, which leads to an underestimation of the total cluster mass if mass segregation is not properly taken into account (Shanahan & Gieles 2015).…”

Radial variation in the stellar mass functions of star clusters

“…The fact that all our model clusters reach similar minimum values of δα may be due to clusters not actually being able to evolve to a state of pure energy equipartition (Merritt 1981;Miocchi 2006;Trenti & van der Marel 2013;Gieles & Zocchi 2015;Bianchini et al 2016), with the minimum δα representing the highest state of energy equipartition a star cluster can reach.…”

“…Gieles et al 2006;Kruijssen et al 2011Kruijssen et al , 2012Renaud & Gieles 2013;Rieder et al 2013), stellar evolution is the initial driver behind cluster evolution and early expansion due to mass loss from high-mass stars. After this early stage, two-body relaxation takes over and the cluster evolves towards a state of partial energy equipartition (Merritt 1981;Miocchi 2006;Trenti & van der Marel 2013;Gieles & Zocchi 2015;Bianchini et al 2016). A natural result of two-body relaxation is the segregation of higher mass stars towards the cluster center while lower mass stars migrate outwards (e.g.…”

The Strong Rotation of M5 (NGC 5904) as Seen from the MIKiS Survey of Galactic Globular Clusters

“…Hence, simple isotropic and nonrotating models (King 1966) are usually adopted to reproduce their observed surface brightness/star count profiles and to derive their structural parameters (e.g., Harris 1996). However, recent N-body simulations indicate that GCs do not attain complete energy equipartition (Trenti & van der Marel 2013; see also Bianchini et al 2016), and they may show differential rotation and complex behaviors of pressure anisotropy, depending on the degree of dynamical evolution suffered and the effect of an external tidal field (e.g., Vesperini et al 2014).…”