On the link between energy equipartition and radial variation in the stellar mass function of star clusters

We make use of N-body simulations to determine the relationship between two observable parameters that are used to quantify mass segregation and energy equipartition in star clusters. Mass segregation can be quantified by measuring how the slope of a cluster's stellar mass function α changes with clustercentric distance r, and then calculating | $\delta _\alpha = \frac{{\rm d} \alpha (r)}{{\rm d} ln(r/r_{\rm m})}$ |⁠, where rm is the cluster's half-mass radius. The degree of energy equipartition in a cluster is quantified by η, which is a measure of how stellar velocity dispersion σ depends on stellar mass m via σ(m) ∝ m−η. Through a suite of N-body star cluster simulations with a range of initial sizes, binary fractions, orbits, black hole retention fractions, and initial mass functions, we present the co-evolution of δα and η. We find that measurements of the global η are strongly affected by the radial dependence of σ and mean stellar mass and the relationship between η and δα depends mainly on the cluster's initial conditions and the tidal field. Within rm, where these effects are minimized, we find that η and δα initially share a linear relationship. However, once the degree of mass segregation increases such that the radial dependence of σ and mean stellar mass become a factor within rm, or the cluster undergoes core collapse, the relationship breaks down. We propose a method for determining η within rm from an observational measurement of δα. In cases where η and δα can be measured independently, this new method offers a way of measuring the cluster's dynamical state.

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