Publication Date:
2016-10-30

Description:
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 r m is the cluster's half-mass radius. The degree of energy equipartition in a cluster is quantified by , which is a measure of how stellar velocity dispersion depends on stellar mass m via ( m ) m – . 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 α and . We find that measurements of the global are strongly affected by the radial dependence of and mean stellar mass and the relationship between and α depends mainly on the cluster's initial conditions and the tidal field. Within r m , where these effects are minimized, we find that and α initially share a linear relationship. However, once the degree of mass segregation increases such that the radial dependence of and mean stellar mass become a factor within r m , or the cluster undergoes core collapse, the relationship breaks down. We propose a method for determining within r m from an observational measurement of α . In cases where and α can be measured independently, this new method offers a way of measuring the cluster's dynamical state.

Print ISSN:
0035-8711

Electronic ISSN:
1365-2966

Topics:
Physics

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