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arXiv · 1907.11965

Further properties of the dynamical clock A+ indicator in a toy model of pure dynamical friction

Mario Pasquato
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Abstract

The Alessandrini A$+$ indicator is a quantitative measure of star cluster dynamical evolution based on the mass-segregation of blue straggler stars. A$+$ is defined as the integral of the cumulative distribution of blue straggler stars with the radius measured in logarithmic scale, minus a term related to the reference population used. In a companion paper I introduced a simplified model of dynamical friction and calculated the A$+$ indicator analytically. Here I show further properties of the time evolution of A$+$, focusing in particular on the physical interpretation of its time derivative $d{A^+}/dt$. I find that $d{A^+}/dt$ is the mean of the reciprocal dyamical friction timescale, weighted by the density of blue straggler stars. I show that it is non-negative (as expected based on monotonicity) due to the density of blue-straggler stars being non-negative and that, for a dynamical friction timescale that is non-decreasing with radius, $d{A^+}/dt$ is also non-decreasing with time, making the A$+$ indicator a convex function.

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Mario Pasquato. 2019-07-27. Further properties of the dynamical clock A+ indicator in a toy model of pure dynamical friction. https://doi.org/10.22201/ia.01851101p.2020.56.01.02

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