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

The Alessandrini A+ indicator is a measure of star cluster dynamical evolu-tion based on the mass-segregation of blue straggler stars. A+ is defined as the integral of the cumulative distribution of blue stragglers over log radius, minus a term related to the reference population used. In a companion paper I introduced a model of dynamical friction and calculated the A+ indicator analytically. Here I show further properties of the time evolution of A+, focusing on the physical interpretation of its time derivative dA+=dt. I find that dA+=dt is the mean of the reciprocal dyamical friction timescale, weighted by the density of blue stragglers. I show that it is non-negative (as expected based on monotonicity) due to the den-sity of blue-stragglers being non-negative and that, for a radially non-decreasing dynamical friction timescale, dA+=dt is also non-decreasing with time, making A+ a convex function.