The Dynamics of Globular Clusters and Elliptical Galaxies

John H Marr

Published 2020-08-04Version 1

Equations of motion are generated for an idealised model spherical galaxy or globular cluster evolving from the epoch of galactic separation until it attains a semi-equilibrium state through gravitational collapse. The theoretical radial surface density is computed and compared with two globular clusters, M15 and M80, and shows a good fit to observational data. The model is contrasted with King's model, and mean cycle time and velocity are computed. The velocity-radius curve is developed, and Gaussian RMS values derived from which half-light radius vs. mass are plotted for 735 spherical objects, including 544 normal ellipticals and compact, massive, and intermediate mass objects. These latter show a linear mean log-log $R-M_{vir}$ slope of ${0.604\pm0.003}$, equivalent to a Faber-Jackson slope of $\gamma=3.66{\pm}0.009$ over a mass range of 7 decades. and a slope of $0.0045\pm0.0001$ on a semi-log plot of $R_{1/2}-\sigma$. Globular clusters, dwarf elliptical and dwarf spherical galaxies show a distinct anomaly on these plots, consistent with the ellipticals containing a supermassive black hole (SMBH) whose mass increases as the velocity dispersion increases, compared with the remaining types of spherical or irregular galaxies without a massive core.