The Dynamics of Globular Clusters and Elliptical Galaxies

TL;DR

This paper models the evolution of spherical galaxies, fitting observational data for globular clusters and ellipticals, revealing relationships between size, mass, and velocity dispersion, and suggesting the presence of supermassive black holes in ellipticals.

Contribution

Develops a theoretical model for spherical galaxy evolution, fitting globular cluster data and analyzing size-mass-velocity relations across galaxy types, highlighting SMBH influence.

Findings

Good fit of the model to globular cluster data.

Linear relation between galaxy radius and mass over seven decades.

Ellipticals show evidence of supermassive black holes affecting dynamics.

Abstract

A model is developed for an idealised spherical galaxy evolving from a uniform mass distribution at the epoch of galactic separation until attaining an equilibrium state through gravitational collapse. The final theoretical radial surface density is computed and shows a good fit to the observational data for two globular clusters, M15 and M80. The 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 544 ellipticals plus compact, massive, and intermediate-mass objects. These 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. Analysis of the equations of motion suggested the generalised rule that all spherical galaxies expand from their initial radius at the epoch of galactic separation to a stable maximum radius of $\simeq1.136$ times their initial radius in their relaxed state.