{
  "id": "2008.01424",
  "version": "v1",
  "published": "2020-08-04T09:14:02.000Z",
  "updated": "2020-08-04T09:14:02.000Z",
  "title": "The Dynamics of Globular Clusters and Elliptical Galaxies",
  "authors": [
    "John H Marr"
  ],
  "comment": "Submitted to MNRAS. 11 pages, 12 figures",
  "categories": [
    "astro-ph.GA"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-04T09:14:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "globular cluster",
      "elliptical galaxies",
      "spherical galaxy",
      "linear mean log-log",
      "intermediate mass objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}