Methods for determining the masses of spherical systems. I. Test particles around a point mass.
Abstract
Mass estimators for spherical systems may be based either on the virial theorem or on moments of the projected mass q= (projected distance) × (radial velocity)^{2}/G. The statistical characteristics of both estimators are derived and discussed for the special case of test particles bound to a massive central object. We illustrate their relative merits by a series of Monte Carlo experiments. We find that the projected mass method is generally more reliable than the virial theorem. We apply our results to three systems: 3C 273, Ml0l, and M3l. The mass of 3C 273 is estimated to be 5 × l0^{13}h^{1} M_{sun} from radial velocities of companion galaxies measured by Stockton. The mass of M101 within ∼400 kpc is found to be about 2 × l0^{12} M_{sun}. The mass of M3l within ∼100 kpc is found to be about 1 × 10^{12} M_{sun}, an order of magnitude larger than given by the virial theorem from the same data, but consistent with the optical and 21 cm rotation curves.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1981
 DOI:
 10.1086/158756
 Bibcode:
 1981ApJ...244..805B
 Keywords:

 Celestial Mechanics;
 Galactic Clusters;
 Mass Distribution;
 Stellar Motions;
 Andromeda Galaxy;
 Monte Carlo Method;
 Quasars;
 Radial Velocity;
 Spheres;
 Spiral Galaxies;
 Statistical Analysis;
 Virial Theorem;
 Astronomy