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 × l013h-1 Msun from radial velocities of companion galaxies measured by Stockton. The mass of M101 within ˜400 kpc is found to be about 2 × l012 Msun. The mass of M3l within ˜100 kpc is found to be about 1 × 1012 Msun, 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.