M/L and velocity anisotropy from observations of spherical galaxies, or must M87 have a massive black hole?

Abstract

An algorithm is developed that determines whether a given set of photometric and spectroscopic observations of a spherical galaxy are consistent with the mass-to-light ratio in the galaxy being constant. If such a model is possible, the value of the mass-to-light ratio and the values of the two independent components of velocity dispersion at each radius are determined. Tests of the algorithm demonstrate its consistency and accuracy when applied to pseudo-data generated from a variety of theoretical models. When the data do not extend to very great radii and must be extrapolated arbitrarily, qualitatively correct results are obtained. The algorithm is applied to M87. The deconvolution technique of Lucy (1974) is used to correct the photometry of Young et al. (1978) for the effects of seeing and a point light source. Velocity dispersion profiles consistent with the observations of Sargent et al. (1978) and of Dressler (1980) combine with the photometry to yield physically plausible models that have constant mass-to-light ratio. |$M/{L}_\text{V}=7.6\,\text{if}\,{A}_\text{v}=0.14$| and D = 16 Mpc. The models returned by different dispersion profiles all involve a tight star cluster at r < 100 pc, in which the velocity dispersion is highly anisotropic towards the outside. The main body of the galaxy, which dominates the light beyond r = 200 pc, has only modest velocity dispersion anisotropy. The constant mass-to-light models of M87 discussed here are very different from that proposed by Duncan & Wheeler (1980) in which the velocity dispersion in the main body of the galaxy is extremely anisotropic. We believe it is difficult to modify their model to conform with the observations of M87 at |$R\gt 80^{\prime{}\prime}$|⁠. The models derived here share important features with those proposed by Gurzadyan & Ozernoi (1980) and by Dressler (1980).