Evidence for a supermassive black hole in the nucleus of M31

Stellar rotation velocities and velocity dispersions along three slit positions in M31 have been measured in seeing σ_*_=0. 5" with the Canada- France-Hawaii Telescope. The velocities and velocity gradients in the semi- stellar nucleus are large. The maximum apparent rotation velocity V is 149 +/- 5 km s^-1^ at r=1. 1. " The apparent velocity dispersion σ is 245 +/- 7 km s^-1^ at the center but ~ 2". The latter is smaller than the central σ=145 km s^-1^ in the bulge. This and the large value of V/σ suggest that the nucleus may be a disk. To search for a central black hole, three-dimensional velocity and velocity dispersion fields are found that fit the observations after projection and seeing convolution. To eliminate problems with the reaction of the Fourier quotient program to stellar population mixes, synthetic apparent spectra are constructed by summing spectra of appropriate V and σ along the line of sight and then summing the seeing contributions of the projected spectra over the whole image. The synthetic spectra are analyzed with the Fourier program in the same way as the real data. Many models are constructed to explore parameter space; e. g. , the trade-off between a central point mass and mass in the visible nucleus. The large velocities and velocity gradients imply that the total mass-to-light ratio M/LV_ rises sharply at r <~ 0. 5" to values greater than 10²^. This is much larger than normal for old stellar populations. Velocity anisotropies are not a major uncertainty because of the rapid rotation. Therefore there is strong evidence for a dark central mass, probably a supermassive black hole. This has a mass of 10⁶. 5^-10⁷^ Mₛun_ if the nucleus is a disk or 10⁷^-10⁸^ Mₛun_ if the nucleus is an ellipsoid with the observed apparent thickness.