Fabry-Perot observations of globular clusters .3. M15

We have used an Imaging Fabry-Perot Spectrophotometer with the Sub-arcsecond Imaging Spectrograph on the Canada-France-Hawaii Telescope to measure velocities for 1534 stars in the globular cluster M15 (NGC 7078) with uncertainties between 0.5 and 10 km s(-1). Combined with previous velocity samples, the total number of stars with measured velocities in M15 is 1597. An average seeing of 0.8 '' allowed us to obtain velocities for 144 stars within 10 '' of the center of M15, including 12 stars within 2 ''. The velocity dispersion profile for M15 remains flat at a value of 11 km s(-1) from a radius of 0.4' into our innermost reliable point at 0.02' (0.06 pc). Assuming an isotropic velocity dispersion tensor, this profile and the previously-published surface brightness profile can be equally well represented either by a stellar population whose M/L varies with radius from 1.7 in solar units at large radii to 3 in the central region, or by a population with a constant M/L of 1.7 and a central black hole of 1000 M(circle dot). A non-parametric mass model that assumes no black hole, no rotation, and isotropy constrains the mass density of M15 to better than 30% at a radius of 0.07 parsecs. The mass-density profile of this model is well represented by a power law with an exponent of -2.2, the value predicted by models of cluster core-collapse. Using the assumption of local thermodynamic equilibrium, we estimate the present-day mass function and infer a significant number of 0.6-0.7 M(circle dot) objects in the central few parsecs, 85% of which maybe in the form of stellar remnants. Not only do we detect rotation; we find that the position angle of the projected rotation axis in the central 10 '' is 100 degrees different from that of the whole sample. We also detect an increase in the amplitude of the rotation at small radii. Although this increase needs to be confirmed with better-seeing data, it may be the result of a central mass concentration. (C) 1997 American Astronomical Society.