THE DYNAMICS OF M15 - OBSERVATIONS OF THE VELOCITY DISPERSION PROFILEAND FOKKER-PLANCK MODELS

We report a new measurement of the velocity dispersion profile within 1' (3 pc) of the center of the globular cluster M15 (NGC 7078), using long-slit spectra from the 4.2 m William Herschel Telescope at La Palm a Observatory. We obtained spatially resolved spectra for a total of 2 3 slit positions during two observing runs. During each run, a set of parallel slit positions was used to map out the central region of the cluster; the position angle used during the second run was orthogonal to that used for the first. The spectra are centered in wavelength nea r the Ca II infrared triplet at 8650 Angstrom, with a spectral range o f about 450 Angstrom. We determined radial velocities by cross-correla tion techniques for 131 cluster members. A total of 32 stars were obse rved more than once. Internal and external comparisons indicate a velo city accuracy of about 4 km s(-1). The velocity dispersion profile ris es from about sigma = 7.2 +/- 1.4 km s(-1) near 1' from the center of the cluster to sigma = 13.9 +/- 1.8 km s(-1) at 20 ''. Inside of 20 '' , the dispersion remains approximately constant at about 10.2 +/- 1.4 km s(-1) with no evidence for a sharp rise near the center. This last result stands in contrast with that of Peterson, Seltzer, & Cudworth w ho found a central velocity dispersion of 25 +/- 7 km s(-1), based on a line-broadening measurement. Our velocity dispersion profile is in g ood agreement with those determined in the recent studies of Gebhardt et al. and Dubath & Meylan. We have developed a new set of Fokker-Plan ck models and have fitted these to the surface brightness and velocity dispersion profiles of M15. We also use the two measured millisecond pulsar accelerations as constraints. The best-fitting model has a mass function slope of x = 0.9 (where 1.35 is the slope of the Salpeter ma ss function) and a total mass of 4.9 x 10(5) M.. This model contains a pproximately 10(4) neutron stars (3% of the total mass), the majority of which lie within 6 '' (0.2 pc) of the cluster center. Since the vel ocity dispersion profile of M15 is well fitted by this postcollapse mo del in which the most massive objects are neutron stars, there appears to be no need to invoke the presence of a massive central black hole in M15.