The dynamics of M15: Observations of the velocity dispersion profile and 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 Palma Observatory. We obtained spatially resolved spectra for a total of 23 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 near the Ca II infrared triplet at 8650 Å, with a spectral range of about 450 Å. We determined radial velocities by cross-correlation techniques for 131 cluster members. A total of 32 stars were observed more than once. Internal and external comparisons indicate a velocity accuracy of about 4 km s^-1. The velocity dispersion profile rises from about σ = 7.2 ± 1.4 km s^-1 near 1′ from the center of the cluster to σ = 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, Seitzer, & Cudworth who found a central velocity dispersion of 25 ± 7 km s^-1, based on a line-broadening measurement. Our velocity dispersion profile is in good agreement with those determined in the recent studies of Gebhardt et al. and Dubath & Meylan. We have developed a new set of Fokker-Planck 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 mass function) and a total mass of 4.9 × 10⁵ M_⊙. This model contains approximately 10⁴ neutron stars (3% of the total mass), the majority of which lie within 6″ (0.2 pc) of the cluster center. Since the velocity dispersion profile of M15 is well fitted by this postcollapse model 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.