Globular Cluster Photometry with the Hubble Space Telescope. V. WFPC2 Study of M15's Central Density Cusp

We describe images of the center of the dense globular cluster M15 (NGC 7078) obtained with the Hubble Space Telescope Wide Field and Planetary Camera 2 (WFPC2). Data taken in the F336W, F439W, and F555W filters (approximately U, B, and V) are used to study the surface density distribution of the $\sim 3\times {10}^4$~stars detected in a 5~arcmin${}^2$ region within $r<2^{\mathrm{\prime }}$ (6.7$$pc) of the cluster center. The surface density of stars in M15 (after correction for the effects of incompleteness and photometric bias/scatter) is well represented by a power law in radius: $N(r)\sim r^{-0.82\pm 0.12}$, over the radial range ${0.3}^{\mathrm{\prime }\mathrm{\prime }}$ (0.017$$pc) to $6^{\mathrm{\prime }\mathrm{\prime }}$. The observed power law is remarkably similar to what is expected if the center of the cluster harbors a massive black hole. Non-parametric estimates of the density profile show a monotonic rise with decreasing radius all the way in to $r={0.3}^{\mathrm{\prime }\mathrm{\prime }}$, the smallest radius at which the density can be reliably measured; there is no indication that the profile flattens at smaller radii. Any flat core of radius larger than $2^{\mathrm{\prime }\mathrm{\prime }}$ (0.11$$pc) in the stellar distribution is ruled out at the $>95$% significance level. The star count profile is consistent with that expected from core-collapse models or with the predicted distribution around a massive (few times ${10}^3{M}_{\odot }$) black hole. The close triplet of bright stars, AC~214, is within ${0.5}^{\mathrm{\prime }\mathrm{\prime }}$ ($1.5\sigma$) of the cluster centroid position.