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 ∼3×10⁴ stars detected in a 5 arcmin² region within r<2′ (6.7 pc) of the cluster center. Realistic simulated images have been used to estimate photometric errors and incompleteness in the star counts, which are strong functions of stellar brightness and radius. We have used a combination of point-spread-function fitting and aperture photometry, a technique that yields more accurate photometry than either method alone on the undersampled WFPC2 images of crowded star fields. The error in photometry is 1σ≲0.05 mag for stars with V<18; this increases to 1σ∼0.2 mag at V=20.5, which is 1.5 mag fainter than the main-sequence turnoff. 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)∼r^-0.82±0.12, over the radial range 0″.3 (0.017 pc) to 6″. The observed power law is remarkably similar to what is expected if the center of the cluster harbors a massive black hole. Nonparametric estimates of the density profile show a monotonic rise with decreasing radius all the way in to r=0″.3, 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″ (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 10³ Script M sign_⊙) black hole. The close triplet of bright stars, AC 214, is within 0″.5 (1.5σ) of the cluster centroid position. The projected density distribution of stars within the central 15″ of M15 departs from circular symmetry at the 95% level, with an ellipticity e=0.05±0.04 (90% confidence limits) at a position angle of +60°±25°, consistent with the rotation measured by Gebhardt et al. (1995) in this region of the cluster.