NONPARAMETRIC-ESTIMATION OF DENSITY PROFILES

We present two nonparametric algorithms for estimating the surface and space density profile of a spherical stellar system directly from a s et of measured positions on the plane of the sky. The algorithms requi re no binning and are able to cope with the amplification of errors as sociated with Abel deconvolution, without the bias that results from a ssuming an ad hoc fitting function. We also show how to estimate confi dence bands for both functions. We apply our algorithms to the determi nation of the density profiles near the center of the Coma galaxy clus ter, and the globular cluster M15. Both systems are found to exhibit a n approximate power-law dependence of space density on radius near the center: roughly r-1 in the case of Coma, and approximately r-2 in the case of M15. We find no evidence for a core in either system. Applica tion of our techniques to other problems, including the construction o f smooth potential solvers for the collisionless N-body problem, is di scussed.