Nonparametric estimation of density profiles

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Abstract
We present two nonparametric algorithms for estimating the surface and space density profile of a spherical stellar system directly from a set of measured positions on the plane of the sky. The algorithms require no binning and are able to cope with the amplification of errors associated with Abel deconvolution, without the bias that results from assuming an ad hoc fitting function. We also show how to estimate confidence bands for both functions. We apply our algorithms to the determination of the density profiles near the center of the Coma galaxy cluster, and the globular cluster M15. Both systems are found to exhibit an 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. Application of our techniques to other problems, including the construction of smooth potential solvers for the collisionless N-body problem, is discussed.

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