Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...413...79m&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 413, no. 1, p. 79-94.
Astronomy and Astrophysics
Astrophysics
62
Astronomical Maps, Hot Stars, Mass To Light Ratios, Stellar Motions, Stellar Systems, Celestial Mechanics, Distribution Functions, Maximum Likelihood Estimates
Scientific paper
We show how to recover the distribution function f(E, L-squared) of an equilibrium population in a spherical stellar system, as well as the gravitational potential Phi(r) in which that population orbits, given its joint distribution of apparent positions and line-of-sight velocities. No assumptions are made about the variation with radius of the mass-to-light ratio or the form of f. Practical nonparametric algorithms are presented for the case of continuous data, as derived from integrated stellar spectra, and discrete data, in the form of individual radial velocities. Ruling out a constant mass-to-light ratio model for any early-type galaxy with a dark halo is shown to require accurate measurement of the line-of-sight velocity distribution at radii extending well beyond the effective radius. In the case of discrete data sets, it is shown that estimates of Phi(r) from samples containing only a few hundred velocities can be rather strongly dependent on presumptions about the smoothness of f.
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