RECOVERING VELOCITY DISTRIBUTIONS VIA PENALIZED LIKELIHOOD

Line-of-sight velocity distributions are crucial for unravelling the d ynamics of hot stellar systems. We present a new formalism based on pe nalized likelihood for deriving such distributions from kinematical da ta, and evaluate the performance of two algorithms that extract N(V) f rom absorption-line spectra and from sets of individual velocities. Bo th algorithms are superior to existing ones in that the solutions are nearly unbiased even when the data are so poor that a great deal of sm oothing is required. In addition, the discrete-velocity algorithm is a ble to remove a known distribution of measurement errors from the esti mate of N(V). The formalism is used to recover the velocity distributi on of stars in five fields near the center of the globular cluster ome ga Centauri. (C) 1997 American Astronomical Society.