  We present a powerful new algorithm that combines both spatial information
(event locations and the point spread function) and spectral information
(photon energies) to separate photons from overlapping sources. We use Bayesian
statistical methods to simultaneously infer the number of overlapping sources,
to probabilistically separate the photons among the sources, and to fit the
parameters describing the individual sources. Using the Bayesian joint
posterior distribution, we are able to coherently quantify the uncertainties
associated with all these parameters. The advantages of combining spatial and
spectral information are demonstrated through a simulation study. The utility
of the approach is then illustrated by analysis of observations of FK Aqr and
FL Aqr with the XMM-Newton Observatory and the central region of the Orion
Nebula Cluster with the Chandra X-ray Observatory.
