  The analysis of individual X-ray sources that appear in a crowded field can
easily be compromised by the misallocation of recorded events to their
originating sources. Even with a small number of sources, that nonetheless have
overlapping point spread functions, the allocation of events to sources is a
complex task that is subject to uncertainty. We develop a Bayesian method
designed to sift high-energy photon events from multiple sources with
overlapping point spread functions, leveraging the differences in their
spatial, spectral, and temporal signatures. The method probabilistically
assigns each event to a given source. Such a disentanglement allows more
detailed spectral or temporal analysis to focus on the individual component in
isolation, free of contamination from other sources or the background. We are
also able to compute source parameters of interest like their locations,
relative brightness, and background contamination, while accounting for the
uncertainty in event assignments. Simulation studies that include event arrival
time information demonstrate that the temporal component improves event
disambiguation beyond using only spatial and spectral information. The proposed
methods correctly allocate up to 65% more events than the corresponding
algorithms that ignore event arrival time information. We apply our methods to
two stellar X-ray binaries, UV Cet and HBC515 A, observed with Chandra. We
demonstrate that our methods are capable of removing the contamination due to a
strong flare on UV Cet B in its companion approximately 40 times weaker during
that event, and that evidence for spectral variability at timescales of a few
ks can be determined in HBC515 Aa and HBC515 Ab.
