  The Chandra Orion Ultradeep project (COUP) observation described in a
companion paper by Getman et al. provides an exceptionally deep X-ray survey of
the Orion Nebula Cluster and associated embedded young stellar objects.
Membership of the region is important for studies of the stellar IMF, cluster
dynamics, and star formation. The COUP study detected 1616 X-ray sources. In
this study we confirm cloud membership for 1315 stars, identify 16 probable
foreground field stars having optical counterparts with discrepant proper
motions, and classify the remaining 285 X-ray sources, of which 51 are lightly
and 234 heavily obscured. The 51 lightly obscured sources without known
counterparts fall into three groups. (i) Sixteen are likely new members of the
Orion Nebula Cluster. (ii) Two with unusually soft and non-flaring X-ray
emission appear to be associated with nebular shocks, and may be new examples
of X-rays produced at the bow shocks of Herbig-Haro outflows. (iii) The
remaining thirty three are very weak uncertain sources, possibly spurious. Out
of 234 heavily absorbed sources without optical or near-infrared counterparts
75 COUP sources are likely new embedded cloud members (with membership for 42
confirmed by powerful X-ray flares), and the remaining 159 are likely
extragalactic AGN seen through the molecular cloud, as argued by a careful
simulation of the extragalactic background population. Finally, a few new
binary companions to Orion stars may have been found, but most cases of
proximate COUP sources can be attributed to chance superpositions in this
crowded field.

Astrophysics