To facilitate the study of X-ray sources fainter than those contained
in the Einstein Medium-Sensitivity Survey (EMSS), we have constructed
a new catalog of sources and fluctuations exceeding 2 sigma significan
ce in 2520 high-latitude Einstein IPCC images. We have employed variou
s tests to validate our source-search algorithm for both high- and low
-significance sources, and to identify and remove the small number of
spurious sources induced by our detection procedure. Based on the know
n vignetting and background characteristics of the IPC and the measure
d X-ray log N-log S relation, we have modeled the number of real sourc
es expected in the catalog in order to evaluate its statistical proper
ties below 4 sigma significance. Our modeling suggests that similar to
13,000 sources in the catalog are real celestial X-ray sources, an in
crease of similar to 9100 over the number found in previous analyses o
f the same IPC images. We find that not only is the reliability of the
Two-Sigma Catalog a function of source significance sigma, it is a fu
nction of off-axis angle on the detector as well. The application of d
ifferent signal-to-noise thresholds at different off-axis angles thus
enables one to tune the reliability of the catalog. The chief motivati
on for studying large numbers of faint X-ray sources is to search for
possible new components of the cosmic X-ray background. To select out
real celestial X-ray sources in the Two-Sigma Catalog, we apply astron
omical catalogs at other wavelengths as filters. For example, the cros
s-correlation of the Two-Sigma Catalog with catalogs from surveys of t
he radio and infrared sky has yielded large samples of faint X-ray sou
rces that are similar to 90% reliable. Optical spectroscopy of 77 unid
entified faint X-ray sources has turned up several surprises, illustra
ting the merits of selecting X-ray sources using a variety of methods:
high-redshift quasars (one at z = 4.30), which are absent in the EMSS
, X-ray-luminous (L(X) approximate to 10(43) ergs s(-1)) radio-loud el
liptical galaxies with optical spectra devoid of emission lines, and i
nfrared-bright active galactic nuclei whose optical spectra are domina
ted by starburst galaxy features. Follow-up observations are scheduled
to determine whether any of these types of objects represent a previo
usly unrecognized component of the X-ray background.