  We use ROSAT PSPC data to study the X-ray properties of a sample of twelve
poor groups that have extensive membership information (Zabludoff and Mulchaey
1997; Paper I). Diffuse X-ray emission is detected in nine of these groups. In
all but one of the X-ray detected groups, the X-ray emission is centered on a
luminous elliptical galaxy. Fits to the surface brightness profiles of the
X-ray emission suggest the presence of two X-ray components in these groups.
The first component is centered on the central elliptical galaxy. The location
and extent of this component, combined with its X-ray temperature and
luminosity, favor an origin in the interstellar medium of the central galaxy.
Alternatively, the central component may be the result of a large-scale cooling
flow. The second X-ray component is detected out to a radius of at least
100-300 kpc. This component follows the same relationships found among the
X-ray temperature, X-ray luminosity and optical velocity dispersion of rich
clusters. This result suggests that the X-ray detected groups are low-mass
versions of clusters and that the extended gas component can properly be called
the intragroup medium, in analogy to the intracluster medium in clusters. We
also find a trend for the position angle of the optical light in the central
elliptical galaxy to align with the position angle of the large-scale X-ray
emission. (Abridged)
