  To test the cooling flow model of early-type galaxies, we obtained a complete
magnitude-limited sample of 34 early-type galaxies, observed with the PSPC and
HRI on ROSAT. The X-ray to optical distribution of galaxies implies a lower
envelope that is consistent with the stellar emission inferred from Cen A. When
this stellar component is removed, the gaseous emission is related to the
optical luminosity by Lx proportional to L_B^m, where m = 3.0-3.5,
significantly steeper than the standard theory (m = 1.7). The dispersion about
the correlation is large, with a full range of 30-100 in Lx for a fixed L_B.
The X-ray temperature is related to the velocity dispersion temperature as Tx
proportional to Tsigma^n, where n = 1.43 +/- 0.21, although for several
galaxies, Tx is about twice Tsigma. The excessively hot galaxies are generally
the most luminous and are associated with the richest environments. We suggest
a model whereby environment influences the X-ray behavior of these galaxies:
early-type galaxies attempt to drive partial or total galactic winds, which can
be stifled by the pressure of their environment. Stifled winds should lead to
hotter and higher luminosity systems, which would occur most commonly in the
richest environments, as observed.
