  A recent analysis of the "Einstein" sample of early-type galaxies has
revealed that at any fixed optical luminosity Lb S0 galaxies have lower mean
X-ray luminosity Lx per unit Lb than ellipticals. Following a previous
analytical investigation of this problem (Ciotti & Pellegrini 1996), we have
performed 2D numerical simulations of the gas flows inside S0 galaxies in order
to ascertain the effectiveness of rotation and/or galaxy flattening in reducing
the Lx/Lb ratio. The flow in models without SNIa heating is considerably
ordered, and essentially all the gas lost by the stars is cooled and
accumulated in the galaxy center. If rotation is present, the cold material
settles in a disk on the galactic equatorial plane. Models with a time
decreasing SNIa heating host gas flows that can be much more complex. After an
initial wind phase, gas flows in energetically strongly bound galaxies tend to
reverse to inflows. This occurs in the polar regions, while the disk is still
in the outflow phase. In this phase of strong decoupling, cold filaments are
created at the interface between inflowing and outflowing gas. Models with more
realistic values of the dynamical quantities are preferentially found in the
wind phase with respect to their spherical counterparts of equal Lb. The
resulting Lx of this class of models is lower than in spherical models with the
same Lb and SNIa heating. At variance with cooling flow models, rotation is
shown to have only a marginal effect in this reduction, while the flattening is
one of the driving parameters for such underluminosity, in accordance with the
analytical investigation.
