The Effects of Galaxy Shape and Rotation on the X-ray Haloes of
  Early-Type Galaxies
  We present a detailed diagnostic study of the observed temperatures of the
hot X-ray coronae of early-type galaxies. By extending the investigation
carried out in Pellegrini (2011) with spherical models, we focus on the
dependence of the energy budget and temperature of the hot gas on the galaxy
structure and internal stellar kinematics. By solving the Jeans equations we
construct realistic axisymmetric three-component galaxy models (stars, dark
matter halo, central black hole) with different degrees of flattening and
rotational support. The kinematical fields are projected along different lines
of sight, and the aperture velocity dispersion is computed within a fraction of
the circularized effective radius. The model parameters are chosen so that the
models resemble real ETGs and lie on the Faber-Jackson and Size-Luminosity
relations. For these models we compute T_* (the stellar heating contribution to
the gas injection temperature) and T_gm (the temperature equivalent of the
energy required for the gas escape). In particular, different degrees of
thermalisation of the ordered rotational field of the galaxy are considered. We
find that T_* and T_gm can vary only mildly due to a pure change of shape.
Galaxy rotation instead, when not thermalised, can lead to a large decrease of
T_*; this effect can be larger in flatter galaxies that can be more
rotationally supported. Recent temperature measurements T_x, obtained with
Chandra, are larger than, but close to, the T_* values of the models, and show
a possible trend for a lower T_x in flatter and more rotationally supported
galaxies; this trend can be explained by the lack of thermalisation of the
whole stellar kinetic energy. Flat and rotating galaxies also show lower L_x
values, and then a lower gas content, but this is unlikely to be due to the
small variation of T_gm found here for them.
