ROSAT temperatures and abundances for a complete sample of elliptical galaxies

We determine X-ray temperatures and abundances for elliptical galaxies drawn from a complete, optically selected sample. The optical magnitude-limited sample consists of 43 galaxies, complete to a (corrected) B magnitude of m(B)(0) = 11.36. Of these, 30 have enough X-ray spectral counts to allow temperature determinations. We find that the temperatures of the X-ray-emitting gas in these elliptical galaxies are correlated with the central stellar velocity dispersions: T proportional to sigma(1.45); this is a shallower trend than the simple thermal relation T proportional to sigma(2). The diffuse gas is substantially hotter than the kinetic temperature of the luminous stars, since kT > mu m(p) sigma(2) for all galaxies with measurable temperatures. This strongly indicates that dark matter halos are characterized by velocity dispersions that exceed those of the luminous stars. We see no evidence of emission from X-ray binaries becoming progressively more dominant in lower luminosity elliptical galaxies. We find that so-called ''supersoft'' sources adhere to the observed kT-sigma relation, so they are no softer than expected for their velocity dispersions. We also find that interstellar medium temperatures and abundances are correlated, with the gas in hotter systems being more enriched than in cooler galaxies. However, no correlation is found between gaseous abundances and stellar abundances, as inferred from Mg-2 indices.