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We determine X-ray temperatures and abundances for elliptical galaxies drawnfrom a complete, optically selected sample. The optical magnitude-limitedsample consists of 43 galaxies, complete to a (corrected) B magnitude ofm_B^o=11.36. Of these, 30 have enough X-ray spectral counts to allowtemperature determinations. We find that the temperatures of the X-ray emittinggas in these ellipticals are correlated with the central stellar velocitydispersions: T ~ sigma^1.45; this is a shallower trend than the simple thermalrelation T ~ sigma^2. The diffuse gas is substantially hotter than the kinetictemperature of the luminous stars, since kT > mu m_p sigma^2 for all galaxieswith measurable temperatures. This strongly indicates that dark matter halosare characterized by velocity dispersions which exceed those of the luminousstars. We see no evidence of emission from X-ray binaries becomingprogressively more dominant in lower luminosity ellipticals. We find thatso-called "supersoft" sources adhere to the observed kT-sigma relation, so theyare no softer than expected for their velocity dispersions. We also find thatISM temperatures and abundances are correlated, with the gas in hotter systemsbeing more enriched than in cooler galaxies. However, no correlation is foundbetween gaseous abundances and stellar abundances, as inferred from Mg_2indices.

[ITAL]ROSAT[/ITAL] Temperatures and Abundances for a Complete Sample of Elliptical Galaxies