Relative Sizes of X-ray and Optical Images of Elliptical Galaxies; Correlation with X-ray Luminosity

Optical parameters of elliptical galaxies are tightly correlated, but their x-ray parameters vary widely. The x-ray luminosity L_x ranges over more than an order of magnitude for ellipticals having similar optical luminosity L_B. The source of this scatter has been elusive. We show here that the dispersion in L_x for fixed optical luminosity L_B correlates strongly with the dimensionless ratio of the sizes of the x-ray and optical images, r_ex/r_e. Specifically, we find that (L_x/L_B) is proportional to (r_{ex}/r_e)^{0.60 \pm 0.30}, a version of the correlation that is independent of distance. This correlation may be a natural result of mergings and tidal truncations that are expected during the formation and early evolution of ellipticals in groups of galaxies. The radial structure of x-ray images also varies: some are compact (e.g. NGC 4649, 7626, 5044), others diffuse (e.g. NGC 4636, 1399)