A MULTIPARAMETRIC ANALYSIS OF THE EINSTEIN SAMPLE OF EARLY-TYPE GALAXIES .3. COMPARISONS WITH THE KAPPA-PARAMETERS

We have extended our bivariate and multivariate statistical analysis of the Einstein sample of early-type galaxies (Fabbiano, Kim, and Trinchieri 1992; Eskridge, Fabbiano, and Rim 1995a, b) to include a consideration of the kappa-parameters defined by Bender, Burstein, and Faber (1992). The kappa-parameters are defined such that kappa(1) scales with virial mass, kappa(3) scales with inner M/L ratio, and kappa(2) is perpendicular to both kappa(1) and kappa(3). The kappa 1-kappa(3) plane is essentially edge-on to the Bender et al. (1992) formulation of the fundamental plane, and the parameter delta kappa(3) describes the scatter about that plane. We find that L(B), L(X), and L(6) are all strongly correlated with kappa(1) Partial Spearman rank analysis shows these trends to be independent of the correlations between the luminosities. There are also significant bivariate trends of both L(X) and L(6) with kappa(3). Partial Spearman rank analysis indicates that the L(X)-kappa(3), trend is the dominant one, thus arguing for a connection between the prominence of X-ray coronae and the inner M/L. This suggests that galaxies with central excesses of dark matter also have more massive extended dark matter halos, providing a mechanism for retaining larger amounts of hot interstellar medium. We find evidence for a correlation between Mg-2 and delta kappa(3) that is independent of correlations of these two parameters with sigma(v) and is enhanced when tested for constant alpha(4). The strengthening of the Mg-2-delta kappa(3) correlation when tested for contant alpha(4) indicates an underlying connection between the scatter about the fundamental plane and the Type II supernova enrichment history of the central regions of elliptical galaxies that is independent of the details of the central structure of individual galaxies. This suggests that the Mg-2-delta kappa(3) trend is not related to the Mg-2 enhancements associated with kinematically decoupled cores seen in some disky elliptical galaxies (e.g., Bender and Surma 1992). It may be that systems with higher inner M/L(e) (at a given mass) were more able to retain the metals generated in early epochs of star formation. Alternatively, systems experiencing more active or prolonged star formation may have produced an excess of baryonic dark matter from stellar remnants that is reflected in their higher M/L(e).