THE FUNDAMENTAL RELATIONS OF ELLIPTIC GALAXIES

We investigate the basic laws that determine the global structure and metal abundance of elliptical galaxies. The existence of the Fundament al Plane has been considered to imply that the virial theorem is the o nly structural constraint for giant ellipticals. However, we show that giant ellipticals do not uniformly cover the Fundamental Plane, but a re located in a band which is not the result of selection effects. Thi s 'Fundamental Band' implies a second constraint between scalelength a nd galaxy mass. On the basis of this result, we present a new framewor k in which the structure and metal abundance of giant ellipticals are determined by only three fundamental relations: M is-proportional-to R [upsilon2], M is-proportional-to R(zeta) and Z is-proportional-to [ups ilon2]xi, where M is the galaxy mass, R is the half-mass radius, [upsi lon2] is the mean square speed of the system's stars and Z is the aver age metallicity of the stellar population; zeta and xi are constants. Xi is uniquely determined from the observations. The value of zeta, ho wever, depends on the assumed scaling laws that relate M and R to the observed luminosity and half-light radius. We assume M/L is-proportion al-to M(eta) and R/R(e) is-proportional-to M(lambda). The two constant s eta and lambda are mutually constrained by observations, but their v alues are not uniquely determined. All the wide variety of observed gl obal correlations can be derived as simple combinations of these funda mental relations. This simple framework provides new insights into the intrinsic differences between giant and dwarf ellipticals. The observ ed universality of the luminosity- and metallicity-velocity dispersion correlations strongly suggests a simple solution within our framework in which zeta, xi and eta adopt the same values for both dwarf and gi ant ellipticals. In this case, we show that the dependence of R/R(e) o n galaxy mass is the only difference between the two galaxy families. We compare this framework with a theoretical scenario of galaxy format ion that combines the hierarchical clustering and the galactic wind mo dels. This picture provides a consistent explanation of the fundamenta l relations of all elliptical galaxies, assuming R/R(e) approximately constant for dwarf ellipticals while, for giant ellipticals, we find t hat R/R(e) must be a decreasing function of galaxy mass.