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In spite of their simple shape, spheroids reveal a very complex nature. Some memory of their formation lies in their dynamical structure and stellar population. The spheroid complexity is strengthened by the systematical presence of super massive black holes (SMBHs) at their nuclear regions, with rather well defined correlations between the SMBH mass and the spheroid luminosity or velocity dispersion (Magorrian et al. 1998; Ferrarese & Merrit 2000; Gebhardt et al. 2000), and the bulge concentration (Graham et al. 2001; Graham, this volume). AGN and QSO activity seem to be intimately associated with SMBHs. On the other hand, observations reveal that the ultra high luminosity infrared galaxies (ULIGs) show evidence of recent galaxy collisions (Sanders and Mirabel 1996); therefore ULIGs may also be linked to the formation of spheroids.

5.1. Relevant observational properties and correlations

Radius, velocity dispersion and surface brightness are related by the fundamental plane (FP) (Bender et al. 1992), which is basically related to the virial theorem and to the M/L ratio inside the effective radius. The use of NIR photometry (Pahre 1998, Pahre et al. 1998a) reduces the effects of the SF history on the M/L ratio and traces the gravitational contribution of dark matter. A homology breaking (dynamical [Busarello et al. 1997; Graham & Colless 1997] and/or photometric [Bertin et al. 2002]), connected to the spheroid formation and evolution, introduces effects difficult to evaluate. The observed evolution of the FP intercept up to z = 0.4 suggests a passive evolution for the stellar population, with a formation redshift of 1.0 - 1.5 (Pahre et al. 1998b, Treu et al. 2001). The change in slope with z is not clear, but the possibility that massive ellipticals could be younger than the less massive ones seems to be ruled out. The scatter of the FP does not show any correlation with metallicity, redshift (age effect), or environment (field or clusters).

The brightness of giant spheroids decreases with size (Kormendy relation, KR; Kormendy 1977; Pahre et al. 1998a), implying that the mean density of spheroids decreases with their mass. It is interesting to note that a similar tendency is shown by dark virialized halos in a hierarchical cosmogony. However, at present it is not clear if the density-mass relation of galaxy spheroids can be explained in terms of the dark halo properties alone or by other processes related to the gas hydrodynamics or to the SF. The observed luminosity evolution agrees with the passive evolution of a star population formed at z gtapprox 1. The Faber-Jackson relation (FJR) may be understood as a combination of the FP and the KR.

The Mg2-velocity dispersion relation shows mainly how the metallicity increases with the mass. The color-magnitude relation involves both metallicity and age. The evolution up to z = 1 of the zero point and of the scatter of this relation suggests a formation redshift gtapprox 2 for most of the field and cluster ellipticals (see Peebles 2003) (even if some uncertainty derives from the sample selection).

From the shape of their isophotes, elliptical galaxies are divided into disky and boxy. It has been suggested that the origin of this dichotomy is related to the mass ratio of the merged disk progenitors (Naab et al. 1999). High resolution observations of the central region of luminous, slowly rotating boxy ellipticals (mainly members of clusters), identify a shallow core, while in faint rapidly rotating disky ellipticals (mainly field galaxies), peaked power-law density profiles were found (Faber et al. 1997; Carollo et al. 1997).

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