On the Invariant Distribution of Galaxies in the re--mie plane out to z   = 0.64
  We study the evolution of the relation between half-light (effective) radius, r_e, and mean surface brightness, mi_e, known as Kormendy relation, out to redshift z=0.64 in V-band restframe on the basis of a large sample of spheroidal galaxies (N=228) belonging to three clusters of galaxies. The present sample constitutes the largest data set for which the Kormendy relation is investigated up to a look-back time of 6 Gyr (H_0= 70 Km/s/Mpc, Omega_M=0.3, Omega_Lambda=0.7). A new fitting procedure, which suitably accounts for selection criteria effects, allows for the first time to study the trend of the slope (beta) and of the intrinsic dispersion (sigma_mi_e) of the Kormendy relation, and the properties of the whole distribution in the r_e -- mi_e, plane as a function of look-back time. The slope beta of the relation does not change from z=0.64 to the present epoch: beta=2.92+/-0.08, implying a tight constraint of 18--28% on the variation of the stellar formation epoch along the sequence of spheroidal galaxies per decade of radius. The intrinsic dispersion of the relation, sigma_i_<mi>_e=0.40+/-0.03, does not vary with redshift and the distribution of galaxy sizes as well as the distribution in the plane of the effective parameters do not vary among the clusters, as proven by the Kolmogorov--Smirnov tests. We conclude that, whatever the mechanism driving galaxy evolution is, it does not affect significantly the properties of bright galaxies in the log(r_e) -- mi_e, plane at least since z=0.64. The evolution of the zeropoint of the Kormendy relation is fully explained by the cosmological dimming in an expanding universe plus the passive luminosity evolution of stellar populations with high formation redshift (z_f>2). 
F. La Barbera (INAF - Osservatorio Astronomico di Capodimonte   INAF-OAC), G. Busarello (INAF-OAC), P. Merluzzi (INAF-OAC), ...