On the Invariant Distribution of Galaxies in the re –<µ>e plane out to z = 0.64

This work deals with the evolution of the relation between half-light (effective) radius, r e , and mean surface brightness, < µ > e , (known as Kormendy relation) at intermediate redshifts. A large sample of spheroids (N ∼ 230) in the three clusters of galaxies A 209 at z = 0.21, AC 118 at z = 0.31, and EIS 0048 at z = 0.64 is analyzed by using ground-based data. Effective parameters have been derived in the R-band for A 209 and AC 118, and in the I-band for EIS 0048, covering closely the same V-band restframe. The slope, β, the intrinsic dispersion, σ (i) <µ>e , and the zeropoint, α, of the r e – < µ > e relation are obtained by a fitting procedure accounting for the selection criteria of the samples. The slope of the Kormendy relation for the three clusters turns out to be the same at all redshifts: we obtain β = 2.91 ± 0.08. We show that this result constrains the formation epoch of galaxy stellar populations to change by less than 18–28% per decade of galaxy radius. Moreover, the intrinsic dispersion of the relation does not vary with redshift, σ (i) <µ>e = 0.31 ± 0.04, and the distributions of galaxies in the plane of the effective parameters do not vary from cluster to cluster, as proven by the Kolmogorov–Smirnov test. 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 – < µ > e plane at least from z = 0.64 to date. The evolution of the zeropoint is compared with predictions of stellar population models: consistently with previous studies, the observed trend can be explained by a pure Tolman signal superposed to the luminosity evolution of stellar populations having a high formation redshift (z f > 2).