Morphological and spectroscopic studies of high redshift clusters indicate that a significant fraction of present-day early-type galaxies was transformed from star forming galaxies at z < 1 .
On the other hand , the slow luminosity evolution of early-type galaxies and the low scatter in their color-magnitude relation indicate a high formation redshift of their stars .
In this paper we construct models which reconcile these apparently contradictory lines of evidence , and we quantify the effects of morphological evolution on the observed photometric properties of early-type galaxies in distant clusters .
We show that in the case of strong morphological evolution the apparent luminosity and color evolution of early-type galaxies are similar to that of a single age stellar population formed at z = \infty , irrespective of the true star formation history of the galaxies .
Furthermore , the scatter in age , and hence the scatter in color and luminosity , is approximately constant with redshift .
These results are consequences of the ‘ ‘ progenitor bias ’ ’ : the progenitors of the youngest low redshift early-type galaxies drop out of the sample at high redshift .
We construct models which reproduce the observed evolution of the number fraction of early-type galaxies in rich clusters and their color and luminosity evolution simultaneously .
Our modelling indicates that \sim 50 % of early-type galaxies were transformed from other galaxy types at z < 1 , and their progenitor galaxies may have had roughly constant star formation rates prior to morphological transformation .
The effect of the progenitor bias on the evolution of the mean M / L ratio and color can be estimated .
The progenitor bias is a linear function of the scatter in the color-magnitude relation produced by age variations , and is maximal if the observed scatter is entirely due to age differences .
After correcting the observed evolution of the mean M / L _ { B } ratio for the maximum progenitor bias we find that the mean luminosity weighted formation redshift of stars in early-type galaxies \langle z _ { * } \rangle = 3.0 ^ { +0.9 } _ { -0.5 } for \Omega _ { m } = 0.3 and \Omega _ { \Lambda } = 0 , and \langle z _ { * } \rangle = 2.0 ^ { +0.3 } _ { -0.2 } for \Omega _ { m } = 0.3 and \Omega _ { \Lambda } = 0.7 .
Our analysis places the star formation epoch of early-type galaxies later than previous studies which ignored the effects of progenitor bias .
The results are consistent with the idea that ( some ) Ly-break galaxies are star forming building blocks of massive early-type galaxies in clusters .