We have compiled a sample of early-type cluster galaxies from 0 < z < 1.3 and measured the evolution of their ellipticity distributions. Our sample contains 487 galaxies in 17 z>0.3 clusters with high quality space-based imaging and a comparable sample of 210 galaxies in 10 clusters at z<0.05. We select early-type galaxies (elliptical and S0 galaxies) that fall within the cluster R_{200}, and which lie on the red-sequence in the magnitude range -19.3 > M_B > -21, after correcting for luminosity evolution. Our ellipticity measurements are made in a consistent manner over our whole sample. We perform extensive simulations to quantify the systematic and statistical errors, and find that it is crucial to use PSF-corrected model fits. We find that neither the median ellipticity, nor the shape of the ellipticity distribution of cluster early-type galaxies evolves with redshift from z ~ 0 to z > 1. These results are strongly suggestive of an unchanging overall bulge-to-disk ratio distribution for cluster early-type galaxies over the last ~8Gyr. This result contrasts with that from visual classifications which show that the fraction of morphologically-selected disk-dominated early-type galaxies, or S0s, is significantly lower at z>0.4 than at z~0. Taking the ellipticity measurements and assuming, as in all previous studies, that the intrinsic ellipticity distribution of both elliptical and S0 galaxies remains constant, then we conclude from the lack of evolution in the observed early-type ellipticity distribution that the relative fractions of ellipticals and S0s do not evolve from z~1 to z=0 for a red-sequence selected samples of galaxies in the cores of clusters of galaxies.
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