Isophote Shapes of Early-Type Galaxies in Massive Clusters at $z\sim1$ and 0

We compare the isophote shape parameter $a_{4}$ of early-type galaxies (ETGs) between $z\sim1$ and 0 as a proxy for dynamics to investigate the epoch at which the dynamical properties of ETGs are established, using cluster ETG samples with stellar masses of $\log(M_{*}/M_{\odot})\geq10.5$ which have spectroscopic redshifts. We have 130 ETGs from the Hubble Space Telescope Cluster Supernova Survey for $z\sim1$ and 355 ETGs from the Sloan Digital Sky Survey for $z\sim0$. We have developed an isophote shape analysis method which can be used for high-redshift galaxies and has been carefully compared with published results. We have applied the same method for both the $z\sim1$ and $0$ samples. We find similar dependence of the $a_{4}$ parameter on the mass and size at $z\sim1$ and 0; the main population of ETGs changes from disky to boxy at a critical stellar mass of $\log(M_{*}/M_{\odot})\sim11.5$ with the massive end dominated by boxy. The disky ETG fraction decreases with increasing stellar mass both at $z\sim1$ and $0$, and is consistent between these redshifts in all stellar mass bins when the Eddington bias is taken into account. Although uncertainties are large, the results suggest that the isophote shapes and probably dynamical properties of ETGs in massive clusters are already in place at $z>1$ and do not significantly evolve in $z<1$, despite significant size evolution in the same galaxy population. The constant disky fraction favors less violent processes than mergers as a main cause of the size and morphological evolution of intermediate mass ETGs in $z<1$.