Environmental impacts on the rest-frame UV size and morphology ofstar-forming galaxies at $z\sim2$

We report the measurement of rest-frame UV size and morphology of H$\alpha$-emission-selected star-forming galaxies (HAEs) in four protoclusters at z $\sim$ 2 (PKS 1138-262, USS 1558-003, PHz G237.0+42.5, and CC 2.2) using archival Hubble Space Telescope Advanced Camera Surveys (HST/ACS) F814W data. We compare the measurement of 122 HAEs in protoclusters detected by HST/ACS to a coeval comparison field sample of 436 HAEs. We find the size distributions of protocluster and field HAEs are similar with typical half-light radius of $\sim$ 2.5 kpc. At fixed stellar mass, there is no significant difference between HAE in protocluster and in field, which is also supported by stacking analyses. This result suggests that the environment does not significantly affect the size of galaxies during the star-forming phase at this epoch. Based on S\'ersic index and non-parametric morphologies, HAE morphologies in both environments at $z\sim2$ in rest-frame UV are consistent with disk-like star-forming galaxies, although we also find $29\% \pm 4\%$ HAEs have peculiar or disturbed morphologies. The fraction of disturbed galaxies is higher in protocluster environment, with $39 \pm 8 \%$ protocluster HAEs showing disturbed morphologies, compared to $26\pm4\%$ in the comparison field. The apparent disturbed morphologies are correlated with higher star-formation activity and may be caused by either in situ giant clumps or mergers.