No evidence for evolution in the typical rest-frame UV sizes or the incidence of morphological disturbance amongst L$_*$ galaxies at 4<z<8

We present the results of a study investigating the sizes and morphologies of redshift 4 < z < 8 galaxies in the CANDELS GOODS-S, HUDF and HUDF parallel fields. Based on non-parametric measurements and incorporating a careful treatment of measurement biases, we quantify the typical size of galaxies at each redshift as the peak of the log-normal size distribution, rather than the arithmetic mean size. Parameterizing the evolution of galaxy half-light radius as $r_{50} \propto (1+z)^n$, we find $n = -0.20 \pm 0.26$ at bright UV-luminosities ($0.3L_{*(z=3)} < L < L_*$) and $n = -0.47 \pm 0.62$ at faint luminosities ($0.12L_* < L < 0.3L_*$). Furthermore, simulations based on artificially redshifting our z~4 galaxy sample show that we cannot reject the null hypothesis of no size evolution. We show that this result is caused by a combination of the size-dependent completeness of high-redshift galaxy samples and the underestimation of the sizes of the largest galaxies at a given epoch. To explore the evolution of galaxy morphology we first compare asymmetry measurements to those from a large sample of simulated single Sersic profiles, in order to robustly categorise galaxies as either `smooth' or `disturbed'. Comparing the disturbed fraction amongst bright ($M_{UV} \leq -20$) galaxies at each redshift to that obtained by artificially redshifting our z~4 galaxy sample, while carefully matching the size and UV-luminosity distributions, we find no clear evidence for evolution in galaxy morphology over the redshift interval 4 < z < 8. Therefore, based on our results, a bright ($M_{UV} \leq -20$) galaxy at z~6 is no more likely to be measured as `disturbed' than a comparable galaxy at z~4, given the current observational constraints.