Morphological Demographics of Galaxies at $z\sim 10-16$: Log-Normal Size Distribution and Exponential Profiles Consistent with the Disk Formation Scenario

We homogeneously investigate the morphological properties of $169$ galaxies at $z\sim 10-16$ with deep JWST NIRCam images employing our established techniques of GALFIT modeling and uncertainty evaluation (systematics+statistics). We obtain effective radii $r_{\mathrm{e}}$ ranging $20-500$ pc, with a distribution significantly broader than the scatter made by the uncertainties. We find that the $r_{\mathrm{e}}$ distribution is well described by a log-normal distribution with a mean of $r_{\mathrm{e}}=133_{-12}^{+13}$ pc and a standard deviation of ${\sigma }_{\mathrm{l}\mathrm{n}{r}_{\mathrm{e}}}=0.52\pm 0.08$. The standard deviation is comparable to that of local galaxies, indicating no significant evolution over $z\sim 0-10$. We also find that the axis ratio distribution is nearly uniform, statistically similar to that of local spirals. We estimate the virial radius $r_{\mathrm{v}\mathrm{i}\mathrm{r}}$ from the stellar masses via the star-formation main sequence and stellar-to-halo mass relation, obtaining a stellar-to-halo size ratio $r_{\mathrm{e}}\mathrm{/}{r}_{\mathrm{v}\mathrm{i}\mathrm{r}}=0.015_{-0.005}^{+0.015}$, which is comparable to those of star-forming galaxies in the local and low-$z$ Universe. Our results of 1) the log-normal $r_{\mathrm{e}}$ distribution, 2) the uniform axis ratio distribution, and 3) a mean radial profile consistent with an exponential profile ($n=1.3\pm 0.6$) suggest that galaxies at $z\sim 10-16$ generally follow the classical galaxy disk formation scenario with a specific disk angular momentum fraction of $j_{\mathrm{d}}\mathrm{/}{m}_{\mathrm{d}}\sim 0.5-1$. Interestingly, we identify two remarkable outliers GN-z11 ($z_{\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}}=10.60$) and GHZ2 ($z_{\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}}=12.34$) with $r_{\mathrm{e}}=55_{-6}^{+5}$ pc and $39\pm 11$ pc, respectively, that may not be explained by disk structures but by AGN or compact star-forming galaxies merging underway in short periods of time, as reproduced in numerical simulations.