On the Size Evolution of a Galactic Disk in Hierarchical Merging of Cold Dark Matter Halos

We investigate the dynamical effects of dark matter subhalos on the structure and evolution of a galactic disk, using semi-analytic method that includes approximated and empirical relations as achieved in detailed numerical simulations of the cold dark matter model. We calculate the upper limit for the size of a galactic disk at a specific redshift $z$, based on the orbital properties of subhalos characterized by their pericentric distances from the center of a host halo. We find that this possibly largest size of a disk as determined by the smallest pericentric distances of subhalos shows the characteristic properties, which are basically in agreement with an observed galactic disk at low and high $z$. Namely, it is found that a massive disk can have a larger size than a less massive one, because of its stability against the destruction effect of subhalos. Also, with fixed mass, the size of a galactic disk at low $z$ can be larger than that at high $z$, reflecting the orbital evolution of subhalos with respect to a host halo. These results suggest that the presence and structure of a galactic disk may be dynamically limited by the interaction with dark matter substructures, especially at high $z$.