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
$z$.
