  By performing $N$-body simulations, we investigated fundamental processes of
collisions between dust aggregates composed of submicron-sized icy dust
monomers. We examined the mass distribution of fragments in the collisional
outcomes in a wide range of the mass ratio and the collision velocity between
colliding dust aggregates. We derived analytic expressions of the mass
distribution of large remnants and small fragments by numerical fitting to the
simulation results. Our analytic formulae for masses of the large remnants can
reproduce the contribution of mass transfer from a large target to a small
projectile, which occurs for a mass ratio of $\gtrsim 3$ and is shown in a
previous study (Hasegawa et al. 2021). We found that the power-law index of the
cumulative mass distribution of the small fragments is independent of the mass
ratio and only weakly dependent on the collision velocity. On the other hand,
the mass fraction of fragments of individual dust monomers decreases with an
increasing total mass of colliding aggregates for a fixed mass ratio. This
tendency implies that multiple hierarchical disruptive collisions (i.e.,
collisions between fragments, collisions between fragments of fragments) are
required for producing a large amount of individual dust monomers via
collisional fragmentation. Our fragment model suggests that the total geometric
cross section integrated over the fragments is estimated to be about the same
order of the geometric cross section of the target.
