Evolution of dust grain size distribution by shattering in the
  interstellar medium: robustness and uncertainty
  Shattering of dust grains in the interstellar medium is a viable mechanism of
small grain production in galaxies. We examine the robustness or uncertainty in
the theoretical predictions of shattering. We identify $P_1$ (the critical
pressure above which the deformation destroys the original lattice structures)
as the most important quantity in determining the timescale of small grain
production, and confirm that the same $P_1/t$ ($t$ is the duration of
shattering) gives the same grain size distribution [$n(a)$, where $a$ is the
grain radius] after shattering within a factor of 3. The uncertainty in the
fraction of shocked material that is eventually ejected as fragments causes
uncertainties in $n(a)$ by a factor of 1.3 and 1.6 for silicate and
carbonaceous dust, respectively. The size distribution of shattered fragments
have minor effects as long as the power index of the fragment size distribution
is less than ~ 3.5, since the slope of grain size distribution $n(a)$
continuously change by shattering and becomes consistent with $n(a)\propto
a^{-3.5}$. The grain velocities as a function of grain radius can have an
imprint in the grain size distribution especially for carbonaceous dust. We
also show that the formulation of shattering can be simplified without losing
sufficient precision.
