Shattering by turbulence as a production source of very small grains

The origin of grain size distribution in the interstellar medium is one of the most fundamental problems in the interstellar physics. In the Milky Way, smaller grains are more abundant in number, but their origins are not necessarily specified and quantified. One of the most efficient drivers of small grain production is interstellar turbulence, in which dust grains can acquire relative velocities large enough to be shattered. Applying the framework of shattering developed in previous papers, we show that small ($a\la 0.01~\micron$) grains reach the abundance level observed in the Milky Way in $\sim 10^8$ yr (i.e. within the grain lifetime) by shattering in warm neutral medium. We also show that if part of grains experience additional shattering in warm ionized medium, carbonaceous grains with $a\sim 0.01~\micron$ are redistributed into smaller sizes. This could explain the relative enhancement of very small carbonaceous grains with $a\sim 3$--100 \AA. Our theory also explains the ubiquitous association between large grains and very small grains naturally. Some tests for our theory are proposed in terms of the metallicity dependence.