Shattering as a source of small grains in the circum-galactic medium
  Observed reddening in the circum-galactic medium (CGM) indicates a
significant abundance of small grains, of which the origin is still to be
clarified. We examine a possible path of small-grain production through
shattering of pre-existing large grains in the CGM. Possible sites where
shattering occurs on a reasonable time-scale are cool clumps with hydrogen
number density $n_\mathrm{H}\sim 0.1$ cm$^{-3}$ and gas temperature
$T_\mathrm{gas}\sim 10^4$ K, which are shown to exist through observations of
Mg II absorbers. We calculate the evolution of grain size distribution in
physical conditions appropriate for cool clumps in the CGM, starting from a
large-grain-dominated distribution suggested from theoretical studies. With an
appropriate gas turbulence model expected from the physical condition of cold
clumps (maximum eddy size and velocity of $\sim$100 pc and 10 km s$^{-1}$,
respectively), together with the above gas density and temperature and the
dust-to-gas mass ratio inferred from observations (0.006), we find that
small-grain production occurs on a time-scale (a few $\times 10^8$ yr)
comparable to the lifetime of cool clumps derived in the literature. Thus, the
physical conditions of the cool clouds are favrourable for small-grain
production. We also confirm that the reddening becomes significant on the above
time-scale. Therefore, we conclude that small-grain production by shattering is
a probable cause for the observed reddening in the CGM. We also mention the
effect of grain materials (or their mixtures) on the reddening at different
redshifts (1 and 2).
