On the grain-size distribution of turbulent dust growth
  It has recently been shown that turbulence in the interstellar medium (ISM)
can significantly accelerate the growth of dust grains by accretion of
molecules, but the turbulent gas-density distribution also plays a crucial role
in shaping the grain-size distribution. The growth velocity, i.e., the rate of
change of the mean grain radius, is proportional to the local gas density if
the growth species (molecules) are well-mixed in the gas. As a consequence,
grain growth happens at vastly different rates in different locations, since
the gas-density distribution of the ISM shows a considerable variance. Here, it
is shown that grain-size distribution (GSD) rapidly becomes a reflection of the
gas-density distribution, irrespective of the shape of the initial GSD. This
result is obtained by modelling ISM turbulence as a Markov process, which in
the special case of an Ornstein-Uhlenbeck process leads to a lognormal
gas-density distribution, consistent with numerical simulations of isothermal
compressible turbulence. This yields an approximately lognormal GSD; the sizes
of dust grains in cold ISM clouds may thus not follow the commonly adopted
power-law GSD with index -3.5, but corroborates the use of a log-nomral GSD for
large grains, suggested by several studies. It is also concluded that the very
wide range of gas densities obtained in the high Mach-number turbulence of
molecular clouds must allow formation of a tail of very large grains reaching
radii of several microns.
