Two-size approximation: a simple way of treating the evolution of grain
  size distribution in galaxies
  Full calculations of the evolution of grain size distribution in galaxies are
in general computationally heavy. In this paper, we propose a simple model of
dust enrichment in a galaxy with a simplified treatment of grain size
distribution by imposing a `two-size approximation'; that is, all the grain
population is represented by small (grain radius a < 0.03 micron) and large (a
> 0.03 micron) grains. We include in the model dust supply from stellar ejecta,
destruction in supernova shocks, dust growth by accretion, grain growth by
coagulation and grain disruption by shattering, considering how these processes
work on the small and large grains. We show that this simple framework
reproduces the main features found in full calculations of grain size
distributions as follows. The dust enrichment starts with the supply of large
grains from stars. At a metallicity level referred to as the critical
metallicity of accretion, the abundance of the small grains formed by
shattering becomes large enough to rapidly increase the grain abundance by
accretion. Associated with this epoch, the mass ratio of the small grains to
the large grains reaches the maximum. After that, this ratio converges to the
value determined by the balance between shattering and coagulation, and the
dust-to-metal ratio is determined by the balance between accretion and shock
destruction. With a Monte Carlo simulation, we demonstrate that the simplicity
of our model has an advantage in predicting statistical properties. We also
show some applications for predicting observational dust properties such as
extinction curves.
