Evolution of dust grain size distribution and grain porosity in galaxies
  The radiative properties of interstellar dust are affected not only by the
grain size distribution but also by the grain porosity. We develop a model for
the evolution of size-dependent grain porosity and grain size distribution over
the entire history of galaxy evolution. We include stellar dust production,
supernova dust destruction, shattering, coagulation, and accretion. Coagulation
is {assumed to be} the source of grain porosity. We use a one-zone model with a
constant dense gas fraction ($\eta_\mathrm{dense}$), which regulates the
balance between shattering and coagulation. We find that porosity develops
after small grains are sufficiently created by the interplay between shattering
and accretion (at age $t\sim 1$ Gyr for star formation time-scale
$\tau_\mathrm{SF}=5$ Gyr) and are coagulated. The filling factor drops down to
0.3 at grain radii $\sim 0.03~\mu$m for $\eta_\mathrm{dense}=0.5$. The grains
are more porous for smaller $\eta_\mathrm{dense}$ because small grains, from
which porous coagulated grains form, are more abundant. We also calculate the
extinction curves based on the above results. The porosity steepens the
extinction curve significantly for silicate, but not much for amorphous carbon.
The porosity also increases the collisional cross-sections and produces
slightly more large grains through the enhanced coagulation; however, the
extinction curve does not necessarily become flatter because of the steepening
effect by porosity. We also discuss the implication of our results for the
Milky Way extinction curve.
