Spectral energy distributions of dust and PAHs based on the evolution of
  grain size distribution in galaxies
  Based on a one-zone evolution model of grain size distribution in a galaxy,
we calculate the evolution of infrared spectral energy distribution (SED),
considering silicate, carbonaceous dust, and polycyclic aromatic hydrocarbons
(PAHs). The dense gas fraction ($\eta_\mathrm{dense}$) of the interstellar
medium (ISM), the star formation time-scale ($\tau_\mathrm{SF}$), and the
interstellar radiation field intensity normalized to the Milky Way value ($U$)
are the main parameters. We find that the SED shape generally has weak
mid-infrared (MIR) emission in the early phase of galaxy evolution because the
dust abundance is dominated by large grains. At an intermediate stage ($t\sim
1$ Gyr for $\tau_\mathrm{SF}=5$ Gyr), the MIR emission grows rapidly because
the abundance of small grains increases drastically by the accretion of
gas-phase metals. We also compare our results with observational data of nearby
and high-redshift ($z\sim 2$) galaxies taken by \textit{Spitzer}. We broadly
reproduce the flux ratios in various bands as a function of metallicity. We
find that small $\eta_\mathrm{dense}$ (i.e.\ the ISM dominated by the diffuse
phase) is favoured to reproduce the 8 $\mu$m intensity dominated by PAHs both
for the nearby and the $z\sim 2$ samples. A long $\tau_\mathrm{SF}$ raises the
8 $\mu$m emission to a level consistent with the nearby low-metallicity
galaxies. The broad match between the theoretical calculations and the
observations supports our understanding of the grain size distribution, but the
importance of the diffuse ISM for the PAH emission implies the necessity of
spatially resolved treatment for the ISM.
