Effects of grain size distribution on the interstellar dust mass growth

Grain growth by the accretion of metals in interstellar clouds (called `grain growth') could be one of the dominant processes that determine the dust content in galaxies. The importance of grain size distribution for the grain growth is demonstrated in this paper. First, we derive an analytical formula that gives the grain size distribution after the grain growth in individual clouds for any initial grain size distribution. The time-scale of the grain growth is very sensitive to grain size distribution, since the grain growth is mainly regulated by the surface to volume ratio of grains. Next, we implement the results of grain growth into dust enrichment models of entire galactic system along with the grain formation and destruction in the interstellar medium, finding that the grain growth in clouds governs the dust content in nearby galaxies unless the grain size is strongly biased to sizes larger than $\sim 0.1 \micron$ or the power index of the grain size distribution is shallower than $\sim -2.5$. The grain growth in clouds contributes to the rapid increase of dust-to-gas ratio at a certain metallicity level (called critical metallicity in Asano et al. 2011 and and Inoue 2011), which we find to be sensitive to grain size distribution. Thus, the grain growth efficiently increase the dust mass not only in nearby galaxies but also in high-redshift quasars, whose metallicities are larger than the critical value. Our recipe for the grain growth is applicable for any grain size distribution and easily implemented into any framework of dust enrichment in galaxies.