Effects of grain size distribution on the interstellar dust mass growth

Abstract

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.Comment: 14 pages, 10 figures, accepted for publication in MNRA

Two-size approximation: a simple way of treating the evolution of grain size distribution in galaxies

“…For α = 1 (δ = 1), this gives the same result as Hirashita & Kuo (2011). For the fiducial case, D/Z ∼ 0.5, which explains the dustto-metal ratio at high metallicity.…”

“…For accretion, we adopt the formulation developed by Hirashita & Kuo (2011), who also considered the dependence on grain size distribution. The increasing rate of dust mass by accre-tion is expressed as…”

“…We adopt the following expression for τ (see eq. 23 of Hirashita & Kuo 2011, applicable for silicate, but carbonaceous dust has a similar time-scale):…”

“…We use the same values as in Hirashita & Kuo (2011); i.e. a0 = 0.1 µm, nH = 10 3 cm −3 , Tgas = 50 K, and S = 0.3.…”

“…With the above definitions, βSN = ǫ sw,l Mswγ/ψ, which is treated as a constant with the instantaneous recycling approximation (Hirashita & Kuo 2011).…”