This paper investigates the main driver of dust mass growth in the interstellar medium (ISM) by using a chemical evolution model of a galaxy with metals (elements heavier than helium) in the dust phase, in addition to the total amount of metals. We consider asymptotic giant branch (AGB) stars, type II supernovae (SNe II), and dust mass growth in the ISM, as the sources of dust, and SN shocks as the destruction mechanism of dust. Furthermore, to describe the dust evolution precisely, our model takes into account the age and metallicity (the ratio of metal mass to ISM mass) dependence of the sources of dust. We have particularly focused on the dust mass growth, and found that in the ISM this is regulated by the metallicity. To quantify this aspect, we introduce a "critical metallicity", which is the metallicity at which the contribution of stars (AGB stars and SNe II) equals that of the dust mass growth in the ISM. If the star-formation timescale is shorter, the value of the critical metallicity is higher, but the galactic age at which the metallicity reaches the critical metallicity is shorter. From observations, it was expected that the dust mass growth was the dominant source of dust in the Milky Way and dusty QSOs at high redshifts. By introducing a critical metallicity, it is clearly shown that the dust mass growth is the main source of dust in such galaxies with various star-formation timescales and ages. The dust mass growth in the ISM is regulated by metallicity, and we emphasize that the critical metallicity serves as an indicator to judge whether the grain growth in the ISM is the dominant source of dust in a galaxy, especially because of the strong, and nonlinear, dependence on the metallicity.

We investigate shattering and coagulation of dust grains in turbulent interstellar medium (ISM). The typical velocity of dust grain as a function of grain size has been calculated for various ISM phases based on a theory of grain dynamics in compressible magnetohydrodynamic turbulence. In this paper, we develop a scheme of grain shattering and coagulation and apply it to turbulent ISM by using the grain velocities predicted by the above turbulence theory. Since large grains tend to acquire large velocity dispersions as shown by earlier studies, large grains tend to be shattered. Large shattering effects are indeed seen in warm ionized medium (WIM) within a few Myr for grains with radius $a\ga 10^{-6}$ cm. We also show that shattering in warm neutral medium (WNM) can limit the largest grain size in ISM ($a\sim 2\times 10^{-5} \mathrm{cm}$). On the other hand, coagulation tends to modify small grains since it only occurs when the grain velocity is small enough. Coagulation significantly modifies the grain size distribution in dense clouds (DC), where a large fraction of the grains with $a<10^{-6}$ cm coagulate in 10 Myr. In fact, the correlation among $R_V$, the carbon bump strength, and the ultraviolet slope in the observed Milky Way extinction curves can be explained by the coagulation in DC. It is possible that the grain size distribution in the Milky Way is determined by a combination of all the above effects of shattering and coagulation. Considering that shattering and coagulation in turbulence are effective if dust-to-gas ratio is typically more than $\sim 1/10$ of the Galactic value, the regulation mechanism of grain size distribution should be different between metal-poor and metal-rich environments.Comment: 15 pages, 10 figures, accepted for publication in MNRA

Abstract. Infrared (IR) luminosity of galaxies originating from dust thermal emission can be used as an indicator of the star formation rate (SFR). Inoue et al. (2000, IHK) have derived a formula for the conversion from dust IR luminosity to SFR by using the following three quantities: the fraction of Lyman continuum luminosity absorbed by gas ( f ), the fraction of UV luminosity absorbed by dust ( ), and the fraction of dust heating from old ( > ∼ 10 8 yr) stellar populations (η). We develop a method to estimate those three quantities based on the idea that the various way of SFR estimates from ultraviolet (UV) luminosity (2000 Å luminosity), Hα luminosity, and dust IR luminosity should return the same SFR. After applying our method to samples of galaxies, the following results are obtained in our framework. First, our method is applied to a sample of starforming galaxies, finding that f ∼ 0.6, ∼ 0.5, and η ∼ 0.4 as representative values. Next, we apply the method to a starburst sample, which shows larger extinction than the star-forming galaxy sample. With the aid of f , , and η, we are able to estimate reliable SFRs from UV and/or IR luminosities. Moreover, the Hα luminosity, if the Hα extinction is corrected by using the Balmer decrement, is suitable for a statistical analysis of SFR, because the same correction factor for the Lyman continuum extinction (i.e. 1/ f ) is applicable to both normal and starburst galaxies over all the range of SFR. The metallicity dependence of f and is also tested: Only the latter proves to have a correlation with metallicity. As an extension of our result, the local (z = 0) comoving density of SFR can be estimated with our dust extinction corrections. We show that all UV, Hα, and IR comoving luminosity densities at z = 0 give a consistent SFR per comoving volume (∼3 × 10 −2 h M yr −1 Mpc −3 ). Useful formulae for SFR estimate are listed.

Dust in galaxies forms and evolves by various processes, and these dust processes change the grain size distribution and amount of dust in the interstellar medium (ISM). We construct a dust evolution model taking into account the grain size distribution, and investigate what kind of dust processes determine the grain size distribution at each stage of galaxy evolution. In addition to the dust production by type II supernovae (SNe II) and asymptotic giant branch (AGB) stars, we consider three processes in the ISM: (i) dust destruction by SN shocks, (ii) metal accretion onto the surface of preexisting grains in the cold neutral medium (CNM) (called grain growth), and (iii) grain-grain collisions (shattering and coagulation) in the warm neutral medium (WNM) and CNM. We found that the grain size distribution in galaxies is controlled by stellar sources in the early stage of galaxy evolution, and that afterwards the main processes that govern the size distribution changes to those in the ISM, and this change occurs at earlier stage of galaxy evolution for a shorter star formation timescale (for star formation time-scales = 0.5, 5 and 50 Gyr, the change occurs about galactic age t ∼ 0.6, 2 and 5 Gyr, respectively). If we only take into account the processes which directly affect the total dust mass (dust production by SNe II and AGB stars, dust destruction by SN shocks, and grain growth), the grain size distribution is biased to large grains (a ∼ 0.2-0.5 µm, where a is the grain radius). Therefore, shattering is crucial to produce small (a 0.01 µm) grains. Since shattering produces a large abundance of small grains (consequently, the surface-tovolume ratio of grains increases), it enhances the efficiency of grain growth, contributing to the significant increase of the total dust mass. Grain growth creates a large bump in the grain size distribution around a ∼ 0.01 µm. Coagulation occurs effectively after the number of small grains is enhanced by shattering, and the grain size distribution is deformed to have a bump at a ∼ 0.03-0.05 µm at t ∼ 10 Gyr. We conclude that the evolutions of the total dust mass and the grain size distribution in galaxies are closely related to each other, and the grain size distribution changes considerably through the galaxy evolution because the dominant dust processes which regulate the grain size distribution change.

We perform smoothed particle hydrodynamics (SPH) simulations of an isolated galaxy with a new treatment for dust formation and destruction. To this aim, we treat dust and metal production self-consistently with star formation and supernova (SN) feedback. For dust, we consider a simplified model of grain size distribution by representing the entire range of grain sizes with large and small grains. We include dust production in stellar ejecta, dust destruction by SN shocks, grain growth by accretion and coagulation, and grain disruption by shattering. We find that the assumption of fixed dust-to-metal mass ratio becomes no longer valid when the galaxy is older than 0.2 Gyr, at which point the grain growth by accretion starts to contribute to the nonlinear rise of dust-to-gas ratio. As expected in our previous one-zone model, shattering triggers grain growth by accretion since it increases the total surface area of grains. Coagulation becomes significant when the galaxy age is greater than ∼ 1 Gyr: at this epoch the abundance of small grains becomes high enough to raise the coagulation rate of small grains. We further compare the radial profiles of dust-to-gas ratio (D) and dustto-metal ratio (D/Z) (i.e., depletion) at various ages with observational data. We find that our simulations broadly reproduce the radial gradients of dust-to-gas ratio and depletion. In the early epoch ( 0.3 Gyr), the radial gradient of D follows the metallicity gradient with D/Z determined by the dust condensation efficiency in stellar ejecta, while the D gradient is steeper than the Z gradient at the later epochs because of grain growth by accretion. The framework developed in this paper is applicable to any SPH-based galaxy evolution simulations including cosmological ones.

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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

To investigate the evolution of dust in a cosmological volume, we perform hydrodynamic simulations, in which the enrichment of metals and dust is treated selfconsistently with star formation and stellar feedback. We consider dust evolution driven by dust production in stellar ejecta, dust destruction by sputtering, grain growth by accretion and coagulation, and grain disruption by shattering, and treat small and large grains separately to trace the grain size distribution. After confirming that our model nicely reproduces the observed relation between dust-to-gas ratio and metallicity for nearby galaxies, we concentrate on the dust abundance over the cosmological volume in this paper. The comoving dust mass density has a peak at redshift z ∼ 1-2, coincident with the observationally suggested dustiest epoch in the Universe. In the local Universe, roughly 10 per cent of the dust is contained in the intergalactic medium (IGM), where only 1/3-1/4 of the dust survives against dust destruction by sputtering. We also show that the dust mass function is roughly reproduced at 10 8 M ⊙ , while the massive end still has a discrepancy, which indicates the necessity of stronger feedback in massive galaxies. In addition, our model broadly reproduces the observed radial profile of dust surface density in the circum-galactic medium (CGM). While our model satisfies the observational constraints for the dust extinction on cosmological scales, it predicts that the dust in the CGM and IGM is dominated by large (> 0.03 µm) grains, which is in tension with the steep reddening curves observed in the CGM.