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

Full calculations of the evolution of grain size distribution in galaxies are in general computationally heavy. In this paper, we propose a simple model of dust enrichment in a galaxy with a simplified treatment of grain size distribution by imposing a `two-size approximation'; that is, all the grain population is represented by small (grain radius a < 0.03 micron) and large (a > 0.03 micron) grains. We include in the model dust supply from stellar ejecta, destruction in supernova shocks, dust growth by accretion, grain growth by coagulation and grain disruption by shattering, considering how these processes work on the small and large grains. We show that this simple framework reproduces the main features found in full calculations of grain size distributions as follows. The dust enrichment starts with the supply of large grains from stars. At a metallicity level referred to as the critical metallicity of accretion, the abundance of the small grains formed by shattering becomes large enough to rapidly increase the grain abundance by accretion. Associated with this epoch, the mass ratio of the small grains to the large grains reaches the maximum. After that, this ratio converges to the value determined by the balance between shattering and coagulation, and the dust-to-metal ratio is determined by the balance between accretion and shock destruction. With a Monte Carlo simulation, we demonstrate that the simplicity of our model has an advantage in predicting statistical properties. We also show some applications for predicting observational dust properties such as extinction curves.Comment: 14 pages, 12 figures, accepted for publication in MNRA

Evolution of dust grain size distribution by shattering in the interstellar medium: robustness and uncertainty

Shattering of dust grains in the interstellar medium is a viable mechanism of small grain production in galaxies. We examine the robustness or uncertainty in the theoretical predictions of shattering. We identify $P_1$ (the critical pressure above which the deformation destroys the original lattice structures) as the most important quantity in determining the timescale of small grain production, and confirm that the same $P_1/t$ ($t$ is the duration of shattering) gives the same grain size distribution [$n(a)$, where $a$ is the grain radius] after shattering within a factor of 3. The uncertainty in the fraction of shocked material that is eventually ejected as fragments causes uncertainties in $n(a)$ by a factor of 1.3 and 1.6 for silicate and carbonaceous dust, respectively. The size distribution of shattered fragments have minor effects as long as the power index of the fragment size distribution is less than ~ 3.5, since the slope of grain size distribution $n(a)$ continuously change by shattering and becomes consistent with $n(a)\propto a^{-3.5}$. The grain velocities as a function of grain radius can have an imprint in the grain size distribution especially for carbonaceous dust. We also show that the formulation of shattering can be simplified without losing sufficient precision.Comment: 12 pages, 7 figures, Accepted for publication in Earth, Planets, and Space (Special Issue: Cosmic Dust V

Observational Test of Environmental Effects on The Local Group Dwarf Spheroidal Galaxies

In this paper, we examine whether tidal forces exerted by the Galaxy or M31 have an influence on the Local Group dwarf spheroidal galaxies (dSphs) which are their companions. We focus on the surface brightness profiles of the dSphs, especially their core radii because it is suggested based on the numerical simulations that tidal disturbance can make core radii extended. We examine the correlation for the dSphs between the distances from their parent galaxy (the Galaxy or M31) and the compactnesses of their surface brightness profiles by using a parameter ``C'' defined newly in this paper. Consequently, we find no significant correlation. We make some remarks on the origin of this result by considering three possible scenarios; tidal picture, dark matter picture, and heterogeneity of the group of dSphs, each of which has been often discussed to understand fundamental properties and formation processes of dSphs.Comment: 14 pages LaTeX, 2 PostScript figures, to appear in ApJ Letter

Evolution of dust content in galaxies probed by gamma-ray burst afterglows

Because of their brightness, gamma-ray burst (GRB) afterglows are viable targets for investigating the dust content in their host galaxies. Simple intrinsic spectral shapes of GRB afterglows allow us to derive the dust extinction. Recently, the extinction data of GRB afterglows are compiled up to redshift $z=6.3$, in combination with hydrogen column densities and metallicities. This data set enables us to investigate the relation between dust-to-gas ratio and metallicity out to high redshift for a wide metallicity range. By applying our evolution models of dust content in galaxies, we find that the dust-to-gas ratio derived from GRB afterglow extinction data are excessively high such that they can be explained with a fraction of gas-phase metals condensed into dust ($f_\mathrm{in}$) $\sim 1$, while theoretical calculations on dust formation in the wind of asymptotic giant branch stars and in the ejecta of Type II supernovae suggest a much more moderate condensation efficiency ($f_\mathrm{in}\sim 0.1$). Efficient dust growth in dense clouds has difficulty in explaining the excessive dust-to-gas ratio at metallicities $Z/\mathrm{Z}_\odot <\epsilon$, where $\epsilon$ is the star formation efficiency of the dense clouds. However, if $\epsilon$ is as small as 0.01, the dust-to-gas ratio at $Z\sim 10^{-2}$ Z$_\odot$ can be explained with $n_\mathrm{H}\gtrsim 10^6$ cm$^{-3}$. Therefore, a dense environment hosting dust growth is required to explain the large fraction of metals condensed into dust, but such clouds should have low star formation efficiencies to avoid rapid metal enrichment by stars.Comment: 7 pages, 3 figures, published in MNRA

Constraining dust formation in high-redshift young galaxies

Core-collapse supernovae (SNe) are believed to be the first significant source of dust in the Universe. Such SNe are expected to be the main dust producers in young high-redshift Lyman $\alpha$ emitters (LAEs) given their young ages, providing an excellent testbed of SN dust formation models during the early stages of galaxy evolution. We focus on the dust enrichment of a specific, luminous LAE (Himiko, $z\simeq 6.6$) for which a stringent upper limit of $52.1~\mu$Jy ($3\sigma$) has recently been obtained from ALMA continuum observations at 1.2 mm. We predict its submillimetre dust emission using detailed models that follow SN dust enrichment and destruction and the equilibrium dust temperature, and obtain a plausible upper limit to the dust mass produced by a single SN: $m_\mathrm{d,SN} < 0.15$--0.45 M$_\odot$, depending on the adopted dust optical properties. These upper limits are smaller than the dust mass deduced for SN 1987A and that predicted by dust condensation theories, implying that dust produced in SNe are likely to be subject to reverse shock destruction before being injected into the interstellar medium. Finally, we provide a recipe for deriving $m_\mathrm{d,SN}$ from submillimetre observations of young, metal poor objects wherein condensation in SN ejecta is the dominant dust formation channel.Comment: 10 pages, 3 figures, accepted for publication in MNRA