Emission from Dust in Galaxies: Metallicity Dependence

Infrared (IR) dust emission from galaxies is frequently used as an indicator of star formation rate (SFR). However, the effect of the dust-to-gas ratio (i.e., amount of the dust) on the conversion law from IR luminosity to SFR has not so far been considered. Then, in this paper, we present a convenient analytical formula including this effect. In order to obtain the dependence on the dust-to-gas ratio, we extend the formula derived in our previous paper, in which a theoretical formula converting IR luminosity to SFR was derived. That formula was expressed as ${\rm SFR}/(M_\odot~{\rm yr}^{-1})=\{3.3\times 10^{-10}(1- \eta)/(0.4-0.2f+0.6\epsilon)\} (L_{\rm IR}/L_\odot)$, where f is the fraction of ionizing photons absorbed by hydrogen, $\epsilon$ is the efficiency of dust absorption for nonionizing photons, $\eta$ is the cirrus fraction of observed dust luminosity, and $L_{\rm IR}$ is the observed luminosity of dust emission in the 8-1000-$\mu$m range. Our formula explains the IR excess of the Galaxy and the Large Magellanic Cloud. In the current paper, especially, we present the metallicity dependence of our conversion law between SFR and $L_{\rm IR}$. This is possible since both f and $\epsilon$ can be estimated via the dust-to-gas ratio, which is related to metallicity. We have confirmed that the relation between the metallicity and the dust-to-gas ratio is applied to both giant and dwarf galaxies. Finally, we apply the result to the cosmic star formation history. We find that the comoving SFR at z=3 calculated from previous empirical formulae is underestimated by a factor of 4-5.