Analytic models of dust temperature in high-redshift galaxies

Abstract

We investigate physical reasons for high dust temperatures ($T_{\mathrm{dust}}\gtrsim 40$ K) observed in some high-redshift ($z>5$) galaxies using analytic models. We consider two models that can be treated analytically: the radiative transfer (RT) model, {where a broad distribution of values for $T_{\mathrm{dust}}$ is considered}, and the one-tempearture (one-$T$) model, which assumes {uniform $T_{\mathrm{dust}}$}. These two extremes {serve to bracket the most realistic scenario}. We adopt the Kennicutt--Schmidt (KS) law to relate stellar radiation field to gas surface density, and vary the dust-to-gas ratio. As a consequence, our model is capable of predicting the relation between the surface density of star formation rate (${\Sigma }_{\mathrm{SFR}}$) or dust mass (${\Sigma }_{\mathrm{dust}}$) and $T_{\mathrm{dust}}$. We show that the high $T_{\mathrm{dust}}$ observed at $z\gtrsim 5$ favour low dust-to-gas ratios ($\lesssim 10^{-3}$). An enhanced star formation compared with the KS law gives an alternative explanation for the high $T_{\mathrm{dust}}$. The dust temperatures are similar between the two (RT and one-$T$) models as long as we use ALMA Bands 6--8. We also examine the relation among ${\Sigma }_{\mathrm{SFR}}$, ${\Sigma }_{\mathrm{dust}}$ and $T_{\mathrm{dust}}$ without assuming the KS law, and confirm the consistency with the actual observational data at $z>5$. In the one-$T$ model, we also examine a clumpy dust distribution, which predicts lower $T_{\mathrm{dust}}$ because of the leakage of stellar radiation. This enhances the requirement of low dust abundance or high star formation efficiency to explain the observed high $T_{\mathrm{dust}}$.

12 pages, 5 figures, Accepted for publication in MNRAS

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