Analytic models of dust temperature in high-redshift galaxies

Abstract

ABSTRACT We investigate physical reasons for high-dust temperatures (Tdust ≳ 40K) 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 Tdust is considered, and the one-tempearture (one-T) model, which assumes uniform Tdust. 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 (ΣSFR) or dust mass (Σdust) and Tdust. We show that the high Tdust observed at $z$ ≳ 5 favour low dust-to-gas ratios (≲ 10−3). An enhanced star formation compared with the KS law gives an alternative explanation for the high Tdust. 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 ΣSFR, Σdust, and Tdust 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 Tdust 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 Tdust.