Analytic models of dust temperature in high-redshift galaxies

TL;DR

This paper uses analytic models to explore why some high-redshift galaxies have very high dust temperatures, highlighting the roles of dust-to-gas ratios and star formation activity in these conditions.

Contribution

It introduces two analytic models, radiative transfer and one-temperature, to predict dust temperature relations and compare with observations of high-redshift galaxies.

Findings

High dust temperatures at z>5 favor low dust-to-gas ratios.

Enhanced star formation can also explain high dust temperatures.

Clumpy dust distribution predicts lower dust temperatures.

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 $T_\mathrm{dust}$.