SIMBAD references

We investigate physical reasons for high-dust temperatures (T_dust ≳ 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 T_dust is considered, and the one-tempearture (one-T) model, which assumes uniform T_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 (Σ_SFR) or dust mass (Σ_dust) and T_dust. We show that the high T_dust 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 T_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 Σ_SFR, Σ_dust, and T_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_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_dust.