Analytic models of dust temperature in high-redshift galaxies

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