Kpc-scale properties of dust temperature in terms of dust mass and star formation activity

We investigate how the dust temperature is affected by local environmental quantities, especially dust surface density (${\mathrm{\Sigma }}_{\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}}$), dust-to-gas ratio (D/G) and interstellar radiation field. We compile multi-wavelength observations in 46 nearby galaxies, uniformly processed with a common physical resolution of $2$kpc. A physical dust model is used to fit the infrared dust emission spectral energy distribution (SED) observed with WISE and Herschel. The star formation rate (SFR) is traced with GALEX ultraviolet data corrected by WISE infrared. We find that the dust temperature correlates well with the SFR surface density (${\mathrm{\Sigma }}_{\mathrm{S}\mathrm{F}\mathrm{R}}$), which traces the radiation from young stars. The dust temperature decreases with increasing D/G at fixed ${\mathrm{\Sigma }}_{\mathrm{S}\mathrm{F}\mathrm{R}}$ as expected from stronger dust shielding at high D/G, when ${\mathrm{\Sigma }}_{\mathrm{S}\mathrm{F}\mathrm{R}}$ is higher than $\sim 2\times {10}^{-3}{\mathrm{M}}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}\mathrm{k}\mathrm{p}{\mathrm{c}}^{-2}$. These measurements are in good agreement with the dust temperature predicted by our proposed analytical model. Below this range of ${\mathrm{\Sigma }}_{\mathrm{S}\mathrm{F}\mathrm{R}}$, the observed dust temperature is higher than the model prediction and is only weakly dependent on D/G, which is possibly due to the dust heating from old stellar population or the variation of SFR within the past ${10}^{10}$yr. Overall, the dust temperature as a function of ${\mathrm{\Sigma }}_{\mathrm{S}\mathrm{F}\mathrm{R}}$ and ${\mathrm{\Sigma }}_{\mathrm{d}\mathrm{u}\mathrm{s}\mathrm{t}}$ predicted by our analytical model is consistent with observations. We also notice that at fixed gas surface density, ${\mathrm{\Sigma }}_{\mathrm{S}\mathrm{F}\mathrm{R}}$ tends to increase with D/G, i.e. we can empirically modify the Kennicutt-Schmidt law with a dependence on D/G to better match observations.