The Physical Drivers of the Luminosity-weighted Dust Temperatures in High-redshift Galaxies

The underlying distribution of galaxies' dust SEDs (i.e., their spectra re-radiated by dust from rest-frame $\sim$3$\mu$m-3mm) remains relatively unconstrained due to a dearth of FIR/(sub)mm data for large samples of galaxies. It has been claimed in the literature that a galaxy's dust temperature -- observed as the wavelength where the dust SED peaks ($\lambda_{peak}$) -- is traced most closely by its specific star-formation rate (sSFR) or parameterized 'distance' to the SFR-M$_\star$ relation (the galaxy 'main sequence'). We present 0.24" resolved 870$\mu$m ALMA dust continuum observations of seven $z=1.4-4.6$ dusty star-forming galaxies (DSFGs) chosen to have a large range of well-constrained luminosity-weighted dust temperatures. We also draw on similar resolution dust continuum maps from a sample of ALESS submillimeter galaxies from Hodge et al. (2016). We constrain the physical scales over which the dust radiates and compare those measurements to characteristics of the integrated SED. We confirm significant correlations of $\lambda_{peak}$ with both L$_{IR}$ (or SFR) and $\Sigma_{\rm IR}$ ($\propto$SFR surface density). We investigate the correlation between $\log_{10}$($\lambda_{peak}$) and $\log_{10}$($\Sigma_{\rm IR}$) and find the relation to hold as would be expected from the Stefan-Boltzmann Law, or the effective size of an equivalent blackbody. The correlations of $\lambda_{peak}$ with sSFR and distance from the SFR-M$_\star$ relation are less significant than those for $\Sigma_{\rm IR}$ or L$_{IR}$; therefore, we conclude that the more fundamental tracer of galaxies' luminosity-weighted integrated dust temperatures are indeed their star-formation surface densities in line with local Universe results, which relate closely to the underlying geometry of dust in the ISM.