Dust temperature in ALMA [C ii]-detected high-z galaxies

Abstract

ABSTRACT At redshift z > 5, the far-infrared (FIR) continuum spectra of main-sequence galaxies are sparsely sampled, often with a single data point. The dust temperature Td,SED, thus has to be assumed in the FIR continuum fitting. This introduces large uncertainties regarding the derived dust mass (Md), FIR luminosity, and obscured fraction of the star formation rate. These are crucial quantities to quantify the effect of dust obscuration in high-z galaxies. To overcome observation limitations, we introduce a new method that combines dust continuum information with the overlying [C $\scriptstyle \rm II$] 158 µm line emission. By breaking the Md–Td,SED degeneracy, with our method, we can reliably constrain the dust temperature with a single observation at 158 µm. This method can be applied to all Atacama Large Millimeter Array (ALMA) and NOEMA [C $\scriptstyle \rm II$] observations, and exploited in ALMA Large Programs such as ALPINE and REBELS targeting [C $\scriptstyle \rm II$] emitters at high-z. We also provide a physical interpretation of the empirical relation recently found between molecular gas mass and [C $\scriptstyle \rm II$] luminosity. We derive an analogous relation linking the total gas surface density and [C $\scriptstyle \rm II$] surface brightness. By combining the two, we predict the cosmic evolution of the surface density ratio $\Sigma _{\rm H_2} / \Sigma _{\rm gas}$. We find that $\Sigma _{\rm H_2} / \Sigma _{\rm gas}$ slowly increases with redshift, which is compatible with current observations at 0 < z < 4.