Dust temperature in ALMA [C <scp>ii</scp>]-detected high-<i>z</i> galaxies

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 $T_{\rm d, SED}$ thus has to be assumed in FIR fitting. This introduces large uncertainties regarding derived mass ($M_{\rm d}$), luminosity, and obscured fraction star formation rate. These crucial quantities quantify effect obscuration high-$z$ galaxies. To overcome observations limitations, we introduce new method that combines information overlying $\hbox{[C $\scriptstyle\rm II $]} 158\mu$m line emission. By breaking $M_{\rm d} - T_{\rm degeneracy, our method, can reliably constrain observation at $158\mu$m. applied all ALMA NOEMA $]}$ exploited Large Programs such as ALPINE REBELS targeting emitters high-$z$. We also provide physical interpretation empirical relation recently found between $molecular$ gas luminosity. derive an analogous linking $total$ surface density brightness. combining two, predict cosmic evolution ratio $\Sigma_{\rm H_2} / \Sigma_{\rm gas}$. find gas}$ slowly increases redshift, which is compatible current $0 < z 4$.