Sommovigo, L.L.SommovigoFerrara, A.A.FerraraCarniani, S.S.CarnianiZANELLA, AnitaAnitaZANELLAPallottini, A.A.PallottiniGallerani, S.S.GalleraniVALLINI, LiviaLiviaVALLINI2025-03-112025-03-1120210035-8711http://hdl.handle.net/20.500.12386/36674At 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<SUB>d,SED</SUB>, thus has to be assumed in the FIR continuum fitting. This introduces large uncertainties regarding the derived dust mass (M<SUB>d</SUB>), 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 M<SUB>d</SUB>-T<SUB>d,SED</SUB> 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.STAMPAenArticle10.1093/mnras/stab7202-s2.0-85108392856http://arxiv.org/abs/2102.08950v1https://academic.oup.com/mnras/article/503/4/4878/61697172021MNRAS.503.4878SFIS/05 - ASTRONOMIA E ASTROFISICAERC sectors::Physical Sciences and Engineering::PE9 Universe sciences: astro-physics/chemistry/biology; solar systems; stellar, galactic and extragalactic astronomy, planetary systems, cosmology, space science, instrumentation