Diagnosing deceivingly cold dusty galaxies at 3.5<z<6: a substantial population of compact starbursts with high infrared optical depths

International audienceUsing NOEMA and ALMA 3mm line scans, we measure spectroscopic redshifts of six new dusty galaxies at 3.56, based on template IR spectrum energy distribution (SED) from known submillimeter galaxies at z=4--6. Dust SED analyses explain the photo-z overestimate from seemingly cold dust temperatures (Td) and steep Rayleigh-Jeans (RJ) slopes, providing additional examples of cold dusty galaxies impacted by the Cosmic Microwave Background (CMB) as found in Jin et al. (2019). We thus study the general properties of the enlarged sample of 10 ``cold" dusty galaxies over 3.5~4, together with the severe impact of the CMB on their RJ observables, paving the way for the diagnostics of optically thick dust in the early universe. Conventional gas mass estimates based on RJ dust continuum luminosities implicitly assume an optically thin case, overestimating gas masses by a factor of 2--3 on average in compact dusty star-forming galaxies