Cold dust and stellar emissions in dust-rich galaxies observed with ALMA: a challenge for SED-fitting techniques

Over the past few years ALMA has detected dust-rich galaxies whose cold dust emission is spatially disconnected from the UV rest-frame emission. This represents a challenge for modeling their spectral energy distributions with codes based on an energy budget between the stellar and dust components. We want to verify the validity of energy balance modeling on a sample of galaxies observed from the UV to the sub-millimeter rest frame with ALMA and decipher what information can be reliably retrieved from the analysis of the full SED and from subsets of wavelengths. We select 17 sources at z~2 in the Hubble Ultra-Deep Field and in the GOODS- South field detected with ALMA and Herschel and for which UV to NIR. rest-frame ancillary data are available. We fit the data with CIGALE exploring different configurations for dust attenuation and star formation histories, considering either the full dataset or one that is reduced to the stellar and dust emission. We compare estimates of the dust luminosities, star formation rates, and stellar masses. The fit of the stellar continuum alone with the starburst attenuation law can only reproduce up to 50% of the total dust luminosity observed by Herschel and ALMA. This deficit is found to be consistent with similar quantities estimated in the COSMOS field and is found to increase with the specific star formation rate. The combined stellar and dust SEDs are well fitted when different attenuation laws are introduced. Shallow attenuation curves are needed for the galaxies whose cold dust distribution is very compact compared to starlight. The stellar mass estimates are affected by the choice of the attenuation law. The star formation rates are robustly estimated as long as dust luminosities are available. The large majority of the galaxies are above the average main sequence of star forming galaxies and one source is a strong starburst.