Dust temperature and mid-to-total infrared color distributions for star-forming galaxies at 0<z<4

We present a new, publicly available library of dust spectral energy distributions (SEDs). These SEDs are characterized by only three parameters: the dust mass (Mdust), the dust temperature (Tdust), and the mid-to-total infrared color (IR8=LIR/L8). The latter measures the relative contribution of PAH molecules to the LIR. We used this library to model star-forming galaxies at 0.5<z<4 in the CANDELS fields, using both individual detections and stacks of Herschel and ALMA imaging, and extending this sample to z=0 using the Herschel Reference Survey. At first order, the dust SED of a galaxy was found independent of stellar mass, but evolving with redshift. We found trends of increasing Tdust and IR8 with redshift and distance from the SFR--Mstar main sequence (MS), and quantified for the first time their intrinsic scatter. Half of the observed variation of these parameters was captured by these empirical relations, with residual scatters of 12% and 0.18 dex, respectively. Second order variations with stellar mass are discussed. Building on these results, we constructed high-fidelity mock galaxy catalogs to predict the accuracy of LIR and Mdust determined from a single flux measurement. Using a single JWST MIRI band, we found that LIR is typically uncertain by 0.15 dex, with a maximum of 0.25 dex when probing the rest-frame 8 um, and this is not significantly impacted by typical redshift uncertainties. On the other hand, we found that ALMA bands 8-to-7 and 6-to-3 measure Mdust at better than 0.2 and 0.15 dex, respectively, and independently of redshift, while bands 9-to-6 only measure LIR at better than 0.2 dex at z>1, 3.2, 3.8, and 5.7, respectively. Starburst galaxies above the MS have LIR significantly underestimated and Mdust overestimated. These results can be used immediately to interpret more accurately the large amount of archival data from Spitzer, Herschel and ALMA. [abridged]