Aims: This paper aims at providing new conservative constraints on the cosmic star-formation (SF) history from the empirical modeling of recent observations in the mid and far infrared.
Methods: We present a new empirical method based on a non-parametric inversion technique. It primarily uses multi-wavelength galaxy counts in the infrared and sub-mm (15, 24, 70, 160, 850 μm), and it does not require any redshift information. This inversion can be considered as a “blind” search for all possible evolutions and shapes of the infrared luminosity function of galaxies, from which the evolution of the star-formation rate density (SFRD) and its uncertainties are derived. The cosmic infrared background (CIRB) measurements are used a posteriori to tighten the range of solutions. The inversion relies only on two hypotheses: (1) the luminosity function remains smooth both in redshift and luminosity; (2) a set of infrared spectral energy distributions (SEDs) of galaxies must be assumed, with a dependency on the total luminosity alone.
Results: The range of SF histories recovered at low redshift is well-constrained and consistent with direct measurements from various redshift surveys. Redshift distributions are recovered without any input into the redshifts of the sources making the counts. A peak of the SFRD at z≃ 2 is preferred, although higher redshifts are not excluded. We also demonstrate that galaxy counts at 160 μm present an excess around 20 mJy that is not consistent with counts at other wavelengths under the hypotheses cited above. Finally, we find good consistency between the observed evolution of the stellar mass density and the prediction from our model of SF history.
Conclusions: Multi-wavelength counts and CIRB (both projected observations) alone, interpreted with a luminosity-dependent library of SEDs, contain enough information to recover the cosmic evolution of the infrared luminosity function of galaxies, and therefore the evolution of the SFRD, with quantifiable errors. Moreover, the inability of the inversion to model perfectly and simultaneously the multi-wavelength infrared counts implies either (i) the existence of a sub-population of colder galaxies; (ii) a larger dispersion of dust temperatures among local galaxies than expected; (iii) a redshift evolution of the infrared SED of galaxies.

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