The HerMES sub-millimetre local and low-redshift luminosity functions

We used wide area surveys over 39 deg$^2$ by the HerMES collaboration, performed with the Herschel Observatory SPIRE multi-wavelength camera, to estimate the low-redshift, $0.02<z<0.5$, monochromatic luminosity functions (LFs) of galaxies at 250, 350 and 500$\,\mu$m. SPIRE flux densities were also combined with Spitzer photometry and multi-wavelength archival data to perform a complete SED fitting analysis of SPIRE detected sources to calculate precise k-corrections, as well as the bolometric infrared (8-1000$\,\mu$m) luminosity functions and their low-$z$ evolution from a combination of statistical estimators. Integration of the latter prompted us to also compute the local luminosity density (LLD) and the comoving star formation rate density (SFRD) for our sources, and to compare them with theoretical predictions of galaxy formation models. The luminosity functions show significant and rapid luminosity evolution already at low redshifts, $0.02<z<0.2$, with L$_{IR}^* \propto (1+z)^{6.0\pm0.4}$ and $\Phi_{IR}^* \propto (1+z)^{-2.1\pm0.4}$, L$_{250}^* \propto (1+z)^{5.3\pm0.2}$ and $\Phi_{250}^* \propto (1+z)^{-0.6\pm0.4}$ estimated using the IR bolometric and the 250$\,\mu$m LFs respectively. Converting our IR LD estimate into an SFRD assuming a standard Salpeter IMF and including the unobscured contribution based on the UV dust-uncorrected emission from local galaxies, we estimate a SFRD scaling of SFRD$_0+0.08 z$, where SFRD$_0\simeq (1.9\pm 0.03)\times 10^{-2} [\mathrm{M}_\odot\,\mathrm{Mpc}^{-3}]$ is our total SFRD estimate at $z\sim0.02$.