Correlations between IR Luminosity, Star Formation Rate, and CO Luminosity in the Local Universe

We exploit the DustPedia sample of galaxies within approximately 40 Mpc, selecting 388 sources, to investigate the correlations between IR luminosity (L$_{\rm IR}$), the star formation rate (SFR), and the CO(1-0) luminosity (L$_{\rm CO}$) down to much lower luminosities than reached by previous analyses. We find a sub-linear dependence of the SFR on L$_{\rm IR}$. Below $\log(\hbox{L}_{\rm IR}/\hbox{L}_\odot)\simeq 10$ or $\hbox{SFR}\simeq 1\,\hbox{M}_\odot\,\hbox{yr}^{-1}$, the SFR/L$_{\rm IR}$ ratio substantially exceeds the standard ratio for dust-enshrouded star formation, and the difference increases with decreasing L$_{\rm IR}$ values. This implies that the effect of unobscured star formation overcomes that of dust heating by old stars, at variance with results based on the $\textit{Planck}$ ERCSC galaxy sample. We also find that the relations between the L$_{\rm CO}$ and L$_{\rm IR}$ or the SFR are consistent with those obtained at much higher luminosities.