PAHs as tracers of the molecular gas in star-forming galaxies

[ Abridged] We combine new CO(1-0) line observations of 24 intermediate redshift galaxies (0.03 < z < 0.28) along with literature data of galaxies at 0 conversion factorof $α_{6.2} = M_{\rm H2}/L_{6.2} = (2.7\pm1.3) \times α_{\rm CO}$, where $α_{\rm CO}$ is the $L'_{\rm CO}$ to $M_{\rm H_2}$ conversion factor. We also find that on galaxy integrated scales, PAH emission is better correlated with cold rather than with warm dust emission, suggesting that PAHs are associated with the diffuse cold dust, which is another proxy for $M_{\rm H_2}$. Focusing on normal SFGs among our sample, we employ the dust continuum emission to derive $M_{\rm H_2}$ estimates and find a constant $M_{\rm H_2}/L_{6.2}$ ratio of $α_{6.2} = 12.3 \ M_{\rm H_2}/{\rm L}_{\odot}$ ($σ\approx 0.3$ dex). We propose that the presented $L_{6.2}-L'_{\rm CO}$ and $L_{6.2}-M_{\rm H_2}$ relations will serve as useful tools for the determination of the physical properties of high-$z$ SFGs, for which PAH emission will be routinely detected by the James Webb Space Telescope.