We present an analysis of CO molecular gas tracers in a sample of 500{mu}m-selected Herschel-ATLAS galaxies at z<0.05 (cz<14990km/s). Using 22-500{mu}m photometry from WISE, IRAS and Herschel, with HI data from the literature, we investigate correlations between warm and cold dust, and tracers of the gas in different phases. The correlation between global CO(3-2) line fluxes and FIR-submillimetre fluxes weakens with increasing IR wavelength ({lambda}>60{mu}m), as a result of colder dust being less strongly associated with dense gas. Conversely, CO(2-1) and HI line fluxes both appear to be better correlated with longer wavelengths, suggesting that cold dust is more strongly associated with diffuse atomic and molecular gas phases, consistent with it being at least partially heated by radiation from old stellar populations. The increased scatter at long wavelengths implies that submillimetre fluxes are a poorer tracer of SFR. Fluxes at 22 and 60{mu}m are also better correlated with diffuse gas tracers than dense CO(3-2), probably due to very-small-grain emission in the diffuse interstellar medium, which is not correlated with SFR. The FIR/CO luminosity ratio and the dust mass/CO luminosity ratio both decrease with increasing luminosity, as a result of either correlations between mass and metallicity (changing CO/H2) or between CO luminosity and excitation [changing CO(3-2)/CO(1-0)].
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