Systematic variation of the 12CO/13CO ratio as a function of star formation rate surface density

We show that the (CO)-C-12/(CO)-C-13 intensity ratio in nearby galaxies varies systematically as a function of the star formation rate surface density (Sigma(SFR)) and gas surface density. The same effect is observed in different transitions, and in the (CO)-C-12/(CO)-O-18 ratio, while the (CO)-C-13/(CO)-O-18 ratio appears to remain constant as a function of Sigma(SFR). We discuss the cause of these variations, considering both changes in the physical state of the gas and chemical changes that lead to abundance variations. We used the observed correlations with (CO)-O-18 to suggest that abundance variations are unlikely to be causing the systematic trend observed with Sigma(SFR), and thus that the mean gas temperature and/or velocity dispersion are systematically higher in higher SFR surface density regions. We present the best-fitting relations between Sigma(SFR) and the (CO)-C-12/(CO)-C-13 and (CO)-C-12/(CO)-O-18 ratios, and discuss how this effect can help us predict CO isotope emission from galaxies across the known Universe.