The Arizona Molecular ISM Survey with the SMT: Variations in the CO(2-1)/CO(1-0) Line Ratio Across the Galaxy Population

The J=1$\rightarrow$0 spectral line of carbon monoxide (CO(1-0)) is the canonical tracer of molecular gas. However, CO(2-1) is frequently used in its place, following the assumption that the higher energy line can be used to infer the CO(1-0) luminosity and molecular gas mass. The use of CO(2-1) depends on a knowledge of the ratio between CO(2-1) and CO(1-0) luminosities, r21. Here we present galaxy-integrated r21 measurements for 122 galaxies spanning stellar masses from 10$^9$ to 10$^{11.5}$ M$_\odot$ and star formation rates (SFRs) from 0.08 to 35 M$_\odot$/yr. We find strong trends between r21 and SFR, SFR surface density, star formation efficiency, and distance from the star formation main sequence (SFMS). We show that the assumption of a constant r21 can introduce biases into the molecular gas trends in galaxy population studies and demonstrate how this affects the recovery of important galaxy scaling relations, including the Kennicutt-Schmidt law and the relation between SFMS offset and star formation efficiency. We provide a prescription which accounts for variations in r21 as a function of SFR and can be used to convert between CO(2-1) and CO(1-0) when only one line is available. Our prescription matches variations in r21 for both AMISS and literature samples and can be used to derive more accurate gas masses from CO(2-1) observations.