The Environmental Dependence of the XCO Conversion Factor

$\mathrm{CO}$ is the most widely used observational tracer of molecular gas. The observable $\mathrm{CO}$ luminosity is translated to ${{\rm{H}}}_{2}$ mass via a conversion factor, ${X}_{\mathrm{CO}}$ , which is a source of uncertainty and bias. Despite variations in ${X}_{\mathrm{CO}}$ , the empirically determined solar neighborhood value is often applied across different galactic environments. To improve understanding of ${X}_{\mathrm{CO}}$ , we employ 3D magnetohydrodynamics simulations of the interstellar medium (ISM) in galactic disks with a large range of gas surface densities, allowing for varying metallicity, far-ultraviolet (FUV) radiation, and cosmic-ray ionization rate (CRIR). With the TIGRESS simulation framework we model the three-phase ISM with self-consistent star formation and feedback, and post-process outputs with chemistry and radiation transfer to generate synthetic CO (1-0) and (2-1) maps. Our models reproduce the observed CO excitation temperatures, line widths, and line ratios in nearby disk galaxies. ${X}_{\mathrm{CO}}$ decreases with increasing metallicity, with a power-law slope of -0.8 for the (1-0) line and -0.5 for the (2-1) line. ${X}_{\mathrm{CO}}$ also decreases at higher CRIR and is insensitive to the FUV radiation. As density increases, ${X}_{\mathrm{CO}}$ first decreases owing to increasing excitation temperature and then increases when the emission is fully saturated. We provide fits between ${X}_{\mathrm{CO}}$ and observable quantities such as the line ratio, peak antenna temperature, and line brightness, which probe local gas conditions. These fits, which allow for varying beam size, may be used in observations to calibrate out systematic biases. We also provide estimates of the CO-dark ${{\rm{H}}}_{2}$ fraction at different gas surface densities, observational sensitivities, and beam sizes.