The environmental dependence of the X_CO conversion factor
  CO is the most widely used observational tracer of molecular gas. The
observable CO luminosity is translated to H_2 mass via a conversion factor,
X_CO, which is a source of uncertainty and bias. Despite variations in X_CO,
the empirically-determined solar neighborhood value is often applied across
different galactic environments. To improve understanding of X_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_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_CO also decreases at higher CRIR, and is
insensitive to the FUV radiation. As density increases, X_CO first decreases
due to increasing excitation temperature, and then increases when the emission
is fully saturated. We provide fits between X_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 H_2 fraction at different gas surface densities,
observational sensitivities, and beam sizes.
