The Physical Drivers and Observational Tracers of CO-to-H2 Conversion Factor Variations in Nearby Barred Galaxy Centers

The CO-to-H${}_2$ conversion factor (${\alpha }_{\mathrm{C}\mathrm{O}}$) is central to measuring the amount and properties of molecular gas. It is known to vary with environmental conditions, and previous studies have revealed lower ${\alpha }_{\mathrm{C}\mathrm{O}}$ in the centers of some barred galaxies on kpc scales. To unveil the physical drivers of such variations, we obtained ALMA Band 3, 6, and 7 observations toward the inner 2 kpc of NGC 3627 and NGC 4321 tracing ${}^{12}$CO, ${}^{13}$CO, and C${}^{18}$O lines on 100 pc scales. Our multi-line modeling and Bayesian likelihood analysis of these datasets reveal variations of molecular gas density, temperature, optical depth, and velocity dispersion, which are among the key drivers of ${\alpha }_{\mathrm{C}\mathrm{O}}$. The central 300 pc nuclei in both galaxies show strong enhancement of temperature $T_{\mathrm{k}}>100$ K and density $n_{{\mathrm{H}}_2}>{10}^3$ cm${}^{-3}$. Assuming a CO-to-H${}_2$ abundance of $3\times {10}^{-4}$, we derive 4-15 times lower ${\alpha }_{\mathrm{C}\mathrm{O}}$ than the Galactic value across our maps, which agrees well with previous kpc-scale measurements. Combining the results with our previous work on NGC 3351, we find a strong correlation of ${\alpha }_{\mathrm{C}\mathrm{O}}$ with low-J ${}^{12}$CO optical depths (${\tau }_{\mathrm{C}\mathrm{O}}$), as well as an anti-correlation with $T_{\mathrm{k}}$. The ${\tau }_{\mathrm{C}\mathrm{O}}$ correlation explains most of the ${\alpha }_{\mathrm{C}\mathrm{O}}$ variation in the three galaxy centers, whereas changes in $T_{\mathrm{k}}$ influence ${\alpha }_{\mathrm{C}\mathrm{O}}$ to second order. Overall, the observed line width and ${}^{12}$CO/${}^{13}$CO 2-1 line ratio correlate with ${\tau }_{\mathrm{C}\mathrm{O}}$ variation in these centers, and thus they are useful observational indicators for ${\alpha }_{\mathrm{C}\mathrm{O}}$ variation. We also test current simulation-based ${\alpha }_{\mathrm{C}\mathrm{O}}$ prescriptions and find a systematic overprediction, which likely originates from the mismatch of gas conditions between our data and the simulations.