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 ($\alpha_\rm{CO}$) is central to measuring the amount and properties of molecular gas. It known vary with environmental conditions, previous studies have revealed lower $\alpha_\rm{CO}$ in centers some barred galaxies on kpc scales. To unveil physical drivers such variations, we obtained ALMA Band 3, 6, 7 observations toward inner 2 NGC 3627 4321 tracing $^{12}$CO, $^{13}$CO, C$^{18}$O lines 100 pc Our multi-line modeling Bayesian likelihood analysis these datasets reveal variations gas density, temperature, optical depth, velocity dispersion, which are among key $\alpha_\rm{CO}$. 300 nuclei both show strong enhancement temperature $T_\rm{k}>100$ K density $n_\rm{H_2}>10^3$ cm$^{-3}$. Assuming a abundance $3\times10^{-4}$, derive 4-15 times than Galactic value across our maps, agrees well kpc-scale measurements. Combining results work 3351, find correlation low-J $^{12}$CO depths ($\tau_\rm{CO}$), as an anti-correlation $T_\rm{k}$. $\tau_\rm{CO}$ explains most variation three galaxy centers, whereas changes $T_\rm{k}$ influence second order. Overall, observed line width $^{12}$CO/$^{13}$CO 2-1 ratio correlate thus they useful observational indicators for variation. We also test current simulation-based prescriptions systematic overprediction, likely originates from mismatch conditions between data simulations.