Physical Properties and HI-to-H2 Transition Across Taurus Linear Edge

Studying the atomic-to-molecular transition is essential for understanding the evolution of interstellar medium. The linear edge of Taurus molecular cloud, clearly identified in the $^{13}$CO(1-0) intensity map, serves as an ideal site for investigating this transition. Utilizing the Arizona Radio Observatory Sub-Millimeter Telescope, we obtained mapping observations of CO(2-1), $^{13}$CO(2-1), and CO(3-2) across this linear edge. The intensity ratio between CO(2-1) and $^{13}$CO(2-1) indicates a lower limit of the $^{12}C/^{13}C$ ratio of $54\pm 17$. Based on multi-transition observations of CO and $^{13}$CO, we performed Markov Chain Monte Carlo (MCMC) fit of the physical properties across this edge using non-Local Thermodynamic Equilibrium analysis with the RADEX code, based on the Large velocity Gradient (LVG) assumption. The number density profile exhibits a pronounced jump coinciding with the H$_2$ infrared emission peak. The cold HI gas within the molecular cloud, manifested as HI-Narrow Self-Absorption (HINSA) features, is detected along the cloud edge. Our quantitative comparison with numerical simulations provides tentative evidence that shocks induced by colliding gas flows may contribute to the atomic-to-molecular phase transition observed along the linear edge.