Probing the Conditions for the H{\i}-to-H$_{2}$ Transition in the Interstellar Medium

In this paper, we investigate the conditions for the HI-to-H$_{2}$ transition in the solar neighborhood by analyzing HI emission and absorption measurements toward 58 Galactic lines of sight (LOSs) along with $^{12}$CO(1$-$0) (CO) and dust data. Based on the accurate column densities of the cold and warm neutral medium (CNM and WNM), we first perform a decomposition of gas into atomic and molecular phases and show that the observed LOSs are mostly HI-dominated. In addition, we find that the CO-dark H$_{2}$, not the optically thick HI, is a major ingredient of the dark gas in the solar neighborhood. To examine the conditions for the formation of CO-bright molecular gas, we analyze the kinematic association between HI and CO and find that the CNM is kinematically more closely associated with CO than the WNM. When CNM components within CO line widths are isolated, we find the following characteristics: spin temperature $<$ 200 K, peak optical depth $>$ 0.1, CNM fraction of $\sim$0.6, and $V$-band dust extinction $>$ 0.5 mag. These results suggest that CO-bright molecular gas preferentially forms in environments with high column densities where the CNM becomes colder and more abundant. Finally, we confront the observed CNM properties with the steady-state H$_{2}$ formation model of Sternberg et al. and infer that the CNM must be clumpy with a small volume filling factor. Another possibility would be that missing processes in the model, such as cosmic-rays and gas dynamics, play an important role in the HI-to-H$_{2}$ transition.