The distribution of the molecular hydrogen in the Milky way

We present the far-ultraviolet fluorescent molecular hydrogen ($H_2$) emission map observed with FIMS/SPEAR for ~76% of the sky. The fluorescent $H_2$ emission is found to be saturated by strong dust extinction at the optically thick, Galactic plane region. However, the extinction-corrected intensity of fluorescent $H_2$ emission is found to have strong linear correlations with the well-known tracers of the cold interstellar medium, such as the E(B-V) color excess, neutral hydrogen column density N(HI), $H{\alpha}$ emission, and CO $J=1{\rightarrow}0$ emission. The all-sky molecular hydrogen column density map is also obtained using a photodissociation region model. We also derive the gas-to-dust ratio, hydrogen molecular fraction ($f_{H2}$), and $CO-to-H_2$ conversion factor ($X_{CO}$) of the diffuse interstellar medium. The gas-to-dust ratio is consistent with the standard value $5.8{\times}10^{21}atoms\;cm^{-2}mag^{-1}$, and the $X_{CO}$ tends to increase with E(B-V), but converges to the Galactic mean value $1.8{\times}10^{20}cm^{-2}K^{-1}km^{-1}s$ at optically thick regions with E(B-V)>2.0.