Fermi-LATγ-Ray Study of the Interstellar Medium and Cosmic Rays in the Chamaeleon Molecular Cloud Complex: A Look at the Dark Gas as Optically Thick H i

We report a Fermi-LAT $\gamma$-ray analysis for the Chamaeleon molecular-cloud complex using a total column density (NH) model based on the dust optical depth at 353 GHz ($\tau_{353}$) with the Planck thermal dust emission model. Gamma rays with energy from 250 MeV to 100 GeV are fitted with the NH model as a function of $\tau_{353}$, NH $\propto$ $\tau_{353}^{1/\alpha}$ ($\alpha$ $\geq$ 1.0), to explicitly take into account a possible nonlinear $\tau_{353}$/NH ratio. We found that a nonlinear relation, $\alpha$$\sim$1.4, gives the best fit to the $\gamma$-ray data. This nonlinear relation may indicate dust evolution effects across the different gas phases. Using the best-fit NH model, we derived the CO-to-H2 conversion factor (XCO) and gas mass, taking into account uncertainties of the NH model. The value of XCO is found to be (0.63-0.76) $\times$10$^{20}$ cm$^{-2}$ K$^{-1}$ km$^{-1}$ s, which is consistent with that of a recent $\gamma$-ray study of the Chamaeleon region. The total gas mass is estimated to be (6.0-7.3) $\times$ 10$^{4}$ Msun, of which the mass of additional gas not traced by standard HI or CO line surveys is 20-40%. The additional gas amounts to 30-60% of the gas mass estimated in the case of optically thin HI and has 5-7 times greater mass than the molecular gas traced by CO. Possible origins of the additional gas are discussed based on scenarios of optically thick HI and CO-dark H2. We also derived the $\gamma$-ray emissivity spectrum, which is consistent with the local HI emissivity derived from LAT data within the systematic uncertainty of $\sim$20%