We report a Fermi -LAT \gamma -ray analysis for the Chamaeleon molecular-cloud complex using a total column density ( N _ { \text { H } } ) model based on the dust optical depth at 353 GHz ( \tau _ { \text { 353 } } ) with the Planck thermal dust emission model .
Gamma rays with energy from 250 MeV to 100 GeV are fitted with the N _ { \text { H } } model as a function of \tau _ { \text { 353 } } , N _ { \text { H } } \propto \tau _ { \text { 353 } } ^ { 1 / \alpha } ( \alpha \geq 1.0 ) , to explicitly take into account a possible nonlinear \tau _ { \text { 353 } } / N _ { \text { H } } 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 N _ { \text { H } } model , we derived the CO-to- \text { H } _ { 2 } conversion factor ( X _ { \text { \scriptsize CO } } ) and gas mass , taking into account uncertainties of the N _ { \text { H } } model .
The value of X _ { \text { \scriptsize CO } } 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 } \text { M } _ { \sun } , of which the mass of additional gas not traced by standard H i 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 H i 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 H i and CO-dark \text { H } _ { 2 } .
We also derived the \gamma -ray emissivity spectrum , which is consistent with the local H i emissivity derived from LAT data within the systematic uncertainty of \sim 20 % .