A Constraint on the Amount of Hydrogen from the CO Chemistry in Debris Disks

The faint CO gases in debris disks are easily dissolved into C by UV irradiation, while CO can be reformed via reactions with hydrogen. The abundance ratio of C/CO could thus be a probe of the amount of hydrogen in the debris disks. We conduct radiative transfer calculations with chemical reactions for debris disks. For a typical dust-to-gas mass ratio of debris disks, CO formation proceeds without the involvement of H$_2$ because a small amount of dust grains makes H$_2$ formation inefficient. We find that the CO to C number density ratio depends on a combination of $n_\mathrm{H}Z^{0.4}\chi^{-1.1}$, where $n_\mathrm{H}$ is the hydrogen nucleus number density, $Z$ is the metallicity, and $\chi$ is the FUV flux normalized by the Habing flux. Using an analytic formula for the CO number density, we give constraints on the amount of hydrogen and metallicity for debris disks. CO formation is accelerated by excited H$_2$ either when the dust-to-gas mass ratio is increased or the energy barrier of chemisorption of hydrogen on the dust surface is decreased. This acceleration of CO formation occurs only when the shielding effects of CO are insignificant. In shielded regions, the CO fractions are almost independent of the parameters of dust grains.