A physical model for the [C II]-FIR deficit in luminous galaxies

Observations of ionized carbon at 158 μm ([C II]) from luminous star-forming galaxies at z ∼ 0 show that their ratios of [C II] to far-infrared (FIR) luminosity are systematically lower than those of more modestly star-forming galaxies. In this paper, we provide a theory for the origin of this so-called [C II] deficit in galaxies. Our model treats the interstellar medium as a collection of clouds with radially stratified chemical and thermal properties, which are dictated by the clouds' volume and surface densities, as well as the interstellar radiation and cosmic ray fields to which they are exposed. [C II] emission arises from the outer, H I-dominated layers of clouds, and from regions where the hydrogen is H₂ but the carbon is predominantly C⁺. In contrast, the most shielded regions of clouds are dominated by CO, and produce little [C II] emission. This provides a natural mechanism to explain the observed [C II]-star formation relation: galaxies' star formation rates are largely driven by the surface densities of their clouds. As this rises, so does the fraction of gas in the CO-dominated phase that produces little [C II] emission. Our model further suggests that the apparent offset in the [C II]-FIR relation for high-z sources compared to those at present epoch may arise from systematically larger gas masses at early times: a galaxy with a large gas mass can sustain a high star formation rate even with a relatively modest surface density, allowing copious [C II] emission to coexist with rapid star formation.