[C II] emission from galactic nuclei in the presence of X-rays

The luminosity of [C II] is used to probe the star formation rate in galaxies, but the correlation breaks down in some active galactic nuclei (AGNs). Models of the [C II] emission from galactic nuclei do not include the influence of X-rays on the carbon ionization balance, which may be a factor in reducing the [C II] luminosity. We calculate the [C II] luminosity in galactic nuclei under the influence of bright sources of X-rays. We solve the balance equation of the ionization states of carbon as a function of X-ray flux, electron, atomic hydrogen, and molecular hydrogen density. These are input to models of [CII] emission from the interstellar medium (ISM) in galactic nuclei. We also solve the distribution of the ionization states of oxygen and nitrogen in highly ionized regions. We find that the dense warm ionized medium (WIM) and dense photon dominated regions (PDRs) dominate the [C II] emission when no X-rays are present. The X-rays in galactic nuclei can affect strongly the C$^+$ abundance in the WIM converting some fraction to C$^{2+}$ and higher ionization states and thus reducing its [C II] luminosity. For an X-ray luminosity > 10$^{43}$ erg/s the [C II] luminosity can be suppressed by a factor of a few, and for very strong sources, >10$^{44}$ erg/s, such as found for many AGNs by an order of magnitude. Comparison of the model with extragalactic sources shows that the [C II] to far-infrared ratio declines for an X-ray luminosity >10$^{43}$ erg/s, in reasonable agreement with our model.