Context. The luminosity of [C II] is used as a probe of 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. Aims. We aim to determine the properties of the ionized carbon and its distribution among highly ionized states in the interstellar gas in galactic nuclei under the influence of X-ray sources. We calculate the [C II] luminosity in galactic nuclei under the influence of bright sources of soft X-rays. Methods. 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 [C II] emission from the interstellar medium (ISM) in galactic nuclei representing conditions in the Galactic central molecular zone and a higher density AGN model. The behavior of the [C II] luminosity is calculated as a function of the X-ray luminosity. We also solve the distribution of the ionization states of oxygen and nitrogen in highly ionized regions. Results. 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 C2+ and higher ionization states and thus reducing its [C II] luminosity. For an X-ray luminosity L(X-ray) 1043 erg s-1 the [C II] luminosity can be suppressed by a factor of a few, and for very strong sources, L(X-ray) > 1044 erg s-1 such as found for many AGNs, the [C II] luminosity is significantly depressed. Comparison of the model with several extragalactic sources shows that the [C II] to far-infrared ratio declines for L(X-ray) 1043 erg s-1, in reasonable agreement with our model. Conclusions. We conclude that X-rays can suppress the C+ abundance and, therefore, the [C II] luminosity of the ISM in active galactic nuclei with a large X-ray flux. The X-ray flux can arise from a central massive accreting black hole and/or from many smaller discrete sources distributed throughout the nuclei. We also find that the lower ionization states of nitrogen and oxygen are also suppressed at high X-ray fluxes in warm ionized gas. © ESO 2015.
