Exceptional AGN-driven turbulence inhibits star formation in the 3C 326N radio-galaxy

We detect bright [CII]158$mu$m line emission from the radio galaxy 3C 326N at z=0.09, which shows weak star formation ($SFR<0.07$M$_{odot}$~yr$^{-1}$) despite having strong H$_2$ line emission and $2times 10^9$M$_{odot}$ of molecular gas. The [CII] line is twice as strong as the 0-0S(1) 17$mu$m H$_2$ line, and both lines are much in excess what is expected from UV heating. We combine infrared Spitzer and Herschel data with gas and dust modeling to infer the gas physical conditions. The [CII] line traces 30 to 50% of the molecular gas mass, which is warm (70<T<100K) and at moderate densities $700<n_{H}<3000$cm$^{-3}$. The [CII] line is broad with a blue-shifted wing, and likely to be shaped by a combination of rotation, outflowing gas, and turbulence. It matches the near-infrared H$_2$ and the Na D optical absorption lines. If the wing is interpreted as an outflow, the mass loss rate would be larger than 20M$_{odot}$/yr, and the depletion timescale shorter than the orbital timescale ($10^8$yr). These outflow rates may be over-estimated because the stochastic injection of turbulence on galactic scales can contribute to the skewness of the line profile and mimic outflowing gas. We argue that the dissipation of turbulence is the main heating process of this gas. Cosmic rays can also contribute to the heating but they require an average gas density larger than the observational constraints. We show that strong turbulent support maintains a high gas vertical scale height (0.3-4kpc) in the disk and can inhibit the formation of gravitationally-bound structures at all scales, offering a natural explanation for the weakness of star formation in 3C 326N. To conclude, the bright [CII] line indicates that strong AGN jet-driven turbulence may play a key role in enhancing the amount of molecular gas (positive feedback) but yet can prevent star formation on galactic scales (negative feedback).