Observations of ionized and neutral gas outflows in radio-galaxies (RGs) suggest that AGN radio jet feedback has a galaxy-scale impact on the host ISM, but it is still unclear how the molecular gas is affected. We present deep Spitzer IRS spectroscopy of 8 RGs that show fast HI outflows. All of these HI-outflow RGs have bright H2 mid-IR lines that cannot be accounted for by UV or X-ray heating. This suggests that the radio jet, which drives the HI outflow, is also responsible for the shock-excitation of the warm H2 gas. In addition, the warm H2 gas does not share the kinematics of the ionized/neutral gas. The mid-IR ionized gas lines are systematically broader than the H2 lines, which are resolved by the IRS (with FWHM up to 900km/s) in 60% of the detected H2 lines. In 5 sources, the NeII line, and to a lesser extent the NeIII and NeV lines, exhibit blue-shifted wings (up to -900km/s with respect to the systemic velocity) that match the kinematics of the outflowing HI or ionized gas. The H2 lines do not show broad wings, except tentative detections in 3 sources. This shows that, contrary to the HI gas, the H2 gas is inefficiently coupled to the AGN jet-driven outflow of ionized gas. While the dissipation of a small fraction (<10%) of the jet kinetic power can explain the dynamical heating of the molecular gas, our data show that the bulk of the warm molecular gas is not expelled from these galaxies.
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