Limited impact of jet induced feedback in the multi-phase nuclear interstellar medium of 4C12.50

Although the ultraluminous infrared radio galaxy 4C12.50 at z=0.12 is a promising candidate to reveal how radio induced feedback may regulate star formation in galaxies, we find no solid evidence for current or past impact of this mechanism on the evolution of this system, neither by clearing out the dusty central cocoon efficiently, nor by suppressing star formation. We study in detail for the first time the hot (>~1500 K) molecular gas in this object. The potential impact of the radio jet on this gas phase, as well as on the star formation activity, are investigated. 4C12.50 hosts (2.1+/-0.4)x1e4 Msun of hot molecular gas. An unusually high rotational temperature T =3020+/-160 K is inferred. The molecular gas mass obeys a power law temperature distribution d(M(H2))/dT ~ T^-5 from T~300 K and up to ~3000 K. Both results support that shocks (probably induced by the radio jet) contribute to the heating and excitation of the hot molecular gas. A molecular outflow is not detected. The coupling of the outflowing ionized and neutral outflows with the hot molecular gas is poor. We find no evidence for star formation supression. NIR and MIR integral field spectroscopy at very high spatial resolution (for instance, with the JWST) would be of key value to further investigate these issues.