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

Context. 4C12.50 (IRAS 13451 +1232) at z = 0:122 is an ultraluminous infared radio galaxy that has often been proposed as a prime candidate for the link between ultraluminous infared galaxies and young radio galaxies. It is also an interesting target to investigate whether and how radio-induced feedback a ffects the evolution of galaxies in the early phases of radio activity. Aims. We study, in detail for the first time, the hot ( >= 1500 K) molecular gas in 4C12.50. The potential impact of the radio jet on this gas phase, as well as on the star formation activity, are investigated. We also study the ionised (including coronal) gas as traced by the near-infrared lines. Methods. Using near-infrared long slit spectroscopy obtained with EMIR on GTC and X-shooter on VLT, we analyse the emission line spectrum of the ionised, coronal, and, specially, the hot molecular gas in the western nucleus hosting the compact radio jet. Based on high spatial resolution ALMA CO(2-1) data, we also revise the location of 4C12.50 in the Kennicutt-Schmidt diagram in order to investigate whether star formation is suppressed. Results. 4C12.50 hosts (2:1 +/- 0:4) x 10(4) M-circle dot hot molecular gas. An unusually high rotational temperature Trot = 3020 +/- 160 K is inferred. The molecular gas mass obeys a power-law temperature distribution, (dMH2)/(dt) proportional to T- 5, from T similar to 300 K and up to similar to 3000 K. Both results support the idea 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 ionised and neutral outflows with the hot molecular gas is poor. Contrary to other studies, we claim that there is no evidence for star formation suppression in this object. Conclusions. If radio-induced feedback can regulate the star formation activity in galaxies, 4C12.50 is a promising candidate to reveal this phenomenon in action. However, we find no solid evidence for a 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 the star formation activity.