Feeding and feedback processes in the Spiderweb proto-intracluster medium

Context. We present a detailed analysis of the thermal, diffuse emission of the proto-intracluster medium (proto-ICM) detected in the halo of the Spiderweb Galaxy at z=2.16, within a radius of ~150 kpc. Aims. Our main goal is to derive the thermodynamic profiles of the proto-ICM, establish the potential presence of a cool core and constrain the classical mass deposition rate (MDR) that may feed the nuclear and the star formation (SF) activity, and estimate the available energy budget of the ongoing feedback process. Methods. We combined deep X-ray data from Chandra and millimeter observations of the Sunyaev-Zeldovich (SZ) effect obtained by the Atacama Large Millimeter/submillimeter Array (ALMA). Results. Thanks to independent measurements of the pressure profile from the ALMA SZ observation and the electron density profile from the available X-ray data, we derived, for the first time, the temperature profile in the ICM of a z> 2 protocluster. It reveals the presence of a strong cool core (comparable to local ones) that may host a significant mass deposition flow, consistent with the measured local SF values. We also find mild evidence of an asymmetry in the X-ray surface brightness distribution, which may be tentatively associated with a cavity carved into the proto-ICM by the radio jets. In this case, the estimated average feedback power would be in excess of ~1043 erg s-1. Alternatively, the asymmetry may be due to the young dynamical status of the halo. Conclusions. The cooling time of baryons in the core of the Spiderweb protocluster is estimated to be ~0.1 Gyr, implying that the baryon cycle in the first stages of protocluster formation is characterized by a high-duty cycle and a very active environment. In the case of the Spiderweb protocluster, we are witnessing the presence of a strongly peaked core that is possibly hosting a cooling flow with a MDR up to 250-1000 M⊙ yr-1, responsible for feeding both the central supermassive black hole (SMBH) and the high star formation rate (SFR) observed in the Spiderweb Galaxy. This phase is expected to be rapidly followed by active galactic nucleus (AGN) feedback events, whose onset may have already left an imprint in the radio and X-ray appearance of the Spiderweb protocluster, eventually driving the ICM into a self-regulated, long-term evolution in less than one Gyr.