Feeding and feedback processes in the Spiderweb proto-intracluster medium

We present the detailed analysis of the thermal, diffuse emission of the proto-intracluster medium (ICM) detected in the halo of the Spiderweb Galaxy at z=2.16, within a radius of $\sim$ 150 kpc. We combined deep X-ray data from Chandra and millimeter observations of the Sunyaev-Zeldovich (SZ) effect obtained by ALMA. Thanks to independent measurements of the pressure profile from 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 the local ones) that may host a significant mass deposition flow, consistent with measured local star formation 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 or, alternatively, may be due to the young dynamical status of the halo. The cooling time of baryons in the core of the Spiderweb Protocluster is estimated to be $\sim$ 0.1 Gyr, implying that the baryon cycle in the first stages of the protocluster formation is characterised 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 possibily hosting a cooling flow with a mass deposition rate up to 250-1000 $M_{\odot}$/yr, responsible for feeding both the central supermassive black hole and the high star formation rate observed in the Spiderweb Galaxy. This phase is expected to be rapidly followed by active galactic nucleus 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.