Using the deepest (370 ksec) Chandra observation of a high-redshift galaxy cluster, we perform a detailed characterization of the intra-cluster medium (ICM) of WARPJ1415.1+3612 at z=1.03. We also explore the connection between the ICM core properties and the radio/optical properties of the brightest cluster galaxy (BCG). We perform a spatially resolved analysis of the ICM to obtain temperature, metallicity and surface brightness profiles. Using the deprojected temperature and density profiles we accurately derive the cluster mass at different overdensities. In addition to the X-ray data, we use archival radio VLA imaging and optical GMOS spectroscopy of the central galaxy to investigate the feedback between the central galaxy and the ICM. The X-ray spectral analysis shows a significant temperature drop towards the cluster center, with a projected value of Tc = 4.6 pm 0.4 keV, and a remarkably high central iron abundance peak, Zc= 3.6 Zsun. The central cooling time is shorter than 0.1 Gyr and the entropy is equal to 9.9 keV cm2. We detect a strong [OII] emission line in the optical spectra of the BCG with an equivalent width of -25 AA, for which we derive a star formation rate within the range 2 - 8 Msun/yr. The VLA data reveals a central radio source coincident with the BCG and a faint one-sided jet-like feature with an extent of 80 kpc. The analysis presented shows that WARPJ1415 has a well developed cool core with ICM properties similar to those found in the local Universe. Its properties and the clear sign of feedback activity found in the central galaxy in the optical and radio bands, show that feedback processes are already established at z~1. In addition, the presence of a strong metallicity peak shows that the central regions have been promptly enriched by star formation processes in the central galaxy already at z > 1.
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