A new distant Giant Radio Galaxy in the Bo\"otes field serendipitously detected by Chandra
Giant Radio Galaxies (GRGs) are the largest single structures in the Universe. Exhibiting extended radio morphology, their projected sizes range from 0.7 Mpc up to 4.9 Mpc. LOFAR has opened a new window on the discovery and investigation of GRGs and, despite the hundreds that are today known, their main growth catalyst is still debated. One natural explanation for the exceptional size of GRGs is their old age. In this context, hard X-ray selected GRGs show evidence of restarting activity, with the giant radio lobes being mostly disconnected from the nuclear source, if any. In this paper, we present the serendipitous discovery of a distant ($z=0.629$), medium X-ray selected GRG in the Bo\"otes field. High-quality, deep Chandra and LOFAR data allow a robust study of the connection between the nucleus and the lobes, at a larger redshift so far inaccessible to coded-mask hard X-ray instruments. The radio morphology of the GRG presented in this work does not show evidence for restarted activity, and the nuclear radio core spectrum does not appear to be GPS-like. On the other hand, the X-ray properties of the new GRG are perfectly consistent with the ones previously studied with Swift/BAT and INTEGRAL at lower redshift. In particular, the bolometric luminosity measured from the X-ray spectrum is a factor of six larger than the one derived from the radio lobes, although the large uncertainties make them formally consistent at $1\sigma$. Finally, the moderately dense environment around the GRG, traced by the spatial distribution of galaxies, supports recent findings that the growth of GRGs is not primarily driven by underdense environments.