We present a 100 ks Chandra observation studying the extended X-ray emission around the powerful z = 1.04 quasar PKS 1229-021 .
The diffuse cluster X-ray emission can be traced out to \sim 15 arcsec ( \sim 120 kpc ) radius and there is a drop in the calculated hardness ratio inside the central 5 arcsec consistent with the presence of a cool core .
Radio observations of the quasar show a strong core and a bright , one-sided jet leading to the SW hot spot and a second hot spot visible on the counter-jet side .
Although the wings of the quasar PSF provided a significant contribution to the total X-ray flux at all radii where the extended cluster emission was detected , we were able to accurately subtract off the PSF emission using ChaRT and marx simulations .
The resulting steep cluster surface brightness profile for PKS 1229-021 appears similar to the profile for the FRII radio galaxy 3C 444 , which has a similarly rapid surface brightness drop caused by a powerful shock surrounding the radio lobes ( Croston et al . ) .
Using a model surface brightness profile based on 3C 444 , we estimated the total cluster luminosity for PKS 1229-021 to be L _ { X } \sim 2 \times 10 ^ { 44 } \hbox { $ erg s ^ { -1 } $ } .
We discuss the difficulty of detecting cool core clusters , which host bright X-ray sources , in high redshift surveys .