We present results obtained from a detailed analysis of a deep Chandra observation of the bright FRII radio galaxy 3C 444 in Abell 3847 cluster .
A pair of huge X-ray cavities are detected along North and South directions from the centre of 3C 444 .
X-ray and radio images of the cluster reveal peculiar positioning of the cavities and radio bubbles .
The radio lobes and X-ray cavities are apparently not spatially coincident and exhibit offsets by \sim 61 kpc and 77 kpc from each other along the North and South directions , respectively .
Radial temperature and density profiles reveal the presence of a cool core in the cluster .
Imaging and spectral studies showed the removal of substantial amount of matter from the core of the cluster by the radio jets .
A detailed analysis of the temperature and density profiles showed the presence of a rarely detected elliptical shock in the cluster .
Detection of inflating cavities at an average distance of \sim 55 kpc from the centre implies that the central engine feeds a remarkable amount of radio power ( \sim 6.3 \times 10 ^ { 44 } erg s ^ { -1 } ) into the intra-cluster medium over \sim 10 ^ { 8 } yr , the estimated age of cavity .
The cooling luminosity of the cluster was estimated to be \sim 8.30 \times 10 ^ { 43 } erg s ^ { -1 } , which confirms that the AGN power is sufficient to quench the cooling .
Ratios of mass accretion rate to Eddington and Bondi rates were estimated to be \sim 0.08 and 3.5 \times 10 ^ { 4 } , respectively .
This indicates that the black hole in the core of the cluster accretes matter through chaotic cold accretion .