Estimating the mechanical power of relativistic jets emanating from active galactic nuclei (AGN) and inflating X-ray cavities into hot atmospheres of elliptical galaxies and galaxy clusters has been a hot topic in X-ray astronomy for the past 30 years. In the current approach, jet powers are derived from sizes of X-ray cavities, which are simplified to have ellipsoidal shapes and lie in the plane of the sky, with their ages determined using additional simplifying assumptions.

The aim of the thesis is to perform a statistical study of the jet powers and enthalpies of X-ray cavities in multi-cavity systems. The student will compare the current approach of jet power estimation with a novel method leveraging machine learning techniques, take into account various possible jet re-orientation scenarios and inclination angles and properly estimate the timescale of cavity inflation. By comparing enthalpies and jet powers of several generations of X-ray cavities for multiple systems, the thesis will hopefully shed more light on the process of jet power estimation, in particular, improving the estimates for previously detached X-ray cavities.