Modelling of Comptonisation in low-mass X-ray binaries in the presence of fast variability

Comptonisation is a physical phenomenon that describes how radiation emitted from a source changes while travelling through a medium. In low-mass X-ray binaries (LMXBs) a compact object, which is a neutron star (NS) or a black-hole (BH), emits X-ray radiation that passes through a medium, called the corona. The corona is in a sense the atmosphere of an LMXB. After passing through the corona, the radiation that reaches our telescopes is observed to oscillate on time-scales of micro-seconds to a few seconds. In this thesis I have developed a mathematical model that explains both the radiation profile received by telescopes and also how that radiation, at different wavelengths, is oscillating as a function of time. By comparing the predictions of the model to real observations, we have concluded that: (a) The LMXBs that contain a neutron star are likely to have a corona that is around a hundred times smaller and 10 times more dense than that of LMXBs containing a black-hole, (b) the size of the corona of BH LMXBs changes reccurently between very large and very small leading to a different interaction between the corona and matter around the BH and (c) the corona around BH LMXBs can be ejected, with the help of magnetic fields, forming the so-called jet and later re-appear in its previous form. Our results have provided, for the first time, quantitative evidence for phenomena that were suggested in the literature decades ago