Growth of RT instability at the accreting magnetospheric boundary of neutron stars

In this paper, we investigate the formation and growth of Rayleigh-Taylor instability (RTI) in an ultra-dense celestial body like a neutron star which gradually accretes mass in it. Such an accretion process occurs at the magnetospheric boundary of the accreting star. Since the density is very high we have considered relativistic degeneracy pressure as well as quantum diffraction effect. Employing quantum hydrodynamic model (QHD), we have carried out the linear and non-linear analysis for this problem. Further by employing standard method we analyzed the instability criteria, its growth rate and other (physical) properties. We obtained four wave modes and analysed the growth rate of RTI and its dependence on various physical parameters. The results obtained here will be helpful in understanding many deep space phenomena. Many observations made by space missions like POLAR, Chandra, Hubble, etc. regarding neutron stars, dwarfs, and nebulae can be explained in a more meaningful way with our theoretical findings.