Rayleigh-Taylor instability in compressible ultra-relativistic degenerate strongly coupled plasma

Dense stars (e.g., white dwarfs) are composed of mainly ultra-relativistic degenerate electrons and strongly coupled ions subjected to a gravitational field. Considering the physical conditions of such systems, in this paper, we investigate the linear Rayleigh-Taylor (R-T) instability in a compressible ultra-relativistic degenerate strongly coupled plasma (SCP) using the generalized hydrodynamic fluid model. The electron fluid is assumed to be inertialess, ultra-relativistic degenerate, and weakly coupled, while the ion fluid is treated as non-degenerate and strongly coupled. The compressibility effects are considered for the ion fluid in terms of the Coulomb coupling parameter and internal energy. The dispersion properties of the R-T instability have been analyzed using the normal mode analysis. For short wavelength perturbations, the R-T instability excites in the presence of compressibility and degeneracy of ultra-relativistic electrons; otherwise, the characteristic internal wave propagates in the plasma medium. The compressibility and strong coupling effects play a decisive role in suppressing the R-T modes in dense degenerate SCP. In the high-frequency kinetic limit, the instability region is observed to be shorter than the low-frequency hydrodynamic limit. The effects of ultra-relativistic degenerate electrons are almost negligible on the growth rates. However, they significantly modify the dispersion properties and R-T instability criterion. The astrophysical applications of the present work have been discussed in the high-density ultra-relativistic plasmas in the finite flame thickness near the center of white dwarfs.