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

Abstract

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.