Modal stability of low-frequency nucleus-acoustic waves in completely degenerate white dwarf cores and their nearly degenerate surroundings

We analyse the characteristic nucleus-acoustic wave (NAW) modes excitable in the completely degenerate (CD) core and in its nearly degenerate (ND) ambience of the ONe (oxygen-neon) and CO (carbon-oxygen) white dwarfs (WDs). It is based on a generalized spherical quantum hydrodynamic plasma model. It consists of non-thermal quantum electrons, classical thermal light nuclear species (LNS), and classical thermal heavy nuclear species (HNS). The inner concentric layer-wise electronic pressures are judiciously modelled. The electronic energy distribution, governed by the Fermi-Dirac (FD) thermostatistical distribution law, involves both the thermodynamical temperature and chemical potential. It emphasizes on the transition state between the thermodynamical temperature (classical) and the Fermi temperature (quantum) for the borderline regions of intermediate degeneracy for the first time. The model closure is obtained with the help of the gravito-electrostatic Poisson formalism. A normal Fourier-centric spherical mode analysis procedurally yields a generalized linear dispersion relation (sextic). It analytically highlights the plasma multiparametric dependency of the hybrid NAW-features. A numerical illustrative platform shows the NAW propagatory and dispersive behaviours in a biscale (hydrokinetic) form with a transcritical demarcation. It is demonstrated that the NAW in ONe (CO) WDs exhibits sensible growth features in the transcritical (supercritical) wave zone. Its temperature-sensitivity is more (less) prominent in ONe (CO) WDs, and so forth. In distinction, a full NAW dispersion portrayal is graphically presented and noticeably interpreted. The tentative asteroseismic implications and applications of the analysis are finally indicated.

Automated summary

We analyze the NAW modes in the CD core and ND ambience of ONe and CO white dwarfs using a quantum hydrodynamic plasma model. The model considers non-thermal quantum electrons, classical thermal light nuclear species, and classical thermal heavy nuclear species. The electronic energy distribution is controlled by the Fermi-Dirac temperature and chemical potential. The dispersion relation shows the multiparametric dependence of the NAW features, and a numerical platform demonstrates the NAW propagation and dispersion behaviors in a biscale form.