Nucleus-acoustic (NA) shock structures (SSs) are formed in a strongly coupled self-gravitating degenerate quantum plasma (SCSGDQP) system (e.g., white dwarfs) for the first time. The reductive perturbation method has been employed to identify the basic features of small, but finite amplitude NA SSs. The SCSGDQP is assumed to be composed of strongly coupled non-degenerate heavy nuclei, weakly coupled degenerate light nuclei, and non-relativistically and ultra-relativistically degenerate electrons. It is shown for the first time that the strong correlation among heavy nuclei acts as a source of dissipation and is responsible for the formation of the NA SSs, and that the NA SSs exist with positive (negative) electrostatic (self-gravitational) potential. It also observed that the effects of ultra-relativistically degenerate electrons and of the dynamics and degenerate pressure of light nuclei significantly modify the basic features (viz., speed, amplitude, and width) of the NA SSs. The implications of our results to the astrophysical compact objects like white dwarfs are briefly discussed.

Heavy nucleus-acoustic (HNA) spherical solitons (SSs) associated with HNA waves (in which the inertia is provided by the heavy and light nuclear species, and restoring force is provided by the degenerate pressure of electron species) in self-gravitating degenerate (super-dense) quantum plasmas have been theoretically investigated. The reductive perturbation method has been employed to derive a modified Korteweg-de Vries equation. The new basic features (e.g., polarity, amplitude, width, etc.) of the HNA SSs (associated with electrostatic and self-gravitational potentials) are identified, and are found to be significantly modified by the effects of ultra-relativistically degenerate electron pressure, dynamics of non-degenerate light and heavy nuclear species, self-gravitational field, and spherical geometry. It is found that depending on the plasma parameters, the HNA SSs with either positive (negative) or negative (positive) electrostatic (self-gravitational) potential exist in such realistic astrophysical plasma systems. The applications of our results in some astrophysical compact objects (containing heavy and light nuclear species, and degenerate electron species) are briefly discussed.

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Nucleus-acoustic (NA) solitary waves (SWs) propagating in a self-gravitating degenerate quantum plasma (SDQP) system (containing non-relativistically degenerate heavy and light nuclei, and non-/ultra-relativistically degenerate electrons) have been theoretically investigated. The modified Korteweg-de Vries (mK-dV) equation has been derived for both planar and non-planar geometry by employing the reductive perturbation technique. It is shown that the NA SWs exist with positive (negative) electrostatic (self-gravitational) potential. It is also observed that the effects of non-/ultra-relativistically degenerate electron pressure, dynamics of non-relativistically light nuclei, spherical geometry, etc. significantly modify the basic features (e.g., amplitude, width, speed, etc.) of the NA SWs. The applications of our results, which are relevant to astrophysical compact objects, like white dwarfs and neutron stars, are briefly discussed.

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