A semi-analytic admixed model formalism to study the stability effects of the inner crust regions against the local collective perturbations in non-rotating neutron stars is proposed. It consists of the viscoelastic heavy neutron-rich nuclei, superfluid neutrons, and degenerate quantum electrons. A normal spherical mode analysis yields a generalized linear dispersion relation multiparametrically mimicking the inner crust features of neutron stars. A hybrid gravito-nucleo-acoustic (GNA) instability mode is found to be excited. It is demonstrated that the electron density and the inner crust curvature act as its accelerating and antidispersive agents. In contrast, the heavy neutron-rich nucleus and neutron densities act as decelerating factors. The heavy nucleus density, electron density, and geometric curvature act as its destabilizers. It is only the neutron density that acts as the GNA stabilizing agent. The heavy neutron-rich nucleus and neutron densities are found to act as dispersive broadening factors to it. The high-$$K$$
K
regions are the more unstable spectral windows indicating that the GNA mode plays a dominant role in the inner crust zone towards the local stability. Its fair reliability is indicated in light of the recent astronomic observed scenarios. It could be useful to explore acoustic mode signatures in non-rotating neutron stars and similar other compact astroobjects.
We employ a quantum hydrodynamic model to investigate the cylindrical acoustic waves excitable in a gyromagnetoactive self-gravitating viscous cylinder comprised of two-component (electron–ion) plasma. The electronic equation of state incorporates the effect of temperature degeneracy. It reveals an expression for the generalized pressure capable of reproducing a completely degenerate (CD) quantum (Fermi) pressure and a completely non-degenerate (CND) classical (thermal) pressure. A standard cylindrical wave analysis, moderated by the Hankel function, yields a generalized linear (sextic) dispersion relation. The low-frequency analysis is carried out procedurally in four distinct parametric special cases of astronomical importance. It includes the quantum (CD) non-planar (cylindrical), quantum (CD) planar, classical (CND) non-planar (cylindrical), and classical (CND) planar. We examine the multi-parametric influences on the instability dynamics, such as the plasma equilibrium concentration, kinematic viscosity, and so forth. It is found that, in the quantum regime, the concentration plays a major role in the system destabilization. In the classical regime, the plasma temperature plays an important role in both the stabilization and destabilization. It is further seen that the embedded magnetic field influences the instability growth dynamics in different multiparametric regimes extensively, and so forth. The presented analysis can hopefully be applicable to understand the cylindrical acoustic wave dynamics leading actively to the formation of astrophysical gyromagnetic (filamentary) structures in diverse astronomical circumstances in both the classical and quantum regimes of astronomical relevance.
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