The nonlinear evolutionary dynamics of gravitational instability in a complex self-gravitating viscoelastic nonthermal polytropic astrofluid is semi-analytically investigated on the Jeansian scales of space and time. The key effects out of fluid buoyancy, thermal fluctuations, and volumetric expansions are concurrently considered and carefully included. A nonlinear normal mode (local) analysis yields a Korteweg-de Vries (KdV) equation with a unique set of multi-parametric coefficients. We provide a numerical platform to demonstrate how the KdV dynamics excites an interesting spectral class of compressive solitary chain patterns as the evolutionary eigenmodes having atypical dynamical behaviour. Their diversified characteristic features are explained elaborately alongside phase-plane analysis. Various stabilizing (destabilizing) and accelerating (decelerating) factors of the instability are illustratively explored together with a validated reliability checkup. The relevancy of our investigated results in the context of super-dense compact astro-objects and their circumvent viscoelastic atmospheres is summarily outlined.
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.
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