Acoustic stability of a self-gravitating cylinder leading to astrostructure formation

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.