Adapted instabilities excited in spherical magnetized viscoelastic astroclouds with extreme dust-fugacity moderations

We investigate the dynamics of the dust acoustic wave (DAW, low-fugacity) and the dust Coulomb wave (DCW, high-fugacity) in self-gravitating magnetized viscoelastic spherical dusty astroclouds. It consists of the inertial dust grains with variable charge alongside the nonthermal electrons and ions in a generalized hydrodynamic framework. A spherical wave analysis yields a unique generalized quadratic dispersion relation. The fluctuations are free from the viscoelasticity effects in the weakly coupled limit (WCL) against the strongly coupled limit (SCL). The electron concentration, dust charge, and magnetic field act as stabilizing and accelerating agencies. The ion density and nonthermality parameters show destabilizing and decelerating effects. The cloud size shows a unique stabilizing feature in the ultralow-frequency domain. Both the DAW and DCW are dispersive in the short-wavelength (acoustic) regime and nondispersive in the long-wavelength (gravitational) regime. The distinctive WCL–SCL scenarios are explicitly compared. The results show correlative consistencies in real astronomic circumstances sketchily. Graphical abstract: The dust acoustic wave (DAW) and the dust Coulomb wave (DCW) in self-gravitating magnetized viscoelastic spherical dusty astroclouds with extreme dust-fugacity moderations are explored. The spatiospectral profiles of (a) Ω and (b) Ω with K and ξ in the SCL (upper row) and in the WCL (lower row) of the HFR in the κ-case are numerically portrayed.[Figure not available: see fulltext.]