Global gravito-electrostatic fluctuations in self-gravitating spherical non-uniform charged dust clouds

We formulate exact non-local linear analysis for identification and characterization of the global collective gravito-electrostatic eigenmodes, discrete oscillations and associated instabilities in interstellar charged dust molecular cloud (DMC) sphere with mass-radius above the stability critical values on the astrophysical fluid scales of space and time. The realistic relevant zeroth-order effects, hitherto remaining unaccounted for, are concurrently included. It avoids using any kind of the Jeansian swindles against usual viewpoint. Armed with the modified Fourier plane-wave method, the dispersion relations (eigenvalues) and amplitude-variations (eigenfunctions) of the relevant perturbations about the inhomogenous equilibrium are procedurally derived and analyzed together with numerical illustrations. It is seen that the entire cloud supports spectrally heterogeneous mixture of the Jeans (gravitational) and electrostatic (acoustic) modes, coupled via quasi-linear discrete oscillations of mixed pattern. The lowest-order non-rigid diffused cloud surface boundary (CSB), sourced by active gravito-electrostatic interplay, is the most unstable interfacial plasma layer. Three distinct and spatio-spectrally isolated classes of global eigenmodes-dispersive, non-dispersive and hybrid types-are keyed together with idiosyncratic prolific features. Dispersive features are prominent in the ultra-high k-regime (acoustic) with modified form due to self-gravitational condensation of the Jeans modes; whereas, non-dispersive characteristics in the ultralow k-regime (gravitational) dominated by the Jeans waves; where, k = 2 pi/lambda is the angular wave number of the fluctuations on the Jeans scale. We further demonstrate that the grain-charge (grain-mass) plays destabilizing (stabilizing) influential role for the electrostatic fluctuations, but stabilizing (destabilizing) role for the self-gravitational counterparts. The results can be useful to realize diverse complex global astrophysical matter stabilities, instability-caused energy-cascading processes and self-gravitational cloud collapse dynamics leading to star clusters and galactic associations.