Gravito-electrostatic fluctuations of a polytropic charged dust cloud

Abstract

An analytical model to explore the weakly nonlinear gravito-electrostatic waves in a field-free polytropic dust molecular cloud on the astrophysical scales of space and time is proposed. The polytrope consists of the lighter electrons, ions and massive dust grains with full ionization. This is a nonthermalized situation due to the cold grains, and the mutually thermalized hot electrons and hot ions. A quasi-hydrostatic equilibrium in one-dimensional (1D, Cartesian) configuration is adopted with presumed global quasi-neutrality. The grain dynamics considered is such that exact gravito-electrostatic equilibrium is facilitated with their first-order perturbed self-gravitational potential. The analytical infrastructure is developed by a standard multi-scale analysis of stretched variables centered on the assumed initially ‘homogeneous’ equilibrium in accordance with the Jeans swindle. We derive a new gravito-electrostatically coupled pair of modified Korteweg–de Vries (m-KdV) equations having unique self-consistent nonlinear sources arising due to gravito-electrostatic intermixed coupling. A detailed numerical shape analysis of the fluctuations is carried out in order to see their parametric excitations as solitary spectral patterns. Interestingly, it is seen that the electrostatic fluctuations undergo bi-periodicity, while the self-gravitational counterparts retain uni-periodicity in phase space. Nontrivial aspects of the results relevant in space and astrophysical environments are summarily indicated.