Nonlinear stability of pulsational mode of gravitational collapse in self-gravitating hydrostatically bounded dust molecular cloud

Abstract

The pulsational mode of gravitational collapse (PMGC) in a hydrostatically bounded dust molecular cloud is responsible for the evolution of tremendous amount of energy during star formation. The source of free energy for this gravito-electrostatic instability lies in the associated self-gravity of the dispersed phase of relatively huge dust grains of solid matter over the gaseous phase of background plasma. The nonlinear stability of the same PMGC in an infinite dusty plasma model (plane geometry approximation for large wavelength fluctuation in the absence of curvature effects) is studied in a hydrostatic kind of homogeneous equilibrium configuration. By the standard reductive perturbation technique, a Korteweg-de Vries (KdV) equation for investigating the nonlinear evolution of the lowest order perturbed self-gravitational potential is developed in a time-stationary (steady-state) form, which is studied analytically as well as numerically. Different nonlinear structures (soliton-like and soliton chain-like) are found to exist in different situations. Astrophysical situations, relevant to it, are briefly discussed.

Acoustic Wave

“…Of course, convective and circulation dynamics which are the primary sources of magnetic field [41], are neglected throughout for simplicity. Similar observations of acoustic kinetics of the formation of soliton-type structures are also found in self-gravitating dust molecular clouds in presence of partially ionized dust grains through the active mechanism of gravito-acoustic coupling processes [27]. Some future scopes including realistic sources of acoustic perturbation of the presented analyses are also pointed out in brief.…”

“…In astrophysics [3,[28][29][30][31][32][35][36][37][38][39][40][41][42][43][44], the primary importance of plasma flows is revealed in such diverse situations as coronal flux tubes, stellar winds, rotating accretion disks, torsional modes, and jets emitted from radio galaxies. This is to argue that the basic understanding of the acoustic wave dynamics in transonic plasma system constitutes an important subject of future interdisciplinary research [5][6][7][8][9][10][11][12][26][27][28][29][30]. This may be useful for development of the appropriate diagnostics for acoustic spectroscopy to measure and characterize the hydrodynamic equilibrium of flowing transonic plasmas [8][9][10].…”

“…Most of the plasma devices of industrial applications like dense plasma focus machine, plasma torches, etc. depend on the plasma flows that violate the static equilibrium [26][27][28][29][30]. In fusion plasmas of future generation too, the static approximation of the equilibrium plasma description may not be suitable to describe the acoustic wave behavior.…”

Nonlinear Gravitoelectrostatic Sheath Fluctuation in Solar Plasma

“…These mathematical analyses may be extended for further investigation of fluctuation and stability with more realistic assumptions like grain rotations, spatial inhomogeneities, different gradient forces, and so forth, taken into account in other astrophysical and space environments. These calculations, although tentative for any concrete application to any sharply specified stellar formation mechanism, may be widely useful in the study of fluctuation-induced dynamics with electrostatic charge fluctuation of dust grains in astrophysical environment of dusty plasmas in the complex form of self-gravitationally collapsing dust cloud [21].…”

“…In the SWP scale of uniform flow, application of the inertia-induced acoustic excitation mechanism [20] may further be carried out for further stability analyses. The basic principles of the nonlinear pulsational mode [21] of the self-gravitational collapse model of charged dust clouds by applying the presented methodology may be another important future application in the self-gravitating solar plasma system.…”