Effect of kappa-modified polarization force on Jeans instability in non-thermal EiBI-gravitating dust clouds

A semi-analytic model formalism is systematically developed to analyze the effects of kappa-distributed lighter constituents and the resulting kappa-modified polarization force on the Jeans instability in EiBI-gravitating dust molecular clouds (DMCs). The lighter constituents (electrons and ions) are considered to follow non-thermal kappa-velocity distribution. The constitutive massive dust grains are treated as EiBI-gravitating fluids. A generalized linear quadratic dispersion relation is derived using spherical normal mode analysis without any quasi-classic approximation. The resulting dispersion relation is analyzed in both the hydrodynamic and kinetic regimes along with their corresponding modified instability criteria. The characteristics of oscillatory and propagatory modes are illustratively analyzed. It is seen that the EiBI gravity introduces a new velocity term, the EiBI-induced velocity, in the dispersion relation. In contrast, the non-thermal kappa-distributed constituents significantly enhance the polarization force against their respective Maxwellian counterparts. The kappa-modified polarization force and the negative EiBI gravity parameter have destabilizing influences, unlike that with the positive EiBI parameter. An enhanced polarization interaction parameter and positive EiBI parameter reduce the real normalized frequency. Consequently, the phase velocity exhibits strong dispersion, increasing with the wavenumber until reaching saturation, after which it transitions into a weakly dispersive regime. These findings provide new theoretical insights on the gravitational collapse mechanisms in the ultracompact Hii regions of dense DMCs towards bounded structure formation.