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A semi-analytic model is developed to study the effects of kappa-distributedlighter constituents and the associated kappa-modified polarization force onthe classical Jeans instability in dust molecular clouds (DMCs). Theconstitutive electrons and ions are considered to follow a nonthermalkappa-velocity distribution law, while the constitutive massive dust grains aretreated as the EiBI-gravitating fluids. A linearized quadratic dispersionrelation is derived using spherical normal mode analysis. The resultingdispersion relation and its corresponding modified instability criteria areanalyzed in the hydrodynamic and kinetic regimes. The oscillatory andpropagating mode characteristics are illustratively analyzed. It is seen thatthe EiBI gravity introduces a new velocity term in the dispersion relation. Incontrast, the nonthermal kappa-distributed constituents significantly enhancethe polarization force against their respective Maxwellian counterparts. Thekappa-modified polarization force and the negative EiBI gravity parameter havedestabilizing influences, unlike the positive EiBI parameter. An enhancedpolarization interaction parameter and a positive EiBI parameter reduce thereal normalized frequency. Consequently, the phase velocity exhibits strongdispersion, increasing with wavenumber until reaching saturation, after whichit transitions into a weakly dispersive regime. These findings provide newinsights into the formation of smaller astrophysical structures via thenon-local Jeans instability in the ultracompact HII regions of dense DMCs.

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