A theoretical model for electromagnetic characterization of a spherical dust molecular cloud equilibrium structure

•A spherical charged dust cloud is electromagnetically characterized.•Weak but finite inertia of the thermal species is considered.•Technique applies the modified Lane–Emden equation and its multi-order solutions.•Cloud surface properties, transitional dynamics and expansions are highlighted.•Besides, application of the model in diverse astrophysical situations is demonstrated.

A theoretical model is developed to study the equilibrium electromagnetic properties of a spherically symmetric dust molecular cloud (DMC) structure on the Jeans scales of space and time. It applies a new technique based on the modified Lane–Emden equation (m-LEE) of polytropic configuration. We consider a spatially inhomogeneous distribution of the massive dust grains in hydrodynamic equilibrium in the framework of exact gravito-electrostatic pressure balancing condition. Although weak relative to the massive grains, but non-zero finite, the efficacious inertial roles of the thermal species (electrons and ions) are included. A full portrayal of the lowest-order cloud surface boundary (CSB) and associated significant parameters is numerically presented. The multi-order extremization of the m  -LEE solutions specifies the CSB existence at a radial point 8.58×10128.58×1012 m relative to the center. It is shown that the CSB gets biased negatively due to the interplay of plasma-boundary wall interaction (global) and plasma sheath–sheath coupling (local) processes. It acts as an interfacial transition layer coupling the bounded and unbounded scale-dynamics of the cloud. The geometrical patterns of the bi-scale plasma coupling are elaborately analyzed. Application of our technique to neutron stars, other observed DMCs and double layers is stressed together with possible future expansion.