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.