Ionizing cylindrical shock in a rotating self-gravitating dusty gas with magnetized isothermal flow

This article analyzes ionizing cylindrical magnetogasdynamic (MGD) shock waves in a rotating, axisymmetric, self-gravitating dusty gas under isothermal conditions. Using Sakurai's power-series method, closed-form similarity solutions are derived up to the first-order approximation in terms of (CU)2, where U is the shock velocity and C is the sound speed. The ambient medium ahead of the shock is assumed to have power-law variations in density, magnetic pressure, and azimuthal and axial velocities. A detailed parametric study highlights how factors such as the adiabatic index γ, dust loading κp, gravitational parameter G0, shock Cowling index C⋆, rotational parameter v⋆A, and density variation index q influence the flow and disturbance energy. The velocity–distance and distance–time profiles confirm the decaying nature of the cylindrical shock. These results offer a valuable benchmark for validating self-similar and numerical solutions and provide novel insights into dusty MGD shocks in astrophysical settings like supernova remnants, protostellar jets, and galactic outflows.