Cylindrical ionizing shock waves in a self-gravitating gas with magnetic field: Power series method

The propagation of cylindrical ionizing shock waves in a self-gravitating ideal gas with axial magnetic field is investigated. The density and magnetic pressure are assumed to be varying according to power law with distance in the undisturbed medium. Approximate analytical solutions are obtained by expanding the flow variables in power series. The zeroth order and first order approximate solutions are discussed. Solutions for zeroth order approximation are constructed in analytical form. Distributions of hydrodynamical quantities for zeroth order approximation are discussed. Also, the effect of various flow parameters, namely shock Cowling number, adiabatic exponent, gravitational parameter and ambient density variation exponent are studied on the flow variables.