Exact Solution for Isothermal Flow behind a Shock Wave in a Self-Gravitating Gas of Variable Density in an Azimuthal Magnetic Field

Similarity solution for the propagation of a spherical shock wave in a self-gravitating perfect gas with an azimuthal magnetic field in the case of isothermal flow is investigated. The density and azimuthal magnetic field strength in the ambient medium are assumed to vary and obey power laws. An exact similarity solution obtained using the McVittie method in the case of isothermal flow is reported for the first time. The obtained solutions show that the radial fluid velocity, density, pressure, magnetic field strength, and the mass tend to zero as the point of symmetry is approached. The effects of the changes in the values of the adiabatic exponent γ and the exponent w in the variation of an initial density are considered in detail. It is shown that the magnetic field strength and mass increase with γ, whereas an increase in w exerts the reverse effect on these flow variables.