Cosmic-ray-modified stellar winds. III - A numerical iterative approach

A numerical iterative method is used to determine the modification of a stellar wind flow with a termination shock by the galactic cosmic rays. A two-fluid model consisting of cosmic rays and thermal stellar wind gas is used in which the cosmic rays are coupled to the background flow via scattering with magnetohydrodynamic waves or irregularities. A polytropic model is used to describe the thermal stellar wind gas, and the cosmic-rays are modeled as a hot, low-density gas with negligible mass flux. The positive galactic cosmic-ray pressure gradient serves to brake the outflowing stellar wind gas, and the cosmic rays modify the location of the critical point of the wind, the location of the shock, the wind fluid velocity profile, and the thermal gas entropy constants on both sides of the shock. The transfer of energy to the cosmic rays results in an outward radial flux of cosmic-ray energy.