Transonic plasma winds with cosmic-rays and waves

Transonic plasma winds are studied under the influence of gravitational potential well in the presence of cosmic rays and self excited Alfven waves. We present interesting features of transonic winds originating from the gravitational potential well for a three-fluid system. The model is comprising of thermal plasma, cosmic rays and Alfven waves. The analysis is carried out on the hydro-dynamical basis with a particular emphasis on cosmic-ray streaming instability and damping mechanism. Boundary conditions on the base of the gravitational potential well will help to explore steady-state transonic wind solutions. A critical analysis on various mass outflow rate is also presented which is applicable to know the behaviour of normal and star-burst galaxies. The dependence of the critical or sonic point is studied for different sets of physical parameters. For the graphical interpretation of the numerical results different contour plots presented to analyze impacts of different mass flow rates. We find that transonic solutions exist for a wide range of parameters. We examine the case very close to the base of the gravitational potential well and the effect of the cosmic ray diffusion is neglected in current study.