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Plasma outflow from a gravitational potential well with cosmic rays and self-excited Alfv\'en waves with cooling and wave damping is studied in the hydrodynamics regime. We study outflows in the presence of cosmic ray and Alfv\'en waves including the effect of cooling and wave damping. We seek physically allowable steady-state subsonic-supersonic transonic solutions. We adopted a multi-fluid hydrodynamical model for the cosmic ray plasma system. Thermal plasma, cosmic rays, and self-excited Alfv\'en waves are treated as fluids. Interactions such as cosmic-ray streaming instability, cooling, and wave damping were fully taken into account. We considered one-dimensional geometry and explored steady-state solutions. The model is reduced to a set of ordinary differential equations, which we solved for subsonic-supersonic transonic solutions with given boundary conditions at the base of the gravitational potential well. We find that physically allowable subsonic-supersonic transonic solutions exist for a wide range of parameters. We studied the three-fluid system (considering only forward-propagating Alfv\'en waves) in detail. We examined the cases with and without cosmic ray diffusion separately. Comparisons of solutions with and without cooling and with and without wave damping for the same set of boundary conditions (on density, pressures of thermal gas, cosmic rays and waves) are presented. We also present the interesting case of a four-fluid system (both forward- and backward-propagating Alfv\'en waves are included), highlighting the intriguing relation between different components., Comment: Outflows --Hydrodynamics-- Cosmic rays -- Alfv\'en waves-- Cooling --Wave Damping

Plasma outflow or wind against a gravitational potential under the influence of cosmic rays is studied in the context of hydrodynamics. Cosmic rays interact with the plasma via hydromagnetic fluctuations. In the process, cosmic rays advect and diffuse through the plasma. We adopt a multi-fluid model in which besides thermal plasma, cosmic rays and self-excited Alfven waves are also treated as fluids. We seek possible physically allowable steady state solutions of three-fluid (one Alfven wave) and four-fluid (two Alfven waves) models with given the boundary conditions at the base of the potential well. Generally speaking, there are two classes of outflows, subsonic and supersonic (with respect to a suitably defined sound speed). Three-fluid model without cosmic ray diffusion can be studied in the same way as the classic stellar wind problem, and is taken as a reference model. When cosmic ray diffusion is included, there are two categories of solutions. One of them resembles the three-fluid model without diffusion, and the other behaves like thermal wind at large distances when the waves wither and cosmic rays are decoupled from the plasma. We also inspect the effect of wave damping mechanisms (such as, nonlinear Landau damping). Roughly speaking, the effect is much smaller in supersonic outflow than in subsonic outflow., Comment: 16 pages, 9 figures, 1 table; Accepted for publication in the Astrophysical Journal