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Kinetic simulations of the solar wind from the subsonic to the supersonic regime

Abstract
We present and discuss a completely self-consistent kinetic simulation of a steady state transonic solar type wind. The equations of motion of an equal number of protons and electrons plunged in a central gravitational field and a self-consistent electric field are integrated numerically. Particles are allowed to make binary collisions with a Coulombian scattering cross-section. The velocity distributions of the particles injected at the boundaries of the simulation domain are taken to be Maxwellian. As anticipated by previous authors we find that the transonic solution implies the existence of a peak in the proton equivalent potential at some distance above the sonic critical point. Collisions appear to be the fundamental ingredient in the process of accelerating the wind to supersonic velocities. For a given temperature at the base of the simulation domain the acceleration efficiency decreases with decreasing density. The reason is that the plasma has to be sufficiently collisional for the heat flux to be converted efficiently into plasma bulk velocity. Concerning the heat flux we find that even when in the vicinity of the sonic point the collisional mean free path of a thermal particle is significantly smaller than the typical scales of variation of the density or the temperature, the electron heat flux cannot be described conveniently by the classical Spitzer-Härm conduction law; not even in most of the subsonic region. Indeed, in the simulations where a transonic wind forms the heat flux has been found to strongly exceed the Spitzer-Härm flux, in opposition to recently published results from multi-moment models. We emphasize that given the high coronal temperatures we use in our simulations (3 times the typical solar values) we do not expect the results presented in this report to be uncritically transposable to the case of the "real" solar wind. In particular, the quantitative aspects of our results must be handled with some care.