  One of the basic properties of the solar wind, that is the high speed of the
fast wind, is still not satisfactorily explained. This is mainly due to the
theoretical difficulty of treating weakly collisional plasmas. The fluid
approach implies that the medium is collision dominated and that the particle
velocity distributions are close to Maxwellians. However the electron velocity
distributions observed in the solar wind depart significantly from Maxwellians.
Recent kinetic collisionless models (called exospheric) using velocity
distributions with a suprathermal tail have been able to reproduce the high
speeds of the fast solar wind. In this letter we present new developments of
these models by generalizing them over a large range of corona conditions. We
also present new results obtained by numerical simulations that include
collisions. Both approaches calculate the heat flux self-consistently without
any assumption on the energy transport. We show that both approaches - the
exospheric and the collisional one - yield a similar variation of the wind
speed with the basic parameters of the problem; both produce a fast wind speed
if the coronal electron distribution has a suprathermal tail. This suggests
that exospheric models contain the necessary ingredients for the powering of a
transonic stellar wind, including the fast solar one.
