Solar wind theory and modelling

The outflow of coronal plasma into interplanetary space is a consequence of the coronal heating process. Therefore the formation of the corona and the acceleration of the solar wind should be treated as a single problem. Traditionally the mass or particle flux emanating from the extended corona has been thought of as being determined by the coronal temperature or scale height and the coronal (base) density. This argument follows from considerations of the momentum balance of the corona-wind system from which one obtains models of a close to hydrostatic corona out to the critical point where the flow becomes supersonic. With this approach to the acceleration of the wind is has been difficult to reconcile the relatively small variation observed in the proton flux at 1 AU with the predicted exponential dependence of the proton flux on the coronal temperature. In this talk we would like to emphasize another approach in which coronal energetics play the primary role. The deposition of energy into the corona through some 'mechanical' energy flux is balanced by the various energy sinks available to the corona and the sum of these processes determine the coronal structure, i.e. its temperature and density. The corona loses energy through heat conduction into the transition region, through radiative losses, and through the gravitational potential energy and kinetic energy put into the solar wind itself. We will show from a series of models of the chromosphere transition region-corona-solar wind system that most of the energy deposited in a magnetically open region will go into the solar wind, with roughly half going into kinetic energy and half into lifting the plasma out of the solar gravity field. The coronal base density will adjust itself in such a way that the heat conductive flux flowing into the transition region is radiated away in the upper chromosphere. The coronal temperature is set by the requirements that most of the deposited energy goes into accelerating the solar wind; the coronal scale height will adjust itself so that the solar wind energy losses conform to the amplitude of the input energy. These processes are modified by the 'mode' of energy deposition, and we will show the effects on coronal structure of changing the parameters describing coronal heating as well as the effects of including a helium fluid in the models. However, the location, scale height and/or form of the energy deposition (i.e. heating or direct acceleration) are not too important for the solar wind, the coronal density and temperature structure will vary with the 'mode' of energy deposition, but the solar wind mass flux depends mainly on the amplitude of the energy flux.