The above constraint requires a coronal energy per proton-electron pair of about 5 keV, to release the fast wind from the Sun’s gravitational potential well and attain its high asymptotic speed. If , there is no critical point, so that if the corona appears gravitationally bound. To obtain a fast flow according to Equation (2), an average temperature of about is needed for and . However, isothermal models, for which , require an infinite amount of internal energy, since formally their enthalpy diverges. Anyway, the key issue of coronal heating is not even addressed in a polytropic model. However, one has to deal with the thermodynamics of the weakly collisional and turbulent corona and wind, a complex problem which requires the kinetic approach. Apparently, in the single-fluid description the coronal temperature profile entirely determines the coronal expansion and solar wind outflow, which is a natural consequence of a hot corona. Here we do not want to address fluid-modelling issues, but refer the reader to the book chapter by Marsch et al. (2003) and further references therein.
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