Supersonic Solutions of the Solar-Wind Equations for Low Coronal Temperatures
J. W. Chamberlain (Rice University)
I have examined the solutions of the three hydrodynamic solar-wind equations for the low-energy wind developed by Durney and for the supersonic ``breezes'' identified by Roberts and Soward. (The breezes are defined by the condition that , the flux of kinetic and conductive energy at infinity, vanishes.) These low-energy domains may have more relevance to planetary blowoff than do the more familiar high-energy solutions in the Parker domain. The low-energy cases admit a ``formal solution'' for the temperature and expansion velocity, discovered in 1961 but not previously exploited. In the Durney solutions, the temperature gradient at infinity is no longer easily obtained from the conductivity parameter, A, since conduction has ceased to be important at large distances from the coronal base.
The Durney solutions extend from the Parker domain to the domain of supersonic breezes, where the variation of coronal temperature, , with A, curiously reverses sign. Consequently, there are two supersonic solutions for values of the ratio (thermal-energy)/(gravitational-energy) = in the range between 0.33333 and about 0.32865. One solution exists for = 0 (a solar breeze) and another for a Durney solar wind, with a different, somewhat larger value of A (or, equivalently, a smaller coronal density). Calculations of temperature and velocity profiles illustrate a distinguishing behavior for each energy domain.