Effect of flow-tube geometry on solar wind properties

A mathematical description of the solar wind flow-tube geometry is proposed. The expansion factor of the flow tube f(r) ( = a/r(2), r is the heliocentric distance and a is the flow-tube cross-section area) increases monotonically from 1 at the coronal base to f(m) at r(c), and approaches its asymptotic value f(infinity) nearly in a width of 2sigma(c). The flow tube with f(m) = f(infinity) is demonstrated to be approximately equivalent to that given by Kopp and Holzer (1976) for the fast solar wind, and it presumably represents slow wind tubes as f(m) is substantially larger than f(infinity). In terms of an Alfven wave-driven solar wind model, the effect of the flow-tube geometry on solar wind properties is examined. It is found that with the same flow conditions at the coronal base an expansion factor which increases monotonically with the radial distance results in a fast solar wind solution, whereas a flow tube which undergoes an expansion-contraction-reexpansion process creates a slow solar wind solution. Among the four flow-tube parameters the maximum expansion factor f(m) has the strongest effect, and the associated Laval-nozzle formed by the contraction and reexpansion of the flow tube plays a crucial role in determining solar wind properties. It is suggested that one must take the effect of the flow-tube geometry into account while constructing reasonable flow-tube models for the slow solar wind.