A semi-analytical approach to time-dependent coronal expansion

In this paper we point out the existence of a special class of solutions to the nonlinear hydrodynamic equations describing the time-dependent solar wind, namely that for which the velocity profile is time-invariant but the density at each point of the corona changes exponentially with time. Theoretical velocity curves are calculated for the case of isothermal expansion and compared with the Parker model for steady-state expansion. These solutions can be used to obtain quantitative estimates for the degree of departure from the latter of a real corona undergoing evolution on a finite time scale.On leave from Los Alamos Scientific Laboratory, Los Alamos, N.M., U.S.A.