Models of coronal hole flows

Models of plasma flow in a coronal hole fall naturally into four classes. These are: (i) radial flow on a streamline along which the divergence is assumed to vary differently than as the square of the radial distance from the Sun; (ii) global flow along streamlines determined in some independent manner; (iii) empirical models originating in, or based strongly on observation; (iv) dynamic models using magnetic and plasma boundary conditions low in the corona to find both the geometry of streamlines and the flow field.To date, models both of ideal coronal holes and of specific observed coronal holes indicate that flow velocities above 100 km s⁺¹, and temperatures of perhaps 2 × 10⁶K are possible at 2R heliocentric distance, where densities of 2 × 10⁵ cm⁺³ have been reported. These velocities are at, or just above the sound speed, although still sub-Alfvénic. There is also general agreement among models of large polar holes that conversion of mechanical wave energy flux into solar wind kinetic energy is occurring in the 2R to 5R range, perhaps occurs even further outwards, and that the magnitude and extent of this energy deposition depends on the size and on the geometrical divergence of the hole.However, each model exhibits distinct weaknesses counteracted only by the complimentary nature of the various types of models. Models in class (i) are simply not global representations, but are tractable when dealing with complex forms of the energy equation or with several ion species. Class (ii) models lack any geometrical information beyond the ad hoc assumption of known streamline geometry, but have the same advantages as those in class (i). Class (iii) models cannot determine streamline geometry within a hole and do not extend further from the Sun than the available data — although they place important constraints on models in the other classes. Class (iv) models are limited to simple forms of the energy equation and/or to quasi-radial flow, but are the only models producing self-consistent streamline geometries through inclusion of transverse magnetic stresses in the momentum equation.Most limitations in coronal hole flow models can be eliminated by using known numerical techniques to combine models in classes (i), (ii), and (iv). This would allow detailed models of coronal holes and corresponding interplanetary conditions to be developed for specific time periods, at the cost of flexibility and possibly also general conceptual understanding. Nevertheless, the concept of a coronal hole is now reasonably well established, and acceptable modelling approaches are rapidly filling the literature. It can be anticipated that the evolution of these models, together with present and future observations, will bring us much nearer to understanding coronal energetics and dynamics.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.