Magnetohydrodynamic tube waves and high speed solar wind streams

It has been widely conjectured that magnetohydrodynamic (MHD) waves may provide the extra momentum or energy required to explain the high speed solar wind streams that originate in coronal holes. Although the magnetic structuring inherent in this problem has been incorporated into models of the bulk flow, this is not generally true of the associated treatments of wave propagation. In particular, as pointed out by Davila (1985), we might generally expect the magnetic geometry to substantially modify those waves whose wavelength is comparable to the hole width. Using both a geometrical optics and an eigenmode approach, Davila addressed the question of wave propagation in a simple uniform width flux slab model of a coronal hole and concluded

1. the hole may act as a ‘leaky wave guide’, i.e., waves travelling along it may leak into the surrounding corona, but
2. the group velocity of waves with periods in a physically relevant range (around 100 s) is downward, indicating that such waves cannot carry energy into the solar wind and therefore cannot be driving it.

We agree with (i) but argue that (ii) results from a mistaken interpretation of a dispersion relation, and is incorrect. Furthermore, we apply the cylindrical tube leaky wave approach of Cally (1986) to a simple coronal hole model, and find two wavetypes with substantial upward energy fluxes. However, of these, we argue that the so-called ‘trig modes’ (geometry modified fast waves) leak so profusely that they are unable to transport energy over the distance required; the non-axisymmetric ‘thin tube’ modes, though, do not suffer from this disability.