5. Conclusions and perspective
In this paper, it has been shown that the properties of coronal continuum waves depend sensitively on the underlying dynamical structure of the chromospheric/photospheric boundary regions. The effect of these regions can be considered in several ways. In our model of coronal magnetic flux tubes, we have incorporated two effects of non-coronal origin that will have a direct effect on the Alfvén velocity and, therefore, on the MHD spectrum. These effects are:
The existence of continuous MHD spectra in inhomogeneous magnetic flux tubes is of fundamental importance for the heating of the solar corona by resonant absorption. Therefore, we studied the continuous spectra of magnetic flux tubes and paid special attention to the changes in the structure of the continuum branches and waves which are introduced by the above two effects.
The equations that determine the continuous spectrum have been written in a form that exploits the usual Alfvén and slow magnetosonic polarization, i.e., the equations are written in terms of the parallel and perpendicular displacement components. These equations clearly reveal that gravity always couples Alfvén and slow magnetosonic continuum waves if the magnetic field is twisted. When the geodesic curvature of the magnetic field, i.e., the variation of the magnetic field strength within a magnetic surface, and the pressure are both non-zero Alfvén and slow magnetosonic continuum waves are also coupled. Therefore, pure Alfvén and slow magnetosonic continuum waves do not exist in coronal loops.
Our numerical results show that continuum branches can still be labeled Alfvén-like and slow-like on the basis of the amplitude ratio of the parallel and perpendicular displacement components. However, the Alfvén-like waves show much larger deviations from the pure ones than the slow-like waves. For Alfvén-like continuum waves the ratio easily reaches values above whereas for slow-like continuum waves the ratio stays below .
By varying the cross-section at the top of the flux tube we have found that the geodesic curvature has a more profound influence on the coupling between Alfvén- and slow-like continuum waves than the gravitational stratification. For example, the ratio typically increases with a factor for Alfvén-like waves going from a straight, constant cross-section, tube to one with a cross-section that is four times larger at the top than at the base.
Since the Alfvén-like continuum waves contain a substantial parallel component they are no longer incompressible. In nonlinear MHD, compressible motions are known to lead to the formation of shocks which can be dissipated easily. Therefore, the question arises how these waves evolve nonlinearly and what their role is for magnetic wave heating of the solar corona. We will report on this issue in a future publication.
© European Southern Observatory (ESO) 1997
Online publication: June 5, 1998