Stability Analysis of Solar Atmospheric Models

           

Principal Investigator

Warren Wood

Department of Mathematics,University of Newcastle

Co-Investigators

Murray Sciffer

Department of Physics, University of Newcastle

Projects

g90 - VPP

This project has studied the stability of equilibrium
magnetic fields evaluated from mathematical
models of the solar atmosphere. These equilibrium models display many of the features of the atmospheric fields detected by recent observations from the satellite SOHO. This investigation looked at the stability properties of the fields as it is believed that when the magnetic fields become unstable then they erupt to heat the upper atmosphere of the Sun. Based on numerical calculations the most unstable fields are those with a quadrupolar structure.

   
         
           

What are the results to date and the future of this work?

The normal modes have been calculated for two dimensional fields for various wave numbers. These calculations show that there are three different sets of modes which arise from the models. There are purely oscillatory modes and the frequency of these modes are plotted for various wave numbers to produce diagnostic diagrams. In addition there are overstable modes which have growth times which do not compare well with any of the observed instability times. The third class of modes are purely growing modes and these have growth times which are the right order of magnitude when compared with eruptive times associated with solar flares.

Some preliminary calculations have been performed on fully three dimensional models but we have not been able to obtain reliable numerical results for these models. Future work in this area will probably require a different approach to the one adopted for our calculations.

What computational techniques are used?

A system of partial differential equations are Fourier analysed in the ignorable direction and the equations are discretized in the remaining two directions. The time dependence is also Fourier analysed and this leads to an eigenvalue problem in which the eigenvalues give information as to the stability of the equilibrium system. The QR algorithm is used to evaluate the eigenvalues using the NAG routines. The NAG routine evaluates all the eigenvalues for the given matrix and so the complete spectrum may be studied.

Publications

M.D.Sciffer, Two Dimensional Stability Analyses of Arcade Structures in the Solar Atmosphere, A.I.P. Annual Conference, 1998, Perth.

           
- Appendix B