An MHD Model of the Solar Corona

Two views of a typical mesh for a 3-D numerical computation of the solar corona. Here 101X75X64 (r,theta,phi) points were used. The r and theta meshes are nonuniform. Click these images to see high resolution JPEG images (134 Kbytes and 199 Kbytes, respectively).

In the calculations presented here, the state of the corona is predicted using a theoretical model based on the magnetohydrodynamic (MHD) equations. To develop a realistic model, photospheric magnetic field data during the time of interest is used to specify the boundary condition on the radial magnetic field (Br). Typically, we use synoptic charts generated from measurements at the Wilcox Solar Observatory or the National Solar Observatory at Kitt Peak. We plan in the future to use data from the SOI/MDI instrument aboard the SOHO spacecraft. The measured photospheric magnetic field, together with a uniform assumed density and temperature at the photosphere, is used to solve the MHD equations to steady state in the corona, expressing the self-consistent interaction of the solar wind with the coronal plasma. The three-dimensional simulation is carried out on a Cray YMP/C90 supercomputer. This gives a prediction of the properties of the coronal plasma (magnetic field, density, temperature, and flow velocity). You can see a movie (384 kbyte MPEG) depicting the relaxation of the magnetic field. This movie shows the field lines every 10 Alfven times during the relaxation to a steady-state solution.

To directly compare our results with observations, we must develop images like those obtained with coronagraphs and during eclipses. Frequently the polarization brightness, pB, is observed. The distribution of pB in the plane of the sky is proportional to the line-of-sight integral of the product of the electron density and a scattering function. Thus, using the plasma density from our model, we generate a pB image to simulate an eclipse image. This image can then be compared to the actual data. Eclipse images generally use radially graded filters to compensate for the rapid fall off of the coronal density with radial distance; we detrend our computed pB in a similar manner.

To predict the structure of the corona prior to an eclipse, we typically use magnetic field data that is about a month old. During solar minimum, the magnetic field on the Sun is changing relatively slowly from day to day, so a prediction of the large-scale structure of the solar corona a month or so in advance can be expected to provide a reasonable forecast of the solar corona. As we approach solar maximum, more care will be needed to use the freshest magnetic data possible.

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