Global Magnetohydrodynamic Modeling of the Solar Corona Using Observed Photospheric Magnetic Fields Lead Investigator: Dr. Jon Linker Science Applications International Corporation linker@iris023.saic.com Other Team Members: Dr. Zoran Mikic Science Applications International Corporation mikic@iris023.saic.com SOI Coordinator: Dr. Todd Hoeksema Stanford University SSSC Lead Programmer: To be determined Abstract We propose to use SOI-MDI magnetograms for the development of realistic three-dimensional magnetohdyrodynamic (MHD) simulations of the solar corona. The magnetograms will be used to deduce the radial magnetic field at the photosphere, which in turn will provide the boundary conditions for our MHD computations. The output from the simulations can be compared with independent observations, such as the LASCO coronograph aboard SOHO, or Mauna Loa Coronameter observations. We have already performed such computations using Wilcox Observatory synoptic maps, and our resulting solutions compare favorably with Mauna Loa and eclipse observations. We will also use SOI-MDI magnetograms to investigate dynamic changes in the corona. In particular, changes in the magnetic flux deduced from sequences of magnetograms can be used to specify the magnetic flux evolution at the solar boundary in our MHD computations. In this manner, the possible role of emerging flux in the initiation of coronal mass ejections can be investigated. Proposed Investigation 1) Introduction The interaction of the solar wind with coronal magnetic fields produces the beautiful structures called helmet streamers that can be seen during solar eclipses. Helmet streamers are dense structures that form in regions where closed coronal magnetic field lines are able to trap the solar wind. These closed-field regions are surrounded by open field lines (coronal holes) along which the solar wind streams to supersonic flow velocities. The self-consistent three-dimensional structure of the solar corona, including these open- and closed-field regions, can be calculated most appropriately using the magnetohydrodynamic (MHD) equations. Such a calculation requires the coupled interaction of magnetic, plasma, and solar gravity forces, including the effect of the solar wind (Parker 1963). Although an idealized MHD calculation of an axisymmetric helmet streamer was performed by Pneuman and Kopp in 1971, it has not been until recently that realistic three-dimensional MHD computations of the solar corona have been developed (Mikic & Linker 1995). These calculations require the distributions of the radial magnetic field, plasma density, and temperature to be specified at the base of the corona as boundary conditions. For our present calculations, we use Wilcox Solar Observatory synoptic maps (collected during a solar rotation by daily measurements of the line-of-sight magnetic field at central meridian) to specify the radial magnetic field at the photosphere. The density and temperature are assumed to be uniform in latitude and longitude at the coronal base (these assumptions will be relaxed in future calculations). A potential magnetic field and a transonic wind solution (Parker, 1963) consistent with the specified boundary conditions is chosen as the initial condition for the time-dependent MHD computation. Of course, since the potential magnetic field and solar wind solutions are not consistent with each other, this is a non-equilibrium state, so that the plasma evolves in time. The MHD equations are integrated in time until a steady-state is reached, when the plasma and magnetic fields have settled into equilbrium. The steady-state solution provides a description of the state of the solar corona, including the detailed distribution of magnetic fields, currents, coronal plasma density, velocity, and temperature. The accuracy of our model has been tested by comparison with observations. We have found that this model reproduces accurately the large-scale structure of the solar corona observed during the solar eclipse of November 3, 1994, in Chile (Mikic & Linker 1995). A comparison with Mauna Loa MK3 coronagraph observations during the solar rotation surrounding the eclipse (Carrington rotation 1888) confirms that the basic large-scale three-dimensional structure of the streamer belt has been captured in the model. These comparisons indicate that the most significant portion of the large-scale structure of the solar corona, including the position and shape of the helmet streamer belt, is determined by the magnetic field distribution on the Sun. The position of the heliospheric current sheet produced by this model also compares favorably with Ulysses observations (Mikic and Linker 1995). 2) Investigation Plan We propose to use SOI-MDI magnetograms to develop boundary conditions for the magnetic field in our coronal simulations. Our first studies will focus on the development of coronal equilibrium solutions for different solar rotations, similar to the computations we have done using Wilcox data. These solutions can be tested with independent SOHO observations and can provide a working model of the solar corona for the coordinated analysis of the diverse data sets available. The higher resolution SOI-MDI magnetograms should provide a significant advance over the Wilcox observatory synoptic charts. We will compare the solutions obtained using these two data sets for co-incident time periods. In our present calculations with the Wilcox data, we use Wang and Sheeley's (1992) procedure to deduce the radial magnetic field at the photosphere. Initially, we will also use this procedure with the SOI-MDI data, but we may examine how the solutions differ when a line-of-sight boundary condition is used. We also plan to investigate the structure of the heliospheric current sheet with our MHD computations. Source-surface models (e.g. Schatten et al. 1969; Altschuler and Newkirk 1969; Hoeksema 1984; Hocksema 1991; Wang and Sheeley 1992) have been used to investigate the interplanetary magnetic field for many years. While this approach has yielded important insights into the structure of the coronal and heliospheric magnetic field, important differences between the model and Ulysses observations have been noted (Smith et al. 1993; Balogh et al.,1995). Initial comparisons of our MHD computations with Ulysses data (Mikic & Linker, 1995) indicate that the MHD computations may provide a means of more accurately mapping phenomena in the solar wind back to their origin in the solar corona. Source-surface models have great utility and are easy to calculate, so a number of researchers are working to improve these calculations (Shulz, 1995; Zhao & Hoeksema, 1995). The MHD computations may help provide guidance for improving these models. The studies described thus far will primarily require "maps" of the Sun's magnetic field, obtained from full-disk SOI-MDI magnetograms acquired during a solar rotation. We also plan to perform studies of coronal dynamics, that will require time sequences of magnetograms. For example, recent theoretical calculations suggest that coronal mass ejections (CMEs) can be initiated by the effect of magnetic nonequilibrium produced by the distortion of magnetic field lines by photospheric shear (Roumeliotis, Sturrock, & Antiochos 1994; Mikic & Linker 1994; Linker & Mikic 1995). The photospheric shear can result from differential rotation (Linker, Mikic, & Schnack 1994). On the other hand, a recent study of the correspondence between disappearing filaments (used as proxies for CMEs) and neighboring emerging flux (Martin & Feynman 1995) implies that CMEs may be initiated by emerging flux. The relative role of these two effects in the initiation of CMEs awaits observational confirmation. We propose to use changes in the magnetic flux deduced from SOI-MDI magnetograms to specify the photospheric magnetic flux evolution in our MHD computations. The coronal consequences of this evolution can be tested and compared with SOHO coronagraph observations. With these computations, the role of emerging flux in initiating CMEs can be assessed. Comparison between these calculations and computations of coronal evolution driven by shear motions will yield new insights into the fundamental processes that drive CME initiation. 3) Summary We have described a program for incorporating SOHO-MDI magnetograms into global MHD computations of the solar corona. The solutions obtained provide a description of the properties of the plasma and magnetic fields in the corona, and can be tested against independent observations, either from other SOHO instruments or ground-based observatories. Our proposed research will require average magnetograms for the full Sun (similar to Wilcox synoptic maps) and time sequences of full disk magnetograms for deducing localized changes in the magnetic flux. We expect our initial efforts to focus on analyzing several selected rotations and time intervals of interest, although eventually a wider sampling of all the synoptic data might be possible. We believe that our MHD computations can provide a useful tool for understanding the diverse data sets that will be available. When possible, we will compute solutions for time intervals that have been identified as of interest for SOHO researchers, and make these solutions available to the research community. References: Altschuler, M.D., & Newkirk, G. 1969, Sol. Phys., 9, 131 Balogh, A., Smith, E.J., Tsurutani, B.T., Southwood, D.J., Forsyth, R.J., & Horbury, T.S. 1995, Science, 268, 1007. Feynman, J., & Martin, S.F. 1995, J. Geophys. Res., 100, 3355. Hoeksema, J.T. 1984, Tech. Rep. CSSA-ASTRO-84-07, Center for Space Science and Astronomy, Stanford University, Calif. Hoeksema, J.T. 1991, Tech. Rep. CSSA-ASTRO-91-01, Center for Space Science and Astronomy, Stanford University, Calif. 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