Martin D. Altschuler

FLARE-PRODUCED CORONAL MHD-FAST-MODE WAVEFRONTS AND MORETON'S WAVE PHENOMENON

The propagation characteristics of MHD fast-mode disturbances, which can emanate from flare regions, are computed for realistic conditions of the solar corona at the times of particular flares. The path of a fast-mode disturbance is determined by the large-scale (global) coronal distributions of magnetic field and density, and can be computed by a general raytracing procedure (eikonal equation) adapted to MHD. We use the coronal (electron) density distribution calculated from daily K-coronameter data, and the coronal magnetic field calculated under the current-free approximation from magnetograph measurements of the photospheric magnetic field. We compare the path and time-development of an MHD fast-mode wavefront emitted from the flare region (as calculated from a realistic model corona for the day of the observed Moreton wave event) with actual observations of the Moreton wave event, and find that the Moreton wave can be identified with the rapidly moving intersection of the coronal fast-mode wavefront and the chromosphere (as hypothesized in our previous paper); the directivity (anisotropic propagation), as well as other characteristics of the propagation of the Moreton wave can be successfully explained.

High resolution mapping of the magnetic field of the solar corona

High resolution KPNO magnetograph measurements of the line-of-sight component of the photospheric magnetic field over the entire dynamic range from 0 to 4000 gauss are used as the basic data for a new analysis of the photospheric and coronal magnetic field distributions. The daily magnetograph measurements collected over a solar rotation are averaged onto a 180 × 360 synoptic grid of equal-area elements. With the assumption that there are no electric currents above the photospheric level of measurement, a unique solution is determined for the global solar magnetic field. Because the solution is in terms of an expansion in spherical harmonics to principal index n = 90, the global photospheric magnetic energy distribution can be analyzed in terms of contributions of different scale-size and geometric pattern. This latter procedure is of value (1) in guiding solar dynamo theories, (2) in monitoring the persistence of the photospheric field pattern and its components, (3) in comparing synoptic magnetic data of different observatories, and (4) in estimating data quality. Different types of maps for the coronal magnetic field are constructed (1) to show the strong field at different resolutions, (2) to trace the field lines which open into interplanetary space and to locate their photospheric origins, and (3) to map in detail coronal regions above (specified) limited photospheric areas.

Magnetic fields and the solar corona

Coronal magnetic fields calculated by the methods developed in Paper I (Altschuler and Newkirk, 1969) and the empirical description of the solar corona of November 1966 derived in Paper II (Newkirket al., 1970) are combined in order to investigate what connection exists between the magnetic fields and the density structure of the corona.To facilitate the comparison of magnetic fields with gross coronal features, magnetic configurations are divided into three classifications - diverging fields (DF), low magnetic arcades (LMA), and high magnetic arcades (HMA). It is found that DFs occur above active plages and correlate primarily with low enhancements in the corona. Magnetic arcades (MA) appear to correlate with coronal streamers, implying that streamers form above the neutral line between extended regions in the photosphere of opposite magnetic polarity.Comparison of the density structure of the corona - as evidenced by rays, arches, and plumes - with the shape of the calculated magnetic field lines shows very satisfactory agreement. This agreement indicates that the potential magnetic field model is reasonably valid in the lower corona (r < 2.5R) and that the density structure of the lower corona correlates with magnetic tubes containing varying amounts of coronal plasma.Density enhancements in the lower corona are investigated with the conclusion that the presence of high intensity magnetic fields in the photosphere implies elevated density in the corona. The geometry of the field determines the morphological form taken by the density enhancement.

On determining the electron density distribution of the solar corona from K-coronameter data

The electron density distribution of the inner solar corona (r ⩽ 2 R⊙) as a function of latitude, longitude, and radial distance is determined from K-coronameter polarization-brightness (pB) data. A Legendre polynomial is assumed for the electron density distribution, and the coefficients of the polynomial are determined by a least-mean-square regression analysis of several days of pB-data. The calculated electron density distribution is then mapped as a function of latitude and longitude. The method is particularly useful in determining the longitudinal extent of coronal streamers and enhancements and in resolving coronal features whose projections on the plane of the sky overlap.

The large-scale solar magnetic field

The large-scale photospheric magnetic field, measured by the Mt. Wilson magnetograph, has been analyzed in terms of surface harmonics (Pnm)(θ)cosmφ and Pnm(θ)sinmφ) for the years 1959 through 1972. Our results are as follows. The single harmonic which most often characterized the general solar magnetic field throughout the period of observation corresponds to a dipole lying in the plane of the equator (2 sectors, n = m = 1). This 2-sector harmonic was particularly dominant during the active years of solar cycles 19 and 20. The north-south dipole harmonic (n = 1, m = 0) was prominent only during quiet years and was relatively insignificant during the active years. (The derived north-south dipole includes magnetic fields from the entire solar surface and does not necessarily correlate with either the dipole-like appearance of the polar regions of the Sun or with the weak polar magnetic fields.) The 4-sector structure (n = m = 2) was prominent, and often dominant, at various times throughout the cycle. A 6-sector structure (n = m = 3) occasionally became dominant for very brief periods during the active years. Contributions to the general solar magnetic field from harmonics of principal index 4 ⩽ n ⩽ 9 were generally relatively small throughout this entire solar cycle with one outstanding exception. For a period of several months prior to the large August 1972 flares, the global photospheric field was dominated by an n = 5 harmonic; this harmonic returned to a low value shortly after the August 1972 flare events. Rapid changes in the global harmonics, in particular, relative and absolute changes in the contributions of harmonics of different principal index n to the global field, imply that the global solar field is not very deep or that very strong fluid flows connect the photosphere with deeper layers.

Improved three-dimensional mapping of the electron density distribution of the solar corona

Three-dimensional maps of the distribution of coronal electron density can now be computed with two radial functions in the series expansion for the density (rather than with only one radial function as shown in our previous paper). With the improved maps we can determine the topological variation of the electron density with radial distance, and thus can (1) distinguish coronal condensations from coronal streamers, (2) trace the structure of a streamer as a function of height, and (3) determine the non-radial orientation of a streamer. We summarize the previous work in concise mathematical notation, show examples of the improved maps derived from two radial functions, and discuss in detail the expectations and limitations of the method. Of great utility are computer-simulated pictures showing the solar corona as it would appear if veiwed from above the north (or south) pole.

Representations of coronal magnetic fields including currents

Coronal electric currents are superposed on the calculated large-scale current-free (potential) magnetic field of the solar corona and the new magnetic configurations are mapped. The results indicate that relatively large coronal electric currents are required before significant topological deviations from the potential magnetic field configuration can be noticed. Thus any agreement between coronal observations and calculated potential magnetic field configurations should not be interpreted to mean that coronal electric currents are necessarily absent or insignificant.

A moving Type IV radio burst and its relation to the coronal magnetic field

A moving Type IV burst, observed with the Culgoora radioheliograph on 1970 April 29, moved out to about 3 R⊙ and attained high circular polarization before fading. The appearance of the moving Type IV source suggests an isolated, self-contained, synchrotron emitting plasmoid. Magnetic field maps of the corona derived from photospheric observations indicate that the plasmoid moved almost radially outward from the flare region along open field lines. To explain the observed source structure and high unipolar polarization, we suggest that a ring of electric current was ejected from the low corona and guided by coronal magnetic field lines; the radio emission was synchrotron radiation generated by mildly-relativistic electrons trapped in the poloidal magnetic field of the ring current.

A possible acceleration mechanism for a solar surge

We examine a non-linear mechanism for a solar surge in which plasma regions of high electrical conductivity and macroscopic dimension can be rapidly accelerated without diffusion of magnetic field. The mechanism is suggested by Rusts observations, which show that surges occur near sunspots in regions of reversed magnetic polarity. For the purposes of numerical calculation, we replace the magnetic field near a polarity reversal in a sunspot by magnetic fields of current loops. The relaxation of the magnetic field generated by two antiparallel coaxial current loops in an incompressible plasma is traced by computer. The results suggest that plasma in the form of a vortex ring can be expelled at the Alfvén velocity from active solar regions.

Tabulation of the harmonic coefficients of the solar magnetic fields

Tables of spherical harmonic coefficients for the global photospheric magnetic field between 1959 and 1974 are now available on microfilm. (These are the same coefficients which were used to construct the maps of the coronal magnetic atlas.)