Sci. Form Vol. 3 (No. 1), pp. 57-58, 1988

Three-Dimensional Structure of the Coronal Magnetic Field

Kazuyuki Hakamada

Department of Engineering Physics, Chubu University, Kasugai, Aichi 487, Japan

Keywords: Corona, Magnetic Field, Three-Dimensional Structure

Abstract. Hot plasma in the corona continuously blows out from the sun as the solar wind into interplanetary space. The solar wind drags the coronal magnetic fields (CMF) out into space, which is observed as the interplanetary magnetic fields (IMF) by space probes. Since the CMF originate from the photospheric magnetic fields (PMF) of the sun, the IMF should have mutual relations with the PMF. However, the pattern of the IMF is very simple, in contrast to the very complicated pattern of the PMF.
Since it is impossible to detect the CMF by ground-based observations, it is necessary to compute the CMF from observational data of the PMF. For this purpose, the PMF is expanded into spherical harmonic series, assuming that the CMF can be computed by scalar magnetic potential. That is, there is no electric current in the corona. Further it is assumed that the scalar potential is equal to zero on a spherical surface of 2.5 solar radii (Rs), and all magnetic field lines are radial from that surface, the so-called "source surface" (ALTSHULER and NEWKIRK, 1969; SHATTEN et al., 1969). The spherical harmonic coefficients are determined from the line-of-sight component of the PMF observed at the Kitt Peak Solar Observatory in the U.S.A. (Harvey, 1984, private communication) with the procedure devised by RIESEBIETER and NEUBAUER (1979). Three components of the CMF can be computed with the spherical harmonic coefficients. Field lines, thus, can be traced with the two-step Runge-Kutta procedure. Figure 1 shows the 3D structure of the CMF. From the figure, it is found that there are many closed field lines near the photosphere. A part of the field lines originating from the photosphere can reach the source surface of 2.5 Rs and go out into the space. Generally, higher order spherical harmonic coefficients contribute to. field lines from the vicinity of active regions in the photosphere, where the magnetic field is also strong. The magnitude of higher order harmonic coefficients rapidly decreases with radial distance from the sun. Then, many field lines from the strong magnetic regions can not reach the source surface. However, the magnitude of lower order spherical harmonic coefficients gradually decreases with radial distance. Therefore the contribution of the lower order harmonic coefficients to the CMF becomes relatively more important than the higher order harmonic coefficients near the source surface. This is the primary reason that the pattern of the IMF is simpler than the one of the PMF.
More details should be referred to in HAKAMADA (1987) and the papers in its references.