Magnetic fields and the structure of the solar corona

Abstract

Several different mathematical methods are described which use the observed line-of-sight component of the photospheric magnetic field to determine the magnetic field of the solar corona in the current-free (or potential-field) approximation. Discussed are (1) a monopole method, (2) a Legendre polynomial expansion assuming knowledge of the radial photospheric magnetic field, (3) a Legendre polynomial expansion obtained from the line-of-sight photospheric field by a least-meansquare technique, (4) solar wind simulation by zero-potential surfaces in the corona, (5) corrections for the missing flux due to magnetograph saturation. We conclude (1) that the field obtained from the monopole method is not consistent with the given magnetic data because of non-local effects produced by monopoles on a curved surface, (2) that the field given by a Legendre polynomial (which is fitted to the measured line-of-sight magnetic field) is a rigorous and self-consistent solution with respect to the available data, (3) that it is necessary to correct for the saturation of the magnetograph (at about 80 G) because fields exceeding 80 G provide significant flux to the coronal field, and (4) that a zero-potential surface at 2.5 solar radii can simulate the effect of the solar wind on the coronal magnetic field.

Time-scales of close-in exoplanet radio emission variability

“…In this section, we describe the process by which the 3D magnetic field structure of cool stars can be determined using a potential-field source surface (PFSS) approach (Altschuler & Newkirk 1969). The magnetic field is assumed to be in a potential state (∇×B = 0) which allows it to be defined in terms of a scalar potential, B = −∇ψ.…”

“…At the source surface, the magnetic field is forced to be purely radial, i.e. B θ = B φ = 0 (Altschuler & Newkirk 1969;Jardine et al 2002). Beyond the source surface, the field remains purely radial, decaying as an inverse square law.…”

Heliocentric distance dependence of the interplanetary magnetic field

“…Knowledge of the large scale structure of the coronal magnetic field is based primarily on magnetograph observations of the line-of-sight component of the field in the photosphere, using the Zeeman effect (see the review of Howard, 1967). The coronal fields are then modeled by calculating the potential field from the measured photospheric field (Newkirk et al, 1968;Schatten, 1968;Schatten et at., 1969;Altschuler and Newkirk, 1969; see also the review by Schatten, 1975). The results can be compared with measured interplanetary fields extrapolated toward the sun or by extrapolation of the coronal field outward (Schatten, 1968;Stenflo, 1971) using the assumption of transport of the field by a radially flowing plasma.…”

Winds and Ejecta from Cool Stars

“…A more useful approach is to tackle the forward problem: to specify the form of the magnetic field and then to predict the observable signatures and compare them with the real observations. This was originally done for the Sun over 30 years ago by taking surface magnetograms and extrapolating a potential coronal field assuming that at some radius (the "source surface") the field is forced open by the effects of the stellar wind to become purely radial (Altschuler & Newkirk, Jr. 1969). Fig.…”