My introduction to the random walk of magnetic flux on the Sun began on the morning of September 16, 1963 when the phone rang in the 60-foot tower telescope at Mount Wilson. Caltech Professor Robert B. Leighton had just returned from IAU Symposium No. 22 in Rottach-Egern, Germany, and was calling to ask me to meet with him in his office later that day. He had an idea for a possible PhD thesis topic. When I met with him back on the Caltech campus, he said that while he was preparing his IAU talk, he realized that the supergranulation could transport magnetic flux from its origin in sunspot groups and ultimately reverse the polar fields of the Sun (Leighton, 1965a). He said that while he was in his hotel room, he considered what would happen if one inserted a concentration of dye into a non-stationary convective flow like the supergranulation. The dye would be swept to the boundaries of the nearby convective cells, and as the pattern of cells evolved, the dye would be swept to new boundaries again and again until the initial concentration was spread over a wide area. He likened the process to a random walk in which the dye was magnetic flux provided by sunspot groups and the convection was the supergranulation.
The implications were obvious. There were two kinds of flux, positive and negative, which spread out independently from their respective sources in a newly erupted sunspot group and canceled where they overlapped. And, of course, the sunspot groups did not have random properties, but satisfied Hale’s law (positive leading polarity in the north and negative in the south during one sunspot cycle, and opposite during the next cycle) and what Hal Zirin would later call Joy’s law (slightly tilted groups in each hemisphere, with their leading parts closer to the equator and their trailing parts closer to the pole of that hemisphere). In the absence of differential rotation and meridional flow, the amount of flux F from each half of the bipolar region would gradually spread out on the surface and eventually coat it with a uniform average flux density , where R is the radius of the Sun. At the nearby pole of the Sun, the contribution of each polarity would increase as the flux began to arrive and then decrease again as it spread further out on the Sun. Because the trailing-polarity flux started closer to the pole, it would arrive sooner than the leading-polarity flux and be more concentrated when it arrived. Thus, the net contribution would have the sign of the trailing-polarity flux and a magnitude of order , where is the initial meridional separation of the leading and following parts of the sunspot group. Moreover, it seemed plausible that the accumulated effect of some 103 sunspot groups that erupt during a given sunspot cycle would be sufficient to reverse the polar fields and replace them with one of opposite polarity.
In the following days, Leighton used idealized ring doublets to represent the longitudinally averaged contribution of sunspot groups, and prepared the punched cards that enabled him to compute the axisymmetric field of the Sun from an equatorial migration of such sources. He acknowledged that I had been working on other topics, but said that measurements to test this new flux-transport hypothesis would make a good thesis project. So while Leighton performed the calculations for his classic paper on flux-transport (Leighton, 1964), I began thinking about measurements that could be used to test the model.
One 11-year sunspot cycle had elapsed since the Babcocks began making daily observations of the Sun’s magnetic field (Babcock and Babcock, 1952), and this interval included the reversal of the polar fields, first at the south pole in 1957 and then at the north pole in 1958 (Babcock and Livingston, 1958; Babcock, 1959). Other reversals were expected, but had not yet been observed. Thus, with the encouragement of Bob Howard, I began looking for indirect evidence of prior polar field reversals on photographic plates that were stored in the basement of the Santa Barbara Street office of the Mount Wilson Observatory. White-light images of the Sun’s disk had been obtained since 1905, and occasionally showed faculae at the poles of the Sun. H and Ca-K images were also available, but provided less of a distinction between the polar and low-latitude fields.
A systematic examination of white-light images obtained during 1905 – 1964 revealed that polar faculae were common in the years around each sunspot minimum, but rare at sunspot maximum (Sheeley Jr, 1964, 1965). Evidently, the polar fields really did reverse around the time of each solar maximum, as predicted by the models of Babcock (1961) and Leighton (1964). However, the yearly averaged numbers of polar faculae occasionally showed short-term fluctuations whose reality was beyond doubt (Sheeley Jr, 1965). Because supergranular diffusion was too slow to cause the polar field to decay appreciably in a year or so, I wondered if intermittent eruptions of flux in the sunspot belts might cause bursts of opposite-polarity flux to arrive at the poles from time to time to suddenly weaken the polar fields. Numerical simulations ultimately showed that the source fluctuations are responsible, but that they must be accompanied by meridional flow in order to reach the poles before they are smoothed out by diffusion (Wang et al., 1989a; Sheeley Jr, 1991).
Aside from Leighton’s (1964) initial flux-transport calculations, there were few numerical studies of flux evolution at that time. Caltech graduate student Phillip Roberts used a true random walk method to extrapolate my measurements of active region fluxes forward in time by a few months and obtained good agreement with the observed fields (Sheeley Jr, 1965, 1966). Leighton experimented with a magneto-kinematic model without meridional flow and was able to reproduce several overall properties of the sunspot cycle (Leighton, 1969). In particular, he obtained the observed equatorward progression of sunspot eruptions (the butterfly diagram) by assuming that the Sun’s internal angular velocity decreases radially outward. However, helioseismology observations have now shown this assumption to be incorrect. As demonstrated by Wang et al. (1991) and Choudhuri et al. (1995), an equatorward progression can be obtained by including meridional circulation with a return flow 1 m s–1 at the base of the convection zone.
The first numerical simulation of the observed large-scale field was performed by Schatten et al. (1972), who combined sources from Mount Wilson Observatory magnetograms with transport by Newton and Nunn (1951) differential rotation and supergranular diffusion at an unspecified rate (presumably in Leighton’s (1964) range of 770 – 1540 km2 s–1). Their simulations exhibited a quasi-rigid rotation poleward of the sunspot belts. Although this rigid rotation was consistent with the rate obtained from cross-correlations of the observed field (Wilcox et al., 1970), Schatten et al. (1972) thought the field ought to exhibit the same differential rotation used as input to the calculations, and supposed that the result was an artifact of their computational technique. Fifteen years elapsed before we realized that the quasi-rigid rotation was caused by the poleward component of flux transport, diffusion plus meridional flow (Sheeley Jr et al., 1987).
© Max Planck Society and the author(s)