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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 
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 
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 
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. 
and 
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 
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 
). 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).
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