1.3 A brief historical survey

While regular observations of sunspots go back to the early seventeenth century, and discovery of the sunspot cycle to 1843, it is the landmark work of George Ellery Hale and collaborators that, in the opening decades of the twentieth century, demonstrated the magnetic nature of sunspots and of the solar activity cycle. In particular, Hale’s celebrated polarity laws established the existence of a well-organized toroidal magnetic flux system, residing somewhere in the solar interior, as the source of sunspots. In 1919, Larmor suggested the inductive action of fluid motions as one of a few possible explanations for the origin of this magnetic field, thus opening the path to contemporary solar cycle modelling. Larmor’s suggestion fitted nicely with Hale’s polarity laws, in that the inferred equatorial antisymmetry of the solar internal toroidal fields is precisely what one would expect from the shearing of a large-scale poloidal magnetic field by an axisymmetric and equatorially symmetric differential rotation pervading the solar interior. However, two decades later T.S. Cowling placed a major hurdle in Larmor’s path - so to speak - by demonstrating that even the most general purely axisymmetric flows could not, in themselves, sustain an axisymmetric magnetic field against Ohmic dissipation. This result became known as Cowling’s antidynamo theorem.

A way out of this quandary was only discovered in the mid-1950’s, when E.N. Parker pointed out that the Coriolis force could impart a systematic cyclonic twist to rising turbulent fluid elements in the solar convection, and in doing so provide the break of axisymmetry needed to circumvent Cowling’s theorem (see Figure 1 ). This groundbreaking idea was put on firm quantitative footing by the subsequent development of mean-field electrodynamics, which rapidly became the theory of choice for solar dynamo modelling. By the late 1970’s, concensus had almost emerged as to the fundamental nature of the solar dynamo, and the $a$ -effect of mean-field electrodynamics was at the heart of it.

Figure 1:

Parker’s view of cyclonic turbulence twisting a toroidal magnetic field (here ribbons pointing in direction $j$ ) into meridional planes $[q,z]$ (reproduced from Figure 1 of Parker, 1955

Figure 2:

The Babcock-Leighton mechanism of poloidal field production from the decay of bipolar active regions showing opposite polarity patterns in each solar hemisphere (reproduced from Figure 8 of Babcock, 1961

Serious trouble soon appeared on the horizon, however, and from no less than four distinct directions. First, it was realized that because of buoyancy effects, magnetic fields strong enough to produce sunspots could not be stored in the solar convection zone for sufficient lengths of time to ensure adequate amplification. Second, numerical simulations of turbulent thermally-driven convection in a thick rotating spherical shell produced magnetic field migration patterns that looked nothing like what is observed on the Sun. Third, and perhaps most decisive, the nascent field of helioseismology succeeded in providing the first determinations of the solar internal differential rotation, which turned out markedly different from those needed to produce solar-like dynamo solutions in the context of mean-field electrodynamics. Fourth, the ability of the $a$ -effect and magnetic diffusivity to operate as assumed in mean-field electrodynamics was also called into question by theoretical calculations and numerical simulations.

It is fair to say that solar dynamo modelling has not yet recovered from this four-way punch, in that nothing remotely resembling concensus currently exists as to the mode of operation of the solar dynamo. As with all major scientific crises, this situation provided impetus not only to drastically redesign existing models based on mean-field electrodynamics, but also to explore new physical mechanisms for magnetic field generation, and resuscitate older potential mechanisms that had fallen by the wayside in the wake of the $a$ -effect - perhaps most notably the so-called Babcock-Leighton mechanism, dating back to the early 1960’s (see Figure 2 ). These post-helioseismic developments, beginning in the mid to late 1980’s, are the primary focus of this review.