3 Early Simulations

The situation turned around in the 1980s, when a confluence of new researchers, improved computing facilities, and high-quality synoptic observations made it possible to begin a more quantitative study of flux transport. During the January 7-10, 1981 meeting of the Solar Physics Division of the American Astronomical Society at Taos, New Mexico, Jay Boris (Director of NRL’s Laboratory for Computational Physics) pointed out that we did not need to listen to speculations about flux transport anymore. We could simulate the evolution of the large-scale field and compare these simulations with synoptic observations from Kitt Peak. So when we returned to NRL, Jay began to write a flux-transport code and I started measuring fluxes in bipolar magnetic regions on Kitt Peak magnetograms. We were soon joined by Rick DeVore, who modified the code for use on the the next generation of computers and used it to simulate the transport of flux in a variety of solar configurations. His analytical and numerical calculations resulted in several papers about magnetic flux transport on the Sun, and a PhD thesis for Princeton University (DeVore, 1986 ).

It was tedious to measure the coordinates and estimate the fluxes of all of the emerging bipolar magnetic regions on the Kitt Peak magnetograms. Thus, we began with the interval 1976-1981, and recorded the coordinates and pole strengths of idealized newly erupting magnetic ‘doublets’. The list included doublets with pole strengths of $21 0.1 × 10 Mx$ or greater. Our first project was to use these measurements to study the evolution of flux in isolated active regions (Sheeley Jr et al., 1983 ). We obtained an effective diffusion rate of $730 ± 250 km2 s-1$ , which overlapped Leighton ’s (1964 ) estimate of $770- 1540 km2 s-1$ , and was much greater than Mosher’s value of $2 -1 200 -400 km s$ (Mosher, 1977 ). Subsequent studies including meridional flow have reduced the diffusion rate, first to $2 -1 600 km s$ (Wang et al., 1989b ) and then to about $2 - 1 500 km s$ (Wang et al., 2002b ).

Next, we simulated the evolution of the Sun’s mean line-of-sight field. The initial result was so encouraging that we extended the source measurements as far as was possible at that time (June 1984), and simulated most of sunspot cycle 21 (DeVore et al., 1985a ,b ; Sheeley Jr et al., 1985 ). The sector pattern of the simulated mean field was relatively insensitive to the details of the flux-transport parameters, and left no doubt that the Sun’s mean field was rooted in flux that had originated in active regions. It was no longer necessary to appeal to unknown primordial fields beneath the Sun’s surface; we were coming out of the dark ages.