The Topology of the Sun's Magnetic Field and the 22-Year Cycle.

Shallow submerged lines of force of an initial axisymmetric dipolar field of 8 X 1021 maxwells are drawn out in longitude by the differential rotation (after the suggestion of Cowling) to produce a spiral wrapping of five turns in the north and south hemispheres after 3 years. The amplification factor approaches 45, with a marked dependence on latitude. Twisting of the irregular flux strands by the faster shallow layers in low latitudes forms "ropes" with local concentrations that are brought to the surface by magnetic buoyancy to produce bipolar magnetic regions (BMR's) with associated sunspots and related activity. The field intensity required for producing BMR's is reached at progressively lower latitudes according to the derived formula sin = + 1.5/(n + 3), where n is the number of years since the beginning of the sunspot cycle. This accounts satisfactorily for 's law and the Maunder "butterfly diagram." Sufficient flux rope for more than 102 BMR's is produced. "Preceding" parts of BMR's expand toward the equator as they age, to be neutralized by merging; "following" parts expand or migrate poleward so that their lines of force neutralize and then replace the initial dipolar field. This process, which involves severing and reconnection of lines of force in the corona, as well as expulsion of flux loops, need be only 1 per cent efficient. The result, after sunspot maximum, is a main dipolar field of reversed polarity. The process repeats itself, so that the initial conditions are reproduced after a complete 22-year magnetic cycle. This model accounts for Hale's laws of sunspot polarity and provides a qualitative explanation of the proponderance of "preceding" spots, of the forward tilt of the axes of older spots, of the recurrence of activity in preferred longitudes, and of Hale's chromospheric "whirls."