Three-Halves Law in Sunspot Cycle Shape,
STANFORD UNIV CA CENTER FOR SPACE SCIENCE AND ASTROPHYSICS
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Annual mean sunspot numbers Rt since 1700 show evidence of a nonlinear effect, first evidenced by the detection of third harmonic in R or - t, the alternating representation of the magnetic 22 year cycle of solar activity. The form of the nonlinearity proves to be a three-halves law Rt 32 power of 100 LR sub lin t83, where L R sub lin t, also an alternating quantity, is a presumed underlying or linearized sunspot number. The nonlinearity is of such a nature as to cause strong semicycles to be sharper than sinusoidal and to produce the inflexion in R or -t noted at sunspot minimum. A search for a physical explanation of a three-halves law reveals that just such a law results because large sunspot groups, such as occur around strong sunspot maxima, enter into the sunspot number, as conventionally defined, over more days than small groups, simply because large groups last longer. Semicycle asymmetry, which cannot result from a simple nonlinear law, is here ascribed to magnetic buoyancy acting preferentially on the antinodal layers of a traveling wave. Profiles for semicycles of different strengths have been constructed on the assumption that the underlying influence is sinusoidal. Each sinusoid is distorted by the three-halves law, and then made unsymmetrical by applying a buoyancy theory for magnetized plasma rising against viscous drag. The majority of past semicycles, including those of the underlying influence that is sinusoidal, and the hypothesis that sunspots result from an upward traveling wave from a submerged 22-year oscillator.