Statistics – Computation
Scientific paper
Feb 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988mnras.230..535b&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 230, Feb. 15, 1988, p. 535-550.
Statistics
Computation
21
Computational Astrophysics, Harmonics, Solar Magnetic Field, Sunspot Cycle, Fourier Analysis, Periodic Variations, Power Spectra, Sine Waves, Solar Planetary Interactions
Scientific paper
Annual mean sunspot numbers R(t) since 1700 show evidence of a non-linear effect, first evidenced by the detection of a third harmonic in R±(t), the alternating representation of the magnetic (22 yr) cycle of solar activity. The form of the non-linearity proves to be a three-halves law R(t) = 100[|Rlin(t)|/83]3/2, where Rlin(t), also an alternating quantity, is a presumed underlying or "linearized" sunspot number. The non-linearity is of such a nature as to cause strong semicycles to be sharper than sinusoidal and to produce the inflexion in R±(t) noted at sunspot minimum. The difference R(t)-|Rlin(t)| is sufficiently like a third harmonic, for semicycles of average strength, to explain the band around 22/3 yr which is noticeable in the spectrum of R±(t). However, the third harmonic alone is not sufficient to account for the observed dependence of semicycle shape on amplitude, whereas the three-halves law accounts economically for a range of effects. A physical explanation of a three-halves law is given.
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