Twenty-three cycles of changing open solar magnetic flux

[1] This paper presents a comparison of various estimates of the open solar flux, deduced from measurements of the interplanetary magnetic field, from the aa geomagnetic index and from photospheric magnetic field observations. The first two of these estimates are made using the Ulysses discovery that the radial heliospheric field is approximately independent of heliographic latitude, the third makes use of the potential-field source surface method to map the total flux through the photosphere to the open flux at the top of the corona. The uncertainties associated with using the Ulysses result are 5%, but the effects of the assumptions of the potential field source surface method are harder to evaluate. Nevertheless, the three methods give similar results for the last three solar cycles when the data sets overlap. In 11-year running means, all three methods reveal that 1987 marked a significant peak in the long-term variation of the open solar flux. This peak is close to the solar minimum between sunspot cycles 21 and 22, and consequently the mean open flux (averaged from minimum to minimum) is similar for these two cycles. However, this similarity between cycles 21 and 22 in no way implies that the open flux is constant. The long-term variation shows that these cycles are fundamentally different in that the average open flux was rising during cycle 21 (from consistently lower values in cycle 20 and toward the peak in 1987) but was falling during cycle 22 (toward consistently lower values in cycle 23). The estimates from the geomagnetic aa index are unique as they extend from 1842 onwards (using the Helsinki extension). This variation gives strong anticorrelations, with very high statistical significance levels, with cosmic ray fluxes and with the abundances of the cosmogenic isotopes that they produce. Thus observations of photospheric magnetic fields, of cosmic ray fluxes, and of cosmogenic isotope abundances all support the long-term drifts in open solar flux reported by Lockwood et al. [1999a, 1999b].