Open magnetic flux: Variation with latitude and solar cycle

Recent Ulysses observations of the heliospheric magnetic field (HMF) reveal that the sun's open magnetic flux in the solar wind, as measured by r(2) Br, is independent of heliographic latitude at solar maximum and at solar minimum. It follows that 4pi r(2) Br at any latitude provides an accurate estimate of the total open flux from the sun. An additional Ulysses result is that long term averages of r(2) Br are very nearly the same at the recent solar maximum as at the preceding minimum. The model of the HMF developed by L. Fisk and his colleagues, which includes several features absent from the well-known Parker model, leads to the prediction that the open flux is relatively constant or perhaps invariant. Motivated by these considerations, Br has been analyzed over the longer interval of four sunspot cycles (20-23) using the archived OMNI field measurements obtained in the ecliptic at 1 AU. Averages of Br, after separation into inward and outward sectors as with Ulysses data, agree within a few percent with previous results based on \Br\, the modulus of the radial component. Averages of Br increase by a factor of about 2 from solar minimum to maximum in cycles 21 and 22 but change only slightly in cycles 20 and 23. The variations in open flux are better correlated with total unsigned flux in the photosphere than with sunspot number, both reaching peak values. after sunspot maximum. The open flux decreases at solar minima and secondary decreases occur when the polar cap fields vanish. It appears that the near equality of the open flux at minimum and maximum observed by Ulysses was, in fact, caused by a time variation with the measurements near maximum being obtained while a secondary decrease was occurring. Thus, the open flux is generally variable and only constant during shorter intervals when the solar field is stable.