We use a flux transport model to simulate the evolution of the Sun's total and open magnetic flux over the last 26 solar cycles . Polar field reversals are maintained by varying the meridional flow speed between 11 and 20 m s À1 , with the poleward-directed surface flow being slower during low-amplitude cycles. If the strengths of the active regions are fixed but their numbers are taken to be proportional to the cycle amplitude, the open flux is found to scale approximately as the square root of the cycle amplitude. However, the scaling becomes linear if the number of active regions per cycle is fixed but their average strength is taken to be proportional to the cycle amplitude. Even with the inclusion of a secularly varying ephemeral region background, the increase in the total photospheric flux between the Maunder minimum and the end of solar cycle 21 is at most $one-third of its minimum-to-maximum variation during the latter cycle. The simulations are compared with geomagnetic activity and cosmogenic isotope records and are used to derive a new reconstruction of total solar irradiance (TSI). The increase in cycle-averaged TSI since the Maunder minimum is estimated to be $1 W m À2 . Because the diffusive decay rate accelerates as the average spacing between active regions decreases, the photospheric magnetic flux and facular brightness grow more slowly than the sunspot number and TSI saturates during the highest amplitude cycles.

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The Sun's polar fields are currently ∼40% weaker than they were during the previous three sunspot minima. This weakening has been accompanied by a corresponding decrease in the interplanetary magnetic field (IMF) strength, by a ∼20% shrinkage in the polar coronal-hole areas, and by a reduction in the solar-wind mass flux over the poles. It has also been reflected in coronal streamer structure and the heliospheric current sheet, which only showed the expected flattening into the equatorial plane after sunspot numbers fell to unusually low values in mid-2008. From latitude-time plots of the photospheric field, it has long been apparent that the polar fields are formed through the transport of trailing-polarity flux from the sunspot latitudes to the poles. To address the question of why the polar fields are now so weak, we simulate the evolution of the photospheric field and radial IMF strength from 1965 to the present, employing a surface transport model that includes the effects of active region emergence, differential rotation, supergranular convection, and a poleward bulk flow. We find that the observed evolution can be reproduced if the amplitude of the surface meridional flow is varied by as little as 15% (between 14.5 and 17 m s −1), with the higher average speeds being required during the long cycles 20 and 23.

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We examine the statistical properties of some 2700 bipolar magnetic regions (BMRs) with magnetic fluxes > 3 x 1020 Mx which erupted during 1976-1986. Empirical rules were used to estimate the fluxes visually from daily magnetograms obtained at the National Solar Observatory/Kitt Peak. Our analysis shows the following: (i) the average flux per BMR declined between 1977 and 1985; (ii) the average tilts of BMRs relative to the east-west line increase toward higher latitudes; (iii)weaker BMRs had larger root-mean-square tilt angles than stronger BMRs at all latitudes; (iv) over the interval 1976-1986, BMRs with their leading poles equatorward of their trailing poles contributed a total of 4 times as much flux as BMRs with 'inverted' tilts, but the relative amount of flux contributed by BMRs with inverted or zero tilts increased as the sunspot cycle progressed; (v) only 4% of BMRs had 'reversed' east-west polarity orientations; (vi) although the northern hemisphere produced far more flux during the rising phase of the sunspot cycle, the southern hemisphere largely compensated for this imbalance during the declining phase; (vii) southern-hemisphere BMRs erupted at systematically higher latitudes than northern-hemisphere ones through most of sunspot cycle 21.

Although most of the magnetic flux observed on the sun originates in the low-latitude sunspot belts, this flux is gradually dispersed over a much wider range of latitudes by supergranular convective motions and meridional circulation. Numerical simulations show how these transport processes interact over the 11-year sunspot cycle to produce a strong "topknot" polar field, whose existence near sunspot minimum is suggested by the observed strength of the interplanetary magnetic field and by the observed areal extent of polar coronal holes. The required rates of diffusion and flow are consistent with the decay rates of active regions and with the rotational properties of the large-scale solar magnetic field.