The Solar Cycle is reviewed. The 11-year cycle of solar activity is characterized by the rise and fall in the numbers and surface area of sunspots. We examine a number of other solar activity indicators including the 10.7 cm radio flux, the total solar irradiance, the magnetic field, flares and coronal mass ejections, geomagnetic activity, galactic cosmic ray fluxes, and radioisotopes in tree rings and ice cores that vary in association with the sunspots. We examine the characteristics of individual solar cycles including their maxima and minima, cycle periods and amplitudes, cycle shape, and the nature of active latitudes, hemispheres, and longitudes. We examine long-term variability including the Maunder Minimum, the Gleissberg Cycle, and the Gnevyshev-Ohl Rule. Short-term variability includes the 154-day periodicity, quasi-biennial variations, and double peaked maxima. We conclude with an examination of prediction techniques for the solar cycle.

The Solar Cycle

We investigate the properties of a kinematic —ux transport solar dynamo model. The model is charac- terized by a solar-like internal diUerential rotation pro—le, a single-cell meridional —ow in the convective envelope that is directed poleward at the surface, and a magnetic diUusivity that is constant within the envelope but decreases sharply at the core-envelope interface. As in earlier —ux transport models of the Babcock-Leighton type, we assume that the poloidal —eld is regenerated as a consequence of the emer- gence at the surface, and subsequent decay, of bipolar active regions exhibiting a systematic tilt with respect to the east-west direction. Inspired by recent simulations of the rise of toroidal magnetic —ux ropes across the solar convective envelope, we model this poloidal —eld regeneration mechanism as a nonlocal source term formulated in such a way as to account for some of the properties of rising —ux ropes revealed by the simulations. For a broad range of parameter values the model leads to solar cycle¨ like oscillatory solutions. Because of the solar-like internal diUerential rotation pro—le used in the model, solutions tend to be characterized by time-latitude (butter—y) diagrams that exhibit both poleward- and equatorward-propagating branches. We demonstrate that the latitudinal shear in the envelope, often omitted in other —ux transport models previously published in the literature, actually has a dominant eUect on the global morphology and period of the solutions, while the radial shear near the core- envelope interface leads to further intensi—cation of the toroidal —eld. On the basis of an extensive parameter space study, we establish a scaling law between the time period of the cycle and the primary parameters of the model, namely the meridional —ow speed, source coefficient, and turbulent diUusion coefficient. In the parameter regime expected to characterize the Sun, we show that the time period of the cycle is most signi—cantly in—uenced by the circulation —ow speed and, unlike for conventional mean —eld a) dynamos, is little aUected by the magnitude of the source coefficient. Finally, we present one speci—c solution that exhibits features that compare advantageously with the observed properties of the solar cycle. Subject headings: diUusionSun: interiorSun: magnetic —eldsSun: rotation

https://iopscience.iop.org/article/10.1086/307269/pdf

A Babcock-Leighton Flux Transport Dynamo with Solar-like Differential Rotation

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 (1713-1996). Polar field reversals are maintained by varying the meridional flow speed between 11 and 20 m s-1, 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-2. 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.

/pdf/modeling-the-sun-s-magnetic-field-and-irradiance-since-1713-4pa23j0v7v.pdf

Modeling the Sun’s Magnetic Field and Irradiance since 1713

Coronal holes, regions of unusually low density and low temperature in the solar corona, are identified as Bartel's M regions, i.e., sources of high-speed wind streams that produce recurrent geomagnetic variations. Throughout the Skylab period the polar caps of the sun were coronal holes, and at lower latitudes the most persistent and recurrent holes were equatorial extensions of the polar caps. The holes rotated 'rigidly' at the equatorial synodic rate. They formed in regions of unipolar photospheric magnetic field, and their internal magnetic fields diverged rapidly with increasing distance from the sun. The geometry of the magnetic field in the inner corona seems to control both the physical properties of the holes and the global distribution of high-speed wind streams in the heliosphere. Phenomenological models for the birth and decay of coronal holes have been proposed.

Coronal holes and high-speed wind streams

: Predicting the peak amplitude of the sunspot cycle is a key goal of solar-terrestrial physics. The precursor method currently favored for such predictions is based on the dynamo model in which large-scale polar fields on the decline of the 11-year solar cycle are converted to toroidal (sunspot) fields during the subsequent cycle. The strength of the polar fields during the decay of one cycle is assumed to be an indicator of peak sunspot activity for the following cycle. Polar fields reach their peak amplitude several years after sunspot maximum; the time of peak strength is signaled by the onset of a strong annual modulation of polar fields due to the 7 1/4-degree tilt of the solar equator to the ecliptic plane. Using direct polar field measurements, now available for four solar cycles, the authors predict that the approaching solar cycle 24 (approx. 2011 maximum) will have a peak smoothed monthly sunspot number of 75 +/- 8, making it potentially the smallest cycle in the last 100 years.

/pdf/sunspot-cycle-24-smallest-cycle-in-100-years-3cu6ewupp0.pdf

Sunspot cycle 24 : Smallest cycle in 100 years?

The magnetic field strength within the polar caps of the sun is an important parameter for both the solar activity cycle and for our understanding of the interplanetary magnetic field. Measurements of the line-of-sight component of the magnetic field generally yield 0.1 to 0.2 mT near times of sunspot minimum. This paper reports measurements of the polar fields made at the Stanford Solar Observatory using the Fe I line at 525.02 nm. It is found that the average flux density poleward of 55 deg latitude is about 0.6 mT peaking to more than 1 mT at the pole and decreasing to 0.2 mT at the polar cap boundary. The total open flux through either polar cap thus becomes about 3 x 10 to the 14th Wb. It is also shown that observed magnetic field strengths vary as the line-of-sight component of nearly radial fields.

The strength of the Sun's polar fields

The strength of the sun's polar fields

A solar telescope has been built at Stanford University to study the organization and evolution of large-scale solar magnetic fields and velocities. The observations are made using a Babcock-type magnetograph which is connected to a 22.9 m vertical Littrow spectrograph. Sun-as-a-star integrated light measurements of the mean solar magnetic field have been made daily since May 1975. The typical mean field magnitude has been about 0.15 G with typical measurement error less than 0.05 G. The mean field polarity pattern is essentially identical to the interplanetary magnetic field sector structure (see near the Earth with a 4 day lag). The differences in the observed structures can be understood in terms of a ‘warped current sheet’ model.

/pdf/the-mean-magnetic-field-of-the-sun-observations-at-stanford-4cvbie8szc.pdf

The mean magnetic field of the Sun: observations at Stanford.

Daily observations of Doppler line shifts made with very low spatial resolution (3′) with the Stanford magnetograph have been used to study the equatorial rotation rate, limb effect on the disk, and the mean meridonial circulation. The equatorial rotation rate was found to be approximately constant over the interval May 1976–January 1977 and to have the value 2.82 μrad s−1 (1.96 km s−1). This average compares favorably with the results of Howard (1977) of 2.83 μrad s−1 for the same time period. The RMS deviation of the daily measurements about the mean value was 1% of the rate (20 m s−1), much smaller than the fluctuations reported by Howard and Harvey (1970) of several per cent. These 1% fluctuations are uncorrelated from day-to-day and may be due to instrumental problems. The limb effect on the disk was studied in equatorial scans (after suppressing solar rotation). A redshift at the center of the disk relative to a position 0.60R⊙ from the center of 30 m s−1 was found for the line Fe i λ5250 A. Central meridian scans were used (after correcting for the limb effect defined in the equatorial scans) to search for the component of mean meridonial circulation symmetric across the equator. A signal is found consistent with a polewards flow of 20 m s−1 approximately constant over the latitude range 10–50°. Models of the solar differential rotation driven by an axisymmetric meridonial circulation and an anisotropic eddy viscosity (Kippenhahn, 1963; Cocke, 1967; Kohler, 1970) predict an equatorwards flow at the surface. However, giant cell convection models (Gilman, 1972, 1976, 1977) predict a mean polewards flow (at the surface). The poleward-directed meridonial flow is created as a by-product of the giant cell convection and tends to limit the differential rotation. The observation of a poleward-directed meridonial circulation lends strong support to the giant cell models over the anisotropic eddy viscosity models.

Large-scale solar velocity fields

A phenomenological model of the interplay between the polar magnetic fields of the Sun and the solar sector structure is discussed. Current sheets separate regions of opposite polarity and mark the sector boundaries in the corona. The sheets are visible as helmet streamers. The solar sector boundary is tilted with respect to central meridian, and boundaries with opposite polarity change are oppositely tilted. The tilt of a given type of boundary [(+, −) or (−, +)] changes systematically during the sunspot cycle as the polarity of the polar fields reverses. Similar reversals of the position of the streamers at the limbs takes place. If we consider (a) a sunspot cycle where the northern polar field is inward (−) during the early part of the cycle and (b) a (+, −) sector boundary at central meridian then the model predicts the following pattern; a streamer at high northern latitudes should be observed over the west limb together with a corresponding southern streamer over the east limb. The current sheet runs now NW-SE. At sunspot maximum the boundary is more in the N-S direction; later when the polar fields have completed their reversal the boundary runs NE-SW and the northern streamer should be observed over the east limb and the southern streamer over the west limb. Observational evidence in support of the model is presented, especially the findings of Hansen, Sawyer and Hansen and Koomen and Howard that the K-corona is highly structured and related to the solar sector structure.

Thomas L. Duvall

Papers

The strength of the Sun's polar fields

The strength of the sun's polar fields

The mean magnetic field of the Sun: observations at Stanford.

Large-scale solar velocity fields

A model combining the polar and the sector structured solar magnetic fields