David H. Hathaway

The Solar Cycle

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. A number of other solar activity indicators also vary in association with the sunspots 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. Individual solar cycles are characterized by their maxima and minima, cycle periods and amplitudes, cycle shape, the equatorward drift of the active latitudes, hemispheric asymmetries, and active longitudes. Cycle-to-cycle variability includes the Maunder Minimum, the Gleissberg Cycle, and the Gnevyshev-Ohl (even-odd) 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 and a closer look at cycles 23 and 24.

A synthesis of solar cycle prediction techniques

A number of techniques currently in use for predicting solar activity on a solar cycle timescale are tested with historical data. Some techniques, e.g., regression and curve fitting, work well as solar activity approaches maximum and provide a month-by-month description of future activity, while others, e.g., geomagnetic precursors, work well near solar minimum but only provide an estimate of the amplitude of the cycle. A synthesis of different techniques is shown to provide a more accurate and useful forecast of solar cycle activity levels. A combination of two uncorrelated geomagnetic precursor techniques provides a more accurate prediction for the amplitude of a solar activity cycle at a time well before activity minimum. This combined precursor method gives a smoothed sunspot number maximum of 154 ± 21 at the 95% level of confidence for the next cycle maximum. A mathematical function dependent on the time of cycle initiation and the cycle amplitude is used to describe the level of solar activity month by month for the next cycle. As the time of cycle maximum approaches a better estimate of the cycle activity is obtained by including the fit between previous activity levels and this function. This Combined Solar Cycle Activity Forecast gives, as of January 1999, a smoothed sunspot maximum of 146 ± 20 at the 95% level of confidence for the next cycle maximum.

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude of a cycle and the length of the previous cycle. This allows for an estimate of the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7–12 years of the cycle.

Variations in the Sun’s Meridional Flow over a Solar Cycle

Solar Meridional Flow The surface of the Sun is composed of plasma that exhibits observable flow patterns. The weakest flow pattern occurs along meridional lines from the equator toward the poles. Hathaway and Rightmire (p. 1350) measured the meridional flow using observations taken with the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory between 1996 and 2009 and found that meridional flow varied with the solar cycle, such that flow was faster during the 2004–2009 minimum than during the 1996–1997 minimum. This finding provides further evidence that the last solar minimum was peculiar by comparison with previous cycles. Observed variations in the Sun’s poleward flow have consequences for models and predictions of the solar cycle. The Sun’s meridional flow is an axisymmetric flow that is generally directed from its equator toward its poles at the surface. The structure and strength of the meridional flow determine both the strength of the Sun’s polar magnetic field and the intensity of sunspot cycles. We determine the meridional flow speed of magnetic features on the Sun using data from the Solar and Heliospheric Observatory. The average flow is poleward at all latitudes up to 75°, which suggests that it extends to the poles. It was faster at sunspot cycle minimum than at maximum and substantially faster on the approach to the current minimum than it was at the last solar minimum. This result may help to explain why this solar activity minimum is so peculiar.

Doppler Measurements of the Suns Meridional Flow

Doppler velocity data obtained with the Global Oscillation Network Group (GONG) instruments in Tucson from 1992 August through 1995 April were analyzed to determine the structure and evolution of the Suns meridional flow. Individual measurements of the flow were derived from line-of-sight velocity images averaged over 17 minutes to remove the p-mode oscillation signal. Typical flow velocities are poleward at approximately 20 m/s, but the results suggest that episodes may occur with much stronger flows. Such variations may help to explain some of the many disparate reports on the strength and structure of the Suns meridional flow.

Evidence That a Deep Meridional Flow Sets the Sunspot Cycle Period

Sunspots appear on the Sun in two bands on either side of the equator that drift toward lower latitudes as each sunspot cycle progresses. We examine the drift of the centroid of the sunspot area toward the equator in each hemisphere from 1874 to 2002 and find that the drift rate slows as the centroid approaches the equator. We compare the drift rate at sunspot cycle maximum with the period of each cycle for each hemisphere and find a highly significant anticorrelation: hemispheres with faster drift rates have shorter periods. These observations are consistent with a meridional counterflow deep within the Sun as the primary driver of the migration toward the equator and the period associated with the sunspot cycle. We also find that the drift rate at maximum is significantly correlated with the amplitude of the following cycle, a prediction of dynamo models that employ a deep meridional flow toward the equator. Our results indicate an amplitude of about 1.2 m s 1 for the meridional flow velocity at the base of the solar convection zone.

Panel achieves consensus prediction of solar cycle 23

In September 1996, a panel of experts on solar cycle prediction techniques met in Boulder, Colorado, to survey forecasts of solar and geomagnetic activity and to arrive at a consensus on how the solar cycle will develop. After two weeks of deliberation, the panel of 12 scientists (from Australia, Germany, the United Kingdom, and the United States) agreed that a large amplitude solar cycle with a smoothed sunspot maximum of approximately 160 is probable near the turn of the century. The amplitude of the predicted cycle is comparable to that of the previous two solar cycles (see Figure 1). Our ability to predict solar and geomagnetic activity is crucial to many technologies, including the operation of low-Earth orbiting satellites, electric power transmission grids, geophysical exploration, and highfrequency radio communications and radars. Because the scale height of Earths upper atmosphere (and thus the drag on satellites in low Earth orbit) depends on the levels of short-wavelength solar radiation and geomagnetic activity, we need to know the profile and magnitude of the next solar and geomagnetic cycle in order to plan for reboosting the Hubble Space Telescope and assembling the International Space Station.

The Solar Acoustic Spectrum and Eigenmode Parameters

The Global Oscillation Network Group (GONG) project estimates the frequencies, amplitudes, and linewidths of more than 250,000 acoustic resonances of the sun from data sets lasting 36 days. The frequency resolution of a single data set is 0.321 microhertz. For frequencies averaged over the azimuthal order m, the median formal error is 0.044 microhertz, and the associated median fractional error is 1.6 × 10−5. For a 3-year data set, the fractional error is expected to be 3 × 10−6. The GONG m-averaged frequency measurements differ from other helioseismic data sets by 0.03 to 0.08 microhertz. The differences arise from a combination of systematic errors, random errors, and possible changes in solar structure.

THE PHOTOSPHERIC CONVECTION SPECTRUM

Spectra of the cellular photospheric flows are determined from observations acquired by the MDI instrument on the SOHO spacecraft. Spherical harmonic spectra are obtained from the full-disk observations. Fourier spectra are obtained from the high-resolution observations. The p-mode oscillation signal and instrumental artifacts are reduced by temporal filtering of the Doppler data. The resulting spectra give power (kinetic energy) per wave number for effective spherical harmonic degrees from 1 to over 3000. Significant power is found at all wavenumbers, including the small wavenumbers representative of giant cells. The time evolution of the spectral coefficients indicates that these small wavenumber components rotate at the solar rotation rate and thus represent a component of the photospheric cellular flows. The spectra show distinct peaks representing granules and supergranules but no distinct features at wavenumbers representative of mesogranules or giant cells. The observed cellular patterns and spectra are well represented by a model that includes two distinct modes – granules and supergranules.

GONG Observations of Solar Surface Flows

Doppler velocity observations obtained by the Global Oscillation Network Group (GONG) instruments directly measure the nearly steady flows in the solar photosphere. The suns differential rotation is accurately determined from single observations. The rotation profile with respect to latitude agrees well with previous measures, but it also shows a slight north-south asymmetry. Rotation profiles averaged over 27-day rotations of the sun reveal the torsional oscillation signal—weak, jetlike features, with amplitudes of 5 meters per second, that are associated with the sunspot latitude activity belts. A meridional circulation with a poleward flow of about 20 meters per second is also evident. Several characteristics of the surface flows suggest the presence of large convection cells.