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Observations show that newly emerging flux tends to appear on the Solar surface at sites where there is flux already. This results in clustering of solar activity. Standard dynamo theories do not predict this effect.
Orbital prediction for satellites in low Earth orbit (LEO) or low planetary orbit depends strongly on exospheric densities. Solar activity forecasting is important in orbital prediction, as the solar UV and EUV inflate the upper atmospheric layers of the Earth and planets, forming the exosphere in which satellites orbit. Geomagnetic effects also relate to solar activity. Because of the complex and ephemeral nature of solar activity, with different cycles varying in strength by more than 100%, many different forecasting techniques have been utilized. The methods range from purely numerical techniques (essentially curve fitting) to numerous oddball schemes, as well as a small subset, called 'Precursor techniques.' The situation can be puzzling, owing to the numerous methodologies involved, somewhat akin to the numerous ether theories near the turn of the last century. Nevertheless, the Precursor techniques alone have a physical basis, namely dynamo theory, which provides a physical explanation for why this subset seems to work. I discuss this solar cycle's predictions, as well as the Sun's observed activity. I also discuss the SODA (Solar Dynamo Amplitude) index, which provides the user with the ability to track the Sun's hidden, interior dynamo magnetic fields. As a result, one may then update solar activity predictions continuously, by monitoring the solar magnetic fields as they change throughout the solar cycle. This paper ends by providing a glimpse into what the next solar cycle (#24) portends.
E. Walter Maunder created his first "Butterfly Diagram" showing the equatorward drift of the sunspot latitudes over the course of each of two solar cycles in 1903. This diagram was constructed from data obtained through the Royal Greenwich Observatory (RGO) starting in 1874. The RGO continued to acquire data up until 1976. Fortunately, the US Air Force (USAF) and the US National Oceanic and Atmospheric Administration (NOAA) have continued to acquire similar data since that time. This combined RGO/USAF/NOAA dataset on sunspot group positions and areas now extends virtually unbroken from the 19th century to the 21st century. The data represented in the Butterfly Diagram contain a wealth of information about solar activity and the solar cycle. Solar activity (as represented by the sunspots) appears at mid-latitudes at the start of each cycle. The bands of activity spread in each hemisphere and then drift toward the equator as the cycle progresses. Although the equator itself tends to be avoided, the spread of activity reaches the equator at about the time of cycle maximum. The cycles overlap at minimum with old cycle spots appearing near the equator while new cycle spots emerge in the mid-latitudes. Large amplitude cycles tend to have activity starting at higher latitudes with the activity spreading to higher latitudes as well. Large amplitude cycles also tend to be preceded by earlier cycles with faster drift rates. These drift rates may be tied to the Sun s meridional circulation - a component in many dynamo theories for the origin of the sunspot cycle. The Butterfly Diagram must be reproduced in any successful dynamo model for the Sun.
The effects of rotation are included in an analytical model for the convective motions in a plane-parallel layer of an ideal fluid. The turbulent stress tensor, formed by taking products and averages of the various velocity components, is calculated for an arbitrary eddy size and shape. Heuristic formulae presented for determining the size and shape of the dominant eddy then give a fully specified stress tensor. Applications for this stress tensor in problems of stellar internal dynamics, heat flow, scalar diffusion, and dynamo theory are suggested. The resultant stresses tend to produce differential rotation profiles with rapidly rotating equators and interiors. The dynamo activity associated with these convective motions tends to occur near the lower boundary of the convection zone.
Assuming that the physical properties of solar-wind ions have remained unchanged over the past 4 billion years, the observation of solar-wind ions in lunar breccias with compaction ages greater than 3.2 billion years places constraints on the nature and origin of the ancient lunar magnetic field. Solar-wind ions would not be expected to occur in old lunar breccias if a surface magnetic field of more than 0.03 gauss was present. Several explanations of this phenomenon are consistent with the global lunar dynamo theory of the origin of the lunar dipole field, including a wandering of the lunar dipole axis, late onset of dynamo action, and reversals of the lunar dipole field, producing a long-term field close to zero. Models invoking external field magnetization as the cause of the ancient lunar magnetic field constrain the dipole axis, precluding field reversals, and do not provide an alternative explanation for the observed occurrence of solar-wind ions in lunar breccias.
The origin and maintenance of planetary magnetic fields are discussed. The discussion is not limited to dynamo theories, although these are almost universally favored. Thermoelectric currents are found to be a possible alternative for Jupiter. Two energy sources for dynamos are considered: convection and precessionally induced fluid flow. The earth is the most favorable planet for precessionally driven dynamo, although Neptune is a possibility. Jupiter is likely to have a convectionally driven dynamo, as may Saturn, but the relevant properties of Saturn are not yet well known. Conclusions for each planet are given.
Long term variations of a planetary magnetic field are one of the few observables available in the study of planetary interiors and dynamo theory. While variations of the geomagnetic field were accessible to direct measurement for centuries, knowledge of the secular variations of other planetary dynamos is limited. New limits on Jovimagnetic secular variations were found by comparison of a Jovian internal field model obtained from the Voyager 1 magnetic field observations at epoch 1979.2 with the epoch 1974.9 Pioneer 11 O4 model. No significant secular variation of either the magnitude or position of the Jovidipole is found for the years 1974.9 through 1979.2, although a small Earth-like variation cannot be ruled out.
Using the 'dynamo theory' method to predict solar activity, an accurate prediction was made for solar cycle 21 by Schatten et al. (1978). Using the same dynamo technique for solar cycle 22, a value for the smoothed sunspot number of 170 + or - 25 is obtained. This large sunspot number is expected to peak in 1990 + or - 1 year. The F(10.7) radio flux is expected to reach a smoothed value of 210 + or - 25 flux units. Since this value is larger than values obtained with prediction schemes based upon 'statistical' and 'periodicity' methods, it provides a useful test for the current methodology, based upon the strength of the sun's polar field near solar minimum. The predicted degree of solar activity is expected to enhance the density and temperature of the earth's thermosphere to values somewhat larger than those found in solar cycle 21. This will have an impact on the orbital lifetime of low altitude satellites.
It is shown that the offset tilted dipole model of Uranus and Neptune, deduced from the spherical harmonic analysis of the Voyager magnetic field observation, can be represented fairly well by the combined field of an axial and an auxiliary dipole; the latter is roughly oriented in the east-west direction and is located near the surface of the core in low latitude. The present dynamo theories of planetary magnetism consider an axial dipolar field as an essential element, since the planetary rotation plays a vital role in the dynamo process. On the other hand, the auxiliary dipoles may be a result of leakage of the toroidal field, like a pair of sunspots on the photosphere, which is also an essential part of the dynamo process.
In this paper, we briefly review the 'dynamo' and 'geomagnetic precursor' methods of long-term solar activity forecasting. These methods depend upon the most basic aspect of dynamo theory to predict future activity, future magnetic field arises directly from the magnification of pre-existing magnetic field. We then generalize the dynamo technique, allowing the method to be used at any phase of the solar cycle, through the development of the 'Solar Dynamo Amplitude' (SODA) index. This index is sensitive to the magnetic flux trapped within the Sun's convection zone but insensitive to the phase of the solar cycle. Since magnetic fields inside the Sun can become buoyant, one may think of the acronym SODA as describing the amount of buoyant flux. Using the present value of the SODA index, we estimate that the next cycle's smoothed peak activity will be about 210 +/- 30 solar flux units for the 10.7 cm radio flux and a sunspot number of 170 +/- 25. This suggests that solar cycle #23 will be large, comparable to cycle #22. The estimated peak is expected to occur near 1999.7 +/- 1 year. Since the current approach is novel (using data prior to solar minimum), these estimates may improve when the upcoming solar minimum is reached.
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
The possibility that the gas-giant planets Jupiter and Saturn undergo solar-type magnetic reversals is examined using dynamo theory and radiotelescope data on decametriic emissions from Jupiter. Possible values are found for the effects of the fluctuating velocity field, the magnetic diffusivity, and change in the rotation rate of a dynamo over a characteristic length. The radio emissions from Jupiter decreased in intensity from 1961-72 and rose steadily to the end of 1978, which could have been caused by a change in the Jovian magnetic field. Since Jupiter may have a small rocky core embedded in metallic hydrogen which comprises 75 percent of the radius of the planet, the planetary magnetic field may extend into the cores of its satellites. The dynamo characteristics, like those of Saturn, would be chaotic, although quasi-periodic reversals could occur over intervals on the order of centuries instead of decades such as with the sun and much longer periods such as with the earth.
Hydromagnetic dynamo theory is applied to the problem of magnetic field amplification in the epoch after recombination but prior to galaxy formation. Large-scale density fluctuations acquire angular momentum from tidal torques exerted by neighboring fluctuations, and small-scale subfluctuations possess helicity due to the Coriolis forces associated with the rotation of the large-scale host fluctuations. Cosmic expansion and the interaction of matter with the ambient radiation field are taken into account. Despite many uncertainties, it is concluded that significant dynamo amplification may have occurred.
Drift measurements perpendicular to the magnetic field are examined, taking into account also some nighttime measurements. Nighttime measurements of drift velocities are more difficult because densities are lower. However, the uncertainty in the drift velocities can be optimized by making use of an approach reported by Kirchhoff (1973). The approach involves a careful selection of the elevation angle of the radar antenna. Measured velocities are discussed along with the magnetospheric perturbation effect. The measurements are compared with conclusions of the dynamo theories.
Abstracts of 63 papers accepted for publication are presented. Topics cover geomagnetism in the context of planetary magnetism, lunar magnetism, the dynamo theory and nondynamo processes, comparative planetary magnetism (terrestrial and outer planets), meteoritic magnetism, and the early solar magnetic field. Author and subject indexes are provided.
What is already known about the structure of the Sun, the motion of its convective zone, and the solar cycle is reviewed. Topics discussed include solar variability, solar 'seismology', velocity patterns, magnetic fields, and the dynamo theory. Observations are needed to determine global properties (solar luminosity and radius), oscillations (p and g models), velocities (variation of rotation with time and depth), and magnetic fields.
Soft X-ray observations are presented of a nearly complete sample of RS Canum Venaticorum systems taken with the Einstein X-ray Observatory. It is shown that the quiescent coronal activity, as measured by the ratio of the X-ray to bolometric flux, is directly proportional to the angular velocity of the star with the active chromosphere in these systems. This relation is found to hold over two decades in angular velocity. It is also found that the stellar surface gravity has no obvious influence on the ratio of the X-ray luminosity to the bolometric luminosity over two decades in surface gravity. It is pointed out that the linear relation between the ratio of the X-ray luminosity to the bolometric luminosity on the one hand, and the angular velocity, on the other, holds important implications for dynamo theories of the generation of stellar magnetic fields.
Alpha, an important parameter in dynamo theory, is proportional to either the kinetic, current, magnetic, or velocity helicity of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first order smoothed equations that describe the alpha effect. In two cases, when alpha is proportional to either the magnetic helicity or velocity helicity, alpha is determined experimentally from two point measurements of the fluctuating fields in incompressible, homogeneous turbulence having arbitrary symmetry. For the other two possibilities, alpha is determined if the turbulence is isotropic.