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Planetary Dynamos

The MAGSAT-program has added significantly to our knowledge of planetary magnetism. The accuracy of observations has been improved such that a reliable extrapolation of the magnetic field to the core surface is now much more feasible than it has been before, and the prospect of further MAGSAT missions raises the expectation that the time dependence of the geomagnetic field will be known with similar accuracy in the future. In the research support it has been attempted to develop dynamo theory with these applications in mind.

Busse, F. H.↗

Magnetic field generation in the cores of terrestrial bodies

Efforts to find some scaling law for the dipole moments of planets seem illusory for, although dynamo theory is still in a rudimentary state, once the critical magnetic Reynolds Number is exceeded it appears that the field strength is determined by the energy source, it it is permissible to treat the core as a heat engine. For this reason the lunar magnetic field is of special significance as the paleomagnetic evidence strongly suggests that the surface field was about 1 G 3.9 by diminishing exponentially to about .02 G 3.2 by ago and completely disappearing some time later.

Runcorn, S. K.↗

The alpha dynamo parameter and measurability of helicities in magnetohydrodynamic turbulence

Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities 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, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two-point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic.

Matthaeus, W. H.↗

Mapping of surface activity on the W UMa-type system VW Cephei

After multifilter photometry of the W UMa-type contact binary VW Cep (P = 6.67 hr; G5V + K0V) in 1986/87 revealed large asymmetries in the light curves believed to be caused by large, cool starspot regions on the surface of the larger stars, in Apr. 1987 it was observed with IUE to study the chromospheres and transition regions of the components. During one complete orbital cycle, three SWP and four LWP low dispersion spectra were obtained, including and then excluding the suspected active region. Phase dependent TR line emission strengths were found, most notably C IV, which is 50 percent stronger when the spot region is most visible. The results could be important because VW Cep represents an extreme case for studying stellar dynamo theory and observations can play a crucial role in the unterstanding of magnetic fields and activity cycles in rapidly rotating solar-like stars.

Bradstreet, David H.↗

The disk-halo connection and the nature of the interstellar medium

Some results on the nature of the interstellar medium that are specifically concerned with the disk-halo interaction are discussed. Over the last five years or so it has become clear that the supernovae rate in our Galaxy is spatially clumped and the consequences of such clumping are superbubbles and supershells fed by tens or hundreds of supernovae per shell. These objects evolve and expand rapidly and soon break out of the disk of the Galaxy, feeding the halo with very significant mass, energy, and momentum. As cooling occurs, gas will rain down onto the disk of the Galaxy completing the cycle. The basic flow of physical quantities from disk to halo and vice versa are discussed. Some of the many implications are noted including aspects of dynamo theory, quasar absorption lines, the theory of galactic coronae, and the nature of the x ray background. The essential difference here with the McKee-Ostriker (1977) theory is that the filling factor of the hot gas in the disk is significantly less than unity.

Norman, Colin A.↗

Solar constant secular changes

A recent model for solar constant secular changes is used to calculate a 'proxy' solar constant for: (1) the past four centuries, based upon the sunspot record, (2) the past nine centuries, based upon C-14 observations and their relation to solar activity, and (3) the next decade, based upon a dynamo theory model for the solar cycle. The proxy solar constant data is tabulated as it may be useful for climate modelers studying global climate changes.

Schatten, Kenneth H.↗

Is the earth's dipole actually inclined with respect to the rotation axis?

Planetary exploration by deep space probes in recent years has shown that the dipole moment of some magnetized planets has a surprisingly large inclination angle with respect to the rotation axis. Applying the method developed for the source surface magnetic field of the sun (a spherical surface of 2.5 solar radii), it is suggested that the main dipole of the earth and the magnetized planets may actually be axial (the magnetic moment being parallel or antiparallel to the rotation axis), and that two or three smaller dipoles near the core surface could be responsible for the apparent inclination of the main dipole. In formulating a dynamo theory of the planetary magnetic field, such a possibility should be considered, as well as the inclined dipole case.

Akasofu, S.-I.↗

Rotation and emission lines in stars and accretion disks

In the accretion disks of quiescent dwarf novae, Doppler mapping studies reveal that Balmer emission lines increase sharply toward the center of the disk, with surface brightnesses scaling roughly as R exp -3/2 varies as Omega(Kep). Similarly, among chromospherically active stars the H-alpha and Ca II H and K emission cores are stronger in the more rapidly rotating stars, with surface brightnesses scaling again roughly as Omega(rot). Since in both cases the emission lines scale linearly with the rotation frequency, it is proposed that the mechanism powering the emission lines in quiescent accretion disks is the same as that in chromospherically active stars, namely, the emergence of magnetic flux generated by the action of a dynamo, and its interaction with the atmosphere. If this empirical connection between disks and stars is in fact due to magnetic dynamos, the range of rotation rates available for testing dynamo theories expands from a factor of 1000 to 10 to the 7th.

Horne, Keith↗

Multiple periodicities in the solar magnetic field - Possible origin in a multiple-mode solar dynamo

The solar magnetic field is generated in an oscillatory mode with a 22 yr full period and gives rise to the 11 yr sunspot cycle. However, analyses of contemporary solar records, as well as other surrogate indicators of solar activity, suggest the presence also of longer term periodicities in the solar magnetic cycle. This paper suggests that the solar dynamo can operate in a multiply periodic state, with several periodicites being generated simultaneously at different depths in the convection zone. A simple two-layer model of the solar convection zone is used to illustrate the physical mechanism of spatially localized, multiple-periodicity-mode dynamo regeneration. The two layers are characterized by differences in their respective turbulent magnetic diffusivities. Although the magnetic modes interact with one another, each mode is produced large in one layer or the other, and has an oscillation period approximately equal to the time characteristic of magnetic diffusion across the layer. The observed complicated periodicity pattern in the solar magnetic field could be a combination of two (or more) dynamo modes generated in this manner. The calculations are carried out using a differential rotation model consistent with recent helioseismological measurements, illustrating the challenge to dynamo theory raised by those observational results.

Boyer, D. W.↗

Nonlinear decay of magnetic helicity in magnetohydrodynamic turbulence with a mean magnetic field

We show that the magnetic helicity associated with fluctuations in homogeneous incompressible magnetohydrodynamic (MHD) turbulence with a mean magnetic field decays in time because of nonlinear processes. Evidence is obtained numerically, by use of both dissipative and nondissipative spectral method simulations. The described effect stands in contrast to expectations based on studies of MHD turbulence without an applied mean field, in which magnetic helicity is transferred nonlinearly to long wavelengths and is preserved in time because of selective decay when dissipation is present. The process of nonlinear decay is described in terms of a generalized ideal helicity invariant and is characterized by the transient production of a mean induced electric field aligned with the applied magnetic field, an effect reminiscent of the alpha effect in dynamo theory. A simple phenomenological model for the decay process is proposed.

Stribling, Troy↗

Helioseismic Constraints on the Gradient of Angular Velocity at the Base of the Solar Convection Zone

The layer of transition from the nearly rigid rotation of the radiative interior to the latitudinal differential rotation of the convection zone plays a significant role in the internal dynamics of the Sun. Using rotational splitting coefficients of the p-mode frequencies, obtained during 1986-1990 at the Big Bear Solar Observatory, we have found that the thickness of the transitional layer is 0.09 +/- 0.04 solar radii (63 +/- 28 Mm), and that most of the transition occurs beneath the adiabatically stratified part of the convection zone, as suggested by the dynamo theories of the 22 yr solar activity cycle.

Kosovichev, A. G.↗

Study of a Solar X-Ray Telescope

The highly structured nature of the outer solar atmosphere seems to be intimately linked to the presence, at the solar surface, of magnetic fields that have been generated inside the Sun and have emerged to the surface. The corona is brightest (and also hottest) at just those locations where the magnetic field has emerged from inside the Sun. Dynamo theory predicts that strong magnetic fields will be generated deep in the solar interior and that bundles or 'ropes' of magnetic flux will float to the surface. When this happens, a magnetically bipolar region will become visible, extending above the surface in a three-dimensional structure. The field lines penetrate through the surface, showing two magnetic poles, and also exhibit a three-dimensional structure above the surface. The structure created by the field emergence is rooted in the (relatively) cool photosphere and extends through the chromosphere and transition region to the corona. Thus, the magnetic field creates a region, called an active region, which contains portions at temperatures from less than 10(exp 4) K to greater than 10(exp 6) K, and is therefore visible at wavelengths from the infrared through x-rays. The locations where the magnetic field leaves and reenters the visible surface are called the 'footpoints' of the coronal structures associated with the magnetic field. The magnetic fields themselves are not directly visible. However, the hot coronal plasma is, for the most part, constrained to follow the direction of the magnetic field lines in the atmosphere. Now, 100 years after the discovery of x-rays by Wilhelm Roentgen in 1896, we can routinely make observations of the solar corona from outside the Earth's atmosphere in this region of the electromagnetic spectrum. As shown by comparing x-ray images with magnetograms, the bright corona over these bipolar magnetic regions consists of closed structures that seem to follow the orientation of the magnetic field. Although we can see down to the photosphere at x-ray wavelengths when observing the disk of the Sun, this part of the solar atmosphere emits so little that far from the peak of its Planck curve it appears dark in x-ray images. This impression of hot plasma following the magnetic field direction is further strengthened by quantitative studies that calculate coronal magnetic field strength and direction based on photospheric measurements and compare them with the observed brightness and location of the x-ray emitting structures. Such comparisons make it clear that, for the most part, the hot plasma conforms to the geometry of the magnetic field and that the coronal brightness is strongly linked to the strength of the magnetic fields which have erupted to the solar surface from the interior. It is also the case that the larger-scale, fainter corona, as well as coronal holes, are strongly influenced by the large-scale solar magnetic field. We may get a small hint of the reason that the coronal plasma outlines the direction of B by examining the thermal conductivity of a hot plasma in the presence of a magnetic field. This quantity has enormously different values in the directions parallel and perpendicular to the field for a coronal temperature of 10(exp 6) K, a particle density of 10(exp 9)/cu cm and a magnetic field strength of 100 G, the conductivity along the field is approximately 13 orders of magnitude greater than that perpendicular to the field. It is therefore not surprising that a parcel of plasma which is locally heated would conduct that heat preferentially in the direction of the field. We also note that the thermal conductivity parallel to the magnetic field increases with temperature T, while the perpendicular conductivity decreases. To the extent that the loop aspect ratio, i.e., the ratio of loop length to loop width, is determined by the thermal conductivity, we would expect that higher temperature loops are longer and thinner than cooler ones. However, if the loop width becomes smaller than the spatial resolution of the observing instrument, this effect will not be directly observable. For organizational purposes, we provide a listing of some scientific objectives for a Solar-B x-ray telescope, arranged in terms of identifiable features in the corona.

Golub, Leon↗

The Fundamental Physical Processes Producing and Controlling Stellar Coronal/ Transition-Region/Chromospheric Activity and Structure

Our LTSA grant supports a long-term collaborative investigation of stellar activity. The project involves current NASA spacecraft and supporting ground-based telescopes, will make use of future missions, and utilizes the extensive archives of IUE, ROSAT, HST, and EUVE. Our interests include observational work (with a nonnegligible groundbased component); specialized processing techniques for imaging and spectral data; and semiempirical modeling, ranging from optically-thin emission measure studies to simulations of optically-thick resonance lines. Collaborations with our cool-star colleagues here in Boulder (at JILA and the High Altitude Observatory) provide access to even broader expertise, particularly on the solar corona, convection, and magnetohydrodynamic phenomena (including "dynamo" theories). The broad-brush of our investigation include the following: (1) where do coronae occur in the Hertzsprung-Russell diagram? (2) the winds of coronal stars: hot, cool, or both? (3) age, activity, rotation relations; (4) atmospheric inhomogeneities; and (5) heating mechanisms, subcoronal flows and flares. Our observation task has been to map the global properties of chromospheres and coronae in the H-R diagram and conduct detailed studies of key objects.

Ayres, Thomas R.↗

Solar Cycle Predictions Near Sunspot Minimum

Observations of solar magnetic activity and the dynamics of the solar convection zone have produced severe constraints on models of the Sun's magnetic dynamo. These constraints are so severe that, at present, we do not have numerical models that can accept the current conditions and then march forward in time to predict future activity. Given this state of solar dynamo theory we are forced to examine previous behavior to discover patterns and trends that afford us some measure of predictability. Here we examine the behavior of several indicators of solar activity near solar minimum that are well correlated with the amplitude of the following solar maximum to predict the level of solar activity over cycle 23. Sunspot numbers, areas, and positions are useful for characterizing solar cycle behavior due to the extent of the data (12 cycles or more). These data exhibit several patterns that relate future activity to past behavior. With the Odd-Even effect the odd numbered cycles have been larger than their even numbered predecessors for each of the last six cycle pairs. With the Amplitude-Period effect short period cycles have been followed by large amplitude cycles and long period cycles have been followed by small amplitude cycles for 10 of the last 13 cycles. With the Maximum-Minimum effect the sunspot number at minimum is directly correlated with the sunspot number at maximum for a given cycle. The geomagnetic indices aa and Ap are also related to solar activity by the connections between disturbances in the solar wind and variations in the Earth's magnetic field. Like the Maximum-Minimum effect for sunspots, the size of the aa and Ap indices at minimum are directly related to the amplitude of the following maximum. The number of geomagnetically disturbed days (days with Ap >= 25) over the course of a cycle is another indicator for the size of the next cycle. The aa and Ap indices can each be separated into a component in phase with the current sunspot cycle and an "extended cycle" component that is directly related to the following cycle. Individually each of these indicators provides some measure of predictive ability for the amplitudes of previous cycles. Taken in combination we find that the predictions are much more accurate. Our multi-variate analysis indicates that a maximum sunspot number of 160 +/- 20 should occur near the end of 1999 for cycle 23.

Hathaway, David H.↗

The Art and Science of Long-Range Space Weather Forecasting

Long-range space weather forecasts are akin to seasonal forecasts of terrestrial weather. We don t expect to forecast individual events but we do hope to forecast the underlying level of activity important for satellite operations and mission pl&g. Forecasting space weather conditions years or decades into the future has traditionally been based on empirical models of the solar cycle. Models for the shape of the cycle as a function of its amplitude become reliable once the amplitude is well determined - usually two to three years after minimum. Forecasting the amplitude of a cycle well before that time has been more of an art than a science - usually based on cycle statistics and trends. Recent developments in dynamo theory -the theory explaining the generation of the Sun s magnetic field and the solar activity cycle - have now produced models with predictive capabilities. Testing these models with historical sunspot cycle data indicates that these predictions may be highly reliable one, or even two, cycles into the future.

Hathaway, David H.↗

On the Origin of Sunspots

It is proposed tha sunspots (and other flux emergence phenomena) originate due ot the presence of fluctuating magnetic fields complementing the regular, mean field in the convection zone. The mean field predicted by dynamo theories is too weak itself to emerge at the surface of the Sun.

sunspots flux emergence solar magnetic fields Sun ↗

Solar Cycle Prediction

Solar cycle predictions are needed to plan long-term space missions; just like weather predictions are needed to plan your next vacation. Fleets of satellites circle the Earth collecting many types of science data, protecting astronauts, and relaying information. All of these satellites are sensitive at some level to solar cycle effects. Predictions of drag on LEO spacecraft are one of the most important. Launching a satellite with less propellant can mean a higher orbit, but unanticipated solar activity and increased drag can make that a Pyrrhic victory. Energetic events at the Sun can produce crippling radiation storms that endanger all assets in space. Testing solar dynamo theories by quantitative predictions of what will happen in 5-20 years is the next arena for solar cycle predictions. I will describe the current state of solar cycle predictions and anticipate how those predictions could be made more accurate in the future.

Pesnell, William Dean↗

Solar Cycle Predictions

Solar cycle predictions are needed to plan long-term space missions; just like weather predictions are needed to plan the launch. Fleets of satellites circle the Earth collecting many types of science data, protecting astronauts, and relaying information. All of these satellites are sensitive at some level to solar cycle effects. Predictions of drag on LEO spacecraft are one of the most important. Launching a satellite with less propellant can mean a higher orbit, but unanticipated solar activity and increased drag can make that a Pyrrhic victory as you consume the reduced propellant load more rapidly. Energetic events at the Sun can produce crippling radiation storms that endanger all assets in space. Solar cycle predictions also anticipate the shortwave emissions that cause degradation of solar panels. Testing solar dynamo theories by quantitative predictions of what will happen in 5-20 years is the next arena for solar cycle predictions. A summary and analysis of 75 predictions of the amplitude of the upcoming Solar Cycle 24 is presented. The current state of solar cycle predictions and some anticipations how those predictions could be made more accurate in the future will be discussed.

Pesnell, William Dean↗