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A boundary-layer solution to a high magnetic Reynolds number R periodic dynamo model shows that: (1) flux expulsion forces the magnetic field into flux sheets; (2) the principal contribution to the alpha effect arises from regions of flow stagnation along a flux sheet; and (3) the alpha effect scales as R exp-1/2. Arguments for these effects persisting in turbulent dynamos are given.
Some questions dealing with the nature and history of a large metallic core within Mercury are considered. These include the existence of a core, its size, whether it is fluid or solid, the timescale for core formation, the geological consequences of core formation, and whether such consequences are consistent with the surface geology. Several indirect lines of evidence are discussed which suggest the presence of a large iron-rich core. A core-formation model is examined in which core infall is accompanied by an increase of 17 km in planetary radius, an increase of 700 K in mean internal temperature, and substantial melting of the mantle. It is argued that if the core differentiated from an originally homogeneous planet, that event must have predated the oldest geological units comprising most of the planetary surface. A convective dynamo model for the source of Mercury's magnetic field is shown to conflict with cosmochemical models that do not predict a substantial radiogenic heat source in the core.
The study of magnetized plasmas in astrophysics is complicated by a number of factors, not the least of which is that in considering magnetic fields in stars or accretion disks, we are considering plasmas with densities well above those we can study in the laboratory. In particular, whereas laboratory plasmas are dominated by the confining magnetic field pressure, stars, and probably accretion disks, have magnetic fields whose beta (ratio of gas pressure to magnetic field pressure) is much greater than 1. Observations of the Sun suggest that under such circumstances the magnetic field breaks apart into discrete flux tubes with a small filling factor. On the other hand, theoretical treatments of MHD turbulence in high-beta plasmas tend to assume that the field is more or less homogeneously distributed throughout the plasma. Here we consider a simple model for the distribution of magnetic flux tubes in a turbulent medium. We discuss the mechanism by which small inhomogeneities evolve into discrete flux tubes and the size and distribution of such flux tubes. We then apply the model to accretion disks. We find that the fibrilation of the magnetic field does not enhance magnetic buoyancy. We also note that the evolution of an initially diffuse field in a turbulent medium, e.g., any uniform field in a shearing flow, will initially show exponential growth as the flux tubes form. This growth saturates when the flux tube formation is complete and cannot be used as the basis for a self-sustaining dynamo effect. Since the typical state of the magnetic field is a collection of intense flux tubes, this effect is of limited interest. However, it may be important early in the evolution of the galactic magnetic field, and it will play a large role in numerical simulations. Finally, we note that the formation of flux tubes is an essential ingredient in any successful dynamo model for stars or accretion disks.
It is shown how the usual nearly-free-electron model for the electrical resistivity of simple liquid metals can be extended to the case of liquid transition metals such as iron. A simple prescription is given for calculating the resistivity at different densities and temperatures. As an application and example of the method, calculations on liquid iron at different densities were carried out and the resistivity of molten iron in the earth's outer core is estimated. The effects of alloying iron with other elements are also considered. The calculated conductivity of the outer core is well within the limit required for the dynamo model of the geomagnetic field and agrees well with some recent shock wave data.
The electrodynamics of the plasmasphere has been a topic of considerable interest. Models predict a space charge buildup, or Alfven layer, at the inner edge of the ring current which opposes the dawn-dusk convection electric field in the magnetosphere and thus shields the plasmasphere from the convection electric field. The current study has the objective to present data from the ISEE 1 double cylindrical probe instrument. All measurements reported were made in the plasmasphere with electron densities of the order of 30-50 or greater per cu cm. The average electric field pattern for quiet conditions is found to be qualitatively consistent with previous average results from whistler measurements and radar backscattering measurements. The magnitudes and gross patterns are in qualitative agreement with representative ionospheric dynamo models. The basic convective flow vectors from the penetration of the magnetospheric electric field tend to follow contours which are parallel to those of the average plasmapause boundary on the nightside.
We will discuss the polar field precursor method for solar activity prediction, which predicts cycle 24 will be significantly lower than recent activity cycles, and some new ideas rejuvenating Babcock's shallow surface dynamo. The polar field precursor method is based on Babcock and Leighton's dynamo models wherein the polar field at solar minimum plays a major role in generating the next cycle's toroidal field and sunspots. Thus, by examining the polar fields of the Sun near solar minimum, a forecast for the next cycle's activity is obtained. With the current low value for the Sun's polar fields, this method predicts solar cycle 24 will be one of the lowest in recent times, with smoothed F10.7 radio flux values peaking near 135 plus or minus 35 (2 sigma), in the 2012-2013 timeframe (equivalent to smoothed Rz near 80 plus or minus 35 [2 sigma]). One may have to consider solar activity as far back as the early 20th century to find a cycle of comparable magnitude. We discuss unusual behavior in the Sun's polar fields that support this prediction. Normally, the solar precursor method is consistent with the geomagnetic precursor method, wherein geomagnetic variations are thought to be a good measure of the Sun's polar field strength. Because of the unusual polar field, the Earth does not appear to be currently bathed in the Sun's extended polar field (the interplanetary field), hence negating the primal cause behind the geomagnetic precursor technique. We also discuss how percolation may support Babcock's original shallow solar dynamo. In this process ephemeral regions from the solar magnetic carpet, guided by shallow surface fields, may collect to form pores and sunspots.
Binary neutron star mergers can produce extreme magnetic fields, some of which can lead to strong magnetar-like remnants. While strong magnetic fields have been shown to affect the dynamics of outflows and angular momentum transport in the remnant, they can also crucially alter the properties of nuclear matter probed in the merger. In this work, we provide a first assessment of the latter, determining the strength of the pressure anisotropy caused by Landau-level quantization and the anomalous magnetic moment. To this end, we perform the first numerical relativity simulation with a magnetic polarization tensor and a magnetic-field-dependent equation of state using a new algorithm we present here, which also incorporates a mean-field dynamo model to control the magnetic field strength present in the merger remnant. Our results show that—in the most optimistic case—corrections to the anisotropy can be in excess of 10% and are potentially largest in the outer layers of the remnant. This work paves the way for a systematic investigation of these effects.
Constraints placed on the thermal evolution of Mercury by the dynamo model of the planet's magnetic field are investigated. It is assumed that Mercury is a differentiated planet possessing an iron-nickel core with a radius approximately three-fourths of the planetary radius, that the mantle is made of silicates with thermal and rheological properties similar to those of earth's upper mantle, and that differentiation was a global process which resulted in the removal of radioactive heat sources from the core and the upward segregation of heat sources in the mantle. These assumptions are found to lead to the conclusion that the existence of a molten core requires the retention of a minimum concentration of heat sources throughout the mantle, the value being comparable to the mantle-wide average concentration for earth. Thus, it is suggested that the differentiation of Mercury could not have resulted in the complete removal of heat sources from the mantle into a crust near the planet's surface.
X-ray observations have provided information about magnetic fields on the sun, and the implications of these observations are discussed. The pattern of small-scale flux emergence is quite different from that of active regions. It is inferred that the small-scale fields originate fairly high in the convective zone, while the fields in active regions have a deeper origin. The small-scale turbulent fields are only loosely related to the fields that define the normal solar cycle. The way in which dynamo models must be modified in the light of these results is indicated.
Magnetic-field observations were carried out for 29 G and K main-sequence stars. The area covering-factors of magnetic regions tends to be greater in the K dwarfs than in the G dwarfs. However, no spectral-type dependence is found for the field strengths, contrary to predictions that pressure equilibrium with the ambient photospheric gas pressure would determine the surface field strengths. Coronal soft X-ray fluxes from the G and K dwarfs correlate well with the fraction of the stellar surface covered by magnetic regions. The dependence of coronal soft X-ray fluxes on photospheric field strengths is consistent with Stein's predicted generation-rates for Alfven waves. These dependences are inconsistent with the one dynamo model for which a specific prediction is offered. Finally, time variability of magnetic fields is seen on the two active stars that have been extensively monitored. Significant changes in magnetic fields are seen to occur on timescales as short as one day.
Magnetic-field observations were carried out for 29 G and K main-sequence stars. The area covering-factors of magnetic regions tends to be greater in the K darfs than in the G dwarfs. However, no spectral-type dependence is found for the field strengths, contrary to predictions that pressure equilibrium with the ambient photospheric gas pressure would determine the surface field strengths. Coronal soft X-ray fluxes from the G and K dwarfs correlate well with the fraction of the stellar surface covered by magnetic regions. The dependence of coronal soft X-ray fluxes on photospheric field strengths is consistent with Stein's predicted generation-rates for Alfven waves. These dependences are inconsistent with the one dynamo model for which a specific prediction is offered. Finally, time variability of magnetic fields is seen on the two active stars that have been extensively monitored. Significant changes in magnetic fields are seen to occur on timescales as short as one day. Previously announced in STAR as N83-24435
The solar coronal complex X-ray structure is now known to involve radiation loops that coincide spatially with the magnetic loops confining the radiating plasma. An effort is presently made to identify primary submodels involved in the global coupling between a mechanical energy reservoir of beta value greater than 1 and a contiguous site of X-ray activity whose beta value is lower than 1. The 'dynamo' model invoked establishes a quantitative connection between mechanical driver properties and the dimensions, field strength, and number density distribution of elemental magnetic loops.
The viability of the solar alpha-omega dynamo model was studied through examination of extreme stellar cases expected to show specific types of deviation from solar behavior. Observational data was taken from studies of main sequence stars with shallow convective zones, fully convective M-dwarfs, and a Pleiades X-ray survey.
The variety of stellar chromospheric and coronal activity provides a framework for understanding solar and stellar magnetic activity. It is pointed out that the recognition of an 11-yr periodicity within the record of sunspot numbers is a relatively recent discovery of just over a century ago. The solar activity cycle is examined, taking into account the sunspot cycle, and solar dynamo models. Time-averaged stellar chromospheric activity levels are considered along with long-term activity fluctuations of cool stars. Attention is given to the direct measurement of stellar magnetic fields, solar luminosity variations, the RS Canum Venaticorum and BY Draconis variables, continuum variations in lower main sequence stars, chromospheric variations in lower main sequence stars, and chromospheric variations in evolved stars.
Two aspects of solar flares are considered from the point of view of circuit theory. First, it is shown that the so-called 'dynamo models', which invoke an analogy between the earth's magnetosphere-ionosphere circuit and the solar corona-photosphere circuit, are ill-founded. Second, the rate of coronal energy release in the impulsive phase of a modest flare is considered, and it is shown that, if the energy going into mass motion can be neglected, the corona must present a resistance of about 0.001 ohm. Classical resistivity, even in a highly filamented circuit, cannot provide so high a resistance. Anomalous resistivity due to ion sound turbulence can provide the required resistance in this case, but is insufficient to explain the very high power levels inferred in some fast spikes.
The Babcock (1961) 'solar dynamo' model and known interactions of the interplanetary magnetic field with the earth's magnetosophere are used to explain the relations found between geomagnetic indices at solar minimum and the sunspot number at the following solar maximum. The work of Kane (1987) is augmented by including recent smoothed aa and Ap indices. A smoothed maximum sunspot number of 163 + or - 40 to peak in October 1990 + or - 9 months for solar cycle 22 is predicted. This value is close to the Schatten and Sofia (1987) value of 170 + or - 25, predicted using more direct solar indicators.
The variability of solar activity over long time scales, given semiquantitatively by measurements of sunspot numbers, is examined as a nonlinear dynamical system. First, a discussion of the data set used and the techniques utilized to reduce the noise and capture the long-term dynamics inherent in the data is presented. Subsequently, an attractor is reconstructed from the data set using the method of time delays. The reconstructed attractor is then used to determine both the dimension of the underlying system and also the largest Lyapunov exponent, which together indicate that the sunspot cycle is indeed chaotic and also low dimensional. In addition, recent techniques of exploiting chaotic dynamics to provide accurate, short-term predictions are utilized in order to improve upon current forecasting methods and also to place theoretical limits on predictability extent. The results are compared to chaotic solar-dynamo models as a possible physically motivated source of this chaotic behavior.
Measurements by the magnetometer on the Pioneer Venus orbiter have established that during conditions of low solar wind dynamic pressure, large-scale magnetic fields are not present in the ionosphere of Venus but that during conditions of high solar wind dynamic pressure the ionosphere of Venus is magnetized. The source of the magnetic field is thought to be currents induced in the ionosphere by the solar wind. We will show that ionospheric polarization electric field can act as a source, or 'battery', producing a small magnetic field, even without any initial magnetic field. We have calculated this polarization source as a function of altitude and solar zenith angle. The magnetic field was then determined using a 2D kinematic dynamo model of the ionosphere of Venus. The magnetic field attains a maximum strength of about 5 nT at a solar zenith angle of about 120 deg. This magnetic field might act as a 'seed' field for magnetic flux ropes and terminator waves.