Audrey L. Summers

Hydromagnetic flow around the magnetosphere

Abstract A magnetohydrodynamic model for the interaction of the solar wind and the geomagnetic field is described, the degree to which the governing equations may be approximated by the simpler equations of the classical Chapman-Ferraro theory combined with gasdynamics is examined, and numerical results for a number of representative cases are presented. In the hydromagnetic model, the magnetosphere boundary and distant tail are represented by tangential and contact discontinuities, and the bow wave by a fast hydromagnetic shock wave. The connectivity of interplanetary and geomagnetic fields, and the asymptotic directions of the wake and shock waves at great distances from the Earth are discussed in terms of properties of these discontinuities. Detailed numerical results for the location of the bow wave, and the density, velocity, and temperature of the flow in the region between the bow wave and the magnetosphere are presented for Mach numbers 5, 8 and 12 for γ = 5 3 and 2. The calculated position of the bow wave is shown to be in good accordance with that observed in shadowgraph photographs of supersonic flow past a model magnetosphere in the Ames Supersonic Free-Flight Wind Tunnel. Results are also presented that illustrate the distortion of the interplanetary magnetic field in the region between the bow and the magnetosphere for cases in which the magnetic field in the incident stream is inclined at 45 and 90° to the free-stream direction.

Solar wind flow past nonmagnetic planets - Venus and Mars

Abstract The hydromagnetic theory of solar wind flow past the Earth has been extended and modified so as to be applicable to nonmagnetic planets, such as Venus and Mars, that have a sufficient ionosphere to deflect the solar plasma around the planet and its atmosphere. The principal difference in the analysis stems from the fact that the current sheath that bounds the solar wind away from the planet is formed by interaction with the ionosphere rather than with the geomagnetic field as in the case of the Earth. After stating the principal assumptions and equations, the theory is applied to determine the shape of the ionosphere boundary, or ionopause, across which the Newtonian approximation for the pressure of the flowing plasma is balanced by the pressure of a stationary ionosphere. Specific numerical results are given for a wide range of ionospheric parameters representative of those proposed for Venus and Mars. The location of the bow wave and the properties of the flow field are then calculated using magnetohydrodynamic and gasdynamic considerations in a manner similar to that employed for the flow of the solar wind plasma past the Earths magnetosphere. Examination of the results reveals a correspondance rule that enables results presently available for the location of the bow wave and the properties of the flow about the Earths magnetosphere to be converted rapidly into those for a nonmagnetic planet by a simple relabeling of the scales. The results are shown to be in general accordance with observations made by Mariner 5 as it flew past Venus, although certain differences near the theoretical location of the ionopause suggest the presence of a thick boundary layer. A similar analysis of the data from Mariners 4,6 and 7 indicates that Mars has a sufficient ionosphere for the theory to be applicable. Further comparison is relatively uninformative beyond revealing no inconsistencies with the theoretical results, however, because Mariner 4 did not approach close enough, and Mariners 6 and 7 were not equipped to make the necessary measurements.

Predictions of the electrical conductivity and charging of the aerosols in Titan's atmosphere

Abstract The electrical conductivity and electrical charge on the aerosols in atmosphere of Titan are computed for altitudes between 0 and 400 km. Ionization of methane and nitrogen due to galactic cosmic rays (GCR) is important at night where these ions are converted to ion clusters such as CH + 5 CH 4 , C 7 H + 7 , C 4 H + 7 , and H 4 C 7 N + . The ubiquitous aerosols observed also play an important role in determining the charge distribution in the atmosphere. Because polycyclic aromatic hydrocarbons (PAHs) are expected in Titans atmosphere and have been observed in the laboratory and found to be electrophilic, we consider the formation of negative ions. During the night, the very smallest molecular complexes accept free electrons to form negative ions. This results in a large reduction of the electron abundance both in the region between 150 and 350 km over that predicted when such aerosols are not considered. During the day time, ionization by photoemission from aerosols irradiated by solar ultraviolet (UV) radiation overwhelms the GCR-produced ionization. The presence of hydrocarbon and nitrile minor constituents substantially reduces the UV flux in the wavelength band from the cutoff of CH 4 at 155 to 200 nm. These aerosols have such a low ionization potential that the bulk of the solar radiation at longer wavelengths is energetic enough to produce a photoionization rate sufficient to create an ionosphere even without galactic cosmic ray (GCR) bombardment. At altitudes below 60 km, the electron and positive ion abundances are influenced by the three-body recombination of ions and electrons. The addition of this reaction significantly reduces the predicted electron abundance over that previously predicted. Our calculations for the dayside show that the peaks of the charge distributions move to larger values as the altitude increases. This variation is the result of the increased UV flux present at the highest altitudes. Clearly, the situation is quite different than that for the night where the peak of the distribution for a particular size is nearly constant with altitude when negative ions are not present. The presence of very small aerosol particles (embryos) may cause the peak of the distribution to decrease from about 8 negative charges to as little as one negative charge or even zero charge. This dependence on altitude will require models of the aerosol formation to change their algorithms to better represent the effect of charged aerosols as a function of altitude. In particular, the charge state will be much higher than previously predicted and it will not be constant with altitude during the day time. Charging of aerosol particles, whether on the dayside or nightside, has a major influence on both the electron abundance and electrical conductivity. The predicted conductivities are within the measurement range of the HASI PWA instrument over most but not all, of the altitude range sampled.

The photometric method of detecting other planetary systems

Abstract The photometric method detects planets orbiting other stars by searching for the reduction in the light flux or the change in the color of the stellar flux that occurs when a planet transits a star. A transit by Jupiter or Saturn would reduce the stellar flux by approximately 1% while a transit by Uranus or Neptune would reduce the stellar flux by 0.1%. A highly characteristic color change with an amplitude approximately 0.1 of that for the flux reduction would also accompany the transit and could be used to verify that the source of the flux reduction was a planetary transit rather than some other phenomenon. Although the precision required to detect major planets is already available with state-of-the-art photometers, the detection of terrestrial-sized planets would require a precision substantially greater than the state-of-the-art and a spaceborne platform to avoid the effects of variations in sky transparency and scintillation. Because the probability is so small of observing a planetary transit during a single observation of a randomly chosen star, the search program must be designed to continuously monitor hundreds or thousands of stars. The most promising approach is to search for large planets with a photometric system that has a single-measurement precision of 0.1%. If it is assumed that large planets will have long-period orbits, and that each star has an average of one large planet, then approximately 104 stars must be monitored continuously. To monitor such a large groups of stars simultaneously while maintaining the required photometric precision, a detector array coupled by a fiber-optic bundle to the focal plane of a moderate aperture (≈ 1 m), wide field of view (≈50°) telescope is required. Based on the stated assumptions, a detection rate of one planet per year of observation appears possible.

EXTERNAL AERODYNAMICS OF THE MAGNETOSPHERE.

The flow of the solar wind past the earth and its magnetosphere constitutes a problem similar in many ways to the familiar, but complex problem of the external aerodynamics of round-nosed bodies in a supersonic stream. It is the purpose of this paper to provide a resume of some of the basic ideas, both theoretical and experimental, that support this correspondence, and to present a connected account of many of the principal quantitative results that have been obtained through application and extension of methods developed originally for the aerodynamics of re-entry vehicles. In addition, the basic concepts of the theory of the solar wind itself are outlined in some detail in order to illustrate the basic unity of the entire theoretical description of the solar wind and its interaction with the geomagnetic field. Finally, extensive discussions of the internal consistency of the theory and the degree to which the results correspond to conditions observed in space are included for the purpose of providing an understanding of the overall reliability of the theory.

On conditions near the neutral points on the magnetosphere boundary

Abstract Conditions near the neutral points are examined from the conventional point of view of fluid flow around a magnetosphere that must adjust its boundary shape in such a way that the gas pressure of the stream is balanced by the magnetic pressure of the bounded geomagnetic field. It is shown that the latter requirement leads in a natural way to the concept of hot, but essentially stationary, plasma trapped in a cusp-shaped region in the vicinity of each neutral point. It is shown, moreover, that there is a flux of about 10 22 protons/sec from each region and that this flux is proportional to the velocity of the solar wind. The area through which these particles stream is inversely proportional to the number density of the solar wind and depends on the angle between the dipole axis and the solar wind direction in such a way that the proton flux may be concentrated into an area 8 times smaller in the summer polar region than the winter polar region. Recent geophysical observations from polar regions, as well as data from laboratory and space experiments, are cited to support the actual existence and physical relevance of the results.

Models of the formation of the solar nebula

Models of the collapse of a protostellar cloud and the formation of the solar nebula reveal that the size of the nebula produced will be the larger of RCF ≡ J2/k2GM3and RV ≡ (GMv/2cc3)12 (where J, M, and cs are the total angular momentum, total mass, and sound speed of the protosetellar material; G is the gravitational constant; k is a number of order unity; and v is the effective viscosity in the nebula). From this result it can be deduced that low-mass nebulas are produced if P ≡ (RV/RCF)2 ⪢ 1; “massive” nebulas result if P ≲ 1. Gravitational instabilities are expected to be important for the evolution of P ⪡ 1 nebulas. The value of J distinguishes most current models of the solar nebula, since P ∝ J−4. Analytic expressions for the surface density, nebular mass flux, and photospheric temperature distributions during the formation stage are presented for some simple models that illustrate the general properties of growing protostellar disks. It does not yet seem possible to rule out either P ⪢ 1 or P < 1 for the solar nebula, but observed or possible heterogeneities in composition and angular-momentum orientation favor P < 1 models.

Saturn's rings: Particle composition and size distribution as constrained by observations at microwave wavelengths: II. Radio interferometric observations

Abstract The sizes, composition, and number of particles comprising the rings of Saturn may be meaningfully constrained by a combination of radar- and radio-astronomical observations. In a previous paper, we have discussed constraints obtained from radar observations. In this paper, we discuss the constraints imposed by complementary “passive” radio observations at similar wavelengths. First, we present theoretical models of the brightness of Saturns rings at microwave wavelengths (0.34–21.0 cm), including both intrinsic ring emission and diffuse scattering by the rings of the planetary emission. The models are accurate simulations of the behavior of realistic ring particles and are parameterized only by particle composition and size distribution, and ring optical depth. Second, we have reanalyzed several previously existing sets of interferometric observations of the Saturn system at 0.83-, 3.71-, 6.0-, 11.1-, and 21.0-cm wavelengths. These observations all have spatial resolution sufficient to resolve the rings and planetary disk, and most have resolution sufficient to resolve the ring-occulted region of the disk as well. Using our ring models and a realistic model of the planetary brightness distribution, we are able to establish improved constraints on the properties of the rings. In particular, we find that: (a) the maximum optical depth in the rings is ∼ 1.5 ± 0.3 referred to visible wavelengths; (b) a significant decrease in ring optical depth from λ3.7 to λ21.0 cm allows us to rule out the possibility that more than ∼30% of the cross section of the rings is composed of particles larger than a meter or so; this assertion is essentially independent of uncertainties in particle adsorption coefficient; and (c) the ring particles cannot be primarily of silicate composition, independently of particle size, and the particles cannot be primarily smaller than ∼0.1 cm, independently of composition.

On the thermal evolution of the terrestrial planets

Physical and chemical constraints for such different planetary objects as the Earth, the Moon and meteorite parent bodies can best be satisfied by thermal history models having high initial temperatures. On the basis of thermal calculations it is suggested that the evolution of the other terrestrial planets (Mars, Venus and Mercury) was also characterized by high initial temperatures. Under these conditions, melting and, consequently, fractionation would set in at an early stage. Because of the resulting redistribution of the long-lived radioactive heat sources and the concentration of these elements in the surface layers, large-scale differentiation could be achieved by partial melting.

Convection and lunar thermal history

The effect of solid convection on the thermal evolution of the Moon is explored for a variety of viscosities, radioactive differentiation efficiencies and initial temperature profiles. Convective heat flux in the models is calculated using an empirical relation derived from the results of laboratory experiments and numerical solutions of the Navier-Stokes equations. The method retains the spherically symmetric approximation and, therefore, greatly facilitates numerical calculations. Results show that even though solid convection may determine the thermal state of the lunar interior, it does not necessarily produce a quasi-steady thermal balance between heat sources and surface loss. An imbalance persists, due to the cooling and growth of the nonconvecting lithosphere. The state of the lithosphere is sensitive to the efficiency of heat source redistribution, while that of the convecting interior depends primarily on rheology. Convecting models have viscosities of 1021–1022 cm2s−1 in their interiors; the central temperature must be above 1100°C. Convection occurring within the first billion years after formation could have led to mare flooding by magma produced in hot zones of convection cells. However, it cannot be shown from model calculations alone that solid convection must have dominated lunar thermal history.