Implications of recent numerical calculations for the fission theory of the origin of the Moon

Recent numerical simulations of fission instabilities in rotating fluid masses give results which are consistent with some requirements of the fission hypothesis for the origin of the moon.     

On the interpretation of Fraunhofer line Doppler shifts at supergranule boundaries

We have used the SPO tower telescope and echelle spectrograph to study differences in the profiles of three Fei lines, between magnetic network and cells. Ca K slit-jaw pictures were used to identify the network and cell areas, and mean network and cell profiles were computed from digitized spectra for the g = 0 lines 4065, 5434, and the g = 1.5 line 5233. The profile bisectors show that the wings of all three lines are red-shifted in the network by between 75–200 m s^–1 relative to the cell profiles. But the redshift decreases in the line core and becomes less than the standard error of 20 m s^–1 near the line core minimum. This disappearance of the redshift at the cores of all 3 lines formed over the height range 250–500 km above _0.5 = 1, argues against a steady downflow at supergranule boundaries. We show that such red-shifted wings and a relatively unshifted core can result if granular convection is suppressed near the network flux tubes, without implying any downflow in the vicinity of these flux tubes. Our results also indicate that searches for large-scale convective velocity patterns should measure shifts of the line core, rather than the line wings which appear to be very sensitive to inhomogeneities in granule structure.Visiting Astronomers, Sacramento Peak Observatory.     

Nonmodal Growth on a Sphere at Various Horizontal Scales

Nonmodal growth (NG) and unstable normal mode growth are considered in spherical geometry. Two groups of initial conditions (IC) are studied: "connected" IC (common in Cartesian studies) and "separated" IC (based on observed conditions prior to cyclogenesis). Time series of growth rates are emphasized in conjunction with eigenmode projections. Projections show that early on normal mode growth was much stronger for connected IC and that NG caused negative growth early on of some variables for separated IC. Projections explain why amplitude, kinetic energy (KE), and potential vorticity have more NG than available potential energy (APE). Though varying between ICs and with initial phase shift, NG increases with wavenumber. For middle wavelengths, NG is significant and positive using connected IC but negative or small using separated IC. Total energy and KE growth rates of short waves are very similar during the first 2 days for both ICs. Amplitude time series closely follow KE in all cases studied. APE has less overlap than does KE between the main modes present, so less NG occurs for APE than for KE. In separated IC cases, APE growth rates evolve consistent with emergence of an unstable normal mode and little NG.     

Steady-state size distributions for collisional populations:: analytical solution with size-dependent strength

The steady-state population of bodies resulting from a collisional cascade depends on how material strength varies with size. We find a simple expression for the power-law index of the population, given a power law that describes how material strength varies with size. This result is extended to the case relevant for the asteroid belt and Kuiper belt, in which the material strength is described by 2 separate power laws—one for small bodies and one for larger bodies. We find that the power-law index of the small body population is unaffected by the strength law for the large bodies, and vice versa. Simple analytical expressions describe a wave that is superimposed on the large body population because of the transition between the two power laws describing the strength. These analytical results yield excellent agreement with a numerical simulation of collisional evolution. These results will help to interpret observations of the asteroids and KBOs, and constrain the strength properties of those objects.     

Mars surface properties observed by earth-based radar at 70-, 12.5-, and 3.8-cm wavelengths

A review of Mars radar data obtained through the 1973 opposition confirms that the surface of the planet has many diverse characteristics. Analysis of the quasi-specular echo component shows changes in apparent reflectivity of at least 5 to 1. If attributed entirely to variations in surface material, these correspond to dielectric constants between 1.6 and 4.0. Values of rms surface slope on 1- to 100-m scales range from as low as 0.5° in tablelands near Vlles Marineris to more than 3.0° (the upper limit for which these analysis techniques are appropriate) in certain other areas such as inside Coprates Chasma itself. There is weak correlation between the small-scale surface characteristics inferred from radar and those inferred from Mariner 9 images, geologic maps derived from those images, and other remote sensing data sets. Topography, a large-scale surface characteristic for which good correlation exists between radar and other data sets, was not considered in this study. A search for guidelines which would allow extrapolation of radar properties to new areas on the basis of those studied has been singularly unsuccessful. Data obtained during the 1973 opposition at Arecibo, Goldstone, and Haystack Observatories indicate that the scattering behavior of Mars varies little over the 70- to 3.8-cm wavelength range. Comparison of 1971 and 1973 Goldstone results shows no detectable variation with time.     

The melting of asteroidal-sized bodies by unipolar dynamo induction from a primordial T Tauri sun

This paper examines the heating of asteroidal parent bodies by electrical induction during early solar evolution and prior to positioning of the sun onto the main sequence. Under the conditions assumed, which include a high initial solar spin rate, interplanetary electric fields of order 1 V/m would have existed in frames of reference comoving with the planets, leading to electrical heating from joule losses in the asteroidal interiors. The mechanism additionally requires the high plasma efflux characteristic of T Tauri objects and the presence of a circumstellar obscuration of the type commonly associated with early stellar objects. The proper combination of circumstellar obscuration, solar spin, solar wind flow, and starting planetary temperatures is shown to lead to asteroidal heating competitive with that found for a class of fossil radioactive species. The time dependence of the solar spin and plasma flow are shaped so as to be consistent with current views on the evolution to T Tauri objects and of the spin down of stars. Calculations also include cases of joint heating by fossil radionuclides and electrical induction, and show a complicated relationship due to the intrinsic nonlinearity of the electrical heating mechanism. Implications regarding the pre-main sequence dynamics of the sun are contained in the hypothesis of electrical heating if the contribution from radionuclides and gravitational accretion can be shown to be insufficient to account for the heating episode. Finally, some consequences of the mechanism applied to planets in the presence of an intense solar wind are considered.     

Self-similar shocked accretion of collisional gas with radiative cooling

We describe similarity solutions that characterize the collapse of collisional gas on to scale-free perturbations in an Einstein–de Sitter universe. We consider the effects of radiative cooling and derive self-similar solutions under the assumption that the cooling function is a power law of density and temperature, Λ( T , ρ )∝ ρ ^3/2 T . We use these results to test the ability of smooth particle hydrodynamics (SPH) techniques to follow the collapse and accretion of shocked, rapidly cooling gas in a cosmological context. Our SPH code reproduces the analytical results very well in cases that include or exclude radiative cooling. No substantial deviations from the predicted central mass accretion rates or from the temperature, density and velocity profiles are observed in well-resolved regions inside the shock radius. This test problem lends support to the reliability of SPH techniques to model the complex process of galaxy formation.