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NASA NTRS1978

Hydrogen emission-line spectra in quasars and active galactic nuclei

An attempt is made to account for the observational fact that the intensity ratios of the lower Balmer lines seen in emission from QSOs, type 1 Seyfert galaxies, and other related active galaxies are not what would be expected from the conventional picture of lines generated in a recombining hydrogen plasma. Previous observations of emission-line intensities in QSOs and Seyfert galaxies are reviewed. The various processes included in the rate coefficients of the calculations are then described, viz., free-free, bound-free, and bound-bound transitions, radiative transfer, and angular-momentum mixing. The strengths of the various emission lines are calculated by using more accurate values for the transition rates, including excitation and deexcitation simultaneously, and providing for finite rates in optically forbidden transitions. Numerical results are presented for the cases of ground-state collisional excitation, reabsorption of the upper Balmer lines, and collisional deexcitation. The results are applied to construct a model for the emission-line gas in a QSO and to discuss limits on models of Seyfert galaxies.

Krolik, J. H.↗

NASA NTRS1978

Fission origin of the moon - Cause and timing

A new scenario is offered for the origin of the moon. It is assumed that the earth formed initially with about the maximum amount of angular momentum consistent with dynamical stability. This state is approximated by the secularly unstable Maclaurin spheroids (highly flattened hamburger-shaped bodies). It is shown that the earth cannot depart from this state at a reasonable rate as long as its viscosity is in the range of liquid rock. Since core formation supplies about 1600 kJ/kg, the earth will not leave this state until core formation is complete. When cooling produces a rise in viscosity, the earth will necessarily evolve along a path which is approximated by the Riemann ellipsoids (which have rapid internal motion). The evolution is toward a Jacobi ellipsoid, but it is intercepted by the development of a third-harmonic (pear-shaped) instability, which is catastrophic and leads to fission. The process of fission itself may be fundamentally analogous to the breaking of a wave in water. We cannot exclude the possibility that some other planets evolved similarly.

Okeefe, J. A.↗

NASA NTRS1979

Method and turbine for extracting kinetic energy from a stream of two-phase fluid

An axial flow separator turbine is described which includes a number of nozzles for delivering streams of a two-phase fluid along linear paths. A phase separator which responsively separates the vapor and liquid is characterized by concentrically related annuli supported for rotation within the paths. The separator has endless channels for confining the liquid under the influence of centrifugal forces. A vapor turbine fan extracts kinetic energy from the liquid. Angular momentum of both the liquid phase and the vapor phase of the fluid is converted to torque.

Elliott, D. G.↗

NASA NTRS1979

Ion beam probing of electrostatic fields

The determination of a cylindrically symmetric, time-independent electrostatic potential V in a magnetic field B with the same symmetry by measurements of the deflection of a primary beam of ions is analyzed and substantiated by examples. Special attention is given to the requirements on canonical angular momentum and total energy set by an arbitrary, nonmonotone V, to scaling laws obtained by normalization, and to the analogy with ionospheric sounding. The inversion procedure with the Abel analysis of an equivalent problem with a one-dimensional fictitious potential is used in a numerical experiment with application to the NASA Lewis Modified Penning Discharge. The determination of V from a study of secondary beams of ions with increased charge produced by hot plasma electrons is also analyzed, both from a general point of view and with application to the NASA Lewis SUMMA experiment. Simple formulas and geometrical constructions are given for the minimum energy necessary to reach the axis, the whole plasma, and any point in the magnetic field. The common, simplifying assumption that V is a small perturbation is critically and constructively analyzed; an iteration scheme for successively correcting the orbits and points of ionization for the electrostatic potential is suggested.

Persson, H.↗

NASA NTRS1978

Space construction base control system

Aspects of an attitude control system were studied and developed for a large space base that is structurally flexible and whose mass properties change rather dramatically during its orbital lifetime. Topics of discussion include the following: (1) space base orbital pointing and maneuvering; (2) angular momentum sizing of actuators; (3) momentum desaturation selection and sizing; (4) multilevel control technique applied to configuration one; (5) one-dimensional model simulation; (6) N-body discrete coordinate simulation; (7) structural analysis math model formulation; and (8) discussion of control problems and control methods.

Source record↗

NASA NTRS1978

Computer experiments on the effect of retrograde stars in disk galaxies

Using large-scale N-body calculations for flat disk galaxies, we examine the effect of reversing the angular momentum for various fractions of the stars upon the global bar-forming mode. The initial conditions for these simulations are based on stationary states of two classes of models: the isochrones studied recently by Kalnajs by means of linear theory, and a model resembling the Schmidt model of our own Galaxy. In both cases, as the fraction of retrograde stars is increased, the growth of the bar-forming mode is inhibited (although not eliminated). These N-body results for the isochrones agree with the predictions of linear theory, quantitatively as well as qualitatively.

Zang, T. A.↗

NASA NTRS1979

Dynamics of a stellar bar

The dynamical properties of a prolate bar have been studied by means of a three-dimensional computer model. The bar pattern rotates in the sense of the total angular momentum. The mean particle motion is a rapid streaming in the direction of pattern rotation as seen from a frame that rotates with the bar. Rotation rates that would be inferred from observation are significantly (2-3 times) faster than the pattern rotation speed. Velocity dispersions are anisotropic with the largest component along the bar. Particles oscillate in the bar potential significantly faster than pattern rotation. About 25% of the star orbits are near 2:2:1 resonance with the slow motion along the bar. Particle motion is highly ordered in the bar. Observable properties are described; where comparisons can be made, observable properties are in agreement with observations of brightness contours, velocity fields, and velocity dispersions. The bar has nearly exponential density profiles.

Miller, R. H.↗

NASA NTRS1979

Coupled motion of rigid bodies about their center of mass

Nontrivial analytical solutions for the coupled motion of two rigid bodies about their center of mass are obtained on the assumptions that the rigid bodies are coupled by a massless rigid boom and that no external forces are acting on the system. Both relative rotational and translational motions of the two bodies are considered. General equations of motion are derived by regarding the two bodies as consisting of two distinct systems of particles and by applying the principle of conservation of angular momentum. It is shown that a basic nontrivial solution can be obtained for the translational problem if an assumption is made concerning the relative orientation of one principal axis of inertia of each body and that fundamental nontrivial solutions are readily obtained for the rotational problem if an additional assumption is made with respect to the symmetry of one body. Certain stability criteria are found for some of these motions by defining regions of constraint for the relative translational and rotational elements.

Jezewski, D. J.↗

NASA NTRS1979

Synchronous rotation in magnetic X-ray binaries

AM Herculis is thought to be a binary stellar system that contains an accreting magnetic degenerate dwarf whose rotation is synchronous with the orbital period. This synchronism is remarkable, particularly because of the small moment of inertia of a degenerate dwarf and the large specific angular momentum of the accreted matter. This paper demonstrates that ohmic dissipation from the magnetic interaction of the stars is capable of bringing about exact synchronism, provided that some other process has brought the rotation period of the degenerate dwarf to the same order of magnitude as the orbital period. It is also shown that magnetostatic interaction in the synchronous state leads to oscillatory drifts in phase about exact synchronism with periods of approximately 1-10 yr. These phase drifts could manifest themselves in long-term periodic variability in the X-ray or optical properties of the source. Accretion torques could excite such oscillatory motions but need not disrupt synchronism once it has been established.

Joss, P. C.↗

NASA NTRS1979

Average photospheric poloidal and toroidal magnetic field components near solar minimum

Average (over longitude and time) photospheric magnetic field components are derived from 3-min Stanford magnetograms made near the solar minimum of cycle 21. The average magnetograph signal is found to behave as the projection of a vector for measurements made across the disk. The poloidal field exhibits the familiar dipolar structure near the poles, with a measured signal in the line Fe I 5250 A of about 1 G. At low latitudes the poloidal field has the polarity of the poles, but is of reduced magnitude (about 0.1 G). A net photospheric toroidal field with a broad latitudinal extent is found. The polarity of the toroidal field is opposite in the northern and southern hemispheres and has the same sense as subsurface flux tubes giving rise to active regions of solar cycle 21. These observations are used to discuss large-scale electric currents crossing the photosphere and angular momentum loss to the solar wind.

Duvall, T. L., Jr.↗

NASA NTRS1979

Tidal interactions in the expanding universe - The formation of prolate systems

The study estimates the magnitude of the anisotropy that can be tidally induced in neighboring initially spherical protostructures, be they protogalaxies, protoclusters, or even uncollapsed density enhancements in the large-scale structure of the universe. It is shown that the linear analysis of tidal interactions developed by Peebles (1969) predicts that the anisotropy energy of a perturbation grows to first order in a small dimensionless parameter, whereas the net angular momentum acquired is of second order. A simple model is presented for the growth of anisotropy by tidal interactions during the nonlinear stage of the development of perturbations. A possible observational test is described of the alignment predicted by the model between the orientations of large-scale perturbations and the positions of neighboring density enhancements.

Binney, J.↗

NASA NTRS1979

How tidal heating in Io drives the Galilean orbital resonance locks

The mechanisms by which orbital resonance locks are maintained among Io, Europa and Ganymede are analyzed, and the effects of the dissipative tides in Jupiter and Io on their establishment and evolution are considered. According to the proposed model, initially all three satellites are in orbits far from the 2:1 commensurabilities or the three body lock. The tide raised on Io damps down the free eccentricity; only modest tidal heating occurs. Subsequently the dissipative tide raised on Jupiter by Io causes Io's orbit to spiral outwards; Io approaches the 2:1 commensurability with Europa. Io's forced eccentricity increases rapidly to a critical value, and thereafter the resonant interaction causes Europa's orbit to expand at half that of Io's orbit. A fluid core is probably formed as the result of tidal heating. Finally Europa approaches the 2:1 commensurability, angular momentum is transferred from Europa's orbit to Ganymede's, and a steady state is attained. On the basis of the observed three-body resonance amplitude (0.066 deg), it is concluded that three-body resonance may have formed less than 500 million years ago; a measurement of the rate of tidal heating in Io may determine the Q value of both Io and Jupiter. Upper and lower limits for the Jovian Q value of 2 million and 20,000 are suggested.

Yoder, C. F.↗

NASA NTRS1979

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Hoots, F. R.↗

NASA NTRS1979

On the interweaving of partial cross sections of different parity

Partial cross sections of definite parity, calculated for electronic-rotational energy transfer in the F +H2 collision system, interweave with increasing total angular momentum J. An explanation, in terms of diabatic curve crossings induced by the centrifugal potential in the body-fixed coordinate system, predicts the interweaving to occur only in systems having half-integer J.

Devries, P. L.↗

NASA NTRS1979

The interaction between giant gaseous protoplanets and the primitive solar nebula

The manner in which a giant gaseous protoplanet becomes embedded in the primitive solar nebula determines surface boundary conditions which must be used in studying the evolution of such objects. On the one hand, if the system resembles a contact binary system, then the envelope of the protoplanet should approach the entropy of the surrounding nebula. On the other hand angular momentum transfer by resonance and tidal effects between the nebula and the protoplanet may cause the nebula to exhibit a zone of avoidance near the protoplanet, thus inhibiting exchange of material. This problem has been studied with a computer program developed by D. N. C. Lin which simulates disk hydrodynamics by particle motions with dissipation. These studies suggest that for expected values of the protoplanet/protosun mass ratios, significant inhibition of mass exchange is likely, so that it is a reasonable next step to undertake protoplanet evolution studies with the imposition of minimum protoplanet surface temperatures.

Cameron, A. G. W.↗

NASA NTRS1980

Some evolutionary considerations of Beta Cephei stars

The evolutionary aspects of massive population 1 stars were investigated. Semiconvection was treated in two different ways, and included mass loss both in the early as well as later spectra stages. The effect of rotation was taken into account and the time evolution of angular momentum of these models was studied. The effect of differential rotation due to the faster rotating interiors and slowed down surface layers are briefly described.

Sreennivasan, S. R.↗

NASA NTRS1980

Tables of stark level transition probabilities and branching ratios in hydrogen-like atoms

The transition probabilities which are given in terms of n prime k prime and n k are tabulated. No additional summing or averaging is necessary. The electric quantum number k plays the role of the angular momentum quantum number l in the presence of an electric field. The branching ratios between stark levels are also tabulated. Necessary formulas for the transition probabilities and branching ratios are given. Symmetries are discussed and selection rules are given. Some disagreements for some branching ratios are found between the present calculation and the measurement of Mark and Wierl. The transition probability multiplied by the statistical weight of the initial state is called the static intensity J sub S, while the branching ratios are called the dynamic intensity J sub D.

Omidvar, K.↗

NASA NTRS1980

Boundary-layer behavior of the flow at the inner edge of black hole accretion disks

The flow of accreting material into black holes from Keplerian disks surrounding them is studied. Solving the system of radial structure equations in Schwarzschild geometry for the case where the kinematic viscosity is constant, the paper discovers a boundary layer at the disk's inner edge, where the flow becomes non-Keplerian. It is also shown that, despite the operation of viscous stresses across this inner edge and the presence of the boundary layer there, very little extra energy or angular momentum is radiated or transported outward from inside that radius - a result many have often assumed but no one has carefully demonstrated. These results constitute a solution to the problem of adequately describing the flow across the inner edge and properly setting the boundary conditions there and at the event horizon.

Stoeger, W. R.↗