Engineering topics
Publications and source records attributed to Wahlquist, H. D..
Doppler tracking experiments using the earth and a distant spacecraft as separated test masses have been used for gravitational wave searches in the low-frequency band. Here we describe the experiment, including the transfer functions of the signals and noises to the Doppler observable, and present the noise statistics and compare them with the pre-experiment noise budget.
From March 21 to April 11, 1993 the Galileo, Mars Observer and Ulysses spacecraft were tracked in a coincidence experiment, searching for low-frequency (milihertz gravitational radiation.
By adopting Nester's 4-dimensional special orthonormal frames, the tetrad equations for vacum gravity are put into explicitly causal and symmetric hyperbolic form, independent of any time slicing or other gauge or coordinate specialization.
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The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.
Since the optimum size of a gravitational wave detector is the wave length, interplanetary dimensions are needed for the mHz band of interest. Doppler tracking of Ulysses will provide the most sensitive attempt to date at the detection of gravitational waves in the low frequency band. The driving noise source is the fluctuations in the refractive index of interplanetary plasma. This dictates the timing of the experiment to be near solar opposition and sets the target accuracy for the fractional frequency change at 3.0 x 10 exp -14 for integration times of the order of 1000 sec. The instrumentation utilized by the experiment is distributed between the radio systems on the spacecraft and the seven participating ground stations of the Deep Space Network and Medicina. Preliminary analysis is available of the measurements taken during the Ulysses first opposition test.
Since condensed massive objects in binary systems should generate observable periodic gravitational radiation, a large fraction of which may appear in one harmonic of the orbital frequency, monochromatic Doppler frequency perturbations were searched for at about 9000 discrete frequencies in the 0.0005-0.0333-Hz band using predetection data taken with the Pioneer 11 spacecraft. The results of the search are presented, and formal sensitivities for the possible signals are discussed. The results are interpreted as observational thresholds for possible incident gravitational wave trains having polarization states and propagation directions that are a priori unknown.
Attention is given to the spectral energy distributions of nine high-redshift quasars between 1250 and 10,000 A. The distributions steepen shortward of about 1200 A in all but one object. The steepening's lack of correlation with QSO luminosity suggests that it arises from absorption by intervening material along the line of sight. Reddening may contribute to the steepening of the QSO continua, if dust lies along the line of sight to the continuum source, and is difficult to assess quantitatively. In QSOs with redshift sufficiently high for Lyman-alpha to be observed at high resolution, it is possible to account for the observed continuum steepening by the Lyman continuum absorption corresponding to the narrow Lyman-alpha absorption lines seen.
Attempts to identify a periodic gravitational wave signal from the binary Geminga in the reduced Doppler data from the Pioneer 10 spacecraft are reported. The study was performed to examine the possibility that the observed 160 min solar oscillation is driven by a gravitational wave from the binary, which has a period exactly one cycle different from the solar oscillation. Three 12 hr passes of Doppler data from Pioneer 10, now beyond the orbit of Neptune, were subjected to FFT analysis to detect a spectral gravitational wave signature. None was found. Least squares analysis of all low noise data from 1981 to characterize the amplitude and phase of a signal from Geminga also produced a null result. Finally, an upper bound was calculated for the polarization component of the potentially observable gravitational strain.
The paper deals with the spectra of six quasars, ranging in redshift from 0.23 to 2.04, obtained with the 45-cm telescope mounted on the IUE satellite. The average emission-line intensity ratio for L-alpha to H beta and the detection of higher-order Lyman emission lines in two objects are found to be inconsistent with a simple optically thick recombination model. The Lyman and Balmer line velocity profiles are identical. The emission lines in 3C 351 can be decomposed into sharp and broad components, with the sharp lines consistent with the recombination model.
IUE observations indicate that the spectrum of 3C 273 is similar to that of other large-redshift quasars. There is a large excess of flux in the range 2400 A to 5300 A, which encompasses the Balmer jump region but which does not appear to be explainable by Balmer emission. The intensity ratio of Lyman-alpha to H-beta is 5.5, in agreement with other measures and a factor 6 smaller than the recombination value. The only absorption lines in the spectrum are due to our Galaxy. There is marginal evidence for a depression of the continuum shortward of the Lyman-alpha emission line, but the errors are too large to warrant any conclusion that 3C 273 has a rich absorption-line spectrum such as that seen in large-redshift quasars. The absence of emission and absorption lines of Fe II leads to the conclusion that resonance fluorescence probably produces the visual Fe II emission lines.
The prospects of using spacecraft Doppler tracking, in NASA missions, for the detection of gravitational waves are examined. The sensitivity limits of such detection are characterized in terms of plasma scintillation, troposphere scintillation, receiver noise, MDA and ODA quantization error, and clock jitter. Current and possible future NASA missions that will involve gravitational wave experiments are briefly reviewed, including the Galileo, solar polar, Halley/Tempel-2, and solar probe missions.
This paper reports a calculation of the effect of gravitational radiation on the observed Doppler shift of a sinusoidal electromagnetic signal transmitted to, and coherently transponded from, distant spacecraft. It is found that the effect of plane gravitational waves on such observations is not intuitively immediate, and in fact depends sensitively on the spacecraft direction, which suggests the possibility of detecting such plane waves by simultaneous Doppler tracking of several spacecraft. The need for broad band gravitational wave observations, the required stabilities of time keeping standards, and astrophysical sources expected in the Very Low Frequency band are briefly discussed.
The MACSYMA file was written to perform these operations and discusses the improvements and additions which are needed to accomplish a complete and efficient implementation. Examples of differential form calculations are displayed.
The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.
The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.
A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.