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The potential of observations of gravitational lens systems for the determination of cosmological constants and for tests of the nature and distribution of dark matter is illustrated. The advantages and disadvantages of gravitational lenses as cosmological probes are evaluated.
Following a few general comments on gravitational lenses from an observer's perspective, the currently available observations of the six known gravitational lenses are summarized. Attention is called to some regularities and peculiarities of the properties of the known lenses and to how they might be interpreted. The most important conclusions, relevant to the dark matter problem, which can be obtained from current observations are that the distributions of mass and light appear to be quite different in at least some of the lensing objects and that objects with projected mass/brightness values about 10 times larger than those ordinarily associated with galaxies exist and are not too rare.
Models of gravitational microlensing at small and large optical depth are presented, with a special emphasis on the time delays between microimages. The time distribution of microimage arrival times is random when the microobjects responsible for the lensing are randomly distributed. If the microobjects are clustered in space, then microimages are clustered in time. In some models there are many pairs of microimages with a very small time separation. It is proposed that the recently discovered recurrent soft gamma-ray burster GB 790107, for which more than 50 bursts were detected, is a single event multiply imaged due to gravitational microlensing by an ensemble of nonrandomly distributed microobjects, perhaps a rich cluster of galaxies. Some observational tests of this hypothesis are proposed. If correct, the hypothesis requires the burster to be at a cosmological distance, perhaps farther away than the most distant quasars.
In this paper, the properties of a special class of inhomogeneous cosmological models and the interaction of the inhomogeneities with the evolution of the background geometry and matter are studied. The cosmological model is chosen so that the initial inhomogeneities evolve into 'plane' gravitational waves propagating through a smooth Bianchi I dust background. It is shown how the inhomogeneities interact with matter, 3 K radiation, and the background geometry, causing the expansion to slow down in some regions and speed up in others. It is also shown how the gravitational waves can produce a 'dragging of the inertial frame' which will affect the observed distribution of matter and 3 K radiation. In particular, this frame-dragging effect can account for a major fraction of the obsserved dipole component between the 3 K background radiation and the rest frame of global matter, an effect usually assumed to have been produced by large-scale local motion.
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.
The observed properties of the six systems generally accepted as gravitational lenses are compared with the properties predicted for the images of point-mass and distributed mass deflectors. Taken as a statistical distribution, the characteristics of the six known systems strongly suggest the existence of a super-massive black hole as the effective deflecting mass in one or more of these systems. If the deflecting mass in a gravitational lens is a black hole, the distance to the deflecting mass can be determined directly from the difference in light travel time along the separate image paths. (No direct solution for the distance to the deflecting mass exists when the deflecting mass is a galaxy or a cluster of galaxies). Geometric parallaxes of objects at 1000 Mpc distance are of obvious importance in a wide variety of cosmological studies.
A cosmological background of gravitational waves induces angular deviations in the propagation of light traversing it. All observed astrophysical sources might therefore have varying apparent positions, with the time dependence set by the wave period. Wavelengths greater than a kiloparsec are examined, so the positions are frozen but in general correlated. Comparison with observed galaxy-galaxy n-point correlation functions provide a spectrum-independent limit on the energy density of gravitational waves with wavelengths between a few tens of kiloparsecs and a few hundred megaparsecs of Omega(GW) less than 0.001.
Global water redistriburtion between the oceans, atmosphere and continents causes changes in the earth's rotation and gravitational field. To conserve water mass, the effect of the small uniform change in sea-level must be considered. Explicit formulas are provided for these sea-level corrections to the gravitational Stokes coefficients, polar motion and length of day. In two recent publications, this sea-level correction term for polar motion was given incorrectly. These errors which arose from normalization conventions with the ocean function are corrected.
It is demonstrated, by an explicit calculation, that a single, isolated Schwarzschild gravitational lens leads to a vanishing net total amplification on its own, without any 'help' from other lenses. It is shown that, in the limit of small M/R (where M is the mass of the lens in geometrical units and R is the distance from the source to the observers), the positive net total amplification, obtained from the classical approximation of the amplification for small impact angle lensing, is balanced by a negative net total amplification from the first-order term in M/R in an approximation of the amplification for large impact angle lensing derived here. The relation of these results to the common interpretation of average flux conservation by gravitational lenses is discussed as due to the collective action of many lenses in a cosmological framework.
The gravitational lens hypothesis is tested for 1613+267 A,B by comparing the detailed line widths and shapes of the 2799-A Mg II and semiforbidden 1909-A C-III lines in each component. Following subtraction of an interpolating polynomial fit to the continua and the determination of a single optimum scaling factor (an amplification ratio of 2.83), reasonable agreement between the profiles of both lines in the two composites is obtained. Comparison of these lines to those in an unrelated quasar with a similar redshift and apparent magnitude does not produce a good match. It is suggested that the observed match in the 1635+267 A,B spectra arises from gravitational lensing.
Gravitationally lensed images of the quasar 0957+561 have been observed at 13 cm wavelength using a six-antenna VLBI array with nearly milliarcsecond resolution. Models of the observed surface brightness distribution of each of the A and B images provide support of the gravitational lens hypothesis. A value of the magnitude of the relative image magnification A/B of 0.64 + or - 0.03 is obtained.
Various Cu-Pb-Al alloys were directionally solidified under 1-g conditions and alternating high-g/low-g conditions (achieved using NSAS's KC-135 aircraft) as a means of studying the influence of interfacial energies and gravitational levels on the resulting microstructures. Directional solidification of low Al content alloys was found to result in samples with coarser more irregular microstructures than in alloys with high Al contents under all the gravity conditions considered. Structures are correlated with interfacial energies, growth rates, and gravitational levels.
The statistical properties of gravitational lensing due to smooth but nonuniform distributions of matter are considered. It is found that a majority of triple images had a parity characteristic for 'shear-induced' lensing. Almost all cases of triple or multiple imaging were associated with large surface density enhancements, and lensing objects were present between the images. Thus, the observed gravitational lens candidates for which no lensing object has been detected between the images are unlikely to be a result of asymmetric distribution of mass external to the image circle. In a model with smoothly variable surface mass density, moderately and highly amplified images tended to be single rather than multiple. An opposite trend was found in models which had singularities in the surface mass distribution.
The evolution of self-gravitating gaseous disks in active galactic nuclei on scales of about 10-1000 pc is investigated. Star formation is a plausible outcome of the Jeans instability operating in a disk which violates the criterion for local stability. Even a low efficiency of star formation would deplete the gaseous disk on a short time scale and create a flat stellar system. These systems can evolve (sphericalize) secularly by means of stellar encounters but this process appears to be too slow to be important. Such flattened stellar systems may be common in the circumnuclear regions of disk galaxies. Conventional viscosities are inefficient in building anew the accretion process even in a cosmological time. Strongly self-gravitating disks are unstable to global nonaxisymmetric modes, which can induce radial inflow of gas in a short dynamical time. The latter effect is studied in a separate paper.
The spherical harmonic equation for the gravitational potential inside the earth is presented. The equation satisfies Poisson's equation and converges uniformly. It obviates the need for downward continuation of the exterior potential with its attendant convergence difficulties but of course requires some knowledge of the earth's density distribution. The equation is used to derive the general expression for the geophysical measurement of the gravitational constant G made inside the earth, such as in boreholes and mine shafts. Numerical evidence is also presented to show that the long- to intermediate-wavelength gravity anomalies can masquerade as the 'fifth force' if not properly corrected for.
The external gravitational field produced by a rigid body of uniform density but irregular shape is formulated in terms of spherical harmonics. The formalism is applied to the Martian satellite Phobos. Based on a three-dimensional shape model of Phobos by Duxbury (1989), the gravitational coefficients up to degree and order 4 for a homogeneous Phobos are computed. In particular, J2 is found to be 0.105. The in-plane libration amplitude of a homogeneous Phobos is predicted to be 0.97 deg, within the rather large uncertainty of the observed value of 0.78 + or - 0.4 deg.
An outline is given that estimates the expected gravitational wave background, based on plausible pregalactic sources. Some cosmologically significant limits can be put on incoherent gravitational wave background arising from pregalactic cosmic evolution. The spectral region of cosmically generated and cosmically limited radiation is, at long periods, P greater than 1 year, in contrast to more recent cosmological sources, which have P approx. 10 to 10(exp -3).
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.