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A survey is presented of current research in the theory of gravitational radiation. The mathematical structure of gravitational radiation is stressed. Furthermore, the radiation problem is treated independently from other problems in gravitation. The development proceeds candidly through three points of view - scalar, rector, and tensor radiation theory - and the corresponding results are stated.
Consideration is given to the possibility of detection of an isotropic background gravitational radiation of a stochastic nature by the method of Doppler tracking of spacecraft. Attention is given in the geometrical optics limit, to the general formula for the frequency shift of an electromagnetic signal in the gravitational radiation field, and it is shown to be gauge independent. The propagation of a free electromagnetic wave in a gravitational radiation field is examined with the conclusion that no resonance phenomena can be expected. Finally, the 'Doppler noise' due to a stochastic background is evaluated, and it is shown to depend on the total energy density of the background and a parameter that is a characteristic of the radiation spectrum and the detection system used.
Topics discussed are gravitational wave detection experiments, the theoretical foundations of gravitational wave physics, black holes, and neutron stars. Particular consideration is given to methods for circumventing the quantum limit for gravitational wave detectors, global problems in numerical relativity, massive black holes and gravitational radiation, the role of binaries in gravitational wave production, and astrophysical sources of gravitational radiation.
The problem of astrophysical sources of detectable gravitational radiation is considered from the stellar-evolution viewpoint. Calculations are presented which indicate that the final stages of evolution may well be dominated by rapidly rotating, collapsing cores which develop nonaxisymmetric configurations. Such events emit large amounts of gravitational radiation which should be detectable in the near future.
Gravitational radiation from spinning ellipsoid of uniform density, finding smaller numerical coefficients than for spinning rod
Gravitational radiation calculation of spinning ellipsoid of uniform density for estimation of energy loss rate of collapsing neutron star
Pulsed gravitational radiation emitted by dense star clusters
Gravitational radiation induced by a test particle falling into an extreme Kerr black hole was investigated analytically. Assuming the radiation is dominated by the infinite sequence of quasi-normal modes which has the limiting frequency m/(2M), where m is an azimuthal eigenvalue and M is the mass of the black hole, it was found that the radiated energy diverges logarithmically in time. Then the back reaction to the black hole was evaluated by appealing to the energy and angular momentum conservation laws. It was found that the radiation has a tendency to increase the ratio of the angular momentum to mass of the black hole, which is completely different from non-extreme case, while the contribution of the test particle is to decrease it.
Emission of gravitational radiation was shown to prevent particles of nonzero rest mass from exceeding the speed of gravitational radiation.
RX J1914.4+2456 is a candidate double-degenerate binary (AM CVn) with a putative 569 s orbital period. If this identification is correct, then it has one of the shortest binary orbital periods known, and gravitational radiation should drive the orbital evolution and mass transfer if the binary is semi-detached. Here we report the results of a coherent timing study of the archival ROSAT data for RX J1914.4+2456. We performed a phase coherent timing analysis using all five ROSAT observations spanning a four-year period. We demonstrate that all the data can be phase connected, and we show that the 1.756 mHz orbital frequency is increasing at a rate of 1.5 +/- 0.4 x 10(exp -17) Hz/s consistent with the expected loss of angular momentum from the binary system via gravitational radiation. In addition to providing evidence for the emission of gravitational waves, our measurement of the orbital v(dot) constrains models for the X-ray emission and the nature of the secondary. If stable mass accretion drives the X-ray flux, then a positive v(dot) is inconsistent with a degenerate donor. A helium burning dwarf is compatible if indeed such systems can have periods as short as that of RX J1914.4+2456, an open theoretical question. Our measurement of a positive v(dot) is consistent with the unipolar induction model of Wu et al. which does not require accretion to drive the X-ray flux. We discuss how future timing measurements of RX J1914.4+2456 (and systems like it) with for example, Chandra and XMM-Newton, can provide a unique probe of the interaction between mass loss and gravitational radiation. We also discuss the importance of such measurements in the context of gravitational wave detection from space, such as is expected in the future with the LISA mission.
Robertson-Walker cosmologies with matter, radiation, and nonzero cosmological constant are examined to determine how much high-frequency gravitational radiation may be present at the current epoch without violating observations. Evolutionary limits due to a maximum redshift requirement, minimum age requirement, and magnitude-redshift relation are used to rule out most M2 models and to restrict singular models to those satisfying an acceleration parameter limit of -4.4-5.6, a matter density limit of less than 4.7, and a radiation density limit of less than 3.4. These limits are compared to direct limits from various experimental searches for a cosmic gravitational radiation background; it is found that several experiments are very close to a significant sensitivity.
The spectral flux of gravitational radiation incident on earth from the Galactic W UMa binaries, unevolved binaries, cataclysmic binaries, neutron star binaries, black hole-neutron star binaries, and close white dwarf binary (CWDB) systems is calculated. The peak values for the strain amplitude hv produced by the binaries are: log hv = -17.0/sq rt Hz at log v = -4.40 Hz for W UMa's; log hv = -16.5/sq rt Hz at log v = -5.50 Hz for unevolved binaries; log hv = -18.2/sq rt Hz at log v = -5.15 Hz for neutron star binaries; log hv = -17.0/sq rt Hz at log v = -4.7 Hz for black hole-neutron star binaries; log hv = -18.0 /sq rt Hz at log v = -4.10 Hz for cataclysmic binaries, and log hv = -27.0/sq rt Hz at log v = -4.0 Hz for CWDBs. The gravitational flux at ultralow frequencies is emitted mainly by unevolved binaries. The integrated flux incident on earth is about 2.4 x 10 to the -9th ergs/sq cm/s.
We discuss spacecraft Doppler tracking searches for gravitational waves in which Doppler data recorded on the ground are linearly combined with Doppler measurements made on board a spacecraft. By using the four-link radio system first proposed by Vessot and Levine, we describe a new method for removing from the combined data the frequency fluctuations due to the Earth troposphere, ionosphere, and mechanical vibrations of the antenna on the ground. This technique provides also a way for reducing by several orders of magnitude, at selected Fourier components, the frequency fluctuations due to other noise sources, such as the clock on board the spacecraft or the antenna and buffeting of the probe by nongravitational forces. In this respect spacecraft Doppler tracking can be regarded as a xylophone detector of gravitational radiation. In the assumption of calibrating the frequency fluctuations induced by the interplanetary plasma, a strain sensitivity equal to 4.7 x 10(exp -18) at 10(exp -3) Hz is estimated. This experimental technique could be extended to other tests of the theory of relativity, and to radio science experiments that rely on high-precision Doppler measurements.
We present a detailed descriptive analysis of the gravitational radiation from black-hole binary mergers of non-spinning black holes, based on numerical simulations of systems varying from equal-mass to a 6:1 mass ratio. Our primary goal is to present relatively complete information about the waveforms, including all the leading multipolar components, to interested researchers. In our analysis, we pursue the simplest physical description of the dominant features in the radiation, providing an interpretation of the waveforms in terms of an implicit rotating source. This interpretation applies uniformly to the full wavetrain, from inspiral through ringdown. We emphasize strong relationships among the l = m modes that persist through the full wavetrain. Exploring the structure of the waveforms in more detail, we conduct detailed analytic fitting of the late-time frequency evolution, identifying a key quantitative feature shared by the l = m modes among all mass-ratios. We identify relationships, with a simple interpretation in terms of the implicit rotating source, among the evolution of frequency and amplitude, which hold for the late-time radiation. These detailed relationships provide sufficient information about the late-time radiation to yield a predictive model for the late-time waveforms, an alternative to the common practice of modeling by a sum of quasinormal mode overtones. We demonstrate an application of this in a new effective-one-body-based analytic waveform model.
RX J0806.3+1527 is a candidate double degenerate binary with possibly the shortest known orbital period. The source shows an $\approx 100 \%$ X-ray intensity modulation at the putative orbital frequency of 3.11 mHz (321.5 s). If the system is a detached, ultracompact binary gravitational radiation should drive spin-up with a magnitude of $\dot\nu \sim 10(exp -16)$ Hi s$(exp -l}$. Efforts to constrain the X-ray frequency evolution to date have met with mixed success, principally due to the sparseness of earlier observations. Here we describe the results of the first phase coherent X-ray monitoring campaign on RX J0806.3+1527 with {\it Chandra) . We obtained a total of 70 ksec of exposure in 6 epochs logarithmically spaced over 320 days. With these data we conclusively show that the X-ray frequency is increasing at a rate of $3.77 \pm\ 0.8 \times l0(exp -16)$ Hz s$(exp -l)$. Using the ephemeris derived from the new data we are able to phase up all the earlier {\it Chandra) and ROSAT data and show they are consistent with a constant $\dot\nu = 3.63 \pm 0.06 \times 10(exp -16)$ Hz s$(exp -1)s over the past decade. This value appears consistent with that recently derived by Israel et al. largely from monitoring of the optical modulation, and is in rough agreement with the solutions reported initially by Hakala et al., based on ground-based optical observations. The large and stable $\dot\nu$ over a decade is consistent with gravitational radiation losses driving the evolution. An intermediate polar (IP) scenario where the observed X-ray period is the spin period of an accreting white dwarf appears less tenable because the observed $\dot\nu$ requires an $\dot m \approx 2 \times 10(exp -8)$ $M-{\odot)$ yr$(exp -l)$, that is much larger than that inferred from the observed X-ray luminosity (although this depends on the uncertain distance and bolometric corrections), and it is difficult to drive such a high $\dot m$ in a binary system with parameters consistent with all the multiwavelength data. If the ultracompact scenario is
A 50-minute period for a binary system harboring an X-ray burster would allow several alternatives for the mass-giving secondary, including an H-shell burning-plus-He degenerate core composite model. The burst properties of X1916-053 are presently used to argue against the He degenerate as well as the He main sequence solutions and to estimate whether, for any of the other solutions, the mass transfer rate could be consistent with that expected from gravitational radiation (GR). Within an uncertainty of a factor of 2, the transfer rate for the composite model solution is consistent with gravitational radiation, but enhancement by other mechanisms should be investigated.
RX J0806.3+1527 is a candidate double degenerate binary with possibly the shortest known orbital period. The source shows an approximately equal to 100% X-ray intensity modulation at the putative orbital frequency of 3.11 mHz (321.5 s). If the system is a detached, ultracompact binary gravitational radiation should drive spin-up with a magnitude of nu(sup dot) approximately 10(exp -16) Hz per second. Efforts to constrain the X-ray frequency evolution to date have met with mixed success, principally due to the sparseness of earlier observations. Here we describe the results of the first phase coherent X-ray monitoring campaign on RX J0806.3+1527 with Chandra. We obtained a total of 70 ksec of exposure in 6 epochs logarithmically spaced over 320 days. With these data we conclusively show that the X-ray frequency is increasing at a rate of 3.77 plus or minus 0.8 x 10(exp -16) Hz per second. Using the ephemeris derived from the new data we are able to phase up all the earlier Chandra and ROSAT data and show they are consistent with a constant nu(sup dot) = 3.63 plus or minus 0.06 x 10(exp -16) Hz per second over the past decade. This value appears consistent with that recently derived by Israel et al. largely from monitoring of the optical modulation, and is in rough agreement with the solutions reported initially by Hakala et al., based on ground-based optical observations. The large and stable nu(sup dot) over a decade is consistent with gravitational radiation losses driving the evolution. An intermediate polar (IP) scenario where the observed X-ray period is the spin period of an accreting white dwarf appears less tenable because the observed nu(sup dot) requires an m(sup dot) approximately equal to 4 x 10 (exp -8) solar mass yr(sup -l), that is much larger than that inferred from the observed X-ray luminosity (although this depends on the uncertain distance and bolometric corrections), and it is difficult to drive such a high m(sup dot) in a binary system with parameters consistent with all the multiwavelength data. If the ultracompact scenario is correct, then the X-ray flux cannot be powered by stable accretion which would drive the components apart, suggesting a new type of energy source (perhaps electromagnetic) may power the X-ray flux.
A scalar potential is used to derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically, the eigenfunctions and eigenfrequencies of isothermal disks are computed, and the way in which these results can be generalized to other disk models is indicated. The (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity are also computed. It is found that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.