The Angular Resolution of Space-Based Gravitational Wave Detectors

Proposed space-based gravitational wave antennas involve satellites arrayed either in an equilateral triangle around the earth in the ecliptic plane (the ecliptic-plane option) or in an equilateral triangle orbiting the sun in such a way that the plane of the triangle is tilted at 60 degrees relative to the ecliptic (the precessing-plane option). In this paper, we explore the angular resolution of these two classes of detectors for two kinds of sources (essentially monochromatic compact binaries and coalescing massive-black-hole binaries) using time-domain expressions for the gravitational waveform that are accurate to 4/2 PN order. Our results display an interesting effect not previously reported in the literature, and underline the importance of including the higher-order PN terms in the waveform when predicting the angular resolution of ecliptic-plane detector arrays.Comment: 13 pages, 6 figures, submitted to Phys Rev D. The current version corrects an error in our original paper and adds some clarifying language. The error also required correction of the graphs now shown in Figures 3 through

A trapped mercury 199 ion frequency standard

Mercury 199 ions confined in an RF quadrupole trap and optically pumped by mercury 202 ion resonance light are investigated as the basis for a high performance frequency standard with commercial possibilities. Results achieved and estimates of the potential performance of such a standard are given

LISA detections of massive black hole inspirals: parameter extraction errors due to inaccurate template waveforms

The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at z <~ 5 with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a ~ 10^6 Msun MBHBs at z = 1 it should be possible to determine the two masses to ~ 0.1% and the sky location to ~ 1 degree. However, those are just the errors due to noise: there will be additional "theoretical" errors due to inaccuracies in our best model waveforms, which are still only approximate. The goal of this paper is to estimate the typical magnitude of these theoretical errors. We develop mathematical tools for this purpose, and apply them to a somewhat simplified version of the MBHB problem, in which we consider just the inspiral part of the waveform and neglect spin-induced precession, eccentricity, and PN amplitude corrections. For this simplified version, we estimate that theoretical uncertainties in sky position will typically be ~ 1 degree, i.e., comparable to the statistical uncertainty. For the mass and spin parameters, our results suggest that while theoretical errors will be rather small absolutely, they could still dominate over statistical errors (by roughly an order of magnitude) for the strongest sources. The tools developed here should be useful for estimating the magnitude of theoretical errors in many other problems in gravitational-wave astronomy.Comment: RevTeX4, 16 pages, 2 EPS figures. Corrected typos, clarified statement

The Effect of the LISA Response Function on Observations of Monochromatic Sources

The Laser Interferometer Space Antenna (LISA) is expected to provide the largest observational sample of binary systems of faint sub-solar mass compact objects, in particular white-dwarfs, whose radiation is monochromatic over most of the LISA observational window. Current astrophysical estimates suggest that the instrument will be able to resolve about 10000 such systems, with a large fraction of them at frequencies above 3 mHz, where the wavelength of gravitational waves becomes comparable to or shorter than the LISA arm-length. This affects the structure of the so-called LISA transfer function which cannot be treated as constant in this frequency range: it introduces characteristic phase and amplitude modulations that depend on the source location in the sky and the emission frequency. Here we investigate the effect of the LISA transfer function on detection and parameter estimation for monochromatic sources. For signal detection we show that filters constructed by approximating the transfer function as a constant (long wavelength approximation) introduce a negligible loss of signal-to-noise ratio -- the fitting factor always exceeds 0.97 -- for f below 10mHz, therefore in a frequency range where one would actually expect the approximation to fail. For parameter estimation, we conclude that in the range 3mHz to 30mHz the errors associated with parameter measurements differ from about 5% up to a factor of 10 (depending on the actual source parameters and emission frequency) with respect to those computed using the long wavelength approximation.Comment: replacement version with typos correcte

Design and implementation of a compliant robot with force feedback and strategy planning software

Force-feedback robotics techniques are being developed for automated precision assembly and servicing of NASA space flight equipment. Design and implementation of a prototype robot which provides compliance and monitors forces is in progress. Computer software to specify assembly steps and makes force feedback adjustments during assembly are coded and tested for three generically different precision mating problems. A model program demonstrates that a suitably autonomous robot can plan its own strategy

Testing Alternative Theories of Gravity using LISA

We investigate the possible bounds which could be placed on alternative theories of gravity using gravitational wave detection from inspiralling compact binaries with the proposed LISA space interferometer. Specifically, we estimate lower bounds on the coupling parameter \omega of scalar-tensor theories of the Brans-Dicke type and on the Compton wavelength of the graviton \lambda_g in hypothetical massive graviton theories. In these theories, modifications of the gravitational radiation damping formulae or of the propagation of the waves translate into a change in the phase evolution of the observed gravitational waveform. We obtain the bounds through the technique of matched filtering, employing the LISA Sensitivity Curve Generator (SCG), available online. For a neutron star inspiralling into a 10^3 M_sun black hole in the Virgo Cluster, in a two-year integration, we find a lower bound \omega > 3 * 10^5. For lower-mass black holes, the bound could be as large as 2 * 10^6. The bound is independent of LISA arm length, but is inversely proportional to the LISA position noise error. Lower bounds on the graviton Compton wavelength ranging from 10^15 km to 5 * 10^16 km can be obtained from one-year observations of massive binary black hole inspirals at cosmological distances (3 Gpc), for masses ranging from 10^4 to 10^7 M_sun. For the highest-mass systems (10^7 M_sun), the bound is proportional to (LISA arm length)^{1/2} and to (LISA acceleration noise)^{-1/2}. For the others, the bound is independent of these parameters because of the dominance of white-dwarf confusion noise in the relevant part of the frequency spectrum. These bounds improve and extend earlier work which used analytic formulae for the noise curves.Comment: 16 pages, 9 figures, submitted to Classical & Quantum Gravit

Orbital evolution of a test particle around a black hole: higher-order corrections

We study the orbital evolution of a radiation-damped binary in the extreme mass ratio limit, and the resulting waveforms, to one order beyond what can be obtained using the conservation laws approach. The equations of motion are solved perturbatively in the mass ratio (or the corresponding parameter in the scalar field toy model), using the self force, for quasi-circular orbits around a Schwarzschild black hole. This approach is applied for the scalar model. Higher-order corrections yield a phase shift which, if included, may make gravitational-wave astronomy potentially highly accurate.Comment: 4 pages, 3 Encapsulated PostScript figure

Prospects for gravitational-wave observations of neutron-star tidal disruption in neutron-star/black-hole binaries

For an inspiraling neutron-star/black-hole binary (NS/BH), we estimate the gravity-wave frequency f_td at the onset of NS tidal disruption. We model the NS as a tidally distorted, homogeneous, Newtonian ellipsoid on a circular, equatorial geodesic around a Kerr BH. We find that f_td depends strongly on the NS radius R, and estimate that LIGO-II (ca. 2006-2008) might measure R to 15% precision at 140 Mpc (about 1 event/yr under current estimates). This suggests that LIGO-II might extract valuable information about the NS equation of state from tidal-disruption waves.Comment: RevTeX, 4 pages, 2 EPS figures. Revised slightly, corrected typo

Gravitational Waves from coalescing binaries: Estimation of parameters

The paper presents a statistical model which reproduces the results of Monte Carlo simulations to estimate the parameters of the gravitational wave signal from a coalesing binary system. The model however is quite general and would be useful in other parameter estimation problems.Comment: LaTeX with RevTeX macros, 4 figure

The Cosmological Constant and Advanced Gravitational Wave Detectors

Interferometric gravitational wave detectors could measure the frequency sweep of a binary inspiral [characterized by its chirp mass] to high accuracy. The observed chirp mass is the intrinsic chirp mass of the binary source multiplied by $(1+z)$, where $z$ is the redshift of the source. Assuming a non-zero cosmological constant, we compute the expected redshift distribution of observed events for an advanced LIGO detector. We find that the redshift distribution has a robust and sizable dependence on the cosmological constant; the data from advanced LIGO detectors could provide an independent measurement of the cosmological constant.Comment: 13 pages plus 5 figure, LaTeX. Revised and final version, to appear in Phys. Rev.