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 Response Function and Parameter Estimation

We investigate the response function of LISA and consider the adequacy of its commonly used approximation in the high-frequency range of the observational band. We concentrate on monochromatic binary systems, such as white dwarf binaries. We find that above a few mHz the approxmation starts becoming increasingly inaccurate. The transfer function introduces additional amplitude and phase modulations in the measured signal that influence parameter estmation and, if not properly accounted for, lead to losses of signal-to-noise ratio.Comment: 4 pages, 2 figures, amaldi 5 conference proceeding

Towards the solution of the relativistic gravitational radiation reaction problem for binary black holes

Here we present the results of applying the generalized Riemann zeta-function regularization method to the gravitational radiation reaction problem. We analyze in detail the headon collision of two nonspinning black holes with extreme mass ratio. The resulting reaction force on the smaller hole is repulsive. We discuss the possible extensions of these method to generic orbits and spinning black holes. The determination of corrected trajectories allows to add second perturbative corrections with the consequent increase in the accuracy of computed waveforms.Comment: Contribution to the Proceedings of the 3rd LISA Symposiu

Macular Bioaccelerometers on Earth and in Space

Space flight offers the opportunity to study linear bioaccelerometers (vestibular maculas) in the virtual absence of a primary stimulus, gravitational acceleration. Macular research in space is particularly important to NASA because the bioaccelerometers are proving to be weighted neural networks in which information is distributed for parallel processing. Neural networks are plastic and highly adaptive to new environments. Combined morphological-physiological studies of maculas fixed in space and following flight should reveal macular adaptive responses to microgravity, and their time-course. Ground-based research, already begun, using computer-assisted, 3-dimensional reconstruction of macular terminal fields will lead to development of computer models of functioning maculas. This research should continue in conjunction with physiological studies, including work with multichannel electrodes. The results of such a combined effort could usher in a new era in understanding vestibular function on Earth and in space. They can also provide a rational basis for counter-measures to space motion sickness, which may prove troublesome as space voyager encounter new gravitational fields on planets, or must re-adapt to 1 g upon return to earth

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

Angular Resolution of the LISA Gravitational Wave Detector

We calculate the angular resolution of the planned LISA detector, a space-based laser interferometer for measuring low-frequency gravitational waves from galactic and extragalactic sources. LISA is not a pointed instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will measure simultaneously both polarization components of incoming gravitational waves, so the data will consist of two time series. All physical properties of the source, including its position, must be extracted from these time series. LISA's angular resolution is therefore not a fixed quantity, but rather depends on the type of signal and on how much other information must be extracted. Information about the source position will be encoded in the measured signal in three ways: 1) through the relative amplitudes and phases of the two polarization components, 2) through the periodic Doppler shift imposed on the signal by the detector's motion around the Sun, and 3) through the further modulation of the signal caused by the detector's time-varying orientation. We derive the basic formulae required to calculate the LISA's angular resolution $\Delta \Omega_S$ for a given source. We then evaluate $\Delta \Omega_S$ for two sources of particular interest: monchromatic sources and mergers of supermassive black holes. For these two types of sources, we calculate (in the high signal-to-noise approximation) the full variance-covariance matrix, which gives the accuracy to which all source parameters can be measured. Since our results on LISA's angular resolution depend mainly on gross features of the detector geometry, orbit, and noise curve, we expect these results to be fairly insensitive to modest changes in detector design that may occur between now and launch. We also expect that our calculations could be easily modified to apply to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil

Solving the Darwin problem in the first post-Newtonian approximation of general relativity

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian(PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for corotating binary(we call it ISCCO). It is found that by the first PN effect, the orbital separation of the binary at the ISCCO becomes small with increase of the compactness of each star, and as a result, the orbital angular velocity at the ISCCO increases. These behaviors agree with previous numerical works.Comment: 33 pages, revtex, 4 figures(eps), accepted for publication in Phys. Rev.

Recovering the stationary phase condition for accurately obtaining scattering and tunneling times

The stationary phase method is often employed for computing tunneling {\em phase} times of analytically-continuous {\em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of this method without considering the barrier boundary effects leads to some misconceptions in the interpretation of the phase times. After reexamining the above barrier diffusion problem where we notice the wave packet collision necessarily leads to the possibility of multiple reflected and transmitted wave packets, we study the phase times for tunneling/reflecting particles in a framework where an idea of multiple wave packet decomposition is recovered. To partially overcome the analytical incongruities which rise up when tunneling phase time expressions are obtained, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a one dimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted waves.Comment: 32 pages, 5 figures, 1 tabl