Data Combinations Accounting for LISA Spacecraft Motion

LISA is an array of three spacecraft in an approximately equilateral triangle configuration which will be used as a low-frequency gravitational wave detector. We present here new generalizations of the Michelson- and Sagnac-type time-delay interferometry data combinations. These combinations cancel laser phase noise in the presence of different up and down propagation delays in each arm of the array, and slowly varying systematic motion of the spacecraft. The gravitational wave sensitivities of these generalized combinations are the same as previously computed for the stationary cases, although the combinations are now more complicated. We introduce a diagrammatic representation to illustrate that these combinations are actually synthesized equal-arm interferometers.Comment: 10 pages, 3 figure

Noise characterization for LISA

We consider the general problem of estimating the inflight LISA noise power spectra and cross-spectra, which are needed for detecting and estimating the gravitational wave signals present in the LISA data. For the LISA baseline design and in the long wavelength limit, we bound the error on all spectrum estimators that rely on the use of the fully symmetric Sagnac combination ($\zeta$). This procedure avoids biases in the estimation that would otherwise be introduced by the presence of a strong galactic background in the LISA data. We specialize our discussion to the detection and study of the galactic white dwarf-white dwarf binary stochastic signal.Comment: 9 figure

Time-Delay Interferometry

Equal-arm interferometric detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector. In order to solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called Time-Delay Interferometry (or TDI). This article provides an overview of the theory and mathematical foundations of TDI as it will be implemented by the forthcoming space-based interferometers such as the Laser Interferometer Space Antenna (LISA) mission. We have purposely left out from this first version of our ``Living Review'' article on TDI all the results of more practical and experimental nature, as well as all the aspects of TDI that the data analysts will need to account for when analyzing the LISA TDI data combinations. Our forthcoming ``second edition'' of this review paper will include these topics.Comment: 51 pages, 11 figures. To appear in: Living Reviews. Added conten

Sensitivity and parameter-estimation precision for alternate LISA configurations

We describe a simple framework to assess the LISA scientific performance (more specifically, its sensitivity and expected parameter-estimation precision for prescribed gravitational-wave signals) under the assumption of failure of one or two inter-spacecraft laser measurements (links) and of one to four intra-spacecraft laser measurements. We apply the framework to the simple case of measuring the LISA sensitivity to monochromatic circular binaries, and the LISA parameter-estimation precision for the gravitational-wave polarization angle of these systems. Compared to the six-link baseline configuration, the five-link case is characterized by a small loss in signal-to-noise ratio (SNR) in the high-frequency section of the LISA band; the four-link case shows a reduction by a factor of sqrt(2) at low frequencies, and by up to ~2 at high frequencies. The uncertainty in the estimate of polarization, as computed in the Fisher-matrix formalism, also worsens when moving from six to five, and then to four links: this can be explained by the reduced SNR available in those configurations (except for observations shorter than three months, where five and six links do better than four even with the same SNR). In addition, we prove (for generic signals) that the SNR and Fisher matrix are invariant with respect to the choice of a basis of TDI observables; rather, they depend only on which inter-spacecraft and intra-spacecraft measurements are available.Comment: 17 pages, 4 EPS figures, IOP style, corrected CQG versio

Implementation of Time-Delay Interferometry for LISA

We discuss the baseline optical configuration for the Laser Interferometer Space Antenna (LISA) mission, in which the lasers are not free-running, but rather one of them is used as the main frequency reference generator (the {\it master}) and the remaining five as {\it slaves}, these being phase-locked to the master (the {\it master-slave configuration}). Under the condition that the frequency fluctuations due to the optical transponders can be made negligible with respect to the secondary LISA noise sources (mainly proof-mass and shot noises), we show that the entire space of interferometric combinations LISA can generate when operated with six independent lasers (the {\it one-way method}) can also be constructed with the {\it master-slave} system design. The corresponding hardware trade-off analysis for these two optical designs is presented, which indicates that the two sets of systems needed for implementing the {\it one-way method}, and the {\it master-slave configuration}, are essentially identical. Either operational mode could therefore be implemented without major implications on the hardware configuration. We then.......Comment: 39 pages, 6 figures, 2 table

Pulsar Timing Sensitivities to Gravitational Waves from Relativistic Metric Theories of Gravity

Pulsar timing experiments aimed at the detection of gravitational radiation have been performed for decades now. With the forthcoming construction of large arrays capable of tracking multiple millisecond pulsars, it is very likely we will be able to make the first detection of gravitational radiation in the nano-Hertz band, and test Einstein's theory of relativity by measuring the polarization components of the detected signals. Since a gravitational wave predicted by the most general relativistic metric theory of gravity accounts for {\it six} polarization modes (the usual two Einstein's tensor polarizations as well as two vector and two scalar wave components), we have estimated the single-antenna sensitivities to these six polarizations. We find pulsar timing experiments to be significantly more sensitive, over their entire observational frequency band ($\approx 10^{-9} - 10^{-6}$ Hz), to scalar-longitudinal and vector waves than to scalar-transverse and tensor waves. At $10^{-7}$ Hz and with pulsars at a distance of $1$ kpc, for instance, we estimate an average sensitivity to scalar-longitudinal waves that is more than two orders of magnitude better than the sensitivity to tensor waves. Our results imply that a direct detection of gravitational radiation by pulsar timing will result into a test of the theory of general relativity that is more stringent than that based on monitoring the decay of the orbital period of a binary system.Comment: 11 pages, 2 figures. Submitted to Phys. Rev.

Data Processing for LISA's Laser Interferometer Tracking System (LITS)

The purpose of this paper is twofold. First, we will present recent results on the data processing for LISA, including algorithms for elimination of clock jitter noise and discussion of the generation of the data averages that will eventually need to be telemetered to the ground. Second, we will argue, based partly on these results, that a laser interferometer tracking system (LITS) that employs independent lasers in each spacecraft is preferable for reasons of simplicity to that in which the lasers in two of the spacecraft are locked to the incoming beam from the third.Comment: 5 pages, Proceedings of the Third LISA Symposium (Golm, Germany, 2000

Optimal statistic for detecting gravitational wave signals from binary inspirals with LISA

A binary compact object early in its inspiral phase will be picked up by its nearly monochromatic gravitational radiation by LISA. But even this innocuous appearing candidate poses interesting detection challenges. The data that will be scanned for such sources will be a set of three functions of LISA's twelve data streams obtained through time-delay interferometry, which is necessary to cancel the noise contributions from laser-frequency fluctuations and optical-bench motions to these data streams. We call these three functions pseudo-detectors. The sensitivity of any pseudo-detector to a given sky position is a function of LISA's orbital position. Moreover, at a given point in LISA's orbit, each pseudo-detector has a different sensitivity to the same sky position. In this work, we obtain the optimal statistic for detecting gravitational wave signals, such as from compact binaries early in their inspiral stage, in LISA data. We also present how the sensitivity of LISA, defined by this optimal statistic, varies as a function of sky position and LISA's orbital location. Finally, we show how a real-time search for inspiral signals can be implemented on the LISA data by constructing a bank of templates in the sky positions.Comment: 22 pages, 15 eps figures, Latex, uses iopart style/class files. Based on talk given at the 8th Gravitational Wave Data Analysis Workshop, Milwaukee, USA, December 17-20, 2003. Accepted for publication in Class. Quant. Gra

TDIR: Time-Delay Interferometric Ranging for Space-Borne Gravitational-Wave Detectors

Space-borne interferometric gravitational-wave detectors, sensitive in the low-frequency (mHz) band, will fly in the next decade. In these detectors, the spacecraft-to-spacecraft light-travel times will necessarily be unequal and time-varying, and (because of aberration) will have different values on up- and down-links. In such unequal-armlength interferometers, laser phase noise will be canceled by taking linear combinations of the laser-phase observables measured between pairs of spacecraft, appropriately time-shifted by the light propagation times along the corresponding arms. This procedure, known as time-delay interferometry (TDI), requires an accurate knowledge of the light-time delays as functions of time. Here we propose a high-accuracy technique to estimate these time delays and study its use in the context of the Laser Interferometer Space Antenna (LISA) mission. We refer to this ranging technique, which relies on the TDI combinations themselves, as Time-Delay Interferometric Ranging (TDIR). For every TDI combination, we show that, by minimizing the rms power in that combination (averaged over integration times $\sim 10^4$ s) with respect to the time-delay parameters, we obtain estimates of the time delays accurate enough to cancel laser noise to a level well below the secondary noises. Thus TDIR allows the implementation of TDI without the use of dedicated inter-spacecraft ranging systems, with a potential simplification of the LISA design. In this paper we define the TDIR procedure formally, and we characterize its expected performance via simulations with the \textit{Synthetic LISA} software package.Comment: 5 pages, 2 figure