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 and Clock-Noise Calibration

The Laser Interferometer Space Antenna is a joint ESA-NASA space-mission to detect and study mHz cosmic gravitational waves. The trajectories followed by its three spacecraft result in unequal- and time-varying arms, requiring use of the Time-Delay Interferometry (TDI) post- processing technique to cancel the laser phase noises affecting the heterodyne one-way Doppler measurements. Although the second-generation formulation of TDI cancels the laser phase noises when the array is both rotating and "flexing", second-generation TDI combinations for which the phase fluctuations of the onboard ultra stable oscillators (USOs) can be calibrated out have not appeared yet in the literature. In this article we present the solution of this problem by generalizing to the realistic LISA trajectory the USO calibration algorithm derived by Armstrong, Estabrook and Tinto for a static configuration.Comment: This article is 17 pages long and contains 2 figure

Gravitational wave detection with single-laser atom interferometers

We present a new general design approach of a broad-band detector of gravitational radiation that relies on two atom interferometers separated by a distance L. In this scheme, only one arm and one laser will be used for operating the two atom interferometers. We consider atoms in the atom interferometers not only as perfect inertial reference sensors, but also as highly stable clocks. Atomic coherence is intrinsically stable and can be many orders of magnitude more stable than a laser. The unique one-laser configuration allows us to then apply time-delay interferometry to the responses of the two atom interferometers, thereby canceling the laser phase fluctuations while preserving the gravitational wave signal in the resulting data set. Our approach appears very promising. We plan to investigate further its practicality and detailed sensitivity analysis.Comment: Paper submitted to General Relativity and Gravitation as part of the prceedings of the International Workshop on Gravitational Waves Detection with Atom Interferometry (Florence, February 2009)

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

The LISA Time-Delay Interferometry Zero-Signal Solution. I: Geometrical Properties

Time-Delay Interferometry (TDI) is the data processing technique needed for generating interferometric combinations of data measured by the multiple Doppler readouts available onboard the three LISA spacecraft. Within the space of all possible interferometric combinations TDI can generate, we have derived a specific combination that has zero-response to the gravitational wave signal, and called it the {\it Zero-Signal Solution} (ZSS). This is a two-parameter family of linear combinations of the generators of the TDI space, and its response to a gravitational wave becomes null when these two parameters coincide with the values of the angles of the source location in the sky. Remarkably, the ZSS does not rely on any assumptions about the gravitational waveform, and in fact it works for waveforms of any kind. Our approach is analogous to the data analysis method introduced by G\"ursel & Tinto in the context of networks of Earth-based, wide-band, interferometric gravitational wave detectors observing in coincidence a gravitational wave burst. The ZSS should be regarded as an application of the G\"ursel & Tinto method to the LISA data.Comment: 29 pages, 17 Figure

Searching for Gravitational Waves with a Geostationary Interferometer

We analyze the sensitivities of a geostationary gravitational wave interferometer mission operating in the sub-Hertz band. Because of its smaller armlength, in the lower part of its accessible frequency band ($10^{-4} - 2 \times 10^{-2}$ Hz) our proposed Earth-orbiting detector will be less sensitive, by a factor of about seventy, than the Laser Interferometer Space Antenna (LISA) mission. In the higher part of its band instead ($2 \times 10^{-2} - 10$ Hz), our proposed interferometer will have the capability of observing super-massive black holes (SMBHs) with masses smaller than $\sim 10^{6}$ M$_{\odot}$. With good event rates for these systems, a geostationary interferometer will be able to accurately probe the astrophysical scenarios that account for their formation.Comment: 33 pages, 9 eps figure