SyZyGy: A Straight Interferometric Spacecraft System for Gravity Wave Observations

We apply TDI, unfolding the general triangular configuration, to the special case of a linear array of three spacecraft. We show that such an array ("SyZyGy") has, compared with an equilateral triangle GW detector of the same scale, degraded (but non-zero) sensitivity at low-frequencies (f<<c/(arrany size)) but similar peak and high-frequency sensitivities to GWs. Sensitivity curves are presented for SyZyGys having various arm-lengths. A number of technical simplifications result from the linear configuration. These include only one faceted (e.g., cubical) proof mass per spacecraft, intra-spacecraft laser metrology needed only at the central spacecraft, placement in a single appropriate orbit can reduce Doppler drifts so that no laser beam modulation is required for ultra-stable oscillator noise calibration, and little or no time-dependent articulation of the telescopes to maintain pointing. Because SyZyGy's sensitivity falls off more sharply at low frequency than that of an equilateral triangular array, it may be more useful for GW observations in the band between those of ground-based interferometers (10-2000 Hz) and LISA (.1 mHz-.1 Hz). A SyZyGy with ~1 light- second scale could, for the same instrumental assumptions as LISA, make obseervations in this intermediate frequency GW band with 5 sigma sensitivity to sinusoidal waves of ~2.5 x 10^-23 in a year's integration.Comment: 13 pages, 6 figures; typos corrected, figure modified, references adde

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

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

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

The Effects of Orbital Motion on LISA Time Delay Interferometry

In an effort to eliminate laser phase noise in laser interferometer spaceborne gravitational wave detectors, several combinations of signals have been found that allow the laser noise to be canceled out while gravitational wave signals remain. This process is called time delay interferometry (TDI). In the papers that defined the TDI variables, their performance was evaluated in the limit that the gravitational wave detector is fixed in space. However, the performance depends on certain symmetries in the armlengths that are available if the detector is fixed in space, but that will be broken in the actual rotating and flexing configuration produced by the LISA orbits. In this paper we investigate the performance of these TDI variables for the real LISA orbits. First, addressing the effects of rotation, we verify Daniel Shaddock's result that the Sagnac variables will not cancel out the laser phase noise, and we also find the same result for the symmetric Sagnac variable. The loss of the latter variable would be particularly unfortunate since this variable also cancels out gravitational wave signal, allowing instrument noise in the detector to be isolated and measured. Fortunately, we have found a set of more complicated TDI variables, which we call Delta-Sagnac variables, one of which accomplishes the same goal as the symmetric Sagnac variable to good accuracy. Finally, however, as we investigate the effects of the flexing of the detector arms due to non-circular orbital motion, we show that all variables, including the interferometer variables, which survive the rotation-induced loss of direction symmetry, will not completely cancel laser phase noise when the armlengths are changing with time. This unavoidable problem will place a stringent requirement on laser stability of 5 Hz per root Hz.Comment: 12 pages, 2 figure

Low energy LIDARs for biomass applications

SilviLaser 2015, La Grande Motte, FRA, 28-/09/2015 - 30/09/2015International audienceA new approach for LIDAR altimetry mission for biomass applications ( tree height measurement ) is explored based on low emitted laser energy at high repetition fr equency. Low energy approach drastical ly reduces the laser induced risks. Altimetry performances meet preliminary science requirements . The proposed instrument design is compatible with a space mission

A hazard model of the probability of medical school dropout in the United Kingdom

From individual level longitudinal data for two entire cohorts of medical students in UK universities, we use multilevel models to analyse the probability that an individual student will drop out of medical school. We find that academic preparedness—both in terms of previous subjects studied and levels of attainment therein—is the major influence on withdrawal by medical students. Additionally, males and more mature students are more likely to withdraw than females or younger students respectively. We find evidence that the factors influencing the decision to transfer course differ from those affecting the decision to drop out for other reasons

Algebraic approach to time-delay data analysis for LISA

Cancellation of laser frequency noise in interferometers is crucial for attaining the requisite sensitivity of the triangular 3-spacecraft LISA configuration. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. Since it is impossible to maintain equal distances between spacecrafts, laser noise cancellation must be achieved by appropriately combining the six beams with appropriate time-delays. It has been shown in several recent papers that such combinations are possible. In this paper, we present a rigorous and systematic formalism based on algebraic geometrical methods involving computational commutative algebra, which generates in principle {\it all} the data combinations cancelling the laser frequency noise. The relevant data combinations form the first module of syzygies, as it is called in the literature of algebraic geometry. The module is over a polynomial ring in three variables, the three variables corresponding to the three time-delays around the LISA triangle. Specifically, we list several sets of generators for the module whose linear combinations with polynomial coefficients generate the entire module. We find that this formalism can also be extended in a straight forward way to cancel Doppler shifts due to optical bench motions. The two modules are infact isomorphic. We use our formalism to obtain the transfer functions for the six beams and for the generators. We specifically investigate monochromatic gravitational wave sources in the LISA band and carry out the maximisiation over linear combinations of the generators of the signal-to-noise ratios with the frequency and source direction angles as parameters.Comment: 27 Pages, 6 figure

Bayesian detection of unmodeled bursts of gravitational waves

The data analysis problem of coherently searching for unmodeled gravitational-wave bursts in the data generated by a global network of gravitational-wave observatories has been at the center of research for almost two decades. As data from these detectors is starting to be analyzed, a renewed interest in this problem has been sparked. A Bayesian approach to the problem of coherently searching for gravitational wave bursts with a network of ground-based interferometers is here presented. We demonstrate how to systematically incorporate prior information on the burst signal and its source into the analysis. This information may range from the very minimal, such as best-guess durations, bandwidths, or polarization content, to complete prior knowledge of the signal waveforms and the distribution of sources through spacetime. We show that this comprehensive Bayesian formulation contains several previously proposed detection statistics as special limiting cases, and demonstrate that it outperforms them.Comment: 18 pages, 3 figures, revisions based on referee comment