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

The White Dwarf -- White Dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes, present the corresponding generalized spectral method needed to characterize such process, and make a comparison between our analytic results and those obtained by applying our method to the simulated data. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.Comment: 36 pages, 15 figure

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

<i>‘What retention’ means to me</i>: the position of the adult learner in student retention

Studies of student retention and progression overwhelmingly appear adopt definitions that place the institution, rather than the student, at the centre. Retention is most often conceived in terms of linear and continuous progress between institutionally identified start and end points. This paper reports on research that considered data from 38 in-depth interviews conducted with individuals who had characteristics often associated with non-traditional engagement in higher education who between 2006 and 2010 had studied an ‘Introduction to HE’ module at one distance higher education institution, some of whom had progressed to further study at that institution, some of whom had not. The research deployed a life histories approach to seek a finer grained understanding of how individuals conceptualise their own learning journey and experience, in order to reflect on institutional conceptions of student retention. The findings highlight potential anomalies hidden within institutional retention rates – large proportions of the interview participants who were not ‘retained’ by the institution reported successful progression to and in other learning institutions and environments, both formal and informal. Nearly all described positive perspectives on lifelong learning which were either engendered or improved by the learning undertaken. This attests to the complexity of individuals’ lives and provides clear evidence that institution-centric definitions of retention and progression are insufficient to create truly meaningful understanding of successful individual learning journeys and experiences. It is argued that only through careful consideration of the lived experience of students and a re-conception of measures of retention, will we be able to offer real insight into improving student retention

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

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

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

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