Introduction to the Analysis of Low-Frequency Gravitational Wave Data

The space-based gravitational wave detector LISA will observe in the low-frequency gravitational-wave band (0.1 mHz up to 1 Hz). LISA will search for a variety of expected signals, and when it detects a signal it will have to determine a number of parameters, such as the location of the source on the sky and the signal's polarisation. This requires pattern-matching, called matched filtering, which uses the best available theoretical predictions about the characteristics of waveforms. All the estimates of the sensitivity of LISA to various sources assume that the data analysis is done in the optimum way. Because these techniques are unfamiliar to many young physicists, I use the first part of this lecture to give a very basic introduction to time-series data analysis, including matched filtering. The second part of the lecture applies these techniques to LISA, showing how estimates of LISA's sensitivity can be made, and briefly commenting on aspects of the signal-analysis problem that are special to LISA.Comment: 20 page

Loosely coherent searches for sets of well-modeled signals

We introduce a high-performance implementation of a loosely coherent statistic sensitive to signals spanning a finite-dimensional manifold in parameter space. Results from full scale simulations on Gaussian noise are discussed, as well as implications for future searches for continuous gravitational waves. We demonstrate an improvement of more than an order of magnitude in analysis speed over previously available algorithms. As searches for continuous gravitational waves are computationally limited, the large speedup results in gain in sensitivity

Removing Line Interference from Gravitational Wave Interferometer Data

We describe a procedure to identify and remove a class of interference lines from gravitational wave interferometer data. We illustrate the usefulness of this technique applying it to prototype interferometer data and removing all those lines corresponding to the external electricity main supply and related features.Comment: Latex 6 pages, 5 figures. To appear in: "Gravitational Wave Detection II". Edt. Rie Sasaki; Universal Academy Press, Inc, Tokyo, Japa

An efficient Matched Filtering Algorithm for the Detection of Continuous Gravitational Wave Signals

We describe an efficient method of matched filtering over long (greater than 1 day) time baselines starting from Fourier transforms of short durations (roughly 30 minutes) of the data stream. This method plays a crucial role in the search algorithm developed by Schutz and Papa for the detection of continuous gravitational waves from pulsars. Also, we discuss the computational cost--saving approximations used in this method, and the resultant performance of the search algorithm.Comment: 4 pages, text only, accepted for publication in the proceedings of the 3rd Amaldi conference on gravitational wave

Gravitational Radiation

Gravity is one of the fundamental forces of Nature, and it is the dominant force in most astronomical systems. In common with all other phenomena, gravity must obey the principles of special relativity. In particular, gravitational forces must not be transmitted or communicated faster than light. This means that when the gravitational field of an object changes, the changes ripple outwards through space and take a finite time to reach other objects. These ripples are called gravitational radiation or gravitational waves. This article gives a brief introduction to the physics of gravitational radiation, including technical material suitable for non-specialist scientists

Searching for continuous gravitational wave signals: the hierarchical Hough transform algorithm

It is well known that matched filtering techniques cannot be applied for searching extensive parameter space volumes for continuous gravitational wave signals. This is the reason why alternative strategies are being pursued. Hierarchical strategies are best at investigating a large parameter space when there exist computational power constraints. Algorithms of this kind are being implemented by all the groups that are developing software for analyzing the data of the gravitational wave detectors that will come online in the next years. In this talk we will report about the hierarchical Hough transform method that the GEO 600 data analysis team at the Albert Einstein Institute is developing. The three step hierarchical algorithm has been described elsewhere. In this talk we will focus on some of the implementational aspects we are currently concerned with.Comment: 9 pages, 1 figure. To appear in the proceedings of the conference ``Gravitational waves: a challenge to theoretical astrophysics'', (June 5-9 2000, Trieste), ICTP Lecture Notes Serie

The response of interferometric gravitational wave detectors

The derivation of the response function of an interferometric gravitational wave detector is a paradigmatic calculation in the field of gravitational wave detection. Surprisingly, the standard derivation of the response wave detectors makes several unjustifiable assumptions, both conceptual and quantitative, regarding the coordinate trajectory and coordinate velocity of the null geodesic the light travels along. These errors, which appear to have remained unrecognized for at least 35 years, render the "standard" derivation inadequate and misleading as an archetype calculation. Here we identify the flaws in the existing derivation and provide, in full detail, a correct derivation of the response of a single-bounce Michelson interferometer to gravitational waves, following a procedure that will always yield correct results; compare it to the "standard", but incorrect, derivation; show where the earlier mistakes were made; and identify the general conditions under which the "standard" derivation will yield correct results. By a fortuitous set of circumstances, not generally so, the final result is the same in the case of Minkowski background spacetime, synchronous coordinates, transverse-traceless gauge metric perturbations, and arm mirrors at coordinate rest.Comment: 10 pages, one figure, as accepted to PR