Detection, Measurement and Gravitational Radiation

TL;DR

This paper develops a statistical framework for assessing the sensitivity of gravitational wave detectors like LIGO and LAGOS, enabling the estimation of signal detectability and parameter accuracy in noisy data, with application to black hole signals.

Contribution

It introduces a method to quantify detector sensitivity and signal parameter uncertainty using probability distributions, applicable to designing and evaluating gravitational wave detectors.

Findings

Quantifies the probability of signal presence in noisy data.

Defines volumes in parameter space for signal parameter estimation.

Applies techniques to LIGO and LAGOS sensitivity to black hole signals.

Abstract

Here I examine how to determine the sensitivity of the LIGO, VIRGO, and LAGOS gravitational wave detectors to sources of gravitational radiation by considering the process by which data are analyzed in a noisy detector. By constructing the probability that the detector output is consistent with the presence of a signal, I show how to (1) quantify the uncertainty that the output contains a signal and is not simply noise, and (2) construct the probability distribution that the signal parameterization has a certain value. From the distribution and its mode I determine volumes $V(P)$ in parameter space such that actual signal parameters are in $V(P)$ with probability $P$. If we are {\em designing} a detector, or determining the suitability of an existing detector for observing a new source, then we don't have detector output to analyze but are interested in the ``most likely'' response of the detector to a signal. I exploit the techniques just described to determine the ``most likely'' volumes $V(P)$ for detector output corresponding to the source. Finally, as an example, I apply these techniques to anticipate the sensitivity of the LIGO and LAGOS detectors to the gravitational radiation from a perturbed Kerr black hole.