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Non-sky-averaged sensitivity curves for space-based gravitational-wave observatories

Vallisneri, Michele and Galley, Chad R. (2012) Non-sky-averaged sensitivity curves for space-based gravitational-wave observatories. Classical and Quantum Gravity, 29 (12). Art. No. 124015. ISSN 0264-9381. http://resolver.caltech.edu/CaltechAUTHORS:20130305-143752417

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Abstract

The signal-to-noise ratio (SNR) is used in gravitational-wave observations as the basic figure of merit for detection confidence and, together with the Fisher matrix, for the amount of physical information that can be extracted from a detected signal. SNRs are usually computed from a sensitivity curve, which describes the gravitational-wave amplitude needed by a monochromatic source of given frequency to achieve a threshold SNR. Although the term 'sensitivity' is used loosely to refer to the detector's noise spectral density, the two quantities are not the same: the sensitivity includes also the frequency- and orientation-dependent response of the detector to gravitational waves and takes into account the duration of observation. For interferometric space-based detectors similar to LISA, which are sensitive to long-lived signals and have constantly changing position and orientation, exact SNRs need to be computed on a source-by-source basis. For convenience, most authors prefer to work with sky-averaged sensitivities, accepting inaccurate SNRs for individual sources and giving up control over the statistical distribution of SNRs for source populations. In this paper, we describe a straightforward end-to-end recipe to compute the non-sky-averaged sensitivity of interferometric space-based detectors of any geometry. This recipe includes the effects of spacecraft motion and of seasonal variations in the partially subtracted confusion foreground from Galactic binaries, and it can be used to generate a sampling distribution of sensitivities for a given source population. In effect, we derive error bars for the sky-averaged sensitivity curve, which provide a stringent statistical interpretation for previously unqualified statements about sky-averaged SNRs. As a worked-out example, we consider isotropic and Galactic-disk populations of monochromatic sources, as observed with the 'classic LISA' configuration. We confirm that the (standard) inverse-rms average sensitivity for the isotropic population remains the same whether or not the LISA orbits are included in the computation. However, detector motion tightens the distribution of sensitivities, so for 50% of sources the sensitivity is within 30% of its average. For the Galactic-disk population, the average and the distribution of the sensitivity for a moving detector turn out to be similar to the isotropic case.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/0264-9381/29/12/124015DOIArticle
https://arxiv.org/abs/1201.3684arXivDiscussion Paper
Additional Information:© 2012 IOP Publishing Ltd. Received 23 January 2012, in final form 20 March 2012. Published 1 June 2012. MV is grateful to J Armstrong, F Estabrook and M Tinto for teaching him about TDI and sensitivity calculations. This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. MV was supported by the LISA Mission Science Office and by the JPL RTD program. CG was supported by an appointment to the NASA Postdoctoral Program at the JPL administered by Oak Ridge Associated Universities through a contract with NASA. Copyright 2012 California Institute of Technology.
Group:TAPIR
Funders:
Funding AgencyGrant Number
NASA/JPL/CaltechUNSPECIFIED
JPL Research and Technology Development FundUNSPECIFIED
NASA Postdoctoral ProgramUNSPECIFIED
Classification Code:PACS numbers: 04.80.Nn, 95.55.Ym
Record Number:10.1088/0264-9381/29/12/124015
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130305-143752417
Official Citation:Michele Vallisneri and Chad R Galley 2012 Class. Quantum Grav. 29 124015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37319
Collection:CaltechAUTHORS
Deposited By: JoAnn Boyd
Deposited On:06 Mar 2013 19:40
Last Modified:11 Dec 2018 00:17

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