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Phase-coherent mapping of gravitational-wave backgrounds using ground-based laser interferometers

Romano, J. D. and Taylor, Stephen and Cornish, Neil J. and Gair, Jonathan R. and Mingarelli, C. M. F. and van Haasteren, R. (2015) Phase-coherent mapping of gravitational-wave backgrounds using ground-based laser interferometers. Physical Review D, 92 (4). Art. No. 042003. ISSN 2470-0010.

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We extend the formalisms developed in Gair et al. [1] and Cornish and van Haasteren [2] to create maps of gravitational-wave backgrounds using a network of ground-based laser interferometers. We show that in contrast to pulsar timing arrays, which are insensitive to half of the gravitational-wave sky (the curl modes), a network of ground-based interferometers is sensitive to both the gradient and curl components of the background. The spatial separation of a network of interferometers, or of a single interferometer at di erent times during its rotational and orbital motion around the Sun, allows for recovery of both components. We derive expressions for the response functions of a laser interferometer in the small-antenna limit, and use these expressions to calculate the overlap reduction function for a pair of interferometers. We also construct maximum-likelihood estimates of the + and -polarization modes of the gravitational-wave sky in terms of the response matrix for a network of ground-based interferometers, evaluated at discrete times during Earth's rotational and orbital motion around the Sun. We demonstrate the feasibility of this approach for some simple simulated backgrounds (a single point source and spatially-extended distributions having only grad or curl components), calculating maximum-likelihood sky maps and uncertainty maps based on the (pseudo)inverse of the response matrix. The distinction between this approach and standard methods for mapping gravitational-wave power is also discussed

Item Type:Article
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URLURL TypeDescription Paper
Mingarelli, C. M. F.0000-0002-4307-1322
van Haasteren, R.0000-0002-6428-2620
Additional Information:Published 18 August 2015. J. D. R. acknowledges support from National Science Foundation Awards No. PHY-1205585 and No. CREST HRD-1242090. This research was in part supported by S. T.’s appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Oak Ridge Associated Universities through a contract with NASA. N. J. C. acknowledges support from National Science Foundation Award No. PHY-1306702 and the NANOGrav Physics Frontier Center, Award No. NSF PFC-1430284. J. G.’s work is supported by the Royal Society. C. M. F. M.’s work is supported by a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme. R. v. H. acknowledges support by NASA through Einstein Fellowship Grant No. PF3-140116. J. D. R. thanks Malik Rakhmanov for useful discussions regarding pseudoinverse calculations when the system of equations is underdetermined. This research has made use of PYTHON and its standard libraries: NUMPY and MATPLOTLIB. We have also made use of MEALPIX (MATLAB implementation of HEALPix [28]), developed by the GWAstro Research Group and available from This work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (, provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council. This paper has been assigned LIGO DCC No. LIGO-P1500065.
Group:Space Radiation Laboratory, TAPIR
Funding AgencyGrant Number
Marie Curie International Outgoing FellowshipUNSPECIFIED
NASA Einstein FellowshipPF3-140116
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Other Numbering System NameOther Numbering System ID
Space Radiation Laboratory2015-37
Issue or Number:4
Record Number:CaltechAUTHORS:20160622-090020070
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68567
Deposited By: Deborah Miles
Deposited On:23 Jun 2016 16:18
Last Modified:09 Mar 2020 13:19

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