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Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays

Gair, Jonathan R. and Romano, Joseph D. and Taylor, Stephen and Mingarelli, Chiara M. F. (2014) Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays. Physical Review D, 90 (8). Art. No. 082001. ISSN 2470-0010. doi:10.1103/PhysRevD.90.082001.

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We describe an alternative approach to the analysis of gravitational-wave backgrounds, based on the formalism used to characterize the polarization of the cosmic microwave background. In contrast to standard analyses, this approach makes no assumptions about the nature of the background and so has the potential to reveal much more about the physical processes that generated it. An arbitrary background can be decomposed into modes whose angular dependence on the sky is given by gradients and curls of spherical harmonics. We derive the pulsar timing overlap reduction functions for the individual modes, which are given by simple combinations of spherical harmonics evaluated at the pulsar locations. We show how these can be used to recover the components of an arbitrary background, giving explicit results for both isotropic and anisotropic uncorrelated backgrounds. We also find that the response of a pulsar timing array to curl modes is identically zero, so half of the gravitational-wave sky will never be observed using pulsar timing, no matter how many pulsars are included in the array. An isotropic, unpolarized and uncorrelated background can be accurately represented using only three modes, and so a search of this type will be only slightly more complicated than the standard cross-correlation search using the Hellings and Downs overlap reduction function. However, by measuring the components of individual modes of the background and checking for consistency with isotropy, this approach has the potential to reveal much more information. Each individual mode on its own describes a background that is correlated between different points on the sky. A measurement of the components that indicates the presence of correlations in the background on large angular scales would suggest startling new physics.

Item Type:Article
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URLURL TypeDescription Paper
Mingarelli, Chiara M. F.0000-0002-4307-1322
Additional Information:© 2014 American Physical Society. Published 1 October 2014; received 17 June 2014. J. G.’s work is supported by the Royal Society. J. D. R. acknowledges support from NSF Grants No. PHY-1205585 and CREST No. HRD-1242090. S. R. T. acknowledges the support of the STFC and the RAS. C.M. F.M. acknowledges the support of the RAS, Universitas 21 and a Marie Curie International Outgoing Fellowship within the 7th European Community Framework Programme. We thank Sanjit Mitra for initial discussions, and Bruce Allen and Chiara Caprini for many e-mail exchanges regarding models for correlated backgrounds. C. M. F. M. thanks Gary Hinshaw for pointing her to Ref. [40], and J. D. R. thanks Graham Woan for useful feedback regarding an earlier draft of the paper. The authors also thank the anonymous referee for useful comments on the manuscript. This research has made use of Python and its standard libraries: numpy and matplotlib. We have also made use of MEALPix (a Matlab implementation of HEALPix [68]), 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.
Funding AgencyGrant Number
Science and Technology Facilities Council (STFC)UNSPECIFIED
Universitas 21UNSPECIFIED
Marie Curie International Outgoing FellowshipUNSPECIFIED
Higher Education Funding Council for EnglandUNSPECIFIED
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Other Numbering System NameOther Numbering System ID
Space Radiation Laboratory2014-16
Issue or Number:8
Classification Code:PACS numbers: 04.80.Nn, 04.30.Db, 07.05.Kf, 95.55.Ym
Record Number:CaltechAUTHORS:20141204-113552353
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Official Citation:Gair, J., Romano, J. D., Taylor, S., & Mingarelli, C. M. F. (2014). Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays. Physical Review D, 90(8), 082001.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52393
Deposited On:04 Dec 2014 20:03
Last Modified:10 Nov 2021 19:40

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