Time-domain implementation of the optimal cross-correlation statistic for stochastic gravitational-wave background searches in pulsar timing data

Sydney J. Chamberlin, Jolien D. E. Creighton, Xavier Siemens, Paul Demorest, Justin Ellis, Larry R. Price, and Joseph D. Romano
Phys. Rev. D 91, 044048 – Published 27 February 2015

Abstract

Supermassive black hole binaries, cosmic strings, relic gravitational waves from inflation, and first-order phase transitions in the early Universe are expected to contribute to a stochastic background of gravitational waves in the 109107Hz frequency band. Pulsar timing arrays (PTAs) exploit the high-precision timing of radio pulsars to detect signals at such frequencies. Here we present a time-domain implementation of the optimal cross-correlation statistic for stochastic background searches in PTA data. Due to the irregular sampling typical of PTA data as well as the use of a timing model to predict the times of arrival of radio pulses, time-domain methods are better-suited for gravitational-wave data analysis of such data. We present a derivation of the optimal cross-correlation statistic starting from the likelihood function, a method to produce simulated stochastic background signals, and a rigorous derivation of the scaling laws for the signal-to-noise ratio of the cross-correlation statistic in the two relevant PTA regimes: the weak-signal limit where instrumental noise dominates over the gravitational-wave signal at all frequencies, and a second regime where the gravitational-wave signal dominates at the lowest frequencies.

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  • Received 30 October 2014

DOI:https://doi.org/10.1103/PhysRevD.91.044048

© 2015 American Physical Society

Authors & Affiliations

Sydney J. Chamberlin*, Jolien D. E. Creighton, and Xavier Siemens

  • Center for Gravitation, Cosmology, and Astrophysics, Department of Physics, University of Wisconsin–Milwaukee, Milwaukee, Wisconsin 53201, USA

Paul Demorest§

  • National Radio Astronomy Observatory, Charlottesville, Virginia 22903 USA

Justin Ellis¶,**

  • Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA

Larry R. Price††

  • LIGO Laboratory, California Institute of Technology, Pasadena, California 91125, USA

Joseph D. Romano‡‡

  • Department of Physics and Astronomy and Center for Gravitational-Wave Astronomy, University of Texas at Brownsville, Brownsville, Texas 78520, USA

  • *sydc@gravity.phys.uwm.edu
  • jolien@gravity.phys.uwm.edu
  • siemens@gravity.phys.uwm.edu
  • §pdemores@nrao.edu
  • Justin.A.Ellis@jpl.nasa.gov
  • **Einstein Fellow
  • ††larryp@caltech.edu
  • ‡‡joe@phys.utb.edu

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Issue

Vol. 91, Iss. 4 — 15 February 2015

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