Detecting a Stochastic Gravitational-Wave Background: The Overlap Reduction Function

Abstract

Detection of a gravitational-wave stochastic background via ground or space-based gravitational-wave detectors requires the cross-correlation of the response of two or more independent detectors. The cross-correlation involves a frequency-dependent factor -- the so-called overlap reduction function or Hellings-Downs curve -- that depends on the relative geometry of each detector pair: i.e., the detector separations and the relative orientation of their antenna patterns (beams). An incorrect formulation of this geometrical factor has appeared in the literature, leading to incorrect conclusions regarding the sensitivity of proposed detectors to a stochastic gravitational-wave background. To rectify these errors and as a reference for future work we provide here a complete, first-principles derivation of the overlap reduction function and assess the nature of the errors associated with the use of the incorrect expression that has appeared in the literature. We describe the behavior of the overlap reduction function in different limiting regimes, and show how the difference between the correct and incorrect expressions can be understood physically.

Removed incorrect references to the Seto and Taruya papers; added explicit expression for the detector transfer function; final published version

References in corpus (10)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities
• Beyond LISA: Exploring Future Gravitational Wave Missions
• Detecting the Cosmic Gravitational Wave Background with the Big Bang Observer
• Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects
• The Sensitivity of Ligo to a Stochastic Background, and its Dependance on the Detector Orientations
• Detecting a gravitational-wave background with next-generation space interferometers
• BBO and the Neutron-Star-Binary Subtraction Problem
• Space missions to detect the cosmic gravitational-wave background
• Mapping the gravitational wave background

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