### 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.

Original language | English (US) |
---|---|

Article number | 062003 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 79 |

Issue number | 6 |

DOIs | |

State | Published - Mar 2 2009 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*79*(6), [062003]. https://doi.org/10.1103/PhysRevD.79.062003

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 79, no. 6, 062003. https://doi.org/10.1103/PhysRevD.79.062003

**Detecting a stochastic gravitational-wave background : The overlap reduction function.** / Finn, Lee S.; Larson, Shane L.; Romano, Joseph D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Detecting a stochastic gravitational-wave background

T2 - The overlap reduction function

AU - Finn, Lee S.

AU - Larson, Shane L.

AU - Romano, Joseph D.

PY - 2009/3/2

Y1 - 2009/3/2

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.79.062003

DO - 10.1103/PhysRevD.79.062003

M3 - Article

AN - SCOPUS:65549162513

VL - 79

JO - Physical Review D

JF - Physical Review D

SN - 0556-2821

IS - 6

M1 - 062003

ER -