Detecting a stochastic gravitational-wave background: The overlap reduction function

Finn, L. S.; Larson, Shane L.; Romano, Joseph D.

doi:10.1103/physrevd.79.062003

Cited by 36 publications

(29 citation statements)

References 20 publications

(33 reference statements)

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“…where · is the expectation value and δ 2 (Ω,Ω ′ ) = δ(cos θ − cos θ ′ )δ(φ− φ ′ ) is the covariant Dirac delta function on the two-sphere [42]. This condition implies that the radiation from different directions are statistically independent.…”

Section: Stochastic Backgroundsmentioning

confidence: 99%

Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays

et al. 2013

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Detecting a stochastic gravitational wave background, particularly radiation from individually unresolvable supermassive black hole binary systems, is one of the primary targets for Pulsar Timing Arrays. Increasingly more stringent upper limits are being set on these signals under the assumption that the background radiation is isotropic. However, some level of anisotropy may be present and the characterisation of the gravitational wave energy density at different angular scales carries important information. We show that the standard analysis for isotropic backgrounds can be generalised in a conceptually straightforward way to the case of generic anisotropic background radiation by decomposing the angular distribution of the gravitational wave energy density on the sky into multipole moments. We introduce the concept of generalised overlap reduction functions which characterise the effect of the anisotropy multipoles on the correlation of the timing residuals from the pulsars timed by a Pulsar Timing Array. In a search for a signal characterised by a generic anisotropy, the generalised overlap reduction functions play the role of the so-called Hellings and Downs curve used for isotropic radiation. We compute the generalised overlap reduction functions for a generic level of anisotropy and Pulsar Timing Array configuration. We also provide an order of magnitude estimate of the level of anisotropy that can be expected in the background generated by super-massive black hole binary systems.

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Section: Stochastic Backgroundsmentioning

confidence: 99%

Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays

et al. 2013

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“…[25,26]. The ORF in turn depends on the frequency of the GW background and the geometry of the PTA, specifically the distance to each pulsar and the angular separation of pulsar pairs.…”

Section: Introductionmentioning

confidence: 99%

Effect of small interpulsar distances in stochastic gravitational wave background searches with pulsar timing arrays

Mingarelli

Sidery

2014

Phys. Rev. D

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One of the primary objectives for pulsar timing arrays (PTAs) is to detect a stochastic background generated by the incoherent superposition of gravitational waves (GWs), in particular from the cosmic population of supermassive black hole binaries. Current stochastic background searches assume that pulsars in a PTA are separated from each other and the Earth by many GW wavelengths. As more millisecond pulsars are discovered and added to PTAs, some may be separated by only a few radiation wavelengths or less, resulting in correlated GW phase changes between close pulsars in the array. Here we investigate how PTA overlap reduction functions (ORFs), up to quadrupole order, are affected by these additional correlated phase changes, and how they are in turn affected by relaxing the assumption that all pulsars are equidistant from the solar system barycenter. We find that in the low-frequency GW background limit of f ∼ 10 −9 Hz, and for pulsars at varying distances from the Earth, these additional correlations only affect the ORFs by a few percent for pulsar pairs at large angular separations, as expected. However, when nearby (order 100 pc) pulsars are separated by less than a few degrees, the correlated phase changes can introduce variations of a few tens of percent in the magnitude of the isotropic ORF, and much larger fractional differences in the anisotropic ORFs-up to 188 in the m ¼ 0, l ¼ 2 ORF for equidistant pulsars separated by 3°. In fact, the magnitude of most of the anisotropic ORFs is largest at small, but nonzero, pulsar separations. Finally, we write down a small angle approximation for the correlated phase changes which can easily be implemented in search pipelines, and for completeness, examine the behavior of the ORFs for pulsars which lie at a radiation wavelength from the Earth.

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“…4. Detailed derivations and discussions of the overlap reduction functions for ground-based laser interferometers, space-based laser interferometers, and pulsar timing arrays can be found in [3][4][5], [6,7], and [8,9], respectively. In Fig.…”

Section: Overlap Reduction Functionmentioning

confidence: 99%

Sensitivity curves for searches for gravitational-wave backgrounds

Thrane

Romano²

2013

Phys. Rev. D

Self Cite

532

645

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We propose a graphical representation of detector sensitivity curves for stochastic gravitationalwave backgrounds that takes into account the increase in sensitivity that comes from integrating over frequency in addition to integrating over time. This method is valid for backgrounds that have a power-law spectrum in the analysis band. We call these graphs "power-law integrated curves." For simplicity, we consider cross-correlation searches for unpolarized and isotropic stochastic backgrounds using two or more detectors. We apply our method to construct power-law integrated sensitivity curves for second-generation ground-based detectors such as Advanced LIGO, space-based detectors such as LISA and the Big Bang Observer, and timing residuals from a pulsar timing array. The code used to produce these plots is available at https://dcc.ligo.org/LIGO-P1300115/public for researchers interested in constructing similar sensitivity curves.

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Detecting a stochastic gravitational-wave background: The overlap reduction function

Cited by 36 publications

References 20 publications

Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays

Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays

Effect of small interpulsar distances in stochastic gravitational wave background searches with pulsar timing arrays

Sensitivity curves for searches for gravitational-wave backgrounds

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