Finite distance effects on the Hellings-Downs curve in modified gravity

2024/07/31 by Domènech, Guillem, Tsabodimos, Apostolos · 3 citations
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2407.21567

Abstract

There is growing interest in the overlap reduction function in pulsar timing array observations as a probe of modified gravity. However, current approximations to the Hellings-Downs curve for subluminal gravitational wave propagation, say v<1, diverge at small angular pulsar separation. In this paper, we find that the ORF for the v<1 case is sensitive to finite distance effects. First, we show that finite distance effects introduce an effective cut-off in the spherical harmonics decomposition at ℓ∼ √(1-v²) kL, where ℓ is the multipole number, k the wavenumber of the gravitational wave and L the distance to the pulsars. Then, we find that the overlap reduction function in the small angle limit approaches a value given by πkL v² (1-v²)² times a normalization factor, exactly matching the value for the autocorrelation recently derived. Although we focus on the v<1 case, our formulation is valid for any value of v.

Cited by

• Simulating a Gaussian stochastic gravitational wave background signal in pulsar timing arrays
• Spatial Correlation between Pulsars from Interfering Gravitational-Wave Sources in Massive Gravity
• Implications of pulsar timing arrays for Gauss-Bonnet Inflation

Related

• Finite distance effects on the Hellings–Downs curve in modified gravity
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• Understanding the gravitational-wave Hellings and Downs curve for pulsar\n timing arrays in terms of sound and electromagnetic waves