Finite distance effects on the Hellings-Downs curve in modified gravity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911982569914368 |
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| author | Domènech, Guillem Tsabodimos, Apostolos |
| author_facet | Domènech, Guillem Tsabodimos, Apostolos |
| contents | 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 $\ell\sim \sqrt{1-v^2} \, kL$, where $\ell$ 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 $πkL\,v^2\,(1-v^2)^2$ 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 $v$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite distance effects on the Hellings-Downs curve in modified gravity Domènech, Guillem Tsabodimos, Apostolos General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics 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 $\ell\sim \sqrt{1-v^2} \, kL$, where $\ell$ 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 $πkL\,v^2\,(1-v^2)^2$ 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 $v$. |
| title | Finite distance effects on the Hellings-Downs curve in modified gravity |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2407.21567 |