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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2311.14159 |
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| _version_ | 1866929554484887552 |
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| author | Kumar, Neha Anil Kamionkowski, Marc |
| author_facet | Kumar, Neha Anil Kamionkowski, Marc |
| contents | Pulsar timing arrays seek and study gravitational waves (GWs) through the angular two-point correlation function of timing residuals they induce in pulsars. The two-point correlation function induced by the standard transverse-traceless GWs is the famous Hellings-Downs curve, a function only of the angle between the two pulsars. Additional polarization modes (vector/scalar) that may arise in alternative-gravity theories have different angular correlation functions. Furthermore, anisotropy, linear, or circular polarization in the stochastic GW background gives rise to additional structure in the two-point correlation function that cannot be written simply in terms of the angular separation of the two pulsars. In this paper, we provide a simple formula for the most general two-point correlation function--or overlap reduction function (ORF)--for a gravitational-wave background with an arbitrary polarization state, possibly containing anisotropies in its intensity and polarization (linear or circular). We provide specific expressions for the ORFs sourced by the general-relativistic transverse-traceless GW modes as well as vector (or spin-1) modes that may arise in alternative-gravity theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14159 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient Computation of Overlap Reduction Functions for Pulsar Timing Arrays Kumar, Neha Anil Kamionkowski, Marc Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Pulsar timing arrays seek and study gravitational waves (GWs) through the angular two-point correlation function of timing residuals they induce in pulsars. The two-point correlation function induced by the standard transverse-traceless GWs is the famous Hellings-Downs curve, a function only of the angle between the two pulsars. Additional polarization modes (vector/scalar) that may arise in alternative-gravity theories have different angular correlation functions. Furthermore, anisotropy, linear, or circular polarization in the stochastic GW background gives rise to additional structure in the two-point correlation function that cannot be written simply in terms of the angular separation of the two pulsars. In this paper, we provide a simple formula for the most general two-point correlation function--or overlap reduction function (ORF)--for a gravitational-wave background with an arbitrary polarization state, possibly containing anisotropies in its intensity and polarization (linear or circular). We provide specific expressions for the ORFs sourced by the general-relativistic transverse-traceless GW modes as well as vector (or spin-1) modes that may arise in alternative-gravity theories. |
| title | Efficient Computation of Overlap Reduction Functions for Pulsar Timing Arrays |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2311.14159 |