Pulsar timing array analysis in a Legendre polynomial basis
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910191244541952 |
|---|---|
| author | Allen, Bruce von Blanckenburg, Arian L. Olum, Ken D. |
| author_facet | Allen, Bruce von Blanckenburg, Arian L. Olum, Ken D. |
| contents | We use Legendre polynomials, previously employed in this context by Lee et al., van Haasteren and Levin, and Pitrou and Cusin, to model signals in pulsar timing arrays. These replace the (Fourier mode) basis of trigonometric functions normally used for data analysis. The Legendre basis makes it simpler to incorporate pulsar modeling effects, which remove constant-, linear-, and quadratic-in-time terms from pulsar timing residuals. In the Legendre basis, this zeroes the amplitudes of the the first three Legendre polynomials. We use this basis to construct an optimal quadratic cross-correlation estimator $\widehatμ$ of the Hellings and Downs (HD) correlation and compute its variance $σ^2_{\widehatμ}$ in the way described by Allen and Romano. Remarkably, if the gravitational-wave background (GWB) and pulsar noise power spectra are (sums of) power laws in frequency, then in this basis one obtains analytic closed forms for many quantities of interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pulsar timing array analysis in a Legendre polynomial basis Allen, Bruce von Blanckenburg, Arian L. Olum, Ken D. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics 85A40 (Primary) 62M15, 42C10 (Secondary) J.2; G.3; G.1.5; I.6.4 We use Legendre polynomials, previously employed in this context by Lee et al., van Haasteren and Levin, and Pitrou and Cusin, to model signals in pulsar timing arrays. These replace the (Fourier mode) basis of trigonometric functions normally used for data analysis. The Legendre basis makes it simpler to incorporate pulsar modeling effects, which remove constant-, linear-, and quadratic-in-time terms from pulsar timing residuals. In the Legendre basis, this zeroes the amplitudes of the the first three Legendre polynomials. We use this basis to construct an optimal quadratic cross-correlation estimator $\widehatμ$ of the Hellings and Downs (HD) correlation and compute its variance $σ^2_{\widehatμ}$ in the way described by Allen and Romano. Remarkably, if the gravitational-wave background (GWB) and pulsar noise power spectra are (sums of) power laws in frequency, then in this basis one obtains analytic closed forms for many quantities of interest. |
| title | Pulsar timing array analysis in a Legendre polynomial basis |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics 85A40 (Primary) 62M15, 42C10 (Secondary) J.2; G.3; G.1.5; I.6.4 |
| url | https://arxiv.org/abs/2510.05913 |