Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array
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2024
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| author | Kimpson, Tom Melatos, Andrew O'Leary, Joseph Carlin, Julian B. Evans, Robin J. Moran, William Cheunchitra, Tong Dong, Wenhao Dunn, Liam Greentree, Julian O'Neill, Nicholas J. Suvorova, Sofia Thong, Kok Hong Vargas, Andrés F. |
| author_facet | Kimpson, Tom Melatos, Andrew O'Leary, Joseph Carlin, Julian B. Evans, Robin J. Moran, William Cheunchitra, Tong Dong, Wenhao Dunn, Liam Greentree, Julian O'Neill, Nicholas J. Suvorova, Sofia Thong, Kok Hong Vargas, Andrés F. |
| contents | Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of $h_0 \approx 2 \times 10^{-15}$. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of $\approx 0.3$ rad in the marginalised one-dimensional posterior for the orbital inclination $ι$, introduced by dropping the so-called `pulsar terms'. Smaller biases $\lesssim 10 \%$ are also observed in other static parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array Kimpson, Tom Melatos, Andrew O'Leary, Joseph Carlin, Julian B. Evans, Robin J. Moran, William Cheunchitra, Tong Dong, Wenhao Dunn, Liam Greentree, Julian O'Neill, Nicholas J. Suvorova, Sofia Thong, Kok Hong Vargas, Andrés F. High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of $h_0 \approx 2 \times 10^{-15}$. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of $\approx 0.3$ rad in the marginalised one-dimensional posterior for the orbital inclination $ι$, introduced by dropping the so-called `pulsar terms'. Smaller biases $\lesssim 10 \%$ are also observed in other static parameters. |
| title | Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array |
| topic | High Energy Astrophysical Phenomena General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2409.14613 |