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Understanding and analysing time-correlated stochastic signals in pulsar timing

van Haasteren, R., & Levin, Y. (2013). Understanding and analysing time-correlated stochastic signals in pulsar timing. Monthly Notices of the Royal Astronomical Society, 428(2), 1147-1159. doi:10.1093/mnras/sts097.

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1202.5932 (Preprint), 862KB
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Creators:
van Haasteren, Rutger1, Author
Levin, Yuri, Author
Affiliations:
1Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, ou_24011

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Free keywords: Astrophysics, Instrumentation and Methods for Astrophysics, astro-ph.IM,General Relativity and Quantum Cosmology, gr-qc
Abstract: Although it is widely understood that pulsar timing observations generally contain time-correlated stochastic signals (TCSSs; red timing noise is of this type), most data analysis techniques that have been developed make an assumption that the stochastic uncertainties in the data are uncorrelated, i.e. "white". Recent work has pointed out that this can introduce severe bias in determination of timing-model parameters, and that better analysis methods should be used. This paper presents a detailed investigation of timing-model fitting in the presence of TCSSs, and gives closed expressions for the post-fit signals in the data. This results in a Bayesian technique to obtain timing-model parameter estimates in the presence of TCSSs, as well as computationally more efficient expressions of their marginalised posterior distribution. A new method to analyse hundreds of mock dataset realisations simultaneously without significant computational overhead is presented, as well as a statistically rigorous method to check the internal consistency of the results. As a by-product of the analysis, closed expressions of the rms introduced by a stochastic background of gravitational-waves in timing-residuals are obtained. Using $T$ as the length of the dataset, and $h_c(1\rm{yr}^{-1})$ as the characteristic strain, this is: $\sigma_{\rm GWB}^2 = h_{c}(1\rm{yr}^{-1})^2 (9\sqrt[3]{2\pi^4}\Gamma(-10/3) / 8008) \rm{yr}^{-4/3} T^{10/3}$.

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Dates: 2012-02-272012-10-022013
Publication Status: Published in print
Pages: 13 pages, 8 figures
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1202.5932
DOI: 10.1093/mnras/sts097
Degree: -

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### Source 1

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Title: Monthly Notices of the Royal Astronomical Society
Source Genre: Journal
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Publ. Info: Oxford : Blackwell Science
Pages: - Volume / Issue: 428 (2) Sequence Number: - Start / End Page: 1147 - 1159 Identifier: ISSN: 1365-8711
CoNE: /journals/resource/1000000000024150