Millisecond and binary pulsars as nature's frequency standards — II. The effects of low-frequency timing noise on residuals and measured parameters

• Published in: Monthly notices of the Royal Astronomical Society 1999-05, Vol.305 (3), p.563-590
• Main Author: Kopeikin, Sergei M.
• Format: Article
• Language: English
• Subjects: binaries: general; methods: data analysis; methods: statistical; pulsars: general
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1046/j.1365-8711.1999.02432.x

Millisecond and binary pulsars are the most stable natural frequency standards. They can be applied to a number of principal problems in modern astronomy and time-keeping metrology, including the search for a stochastic gravitational wave background in the early Universe, testing general relativity and establishing a new ephemeris time-scale. The full exploration of pulsar properties requires that proper unbiased estimates of the spin and orbital parameters be obtained, a problem which deserves special investigation. These estimates depend essentially on the random noise component being revealed in the residuals of time of arrival (TOA) and having various physical origins. In the present paper, the influence of low-frequency (‘red’) timing noise with spectral indices from 1 to 6 on TOA residuals, variances, and covariances of the estimates of measured parameters of single and binary pulsars is studied. In order to determine the functional dependence of these quantities on time, an analytical technique for processing observational data in the time domain is developed. Data processing in the time domain is more informative, because it takes into account both the stationary and non-stationary components of noise. Data processing in the frequency domain is valid if and only if the noise is stationary. Our analysis includes a simplified timing model of a binary pulsar in a circular orbit and a procedure for estimating pulsar parameters and residuals under the influence of red noise. We reconfirm, in accordance with the results of previous authors, that uncorrelated white noise in the errors of measurements of TOA causes gradually decreasing residuals, variances and covariances of all parameters. On the other hand, we show that any low-frequency, correlated noise of terrestrial or/and astrophysical origin that is present causes the residuals, variances and covariances of certain parameters to increase with time. Hence, the low-frequency noise corrupts our observations and reduces the experimental possibilities for better tests of general relativity theory. At the same time, the rate of growth of residuals and variances of parameters can give valuable information about the red noise itself. We also treat in detail the influence of polynomial drift of noise on the residuals and fitting parameters, in order to avoid confusion with red noise without polynomial drift. Results of the analytic analysis are used for discussion of a statistic describing the stabilities o