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

Millisecond and binary pulsars are the most stable natural frequency standa rds. They can be applied to a number of principal problems in modern astron omy and time-keeping metrology, including the search for a stochastic gravi tational 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. Th ese estimates depend essentially on the random noise component being reveal ed in the residuals of time of arrival (TOA) and having various physical or igins. In the present paper, the influence of low-frequency ('red') timing noise with spectral indices from 1 to 6 on TOA residuals, variances, and co variances of the estimates of measured parameters of single and binary puls ars is studied. In order to determine the functional dependence of these qu antities on time, an analytical technique for processing observational data in the time domain is developed. Data processing in the time domain is mor e informative, because it takes into account both the stationary and nonsta tionary components of noise. Data processings in the frequency domain is va lid if and only if the noise is stationary. Our analysis includes a simplif ied timing model of a binary pulsar in a circular orbit and a procedure for estimating pulsar parameters and residuals under the influence of red nois e. We reconfirm, in accordance with the results of previous authors, that u ncorrelated white noise in the errors of measurements of TOA causes gradual ly decreasing residuals, variances and covariances of all parameters. On th e other hand, we show that any low-frequency, correlated noise of terrestri al or/and astrophysical origin that is present causes the residuals, varian ces 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 t ime, the rate of growth of residuals and variances of parameters can give v aluable information about the red noise itself. We also treat in detail the influence of polynomial drift of noise on the residuals and fitting parame ters, in order to avoid confusion with red noise without polynomial drift. Results of the analytic analysis are used for discussion of a statistic des cribing the stabilities of kinematic (PT) and dynamic (BPT) pulsar time-sca les.