Arrival-time analysis for a millisecond pulsar

Arrival times from a fast, quiet pulsar can be used to obtain accurate determinations of pulsar parameters. In the case of the millisecond pulsar, PSR 1937 + 214, the remarkably small rms residual to the timing fit indicates that precise measurements of position, proper motion and perhaps even trigonometric parallax will be possible (Backer 1984). The variances in these parameters, however, will depend strongly on the nature of the underlying noise spectrum. We demonstrate that for very red spectrai.e. those dominated by low-frequency noise, the uncertainties can be larger than the present estimates (based on a white-noise model) and can even grow with the observation period. The possibility of improved parameter estimation through prewhitening’ the data and the application of these results to other pulsar observations are briefly discussed. The post-fit rms residual of PSR 1937 + 214 may be used to limit the energy density of a gravitational radiation background at periods of a few months to years. However, fitting the pulsar position and pulse-emission times filters out significant amounts of residual power, especially for observation periods of less than three years. Consequently the present upper bound on the energy density of gravitational waves Ω_g