In this expression is a geometric factor dependent on the line-of-sight direction to the pulsar and the propagation and polarisation vectors of the gravitational wave of dimensionless amplitude . The timing noise intrinsic to the pulsar is characterised by the function . The result of a cross-correlation between pulsars i and j is then
where the bracketed terms indicate cross-correlations. Since the wave function and the noise contributions from the two pulsars are independent quantities, the cross correlation tends to as the number of residuals becomes large. Summing the cross-correlation functions over a large number of pulsar pairs provides additional information on this term as a function of the angle on the sky . This allows the separation of the effects of terrestrial clock and solar system ephemeris errors from the GWB .
Applying the timing array concept to the present database of long-term timing observations of millisecond pulsars does not improve on the limits on the GWB discussed above. The sky distribution of these pulsars, seen in the left panel of Fig. 26, shows that their angular separation is rather low. To achieve optimum sensitivity it is desirable to have an array consisting of pulsar clocks distributed isotropically over the whole sky. The flood of recent discoveries of nearby binary and millisecond pulsars has resulted in essentially such a distribution, shown in the right panel of Fig. 26 .
A number of long-term timing projects are now underway to monitor these millisecond pulsars with a goal of detecting low-frequency gravitational radiation. At Arecibo, regular timing of a dozen or more millisecond pulsars has been carried out following the completion of the upgrade to the telescope in 1997. A summary of these observations is shown in Fig. 27 . The rms timing residuals for several of the pulsars are now approaching the 100 ns level. This degree of precision demands a high level of commitment to investigate possible causes of systematic errors in the signal path through the telescope. Combining datasets from several observatories is also challenging. The Berkeley pulsar group lead by Don Backer  are among the most active observers in this area. Backer and collaborators have now installed identical sets of datataking equipment at a number of radio telescopes around the world in an attempt to ensure a homogeneous set of residuals. Continued timing of these millisecond pulsars in the coming years should greatly improve the sensitivity and will perhaps allow the detection of gravitational waves, as opposed to upper limits, in the not-too-distant future.
|Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
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