5.3 Going further5 Pulsars as Gravitational Wave 5.1 Limits from individual pulsars

5.2 A pulsar timing array 

The idea of using timing data for a number of pulsars distributed on the sky to detect gravitational waves was first proposed by Hellings & Downs [96]. Such a ``timing array'' of pulsars would have the advantage over a single arm in that, through a cross-correlation analysis of the residuals for pairs of pulsars distributed over the sky, it should be possible to separate the timing noise of each pulsar from the signature of the GWB, which would be common to all pulsars in the array. To quantify this, consider the fractional frequency shift observed for the i th pulsar in the array:


In this expression tex2html_wrap_inline9689 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 tex2html_wrap_inline9691 . The timing noise intrinsic to the pulsar is characterised by the function tex2html_wrap_inline9693 . 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 tex2html_wrap_inline9699 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 [95]. This allows the separation of the effects of terrestrial clock and solar system ephemeris errors from the GWB [79].

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 .


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Figure 26: Hammer-Aitoff projections showing the known Galactic disk millisecond pulsar population in 1990 and 2001. The impact of the new discoveries is seen by comparing the sample circa 1990, where all the known sources had been discovered at Arecibo, with the present sample where the sources are much more uniformly distributed on the sky.

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 [10] 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.


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Figure 27: Arecibo timing residuals of millisecond pulsars monitored by groups at Berkeley and Princeton on a regular basis as part of a long-term project to detect low-frequency gravitational waves. The level of precision being achieved is well below the vertical bars surrounding each set of residuals (tex2html_wrap_inline9701 s).

5.3 Going further5 Pulsars as Gravitational Wave 5.1 Limits from individual pulsars

image Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
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