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
gravity 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 [73]. This allows, in principle, the separation of the effects of terrestrial clock and solar system ephemeris errors from the GWB [61].

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.
17, 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 by the all-sky searches has resulted in essentially such
a distribution, shown in the right panel of Fig.
17
. Continued timing of these pulsars in the coming years should
greatly improve the sensitivity and will perhaps allow the
detection of gravity waves, as opposed to upper limits, in the
future.

Binary and Millisecond Pulsars
D. R. Lorimer (dunc@mpifr-bonn.mpg.de)
http://www.livingreviews.org/lrr-1998-10
© Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |