would be due to the measurement uncertainties and intrinsic
timing noise from the neutron star. Detweiler [54] showed that a GWB with a flat energy spectrum in the frequency
band
would result in an additional contribution to the timing
residuals
. The corresponding wave energy density
(for
) is
An upper limit to
can be obtained from a set of timing residuals by assuming the
rms scatter is entirely due to this effect (
). These limits are commonly expressed as a fraction of
the energy density required to close the Universe:
where the Hubble constant
km s
Mpc.
Romani & Taylor [133] applied this technique to a set of TOAs for PSR B1237+12
obtained from regular observations over a period 11 years as part
of the JPL pulsar timing programme [58]. This pulsar was chosen on the basis of its relatively low
level of timing activity by comparison with the youngest pulsars,
whose residuals are ultimately plagued by timing noise (§
4.4). By ascribing the rms scatter in the residuals (
ms) to the GWB, Romani & Taylor placed a limit of
for a centre frequency
Hz.
This limit, already well below the energy density required to
close the Universe, was further reduced following the long-term
timing measurements of millisecond pulsars at Arecibo by Taylor
and collaborators (§
4.4). In the intervening period, more elaborate techniques had been
devised [30
,
37,
145] to look for the likely signature of a GWB in the frequency
spectrum of the timing residuals and to address the possibility
of ``fitting out'' the signal in the TOAs. Following [30], it is convenient to define
, the energy density of the GWB per logarithmic frequency
interval relative to
. With this definition, the power spectrum of the GWB
can be written [77,
37] as
where
is frequency in cycles per year. The timing residuals for
B1937+21 shown in Fig.
16
are clearly non-white and, as we saw in §
4.4, limit its timing stability for periods > 2 yr. The residuals
for PSR B1855+09 clearly show no systematic trends and are in
fact consistent with the measurement uncertainties alone. Based
on these data, and using a rigorous statistical analysis,
Thorsett & Dewey [156] place a 95% confidence upper limit of
for
Hz. This limit is difficult to reconcile with most cosmic string
models for galaxy formation [38,
156].
For those pulsars in binary systems, an additional clock for
measuring the effects of gravitational waves is the orbital
period. In this case, the range of frequencies is not limited by
the time span of the observations, allowing the detection of
waves with periods as large as the light travel time to the
binary system [30]. The most stringent results presently available are based on
B1855+09 limit
in the frequency range
Hz. Kopeikin [88] has recently presented this limit and discusses the methods in
detail.
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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 |