5.2 A pulsar timing array5 Pulsars as Gravitational Wave 5 Pulsars as Gravitational Wave

5.1 Limits from individual pulsars 

In the ideal case, the change in the observed frequency caused by the GWB should be detectable in the set of timing residuals after the application of an appropriate model for the rotational, astrometric and, where necessary, binary parameters of the pulsar. As discussed in §  4, all other effects being negligible, the rms scatter of these residuals tex2html_wrap_inline9645 would be due to the measurement uncertainties and intrinsic timing noise from the neutron star. Detweiler [68] showed that a GWB with a flat energy spectrum in the frequency band tex2html_wrap_inline9647 would result in an additional contribution to the timing residuals tex2html_wrap_inline9649 . The corresponding wave energy density tex2html_wrap_inline9651 (for tex2html_wrap_inline9653) is


An upper limit to tex2html_wrap_inline9651 can be obtained from a set of timing residuals by assuming the rms scatter is entirely due to this effect (tex2html_wrap_inline9657). These limits are commonly expressed as a fraction of tex2html_wrap_inline9659 the energy density required to close the Universe:


where the Hubble constant tex2html_wrap_inline9661 .

Romani & Taylor [205] applied this technique to a set of TOAs for PSR B1237+12 obtained from regular observations over a period of 11 years as part of the JPL pulsar timing programme [73]. 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 (§  4.3). By ascribing the rms scatter in the residuals (tex2html_wrap_inline9663 ms) to the GWB, Romani & Taylor placed a limit of tex2html_wrap_inline9665 for a centre frequency tex2html_wrap_inline9667 .

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 (§  4.3). In the intervening period, more elaborate techniques had been devised [29Jump To The Next Citation Point In The Article, 36Jump To The Next Citation Point In The Article, 228] 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 [29Jump To The Next Citation Point In The Article] it is convenient to define tex2html_wrap_inline9669, the energy density of the GWB per logarithmic frequency interval relative to tex2html_wrap_inline9659 . With this definition, the power spectrum of the GWB, tex2html_wrap_inline9673, can be written [99, 36] as


where tex2html_wrap_inline9675 is frequency in cycles per year. The timing residuals for B1937+21 shown in Fig.  25 are clearly non-white and, as we saw in §  4.3, limit its timing stability for periods tex2html_wrap_inline9677 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 [249Jump To The Next Citation Point In The Article] place a 95% confidence upper limit of tex2html_wrap_inline9679 for tex2html_wrap_inline9681 . This limit is difficult to reconcile with most cosmic string models for galaxy formation [40, 249].


Click on thumbnail to view imageClick on thumbnail to view image

Figure 25: Timing residuals for PSRs B1855+09 (left panel) and B1937+21 (right panel) obtained from almost a decade of timing at Arecibo (Kaspi, Taylor & Ryba 1994 [117Jump To The Next Citation Point In The Article]).

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 [29]. The most stringent results presently available are based on the B1855+09 limit tex2html_wrap_inline9683 in the frequency range tex2html_wrap_inline9685 . Kopeikin [118] has recently presented this limit and discusses the methods in detail.

5.2 A pulsar timing array5 Pulsars as Gravitational Wave 5 Pulsars as Gravitational Wave

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