Other
Scientific paper
Oct 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phrvd..56.4455k&link_type=abstract
Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 56, Issue 8, 15 October 1997, pp.4455-4469
Other
14
Gravitational Wave Detectors And Experiments, Stochastic Processes, Gravitational Radiation Detectors, Mass Spectrometers, And Other Instrumentation And Techniques, Pulsars
Scientific paper
Fundamental limits on the energy density Ωg of the ultralow-frequency primordial gravitational wave background (GWB) radiation which can be obtained from the measurement of secular variations of orbital parameters of binary pulsars are explored. For analytical convenience we choose the simple timing model comprised of the binary system with a pulsar on a circular orbit and a remote observer on the Earth whose motion about the barycenter of the Solar System is assumed to be known with sufficient accuracy. The primordial gravitational waves bring about stochastic noise fluctuations in the times of arrival of the pulsar pulses which include (as our analysis shows) both nonstationary and stationary components. The latter part of the noise is supposed to have spectral power ~Ωg/f5, where f is the frequency of a gravitational wave intersecting or passing near the line of sight and Ωg is the energy density of the GWB radiation. An analytical technique of processing observational data in the time domain is worked out to determine the functional dependence of the pulsar timing residuals and variances of spin and orbital parameters of the binary pulsar with time. This technique enables us to prove that the procedure of fitting the pulsar's spin and orbital parameters acts not only as a low frequency filter of the background noise but also eliminates the nonstationary component of the noise so that the post-fit timing residuals contain only a stationary component. In order to keep the calculations manageable we idealize the observations by assuming that they are uniformly spaced and extend over an integral number of orbital revolutions N which is taken so large that any sum over all observation points can be approximated by an integral over the observing period T. The integrals one meets in calculations are divergent because of the existence of an algebraic singularity in the spectrum of the stochastic gravitational wave background as the frequency approaches the point f=0. To avoid this difficulty a powerful method of analytical continuation of Riesz is applied for regularization of all divergent integrals in order to convert them into finite expressions. The regularization procedure enables us to show that the divergent behavior of the spectrum of background gravitational radiation is irrelevant in the treatment of post-fit residuals because of a mutual cancellation of all singular expressions. Our calculations clearly demonstrate that the observed secular variations both of orbital period Pb and of semimajor axis x projected onto the line of sight can be effectively used to set a limit on the energy density Ωg of the GWB radiation in the frequency range 1/L
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