Imprints of relic gravitational waves on pulsar timing

Relic gravitational waves （RGWs）, a background originating during inflation, would leave imprints on pulsar timing residuals. This makes RGWs an important source for detection of RGWs using the method of pulsar timing. In this paper, we discuss the effects of RGWs on single pulsar timing, and quantitatively analyze the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noises in pulsar timing residuals are understood, even though simultaneously observing multiple millisecond pulsars is a more powerful technique for extracting gravitational wave signals. We correct the normalization of RGWs using observations of the cosmic microwave background （CMB）, which leads to the amplitudes of RGWs being reduced by two orders of magnitude or so compared to our previous works. We obtained new constraints on RGWs using recent observations from the Parkes Pulsar Timing Array, employing the tensor-to-scalar ratio r = 0.2 due to the tensor-type polarization observations of CMB by BICEP2 as a reference value, even though its reliability has been brought into question. Moreover, the constraints on RGWs from CMB and Big Bang nucleosynthesis will also be discussed for comparison.

Pulsar timing residuals due to individual non-evolving gravitational wave sources

The pulsar timing residuals induced by gravitational waves from non- evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will analyze the various effects due to different parameters. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The or- bits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also be studied in detail. We find that the effects of the related parameters are quite different, and some of them display certain regularities.