Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects

Using a statistically rigorous analysis method, we place limits on the existence of an isotropic stochastic gravitational wave background using pulsar timing observations. We consider backgrounds whose characteristic strain spectra may be described as a power-law dependence with frequency. Such backgrounds include an astrophysical background produced by coalescing supermassive black-hole binary systems and cosmological backgrounds due to relic gravitational waves and cosmic strings. Using the best available data, we obtain an upper limit on the energy density per unit logarithmic frequency interval of \Omega^{\rm SMBH}_g(1/8yr) h^2 <= 1.9 x 10^{-8} for an astrophysical background which is five times more stringent than the earlier Kaspi et al. (1994) limit of 1.1 x 10^{-7}. We also provide limits on a background due to relic gravitational waves and cosmic strings of \Omega^{\rm relic}_g(1/8yr) h^2 <= 2.0 x 10^{-8} and \Omega^{\rm cs}_g(1/8yr) h^2 <= 1.9 x 10^{-8} respectively. All of the quoted upper limits correspond to a 0.1% false alarm rate together with a 95% detection rate. We discuss the physical implications of these results and highlight the future possibilities of the Parkes Pulsar Timing Array project. We find that our current results can 1) constrain the merger rate of supermassive binary black hole systems at high red shift, 2) rule out some relationships between the black hole mass and the galactic halo mass, 3) constrain the rate of expansion in the inflationary era and 4) provide an upper bound on the dimensionless tension of a cosmic string background.