Pulsar timing limits on very low frequency stochastic gravitational radiation

A low-frequency, stochastic gravitational radiation background can be detected through the irregularities it induces in pulsar arrival times. Here, we present an optimal statistical framework for analysis of timing data from a single pulsar, correcting an error in previous treatments. Observations of PSR B1855+09 yield an upper limit (95% confidence) of 1.0×${10}^{-8\mathrm{}}$ or (90% confidence) 4.8×${10}^{-9\mathrm{}}$ of the closure density at frequency 4.4×${10}^{-9\mathrm{}}$ Hz. This result probably rules out cosmological models that use cosmic strings as seeds for galaxy formation. Combined observations of four binary pulsars yield weaker limits at frequencies as low as ${10}^{-12\mathrm{}}$ Hz.