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 1.0x10(-8) or (90% confidence) 4.8X10(-9) of the closure density at frequency 4.4X10(-9) 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) Hz.