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A stochastic spectrum of gravitational wave background radiation (GBR) from the early universe will produce unmodeled perturbations to the arrival times of an array of millisecond pulsars. These perturbations will have a set of distinct angular signatures that can be separated from other effects such as clock noise and ephemeris errors. We present a method for analyzing the angular correlations in pulsar timing residuals in order to detect such radiation.
We construct a set of angular basis functions appropriate to the induced angular correlations in pulsar timing residuals. Sinusoids are used for the temporal basis functions. Using a simulated GBR spectrum, we artificially produce idealized timing residuals at the positions of pulsars, including both the contributions at the solar system (correlated) and at the individual pulsars (uncorrelated). Using our method, we consider the success with which we can recover the input simulated GBR. The inevitable noise due to the uncorrelated effects of the GBR at each pulsar limits this method. In addition, although there are only five instantaneous free parameters, we find that ${_>\atop^{\sim}} 9$ pulsars are required for reasonable results. The choice of coordinate system orientation is a small effect. This method is promising, but application to unevenly sampled real data with uneven observational errors will be complicated.
