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Abstract

We present two methods for determining the significance of a stochastic gravitational-wave background affecting a pulsar-timing array, where detection is based on recovering evidence for correlations between different pulsars, i.e. spatial correlations. Nulling these spatial correlations is crucial to understanding the response of our detection statistic under the null hypothesis so that we can properly assess the significance of plausible signals. The usual approach of creating many noise-only simulations is, albeit useful, undesirable since in that case detection significance is predicated on our (incomplete) understanding of all noise processes. Alternatively, destroying any possible correlations in our real datasets and using those (containing all actual noise features) is a much superior approach. In our first method, we perform random phase shifts in the signal-model basis functions, which has the effect of eliminating signal phase coherence between pulsars, while keeping the statistical properties of the pulsar timing residuals intact. We also explore a method to null correlations between pulsars by using a "scrambled" overlap-reduction function in the signal model for the array. This scrambled overlap-reduction function should be effectively orthogonal to what we expect of a real background signal. We demonstrate the efficacy of these methods in a set of simulated datasets that contain a stochastic gravitational wave background, using Bayesian model selection to compare models that do, or do not, account for the correlation between pulsars induced by this signal. Finally, we introduce an overarching formalism under which these two techniques can be seen as natural companions to each other. These methods are immediately applicable to all current pulsar-timing array datasets, and should become standard tools for future analyses.