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Incredible progress on the theoretical uncertainty of the spatialcorrelations of the stochastic gravitational wave (GW) background were recentlymade. However, it remains to realize the impact of this theoretical uncertaintyon PTA cross correlations analysis. This paper pushes forward in thisdirection, as a proof--of--principle: showing the potential role thattheoretical uncertainty has on unburying the stochastic GW background signal innoisy PTA cross correlation measurements. We consider both a mock data set andthe noise--marginalized 12.5 years NANOGrav spatial correlation measurements,and find optimistic conclusions regardless of the physical content of the GWbackground and the nature of the noise in the data. Very briefly, we showthrough various cases a modest result that looking out for a stochastic signalis better when two of its moments are utilized. Or, in terms of GWs, we showthat the theoretical uncertainty can play a substantial role in the hunt forthe stochastic GW background.

Hunting the stochastic gravitational wave background in pulsar timing array cross correlations through theoretical uncertainty