Nonlinear corrections of overlap reduction functions for pulsar timing arrays

Abstract

Recent pulsar timing array experiments have reported a hint of gravitational stochastic background in nHz band frequency. Further confirmation might rely on whether the signature of the signals is consistent with that sketched by overlap reduction functions, known as Hellings-Downs curves. This paper investigates the nonlinear corrections of overlap reduction functions in the presence of non-Gaussianity, in which the self-interaction of gravity is first taken into account. Expanding Einstein field equations and geodesic equations into the nonlinear regime, we obtain nonlinear corrections for the timing residuals of pulsar timing, and theoretically study the overlap reduction functions for pulsar timing arrays. In the event of considerable correction from the three-point correlations of gravitational waves, the shapes of the overlap reduction functions with nonlinear corrections can be differentiated from Hellings-Downs curves.