Non-linear corrections of overlap reduction functions for pulsar timing arrays

TL;DR

This paper explores non-linear corrections to overlap reduction functions in pulsar timing arrays, considering gravitational self-interactions and non-Gaussianity, which could distinguish real signals from the Hellings-Downs curves.

Contribution

It introduces a theoretical framework for non-linear corrections to overlap reduction functions, accounting for gravitational self-interactions and non-Gaussianity in pulsar timing data.

Findings

Order-one correction from three-point correlations of gravitational waves

Non-linear corrections alter the shape of overlap reduction functions

Potential to distinguish non-linear effects from standard Hellings-Downs curves

Abstract

The signals from international pulsar timing arrays have presented a hint of gravitational stochastic background in nHz band frequency. Further confirmation will be based on whether the signals follow the angular correlation curves formulated by the overlap reduction functions, known as Hellings-Downs curves. This paper investigates the non-linear corrections of overlap reduction functions in the present of non-Gaussianity, in which the self-interaction of gravity is first taken into considerations. Based on perturbed Einstein field equations for the second order metric perturbations, and perturbed geodesic equations to the second order, we obtain non-linear corrections for the timing residuals of pulsar timing, and theoretically study corresponding overlap reduction functions for pulsar timing arrays. There is order-one correction for the overlap reduction functions from the three-point correlations of gravitational waves, and thus the shapes of the overlap reduction functions with non-linear corrections can be distinguished from the Hellings-Downs curves.