Overlap reduction functions for pulsar timing arrays and astrometry

TL;DR

This paper introduces an efficient method to compute the overlap reduction functions for gravitational wave detection via pulsar timing arrays and astrometry, applicable to various gravitational wave polarizations.

Contribution

It provides a general technique for calculating correlation functions for gravitational waves in pulsar timing and astrometry, including alternative gravity modes, with accessible code.

Findings

Calculates overlap reduction functions for spin-2 and spin-1 gravitational waves.

Provides a versatile, implementable method for future gravitational wave data analysis.

Includes code to facilitate application of the method in research.

Abstract

We present an efficient technique for calculating the angular two-point correlation functions (or ``overlap reduction functions'') induced by gravitational waves in both the pulse arrival times of pulsars and in the angular deflections of distant sources. In the most general case, there are six auto- and cross-correlations for the pulse arrival times and the two components of the angular deflection. We provide results for spin-2 (i.e., general-relativistic) gravitational waves as well as the spin-1 modes that may arise in alternative-gravity theories. These calculations can be easily implemented for future analysis or study, and we provide code to do so.