# Ephemeris Errors and the Gravitational Wave Signal: Harmonic Mode Coupling in Pulsar Timing Array Searches

## TL;DR

Detecting a gravitational wave background with pulsar timing arrays requires careful array design to distinguish true signals from ephemeris and clock errors, emphasizing the importance of array geometry and pulsar distribution.

## Contribution

This paper provides a spherical harmonic analysis of pulsar timing residuals to quantify how array geometry affects contamination from ephemeris and clock errors, proposing methods to mitigate these effects.

## Key findings

- At least 9 well-spaced pulsars are needed to separate gravitational wave signals from errors.
- Uniform pulsar distributions can reduce contamination in large arrays.
- Pulsars following the galactic distribution are always affected by ephemeris errors.

## Abstract

Any unambiguous detection of a stochastic gravitational wave background by a pulsar timing array will rest on the measurement of a characteristic angular correlation between pulsars. The ability to measure this correlation will depend on the geometry of the array. However, spatially correlated sources of noise, such as errors in the planetary ephemeris or clock errors, can produce false-positive correlations. The severity of this contamination will also depend on the geometry of the array. This paper quantifies these geometric effects with a spherical harmonic analysis of the pulsar timing residuals. At least 9 well-spaced pulsars are needed to simultaneously measure a gravitational wave background and separate it from ephemeris and clock errors. Uniform distributions of pulsars can eliminate the contamination for arrays with large numbers of pulsars, but pulsars following the galactic distribution of known millisecond pulsars will always be affected. We quantitatively demonstrate the need for arrays to include many pulsars and for the pulsars to be distributed as uniformly as possible. Finally, we suggest a technique to cleanly separate the effect of ephemeris and clock errors from the gravitational wave signal.