Analytic series expansion of the overlap reduction function for gravitational wave search with pulsar timing arrays

Abstract

In our previous paper \cite{PTA1} we derived a generic expression for the pulse redshift the main observable for the Pulsar Timing Array (PTA) experiment for detection of gravitational waves for all possible polarizations induced by modifications of general relativity (GR). In this work we provide a generic expression of the overlap reduction function for PTA without using the short wavelength approximation for tensorial polarization. We are convinced, that the short wavelength approximation is not applicable to the overlap reduction function for PTA's, since the removal of the exponential terms in the integrand would lead to poles for $x,y$ and $l$ polarizations and discontinuities for $+$ and $\times$. In this work we provide a series expansion to calculate the integral exactly and investigate the behaviour of the series for short wavelength values via numerical evaluation of the analytical series. We find a disagreement for the limit of co-located pulsars with the Hellings \& Downs curve.

arXiv commentSupplemental material is attached in the main text and Mathematica notebooks are also attached in the source

References in corpus (9)

• A Double-Pulsar System - A Rare Laboratory for Relativistic Gravity and Plasma Physics
• The international pulsar timing array project: using pulsars as a gravitational wave detector
• Search templates for gravitational waves from inspiraling binaries: Choice of template spacing
• The Parkes Pulsar Timing Array Project
• The International Pulsar Timing Array: Second data release
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• Stochastic backgrounds in alternative theories of gravity: overlap reduction functions for pulsar timing arrays
• Pulse redshift of pulsar timing array signals for all possible gravitational wave polarizations in modified general relativity
• Gravitational wave polarization from combined Earth-space detectors

Cited by in corpus (5)

• Full analytic expression of overlap reduction function for gravitational wave background with pulsar timing arrays
• Non-linear corrections of overlap reduction functions for pulsar timing arrays
• Unveiling the existence of nontensorial gravitational-wave polarizations from individual supermassive black hole binaries with pulsar timing arrays
• Overlap reduction function for gravitational wave detectors in an expanding Universe
• Series expansion of the overlap reduction function for scalar and vector polarizations for gravitational wave search with pulsar timing arrays