The effect of small inter-pulsar distance variations in stochastic gravitational wave background searches with Pulsar Timing Arrays

Abstract

One of the primary objectives for Pulsar Timing Arrays (PTAs) is to detect a stochastic background generated by the incoherent superposition of gravitational waves (GWs), in particular from the cosmic population of supermassive black hole binaries. Current stochastic background searches assume that pulsars in a PTA are separated from each other and the Earth by many GW wavelengths. As more millisecond pulsars are discovered and added to PTAs, some may be separated by only a few radiation wavelengths or less, resulting in correlated GW phase changes between close pulsars in the array. Here we investigate how PTA overlap reduction functions (ORFs), up to quadrupole order, are affected by these additional correlated phase changes, and how they are in turn affected by relaxing the assumption that all pulsars are equidistant from the solar system barycenter. We find that in the low frequency GW background limit of $f\sim 10^{-9}$~Hz, and for pulsars at varying distances from the Earth, that these additional correlations only affect the ORFs by a few percent for pulsar pairs at large angular separations, as expected. However when nearby (order 100 pc) pulsars are separated by less than a few degrees, the correlated phase changes can introduce variations of a few tens of percent in the magnitude of the isotropic ORF, and much larger fractional differences in the anisotropic ORFs-- up to 188 in the $m=0$, $l=2$ ORF for equidistant pulsars separated by 3 degrees. In fact, the magnitude of most of the anisotropic ORFs is largest at small, but non-zero, pulsar separations. Finally, we write down a small angle approximation for the correlated phase changes which can easily be implemented in search pipelines, and for completeness, examine the behavior of the ORFs for pulsars which lie at a radiation wavelength from the Earth.

16 pages, 8 figures, submitted to PRD

References in corpus (6)

• Tests of general relativity from timing the double pulsar
• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• Gravitational waves from resolvable massive black hole binary systems and observations with Pulsar Timing Arrays
• Binary super-massive black hole environments diminish the gravitational-wave signal in the pulsar timing band
• Detecting a Stochastic Gravitational-Wave Background: The Overlap Reduction Function
• Constraint on the early Universe by relic gravitational waves: From pulsar timing observations

Cited by in corpus (4)

• Gravitational-wave sensitivity curves
• The Local Nanohertz Gravitational-Wave Landscape From Supermassive Black Hole Binaries
• Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data
• Gravitational Waves, Extreme Astrophysics, and Fundamental Physics with Precision Pulsar Timing