On the overlap reduction function of pulsar timing array searches for gravitational waves in modified gravity
Year: 2024
Type: article
Abstract: Pulsar timing array (PTA) searches for gravitational waves (GWs) aim to detect a characteristic correlation pattern in the timing residuals of galactic millisecond pulsars. This pattern is described by the PTA overlap reduction function (ORF) Γ a b ( ξ a b ) , which is known as the Hellings–Downs (HD) curve in general relativity (GR). In theories of modified gravity, the HD curve often receives corrections. Assuming, e.g. a subluminal GW phase velocity, one finds a drastically enhanced ORF in the limit of small angular separations between pulsar a and pulsar b in the sky, ξ a b → 0 . In particular, working in harmonic space and performing an approximate resummation of all multipole contributions, the auto correlation coefficient Γ aa seems to diverge. In this paper, we confirm that this divergence is unphysical and provide an exact and analytical expression for Γ aa in dependence of the pulsar distance La and the GW phase velocity v ph . In the GR limit and assuming a large pulsar distance, our expression reduces to Γ a a = 1 . In the case of subluminal phase velocity, we show that the regularization of the naive divergent result is a finite-distance effect, meaning that Γ aa scales linearly with fLa , where f is the GW frequency. For superluminal phase velocity (subluminal group velocity), which is relevant in the case of massive gravity, we correct an earlier analytical result for Γ ab . Our results pave the way for fitting modified-gravity theories with nonstandard phase velocity to PTA data, which requires a proper understanding of the auto correlation coefficient Γ aa .
Source: Classical and Quantum Gravity
Institutions: University of Münster, Deutsches Elektronen-Synchrotron DESY
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,165
Funders: Strong, Deutsche Forschungsgemeinschaft
OpenAlex ID: W4404797817