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Efficient Computation of Overlap Reduction Functions for Pulsar Timing Arrays.

Neha Anil Kumar1, Marc Kamionkowski1

  • 1William H. Miller III Department of Physics and Astronomy, <a href="https://ror.org/00za53h95">Johns Hopkins University</a>, 3400 North Charles Street, Baltimore, Maryland 21218, USA.

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Pulsar timing arrays detect gravitational waves (GWs) using correlation functions. This study presents a general formula for these functions, accounting for arbitrary polarization and anisotropy in GW backgrounds.

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Area of Science:

  • * Astrophysics
  • * Gravitational Wave Astronomy
  • * Theoretical Physics

Background:

  • * Pulsar timing arrays (PTAs) are key instruments for detecting stochastic gravitational wave (GW) backgrounds.
  • * The standard signal in PTAs is characterized by the Hellings-Downs curve, dependent only on pulsar separation.
  • * Alternative gravity theories may introduce additional GW polarization modes and anisotropic backgrounds.

Purpose of the Study:

  • * To derive a generalized formula for the two-point correlation function (overlap reduction function, ORF) of GWs.
  • * To accommodate arbitrary polarization states, including linear and circular polarization.
  • * To incorporate anisotropies in GW intensity and polarization within the ORF.

Main Methods:

  • * Developed a comprehensive mathematical framework for the GW overlap reduction function (ORF).
  • * Extended the ORF to include contributions from transverse-traceless GW modes and vector (spin-1) modes.
  • * Analyzed the impact of arbitrary polarization and anisotropy on the ORF.

Main Results:

  • * Provided a simple, general formula for the most encompassing ORF.
  • * Demonstrated how anisotropy and non-standard polarizations modify the ORF beyond the Hellings-Downs curve.
  • * Derived specific ORF expressions for general-relativistic and alternative-gravity modes.

Conclusions:

  • * The generalized ORF framework is essential for interpreting PTA data with complex GW backgrounds.
  • * This work advances the search for GWs and the testing of alternative gravity theories.
  • * The derived formulas will enhance the sensitivity and scope of gravitational wave detection with PTAs.