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Journal Article

Rapid refitting techniques for Bayesian spectral characterization of the gravitational wave background using pulsar timing arrays


van Haasteren,  Rutger
Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society;

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Lamb, W. G., Taylor, S. R., & van Haasteren, R. (2023). Rapid refitting techniques for Bayesian spectral characterization of the gravitational wave background using pulsar timing arrays. Physical Review D, 108(10): 103019. doi:10.1103/PhysRevD.108.103019.

Cite as: https://hdl.handle.net/21.11116/0000-000E-0915-1
Pulsar timing arrays (PTAs) have recently found evidence for a
nanohertz-frequency stochastic gravitational-wave background (SGWB).
Constraining its spectral characteristics will reveal its origins. To achieve
this, we must understand how data and modeling conditions in each pulsar
influence the precision and accuracy of SGWB spectral recovery, typically
requiring many Bayesian analyses on real data sets and large-scale simulations
that are slow and computationally taxing. To combat this, we have developed
several new rapid approaches that operate on intermediate SGWB analysis
products. These techniques refit SGWB spectral models to previously computed
Bayesian posterior estimates of the timing power spectra. We test our new
techniques on simulated PTA data sets and the NANOGrav 12.5-year data set,
where in the latter our refit posterior achieves a Hellinger distance --
bounded between 0 for identical distributions and 1 for zero overlap -- from
the current full production-level pipeline that is < 0.1. Our techniques are ~
$10^2$--$10^4$ times faster than the production-level likelihood and scale much
more favorably (sub-linearly) as a PTA is expanded with new pulsars or
observations. Our techniques also allow us to demonstrate conclusively that
SGWB spectral characterization in PTA data sets is driven by the longest-timed
pulsars and the best-measured power spectral densities. Indeed, the
common-process spectral properties found in the NANOGrav 12.5-year data set are
given by analyzing only the ~14 longest-timed pulsars out of the full 45 pulsar
array, and we find that the 'shallowing' of the common-process power-law model
occurs when gravitational-wave frequencies higher than ~50 nanohertz are
included. The implementation of our techniques is openly available as a
software suite to allow fast and flexible PTA SGWB spectral characterization
and model selection.