Abstract
The stochastic gravitational wave background for pulsar timing arrays is often modeled by a Gaussian ensemble which is isotropic and unpolarized. However, the Universe has a discrete set of polarized gravitational wave sources at specific sky locations. Can we trust that the Gaussian ensemble is an accurate description? To investigate this, we explicitly construct an ensemble containing individual binary sources with circular orbits. The orbital inclination angles are randomly distributed, hence the individual sources are elliptically polarized. We then compute the first two moments of the Hellings and Downs correlation, as well as the pulsar-averaged correlation mean and (cosmic) variance. The first moments are the same as for a previously studied ensemble of circularly polarized sources. However, the second moments, and hence the variances, are different for the two ensembles. While neither discrete source model is exactly described by a Gaussian ensemble, we show that in the limit of large , the differences are small.
- Received 30 January 2024
- Accepted 22 February 2024
DOI:https://doi.org/10.1103/PhysRevD.109.083038
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.
Published by the American Physical Society