Year: 2026
Type: preprint
Abstract: What is the optimal power spectrum estimator on ultra-large scales where the plane-parallel approximation breaks down? Conventional estimators, such as the Yamamoto estimator, are only optimal in the plane-parallel limit, while their associated window functions are typically approximated by truncating a slowly converging infinite series. We address two outstanding challenges in the analysis of wide-angle power spectra. First, we derive the optimal estimator for a broad class of clustering signals and show that it is equivalent to a previously proposed two-$\ell$ generalization of the Yamamoto estimator. Second, we show how to write the exact two-$\ell$ window function as a finite number of terms that can be efficiently evaluated using FFTs. Our results apply to a wide range of observables, including redshift-space distortions (RSDs) and large-scale radial-velocity reconstruction from the kinetic Sunyaev-Zel'dovich effect. Focusing on linear-theory RSDs, we validate the finite window-function representation numerically and show that the two-$\ell$ estimator can yield order-unity improvements in the signal-to-noise ratio of ultra-large-scale power spectrum measurements.
Source: arXiv (Cornell University)
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, National Aeronautics and Space Administration, Government of Canada, Industry Canada, Institut Périmètre de physique théorique, Office of Science, Natural Sciences and Engineering Research Council of Canada, High Energy Physics, Lawrence Berkeley National Laboratory
Awards: G2066175637, Kinetic Sunyaev-Zeldovich Velocity Reconstruction with the Simons Observatory, G4326592670, G443619643, CDS&E: Probabilistic modeling of fields and point clouds in cosmology, HIGH ENERGY PHYSICS RESEARCH: EXPERIMENTAL & THEORETICAL, HIGH ENERGY PHYSICS RESEARCH: EXPERIMENTAL & THEORETICAL
OpenAlex ID: W7167686997
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