An optimal FFT-based anisotropic power spectrum estimator. Issue 7 (3rd July 2017)

• Record Type: Journal Article
• Authors: Hand, Nick; Li, Yin; Slepian, Zachary; Seljak, Uroš
• Is Part Of: Journal of cosmology and astroparticle physics. Volume 2017:Issue 7(2017)
• Page Start: 002
• Page End: 002
• Publication Date: 2017-07-03
• Subjects: cosmological simulations -- power spectrum -- redshift surveys; Cosmology -- Periodicals; Astrophysics -- Periodicals; 523.0105
• DOI: 10.1088/1475-7516/2017/07/002
• Languages: English
• ISSNs: 1475-7516

Abstract

Abstract: Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTs of the Cartesian approach. For the hexadecapole ( ℓ = 4 ), this translates to 40% fewer FFTs, with increased savings for higher ℓ . The reduction in wall-clock time enables the calculation of finely-binned wedges in P ( k, μ), obtained by computing multipoles up to a large ℓmax and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≃ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓmax, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓmax =16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ8, as compared to a 54% increase with ℓmax =4 .