Fast estimators for redshift-space clustering

By R. Scoccimarro. 2015

161 citations recorded by the source corpus.

Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only Fast Fourier Transforms (FFTs) of the overdensity field multipoles for a given survey geometry, compute the power spectrum monopole, quadrupole and hexadecapole, and generalize such estimators to the bispectrum. Using realistic mock catalogs we compare the signal to noise of two estimators for the power spectrum hexadecapole that require different number of FFTs and measure the bispectrum monopole, quadrupole and hexadecapole. The resulting algorithm is very efficient, e.g. for the BOSS survey requires about three minutes for $\ell=0,2,4$ power spectra for scales up to $k=0.3~h/$Mpc and about fifteen additional minutes for $\ell=0,2,4$ bispectra for all scales and triangle shapes up to $k=0.2~h/$Mpc on a single core. The speed of these estimators is essential as it makes possible to compute covariance matrices from large number of realizations of mock catalogs with realistic survey characteristics, and paves the way for improved constrains of gravity on cosmological scales, inflation and galaxy bias.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/6f51e4e5657f1076e5c9e496fdf66b5a1e74128b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Instrumentation

Citations in the corpus

Consistent modeling of velocity statistics and redshift-space distortions in one-loop perturbation theory (2020, unknown): “produce power spectrum multipoles P`(k) [92, 105–107].”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Fourier space (2016, methodology): “(5) Following Bianchi et al. (2015) and Scoccimarro (2015) we can write A0(k) = ∫ drD(r)eik·r , (6) Bxy(k) = ∫ dr rxry |r|2 D(r)e ik·r , (7) which allows these quantities to be calculated with FFTs.”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space (2016, methodology): “This integral was recently found to be evaluable using Fast Fourier transformations (FFTs; Bianchi et al. 2015; Scoccimarro 2015) instead of the expensive direct summation.”
nbodykit: An Open-source, Massively Parallel Toolkit for Large-scale Structure (2017, methodology): “This estimator improves the FFT-based estimator presented by Bianchi et al. (2015) and Scoccimarro (2015), building on the ideas of previous power spectrum estimators (Feldman et al. 1994; Yamamoto et al. 2006), and in particular, the treatment of the anisotropic 2PCF using spherical harmonics of…”
The Quijote Simulations (2019, methodology): “We use a Fast Fourier Transform (FFT) based estimator similar to the estimators described in Sefusatti & Scoccimarro (2005), Scoccimarro (2015), and Sefusatti et al. (2016).”
Accurate estimators of correlation functions in Fourier space (2015, unknown): “(49) can take advantage of the integral representation of the Dirac delta, so that (see Scoccimarro 2015, for extensions to redshift-space) B̂(k1, k2, k3) = 1 VB ∫ d3x (2π)3 ∫ k1 d3q1 ∫ k2 d3q2 ∫ k3 d3q3 ×δq1 δq2 δq3 e iq123·x = 1 VB ∫ d3x (2π)3 3∏ i=1 Iki(x) , (52) where the integrals Ik(x) ≡ ∫ k…”
Combining full-shape and BAO analyses of galaxy power spectra: a 1.6% CMB-independent constraint on H0 (2020, methodology): “[86, 87], computing the multipole power from the data-set combined with a set of random points.”
The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample (2016, methodology): “In order to make use of new estimators based on fast Fourier transforms (FFT; Bianchi et al. 2015; Scoccimarro 2015), their analaysis uses the power spectrum clustering wedges, filtering out the information of Legendre multipoles ` > 4.”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies (2016, methodology): “An extension of this estimator based the Yamamoto estimator (Yamamoto et al. 2006) for the quadrupole of the bispectrum would be possible (see Scoccimarro 2015), although for simplicity (especially on the modelling) we do not consider this quantity here.”