Fast estimation of polarization power spectra using correlation functions

By G. Chon, A. Challinor, S. Prunet, E. Hivon, Istvan Szapudi. 2003

202 citations recorded by the source corpus.

We present a fast method for estimating the cosmic microwave background polarization power spectra using unbiased estimates of heuristically weighted correlation functions. This extends the O(N 3/2 pix) method of Szapudi et al. to polarized data. If the sky coverage allows the correlation functions to be estimated over the full range of angular separations, they can be inverted directly with integral transforms and clean separation of the electric (E) and magnetic (B) modes of polarization is obtained exactly in the mean. We assess the level of E-B mixing that arises from apodized integral transforms when the correlation function can only be estimated for a subset of angular scales, and show that it is significant for small-area observations. We introduce new estimators to deal with this case on the spherical sky that preserve E-B separation; their construction requires an additional integration of the correlation functions but the computational cost is negligible. We illustrate our methods with application to a large-area survey with parameters similar to Planck, and the small-area Background Imaging of Cosmic Extragalactic Polarization experiment. In both cases we show that the errors on the recovered power spectra are close to theoretical expectations.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/5c602f05ed692d646085857b36fec93cd1c73270

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In Astronomy and Astrophysics

Citations in the corpus

An improved source-subtracted and destriped 408 MHz all-sky map (2014, methodology): “We also compute the angular power spectrum of the different maps using the PolSpice pseudo-C` code (Chon et al. 2004).”
A Measurement of the CMB ⟨EE⟩ Spectrum from the 2003 Flight of BOOMERANG (2005, background): “…window function, F XY ℓ is the transfer function measured by signal-only Monte Carlo simulations, ÑXYℓ is the noise bias measured by noise-only Monte Carlo simulations, +Kℓℓ′ is the primary coupling kernel and −Kℓℓ′ describes the geometric leakage between E-modes and Bmodes (Chon et al. 2004).”
Toward an understanding of foreground emission in the BICEP2 region (2014, methodology): “Our power spectrum estimator is based on PolSpice [43].”
MEASUREMENT OF COSMIC MICROWAVE BACKGROUND POLARIZATION POWER SPECTRA FROM TWO YEARS OF BICEP DATA (2009, methodology): “In the following, we describe in detail the Spice pipeline.”
Cosmological Parameters from the 2003 Flight of BOOMERANG (2005, methodology): “The effect of reduced sky coverage and/or pixel weighting is accounted for by computing all coupling kernels following Hivon et al. 20 http://cmb.phys.cwru.edu/boomerang http://oberon.roma1.infn.it/boomerang/b2k (2001) and Chon et al. (2004).”
Planck intermediate results. LVII. Joint Planck LFI and HFI data processing (2020, methodology): “as computed with PolSpice (Chon et al. 2004) over the Planck 2018 common polarization mask.”
Core Cosmology Library: Precision Cosmological Predictions for LSST (2018, unknown): “20) as ξab± = ∑ ` 2`+ 1 4π (±1)sb Cab±` d`sa,±sb(θ), (33) where d`mm′ are the Wigner-d matrices (Ng & Liu 1999; Chon et al. 2004) and we have defined the power spectra Cab±` ≡ ( CaEbE` ± CaBbB` ) +i ( CaBbE` ∓ CaEbB` ) , (34) 12 Note that the transfer functions are defined here for the full…”
KiDS+GAMA : cosmology constraints from a joint analysis of cosmic shear, galaxy-galaxy lensing, and angular clustering (2017, methodology): “This ansatz is very similar to the ‘Spice/PolSpice’ methods (e.g. Chon et al. 2004; Becker et al. 2016), except that we calculate correlation functions via direct galaxy pair counts instead of passing through map-making and pseudo-C estimation steps first.”
A unified pseudo-Cℓ framework (2018, methodology): “…this reason, pseudo-C` algorithms (Peebles 1973; Wandelt et al. 2001; Szapudi et al. 2001; Wandelt et al. 2001; Hivon et al. 2002; Hansen et al. 2002; Chon et al. 2004; Tristram et al. 2005) have become a popular alternative that preserves the `3max scaling of spherical harmonic transforms (and…”
H i intensity mapping: a single dish approach (2012, methodology): “This was achieved by using the Polspice5 software, which calculates the power spectrum from the 2-point pixel correlation function (Szapudi et al. 2001; Chon et al. 2004).”
Planck intermediate results. XXII. Frequency dependence of thermal emission from Galactic dust in intensity and polarization (2014, background): “9.0 (Chon et al. 2004), corrected for the masking, beam, and pixel window e ﬀ ect.”