Residual noise covariance for Planck low-resolution data analysis
University of Helsinki, Department of Physics,
PO Box 64, 00014
e-mail: email@example.com; firstname.lastname@example.org
2 Helsinki Institute of Physics, PO Box 64, 00014 Helsinki, Finland
3 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena CA 91109, USA
4 Astrophysics Group, Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, UK
5 Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK
6 Dipartimento di Fisica, Universitá di Roma “La Sapienza”, p.le A. Moro 2, 00185 Roma, Italy
7 Dipartimento di Fisica, Universitá di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy
8 Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley CA 94720, USA
9 Metsähovi Radio Observatory, Helsinki University of Technology, Metsähovintie 114, 02540 Kylmälä, Finland
10 Laboratoire Astroparticule & Cosmologie (APC) – UMR 7164, CNRS, Université Paris Diderot, 10 rue A. Domon et L. Duquet, 75205 Paris Cedex 13, France
11 Space Sciences Laboratory, University of California Berkeley, Berkeley CA 94720, USA
12 INAF-IASF Bologna, Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna Istituto Nazionale di Astrofisica, via Gobetti 101, 40129 Bologna, Italy
13 Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
14 Centre of Mathematics for Applications, University of Oslo, PO Box 1053 Blindern, 0316 Oslo, Norway
15 INFN, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy
16 INAF-OAB, Osservatorio Astronomico di Bologna Istituto Nazionale di Astrofisica, via Ranzani 1, 40127 Bologna, Italy
17 Warsaw University Observatory, Aleje Ujazdowskie 4, 00478 Warszawa, Poland
18 Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
19 Department of Physics, Blackett Laboratory, Imperial College London, South Kensington campus, London, SW7 2AZ, UK
20 INFN, Sezione di “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy
21 Instituto de Fisica de Cantabria, CSIC-Universidad de Cantabria, Avda. Los Castros s/n, 39005 Santander, Spain
22 ASI Science Data Center, c/o ESRIN, via G. Galilei snc, 00044 Frascati, Italy
23 INAF-Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
Accepted: 15 June 2010
Aims. We develop and validate tools for estimating residual noise covariance in Planck frequency maps, we also quantify signal error effects and compare different techniques to produce low-resolution maps.
Methods. We derived analytical estimates of covariance of the residual noise contained in low-resolution maps produced using a number of mapmaking approaches. We tested these analytical predictions using both Monte Carlo simulations and by applying them to angular power spectrum estimation. We used simulations to quantify the level of signal errors incurred in the different resolution downgrading schemes considered in this work.
Results. We find excellent agreement between the optimal residual noise covariance matrices and Monte Carlo noise maps. For destriping mapmakers, the extent of agreement is dictated by the knee frequency of the correlated noise component and the chosen baseline offset length. Signal striping is shown to be insignificant when properly dealt with. In map resolution downgrading, we find that a carefully selected window function is required to reduce aliasing to the subpercent level at multipoles, ℓ > 2Nside, where Nside is the HEALPix resolution parameter. We show that, for a polarization measurement, reliable characterization of the residual noise is required to draw reliable constraints on large-scale anisotropy.
Conclusions. Methods presented and tested in this paper allow for production of low-resolution maps with both controlled sky signal error level and a reliable estimate of covariance of the residual noise. We have also presented a method for smoothing the residual noise covariance matrices to describe the noise correlations in smoothed, bandwidth-limited maps.
Key words: cosmic microwave background / cosmology: observations / methods: data analysis / methods: numerical
© ESO, 2010