Residual noise covariance for Planck low-resolution data analysis

¹ University of Helsinki, Department of Physics, PO Box 64, 00014 Helsinki, Finland
e-mail: reijo.t.keskitalo@jpl.nasa.gov; reijo.keskitalo@gmail.com
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

Received: 31 May 2009
Accepted: 15 June 2010

Abstract

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 > 2N_side, where N_side 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.