Planck 2013 results. XXXI. Consistency of the Planck data

¹ APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France
² Aalto University Metsähovi Radio Observatory and Dept of Radio Science and Engineering, PO Box 13000, 00076 Aalto, Finland
³ African Institute for Mathematical Sciences, , 6-8 Melrose Road, 7945 Muizenberg, Cape Town, South Africa
⁴ Agenzia Spaziale Italiana Science Data Center, , Via del Politecnico snc, 00133 Roma, Italy
⁵ Agenzia Spaziale Italiana, Viale Liegi 26, Roma, Italy
⁶ Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
⁷ Astrophysics & Cosmology Research Unit, School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, , Westville Campus, Private Bag X54001, 4000 Durban, South Africa
⁸ CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
⁹ CNRS, IRAP, 9 Av. Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
¹⁰ California Institute of Technology, Pasadena, California, USA
¹¹ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹² Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, USA
¹³ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁴ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁵ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁶ Departamento de Física, Universidad de Oviedo, , Avda. Calvo Sotelo s/n, 33007 Oviedo, Spain
¹⁷ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
¹⁸ Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA
¹⁹ Department ofPhysics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁰ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, , Los Angeles, CA 90089, USA
²¹ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²² Department of Physics, Florida State University, , Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
²³ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00014 Helsinki, Finland
²⁴ Department of Physics, Princeton University, , Princeton, New Jersey, USA
²⁵ Department of Physics, University of California, , Santa Barbara, California, USA
²⁶ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
²⁷ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
²⁸ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy
²⁹ Dipartimento di Fisica, Università La Sapienza, , P.le A. Moro 2, 00185 Roma, Italy
³⁰ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, 20133 Milano, Italy
³¹ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, 34127 Trieste, Italy
³² Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, 00133 Roma, Italy
³³ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
³⁴ Dpto. Astrofísica, Universidad de La Laguna (ULL), , 38206, La Laguna, Tenerife, Spain
³⁵ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, 28691 Villanueva de la Cañada, Madrid, Spain
³⁶ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
³⁷ Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Väisäläntie 20, Piikkiö 21500, Finland
³⁸ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, USA
³⁹ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, 00014 Helsinki, Finland
⁴⁰ INAF – Osservatorio Astronomico di Padova, , Vicolo dell’Osservatorio 5, 35122 Padova, Italy
⁴¹ INAF – Osservatorio Astronomico di Roma, , via di Frascati 33, 00040 Monte Porzio Catone, Italy
⁴² INAF – Osservatorio Astronomico di Trieste, , via G.B. Tiepolo 11, 34143 Trieste, Italy
⁴³ INAF/IASF Bologna, via Gobetti 101, 40129 Bologna, Italy
⁴⁴ INAF/IASF Milano, via E. Bassini 15, 20133 Milano, Italy
⁴⁵ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁴⁶ INFN, Sezione di Roma 1, Università di Roma Sapienza, , P.le Aldo Moro 2, 00185 Roma, Italy
⁴⁷ INFN/National Institute for Nuclear Physics, , Via Valerio 2, 34127 Trieste, Italy
⁴⁸ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁴⁹ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁵⁰ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁵¹ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁵² Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁵³ Institut d’Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91405 Orsay, France
⁵⁴ Institut d’Astrophysique de Paris, CNRS (UMR 7095), , 98bis boulevard Arago, 75014 Paris, France
⁵⁵ Institute for Space Sciences, Bucharest-Magurale, Romania
⁵⁶ Institute of Astronomy, University of Cambridge, , Madingley Road, Cambridge CB3 0HA, UK
⁵⁷ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0315 Oslo, Norway
⁵⁸ Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Apartado Postal 51 y 216, 72000 Puebla, México
⁵⁹ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, 38200, La Laguna, Tenerife, Spain
⁶⁰ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁶¹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁶² Jodrell Bank Centre for Astrophysics, Alan Turing Building, School ofPhysics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁶³ Kavli Institute for Cosmology Cambridge, , Madingley Road, Cambridge, CB3 0HA, UK
⁶⁴ LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
⁶⁵ LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, 75014 Paris, France
⁶⁶ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁶⁷ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁶⁸ Laboratoire de Physique Subatomique et de Cosmologie, Université Joseph Fourier Grenoble I, CNRS/IN2P3, Institut National Polytechnique de Grenoble, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁶⁹ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁷⁰ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷¹ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁷² National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁷³ Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁷⁴ Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena, CA, 91125, USA
⁷⁵ SB-ITP-LPPC, EPFL, 1015, Lausanne, Switzerland
⁷⁶ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁷⁷ School of Physics and Astronomy, Cardiff University, , Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁷⁸ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁷⁹ Space Sciences Laboratory, University of California, , Berkeley, California, USA
⁸⁰ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁸¹ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
⁸² UPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
⁸³ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁸⁴ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
⁸⁵ University of Granada, Instituto Carlos I de Física Teórica y Computacional, Granada, Spain
⁸⁶ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 2 March 2014
Accepted: 29 July 2014

Abstract

The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70 GHz (amplifier) and 100 GHz (bolometer) channels. Based on different instrument technologies, with feeds located differently in the focal plane, analysed independently by different teams using different software, and near the minimum of diffuse foreground emission, these channels are in effect two different experiments. The 143 GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved foreground emission. In this paper, we analyse the level of consistency achieved in the 2013 Planck data. We concentrate on comparisons between the 70, 100, and 143 GHz channel maps and power spectra, particularly over the angular scales of the first and second acoustic peaks, on maps masked for diffuse Galactic emission and for strong unresolved sources. Difference maps covering angular scales from 8° to 15′ are consistent with noise, and show no evidence of cosmic microwave background structure. Including small but important corrections for unresolved-source residuals, we demonstrate agreement (measured by deviation of the ratio from unity) between 70 and 100 GHz power spectra averaged over 70 ≤ ℓ ≤ 390 at the 0.8% level, and agreement between 143 and 100 GHz power spectra of 0.4% over the same ℓ range. These values are within and consistent with the overall uncertainties in calibration given in the Planck 2013 results. We also present results based on the 2013 likelihood analysis showing consistency at the 0.35% between the 100, 143, and 217 GHz power spectra. We analyse calibration procedures and beams to determine what fraction of these differences can be accounted for by known approximations or systematicerrors that could be controlled even better in the future, reducing uncertainties still further. Several possible small improvements are described. Subsequent analysis of the beams quantifies the importance of asymmetry in the near sidelobes, which was not fully accounted for initially, affecting the 70/100 ratio. Correcting for this, the 70, 100, and 143 GHz power spectra agree to 0.4% over the first two acoustic peaks. The likelihood analysis that produced the 2013 cosmological parameters incorporated uncertainties larger than this. We show explicitly that correction of the missing near sidelobe power in the HFI channels would result in shifts in the posterior distributions of parameters of less than 0.3σ except for A_s, the amplitude of the primordial curvature perturbations at 0.05 Mpc^-1, which changes by about 1σ. We extend these comparisons to include the sky maps from the complete nine-year mission of the Wilkinson Microwave Anisotropy Probe (WMAP), and find a roughly 2% difference between the Planck and WMAP power spectra in the region of the first acoustic peak.