Planck 2015 results

XVI. Isotropy and statistics of the CMB

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, Muizenberg, Cape Town, South Africa
⁴ Agenzia Spaziale Italiana Science Data Center, via del Politecnico snc, 00133 Roma, Italy
⁵ Aix Marseille Université, CNRS, LAM (Laboratoire d’Astrophysique de Marseille) UMR 7326, 13388 Marseille, France
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 CRANN, Trinity College, Dublin, Ireland
¹¹ California Institute of Technology, Pasadena, California CA 91125, USA
¹² Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹³ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹⁴ Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, USA
¹⁵ Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain
¹⁶ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁷ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁸ Département de Physique Théorique, Université de Genève, 24 Quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁹ Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna, Tenerife, Spain
²⁰ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33003 Oviedo, Spain
²¹ Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain
²² Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario, Canada
²³ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²⁴ Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²⁵ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁶ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁷ Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
²⁸ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, 00100 Helsinki, Finland
²⁹ Department of Physics, Princeton University, Princeton, New Jersey NJ 08544, USA
³⁰ Department of Physics, University of California, Santa Barbara, California CA 93106, USA
³¹ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³² Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³³ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³⁴ Dipartimento di Fisica, Università La Sapienza, P. le A. Moro 2, Roma, Italy
³⁵ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16 Milano, Italy
³⁶ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, Trieste, Italy
³⁷ Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1 Roma, Italy
³⁸ Discovery Center, Niels Bohr Institute, 17 Blegdamsvej, Copenhagen, Denmark
³⁹ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain
⁴⁰ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴¹ Facoltà di Ingegneria, Università degli Studi e-Campus, via Isimbardi 10, 22060 Novedrate (CO), Italy
⁴² Gran Sasso Science Institute, INFN, viale F. Crispi 7, 67100 L’ Aquila, Italy
⁴³ HGSFP and University of Heidelberg, Theoretical Physics Department, Philosophenweg 16, 69120 Heidelberg, Germany
⁴⁴ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁴⁵ INAF–Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, Italy
⁴⁶ INAF–Osservatorio Astronomicodi Roma, via di Frascati 33, Monte Porzio Catone, Italy
⁴⁷ INAF–Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, Trieste, Italy
⁴⁸ INAF/IASF Bologna, via Gobetti 101, Bologna, Italy
⁴⁹ INAF/IASF Milano, via E. Bassini 15, Milano, Italy
⁵⁰ INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
⁵¹ INFN, Sezione di Roma 1, Università di Roma Sapienza, Piazzale Aldo Moro 2, 00185 Roma, Italy
⁵² INFN, Sezione di Roma 2, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1 Roma, Italy
⁵³ INFN/National Institute for Nuclear Physics, via Valerio 2, 34127 Trieste, Italy
⁵⁴ IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Grenoble Alpes, IPAG; CNRS, IPAG, 38000 Grenoble, France
⁵⁵ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁵⁶ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁵⁷ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁵⁸ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, Grenoble, France
⁵⁹ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁶⁰ Institut d’Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, 91440 Orsay, France
⁶¹ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98 bis Boulevard Arago, 75014 Paris, France
⁶² Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, 52056 Aachen, Germany
⁶³ Institute for Space Sciences, Bucharest-Magurale, 077125 Romania
⁶⁴ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁵ Institute of Theoretical Astrophysics, University of Oslo, Blindern, 0371 Oslo, Norway
⁶⁶ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, 38205 Tenerife, Spain
⁶⁷ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, 39005 Santander, Spain
⁶⁸ Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy
⁶⁹ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁷⁰ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷¹ Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA
⁷² Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷³ Kazan Federal University, 18 Kremlyovskaya St., 420008 Kazan, Russia
⁷⁴ LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
⁷⁵ LERMA, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, France
⁷⁶ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁷ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁷⁸ Laboratoire de Physique Subatomique et Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, 53 rue des Martyrs, 38026 Grenoble Cedex, France
⁷⁹ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁸⁰ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁸¹ Lebedev Physical Institute of the Russian Academy of Sciences, Astro Space Centre, 84/32 Profsoyuznaya st., GSP-7, 117997 Moscow, Russia
⁸² Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, 10617 Taipei, Taiwan
⁸³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁸⁴ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁸⁵ National University of Ireland, Department of Experimental Physics, Maynooth, Co. Kildare, Ireland
⁸⁶ Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland
⁸⁷ Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
⁸⁸ Optical Science Laboratory, University College London, Gower Street, London, UK
⁸⁹ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁹⁰ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁹¹ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁹² Simon Fraser University, Department of Physics, 8888 University Drive, Burnaby BC, Canada
⁹³ Sorbonne Université-UPMC, UMR 7095, Institut d’Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris, France
⁹⁴ Space Research Institute (IKI), Russian Academy of Sciences, Profsoyuznaya Str, 84/32, 117997 Moscow, Russia
⁹⁵ Space Sciences Laboratory, University of California, Berkeley, California, USA
⁹⁶ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁹⁷ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
⁹⁸ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
⁹⁹ Theory Division, PH-TH, CERN, 1211, Geneva 23, Switzerland
¹⁰⁰ UPMC Univ Paris 06, UMR 7095, 98 bis Boulevard Arago, 75014 Paris, France
¹⁰¹ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
¹⁰² University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, 18071 Granada, Spain
¹⁰³ University of Granada, Instituto Carlos I de Física Teórica y Computacional, 18071 Granada, Spain
¹⁰⁴ University of Heidelberg, Institute for Theoretical Physics, Philosophenweg 16, 69120 Heidelberg, Germany
¹⁰⁵ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

^⋆ Corresponding author: A. J. Banday, e-mail: anthony.banday@irap.omp.eu

Received: 5 June 2015
Accepted: 7 September 2015

Abstract

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The “Cold Spot” is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.