Planck 2013 results. IV. Low Frequency Instrument beams and window functions

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, Metsähovintie 114, 02540 Kylmälä, 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 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 CITA, University of Toronto, 60 St. George St., Toronto, ON M5S 3H8, Canada
⁸ CNRS, IRAP, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France
⁹ California Institute of Technology, Pasadena, California, USA
¹⁰ Centre for Theoretical Cosmology, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
¹¹ Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain
¹² Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, California, USA
¹³ Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain
¹⁴ DSM/Irfu/SPP, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
¹⁵ DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
¹⁶ Département de Physique Théorique, Université de Genève, 24 quai E. Ansermet, 1211 Genève 4, Switzerland
¹⁷ Departamento de Física Fundamental, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain
¹⁸ Departamento de Física, Universidad de Oviedo, Avda. Calvo Sotelo s/n, Oviedo, Spain
¹⁹ Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, Ontario, Canada
²⁰ Department of Astrophysics/IMAPP, Radboud University Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands
²¹ Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA
²² Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada
²³ Department of Physics and Astronomy, Dana and David Dornsife College of Letter, Arts and Sciences, University of Southern California, Los Angeles, CA 90089, USA
²⁴ Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
²⁵ Department of Physics, Florida State University, Keen Physics Building, 77 Chieftan Way, Tallahassee, Florida, USA
²⁶ Department of Physics, Gustaf Hällströmin katu 2a, University of Helsinki, Helsinki, Finland
²⁷ Department of Physics, Princeton University, Princeton, New Jersey, USA
²⁸ Department of Physics, University of California, One Shields Avenue, Davis, California, USA
²⁹ Department of Physics, University of California, Santa Barbara, California, USA
³⁰ Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois, USA
³¹ Dipartimento di Fisica e Astronomia G. Galilei, Università degli Studi di Padova, via Marzolo 8, 35131 Padova, Italy
³² Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, via Saragat 1, 44122 Ferrara, Italy
³³ Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, Roma, Italy
³⁴ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria, 16, Milano, Italy
³⁵ Dipartimento di Fisica, Università degli Studi di Trieste, via A. Valerio 2, Trieste, Italy
³⁶ Dipartimento di Fisica, Università di Roma Tor Vergata, via della Ricerca Scientifica, 1, Roma, Italy
³⁷ Discovery Center, Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark
³⁸ Dpto. Astrofísica, Universidad de La Laguna (ULL), 38206, La Laguna, Tenerife, Spain
³⁹ European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain
⁴⁰ European Space Agency, ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
⁴¹ Haverford College Astronomy Department, 370 Lancaster Avenue, Haverford, Pennsylvania, USA
⁴² Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
⁴³ INAF – Osservatorio Astrofisico di Catania, via S. Sofia 78, Catania, Italy
⁴⁴ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, Padova, Italy
⁴⁵ INAF – Osservatorio Astronomico di Roma, via di Frascati 33, Monte Porzio Catone, Italy
⁴⁶ INAF – Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, Trieste, Italy
⁴⁷ INAF Istituto di Radioastronomia, via P. Gobetti 101, 40129 Bologna, 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, P.le Aldo Moro 2, 00185 Roma, Italy
⁵² IPAG: Institut de Planétologie et d’Astrophysique de Grenoble, Université Joseph Fourier, Grenoble 1/CNRS-INSU, UMR 5274, 38041 Grenoble, France
⁵³ ISDC Data Centre for Astrophysics, University of Geneva, Ch. d’Ecogia 16, Versoix, Switzerland
⁵⁴ IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, 411 007 Pune, India
⁵⁵ Imperial College London, Astrophysics group, Blackett Laboratory, Prince Consort Road, London, SW7 2AZ, UK
⁵⁶ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁵⁷ Institut Néel, CNRS, Université Joseph Fourier Grenoble I, 25 rue des Martyrs, Grenoble, France
⁵⁸ Institut Universitaire de France, 103 bd Saint-Michel, 75005 Paris, France
⁵⁹ Institut d’Astrophysique Spatiale, CNRS (UMR 8617) Université Paris-Sud 11, Bâtiment 121, Orsay, France
⁶⁰ Institut d’Astrophysique de Paris, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
⁶¹ Institute for Space Sciences, Bucharest-Magurale, Romania
⁶² Institute of Astronomy and Astrophysics, Academia Sinica, Taipei, Taiwan
⁶³ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
⁶⁴ Institute of Theoretical Astrophysics, University of Oslo, Blindern, Oslo, Norway
⁶⁵ Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, Tenerife, Spain
⁶⁶ Instituto de Física de Cantabria (CSIC-Universidad de Cantabria), Avda. de los Castros s/n, Santander, Spain
⁶⁷ Istituto di Fisica del Plasma, CNR-ENEA-EURATOM Association, via R. Cozzi 53, Milano, Italy
⁶⁸ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA
⁶⁹ Jodrell Bank Centre for Astrophysics, Alan Turing Building, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, UK
⁷⁰ Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
⁷¹ LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
⁷² LERMA, CNRS, Observatoire de Paris, 61 avenue de l’Observatoire, Paris, France
⁷³ Laboratoire AIM, IRFU/Service d’Astrophysique – CEA/DSM – CNRS – Université Paris Diderot, Bât. 709, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
⁷⁴ Laboratoire Traitement et Communication de l’Information, CNRS (UMR 5141) and Télécom ParisTech, 46 rue Barrault, 75634 Paris Cedex 13, France
⁷⁵ 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
⁷⁶ Laboratoire de Physique Théorique, Université Paris-Sud 11 & CNRS, Bâtiment 210, 91405 Orsay, France
⁷⁷ Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁷⁸ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁷⁹ McGill Physics, Ernest Rutherford Physics Building, McGill University, 3600 rue University, Montréal, QC, H3A 2T8, Canada
⁸⁰ MilliLab, VTT Technical Research Centre of Finland, Tietotie 3, Espoo, Finland
⁸¹ Niels Bohr Institute, Blegdamsvej 17, Copenhagen, Denmark
⁸² Observational Cosmology, Mail Stop 367-17, California Institute of Technology, Pasadena, CA 91125, USA
⁸³ SB-ITP-LPPC, EPFL, CH-1015, Lausanne, Switzerland
⁸⁴ SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy
⁸⁵ School of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade, Cardiff, CF24 3AA, UK
⁸⁶ School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK
⁸⁷ Space Sciences Laboratory, University of California, Berkeley, California, USA
⁸⁸ Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Zelenchukskiy region, 369167 Karachai-Cherkessian Republic, Russia
⁸⁹ Stanford University, Dept of Physics, Varian Physics Bldg, 382 via Pueblo Mall, Stanford, California, USA
⁹⁰ Sub-Department of Astrophysics, University of Oxford, Keble Road, Oxford OX1 3RH, UK
⁹¹ Theory Division, PH-TH, CERN, 1211 Geneva 23, Switzerland
⁹² UPMC Univ Paris 06, UMR7095, 98bis boulevard Arago, 75014 Paris, France
⁹³ Université de Toulouse, UPS-OMP, IRAP, 31028 Toulouse Cedex 4, France
⁹⁴ University of Granada, Departamento de Física Teórica y del Cosmos, Facultad de Ciencias, Granada, Spain
⁹⁵ Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

Received: 22 March 2013
Accepted: 1 March 2014

Abstract

This paper presents the characterization of the in-flight beams, the beam window functions, and the associated uncertainties for the Planck Low Frequency Instrument (LFI). Knowledge of the beam profiles is necessary for determining the transfer function to go from the observed to the actual sky anisotropy power spectrum. The main beam distortions affect the beam window function, complicating the reconstruction of the anisotropy power spectrum at high multipoles, whereas the sidelobes affect the low and intermediate multipoles. The in-flight assessment of the LFI main beams relies on the measurements performed during Jupiter observations. By stacking the datafrom multiple Jupiter transits, the main beam profiles are measured down to –20 dB at 30 and 44 GHz, and down to –25 dB at 70 GHz. The main beam solid angles are determined to better than 0.2% at each LFI frequency band. The Planck pre-launch optical model is conveniently tuned to characterize the main beams independently of any noise effects. This approach provides an optical model whose beams fully reproduce the measurements in the main beam region, but also allows a description of the beams at power levels lower than can be achieved by the Jupiter measurements themselves. The agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band. The simulated beams are used for the computation of the window functions for the effective beams. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer bandshapes. The total uncertainties in the effective beam window functions are: 2% and 1.2% at 30 and 44 GHz, respectively (at ℓ ≈ 600), and 0.7% at 70 GHz (at ℓ ≈ 1000).