Euclid: Fast two-point correlation function covariance through linear construction

Astronomy and Astrophysics, vol. 666, pp. A129

Abstract

We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy–Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (random-to-data objects’ ratio M ≫ 1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs with a size of M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of the two. We show that the LC covariance estimate is unbiased. We validated the method with PINOCCHIO simulations in the range r = 20 − 200 h−1 Mpc. With M = 50 and with 2 h−1 Mpc bins, the theoretical speedup of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and present a formula for the covariance of covariance.

Authors 97

1. Elina Keihänen

   University of Helsinki

   Affiliation as printed

   Department of Physics, PO Box 64 00014 University of Helsinki, Finland

2. V. Lindholm

   University of Helsinki · Helsinki Institute of Physics

   Affiliation as printed

   Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland

3. Pierluigi Monaco

   University of Trieste · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe

   Affiliation as printed

   Dipartimento di Fisica – Sezione di Astronomia, Universitá di Trieste, Via Tiepolo 11, 34131 Trieste, Italy

   IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy

   INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

   INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy

4. L Blot

   Max Planck Institute for Astrophysics

   Affiliation as printed

   Max-Planck-Institut für Astrophysik, Karl-Schwarzschild Str. 1, 85741 Garching, Germany

5. C. Carbone

   National Institute for Astrophysics

   Affiliation as printed

   INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy

6. K. Kiiveri

   University of Helsinki · Helsinki Institute of Physics

   Affiliation as printed

   Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland

7. Ariel G. Sánchez

   Max Planck Institute for Extraterrestrial Physics

   Affiliation as printed

   Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany

8. A. Viitanen

   University of Helsinki · Helsinki Institute of Physics

   Affiliation as printed

   Department of Physics and Helsinki Institute of Physics, Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland

9. J. Väliviita

   University of Helsinki · Helsinki Institute of Physics

   Affiliation as printed

   Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland

10. Adam Amara

    University of Portsmouth

    Affiliation as printed

    Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK

11. N. Auricchio

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

12. Marco Baldi

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

    Dipartimento di Fisica e Astronomia "Augusto Righi" – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

13. D. Bonino

    Osservatorio Astrofisico di Torino

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy

14. E. Branchini

    Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa

    Affiliation as printed

    Dipartimento di Fisica, Universitá degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy

    INFN-Sezione di Roma Tre, Via della Vasca Navale 84, 00146 Roma, Italy

15. M. Brescia

    Astronomical Observatory of Capodimonte

    Affiliation as printed

    INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy

16. J. Brinchmann

    Universidade do Porto · Institute of Astrophysics and Space Sciences · Centro de Astrofísica da Universidade do Porto

    Affiliation as printed

    Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal

17. S. Camera

    Istituto Nazionale di Fisica Nucleare, Sezione di Torino · Osservatorio Astrofisico di Torino · University of Turin

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    Dipartimento di Fisica, Universitá degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy

    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy

    INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy

18. V. Capobianco

    Osservatorio Astrofisico di Torino

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy

19. J. Carretero

    Institute for High Energy Physics · Barcelona Institute of Science and Technology · Port d'Informació Científica

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    Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain

    Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain

    Institut de Física d'Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain

    Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain

20. M. Castellano

    Astronomical Observatory of Rome · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy

21. S. Cavuoti

    Astronomical Observatory of Capodimonte · Istituto Nazionale di Fisica Nucleare, Sezione di Napoli · University of Naples Federico II

    Affiliation as printed

    Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy

    INAF-Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy

    INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy

    Department of Physics "E. Pancini", University Federico II, Via Cinthia 6, 80126 Napoli, Italy

22. A. Cimatti

    Arcetri Astrophysical Observatory · University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Universitá di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

    INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy

    Dipartimento di Fisica e Astronomia "Augusto Righi" – Alma Mater Studiorum Universitá di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

23. R. Clédassou

    Centre National d'Études Spatiales · Institut National de Physique Nucléaire et de Physique des Particules

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    Centre National d’Etudes Spatiales, Toulouse, France

    Institut national de physique nucléaire et de physique des particules, 3 rue Michel-Ange, 75794 Paris Cedex 16, France

    Centre National d'Etudes Spatiales, Toulouse, France

24. G. Congedo

    Royal Observatory · University of Edinburgh

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    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

25. L. Conversi

    European Space Agency · European Space Astronomy Centre · European Space Research Institute

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    ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain

    European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy

26. Y. Copin

    Lyon 1 Université · Centre National de la Recherche Scientifique · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France

27. L. Corcione

    Osservatorio Astrofisico di Torino

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy

28. Mark S. Cropper

    University College London

    Affiliation as printed

    Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK

29. A. Da Silva

    University of Lisbon · Institute of Astrophysics and Space Sciences

    Affiliation as printed

    Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal

    Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

30. Hubert Degaudenzi

    University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva, ch. dÉcogia 16, 1290 Versoix, Switzerland

31. Marian Douspis

    Centre National de la Recherche Scientifique · Université Paris-Saclay · Institut d'Astrophysique Spatiale

    Affiliation as printed

    Université Paris-Saclay, CNRS, Institut d’astrophysique spatiale, 91405 Orsay, France

    Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405 Orsay, France

32. F. Dubath

    University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva, ch. dÉcogia 16, 1290 Versoix, Switzerland

33. C. A. J. Duncan

    University of Oxford

    Affiliation as printed

    Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK

34. X. Dupac

    European Space Astronomy Centre

    Affiliation as printed

    ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain

35. S. Dusini

    Istituto Nazionale di Fisica Nucleare, Sezione di Padova

    Affiliation as printed

    INFN-Padova, Via Marzolo 8, 35131 Padova, Italy

36. A. Ealet

    Lyon 1 Université · Centre National de la Recherche Scientifique · Institut de Physique des 2 Infinis de Lyon

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    Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France

37. S. Farrens

    Centre National de la Recherche Scientifique · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · Astrophysique, Instrumentation et Modélisation

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    AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, 91191 Gif-sur-Yvette, France

38. S. Ferriol

    Lyon 1 Université · Centre National de la Recherche Scientifique · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Univ Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France

39. M. Frailis

    Trieste Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

40. Enrico Franceschi

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

41. M. Fumana

    National Institute for Astrophysics

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    INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy

42. Bryan R. Gillis

    Royal Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

43. C. Giocoli

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

    Affiliation as printed

    Istituto Nazionale di Astrofisica (INAF) – Osservatorio di Astrofisica e Scienza dello Spazio (OAS), Via Gobetti 93/3, 40127 Bologna, Italy

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy

44. A. Grazian

    Osservatorio Astronomico di Padova

    Affiliation as printed

    INAF-Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy

    INAF-Osservatorio Astronomico di Padova, Via dell'Osservatorio 5, 35122 Padova, Italy

45. Frank U. Grupp

    Max Planck Institute for Extraterrestrial Physics · Ludwig-Maximilians-Universität München

    Affiliation as printed

    Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany

    Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany

46. L. Guzzo

    University of Milan · Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Milano

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    Dipartimento di Fisica “Aldo Pontremoli”, Universitá degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy

    INAF-Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy

    INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy

    Dipartimento di Fisica "Aldo Pontremoli", Universitá degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy

47. S. V. H. Haugan

    University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern 0315 Oslo, Norway

48. Henk Hoekstra Aachen Leiden Observatory

    Leiden University · Leiden Observatory

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    Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands

49. W. A. Holmes

    Jet Propulsion Laboratory

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    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

50. F. Hormuth

    von Hoerner & Sulger (Germany)

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    von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany

51. K. Jahnkę

    Max Planck Institute for Astronomy

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    Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

52. M Kümmel

    Ludwig-Maximilians-Universität München

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    Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany

53. Smaïn Kermiche

    Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules

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    Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France

54. A. Kiessling

    Jet Propulsion Laboratory

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    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

55. T. Kitching

    University College London

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    Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK

56. Martin Kunz

    University of Geneva

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    Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland

57. Hannu Kurki-Suonio

    University of Helsinki · Helsinki Institute of Physics

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    Department of Physics, PO Box 64 00014 University of Helsinki, Finland

    Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland

58. S. Ligori

    Osservatorio Astrofisico di Torino

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    INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy

59. Per Barth Lilje

    University of Oslo

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    Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern 0315 Oslo, Norway

60. Ivan Lloro

    Netherlands Institute for Radio Astronomy

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    NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands

61. E. Maiorano

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

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    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

62. O. Mansutti

    Trieste Astronomical Observatory

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    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

63. O. Marggraf

    University of Bonn

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    Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

64. F. Marulli

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

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    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

    Dipartimento di Fisica e Astronomia "Augusto Righi" – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

65. R. Massey

    Durham University

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    Department of Physics, Institute for Computational Cosmology, Durham University, South Road, DH1 3LE Durham, UK

66. M. Melchior

    FHNW University of Applied Sciences and Arts Northwestern Switzerland

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    University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland

67. Massimo Meneghetti

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics

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    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

    INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy

68. George L. Meylan

    École Polytechnique Fédérale de Lausanne

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    Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland

69. M. Moresco

    Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

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    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

    Dipartimento di Fisica e Astronomia "Augusto Righi" – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

70. Lauro Moscardini

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · Osservatorio di Astrofisica e Scienza dello Spazio · National Institute for Astrophysics · University of Bologna

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    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

    Dipartimento di Fisica e Astronomia "Augusto Righi" – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

71. Emiliano Munari

    Trieste Astronomical Observatory

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    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

72. S.-M Niemi

    European Space Agency · European Space Research and Technology Centre

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    European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

73. S. Paltani

    University of Geneva

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    Department of Astronomy, University of Geneva, ch. dÉcogia 16, 1290 Versoix, Switzerland

74. FABIO PASIAN

    Trieste Astronomical Observatory

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    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

75. K. Pedersen

    Aarhus University

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    Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, 8000 Aarhus C, Denmark

76. V. Pettorino

    Centre National de la Recherche Scientifique · Université Paris Cité · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · Astrophysique, Instrumentation et Modélisation

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    Université Paris-Saclay, Université Paris Cité, CEA, CNRS, Astrophysique, Instrumentation et Modélisation Paris-Saclay, 91191 Gif-sur-Yvette, France

77. S. Pires

    Centre National de la Recherche Scientifique · Commissariat à l'Énergie Atomique et aux Énergies Alternatives · Université Paris-Saclay · Astrophysique, Instrumentation et Modélisation

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    AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, 91191 Gif-sur-Yvette, France

78. Gianluca Polenta

    Agenzia Spaziale Italiana

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    Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy

79. Maurice Poncet

    Centre National d'Études Spatiales

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    Centre National d’Etudes Spatiales, Toulouse, France

    Centre National d'Etudes Spatiales, Toulouse, France

80. Lucia Aurelia Popa

    Institute of Space Science - INFLPR Subsidiary

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    Institute of Space Science, Bucharest 077125, Romania

81. F. Raison

    Max Planck Institute for Extraterrestrial Physics

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    Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany

82. Alessandro Renzi

    University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova

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    Dipartimento di Fisica e Astronomia “G.Galilei”, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy

    INFN-Padova, Via Marzolo 8, 35131 Padova, Italy

    Dipartimento di Fisica e Astronomia "G.Galilei", Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy

83. Jason D. Rhodes

    Jet Propulsion Laboratory

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    Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

84. E. Romelli

    Trieste Astronomical Observatory

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    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

85. Roberto P. Saglia

    Max Planck Institute for Extraterrestrial Physics · Ludwig-Maximilians-Universität München

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    Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany

    Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany

86. Barbara Sartoris

    Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy

    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

87. T. Schrabback

    University of Bonn

    Affiliation as printed

    Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany

88. Aurelia Secroun

    Centre National de la Recherche Scientifique · Aix-Marseille Université · Centre de physique des particules de Marseille · Institut National de Physique Nucléaire et de Physique des Particules

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    Aix-Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France

89. Gregor Seidel

    Max Planck Institute for Astronomy

    Affiliation as printed

    Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

90. C. Sirignano

    University of Padua · Istituto Nazionale di Fisica Nucleare, Sezione di Padova

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “G.Galilei”, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy

    INFN-Padova, Via Marzolo 8, 35131 Padova, Italy

    Dipartimento di Fisica e Astronomia "G.Galilei", Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy

91. Gabriele Sirri

    Istituto Nazionale di Fisica Nucleare, Sezione di Bologna

    Affiliation as printed

    INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

92. Luca Stanco

    Istituto Nazionale di Fisica Nucleare, Sezione di Padova

    Affiliation as printed

    INFN-Padova, Via Marzolo 8, 35131 Padova, Italy

93. Christian Surace

    Centre National de la Recherche Scientifique · Aix-Marseille Université

    Affiliation as printed

    Aix-Marseille Univ, CNRS, CNES, LAM, Marseille, France

94. Pau Tallada-Crespí

    Port d'Informació Científica · Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas

    Affiliation as printed

    Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain

    Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain

    Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain

95. Daniele Tavagnacco

    Trieste Astronomical Observatory

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

96. A. N. Taylor

    Royal Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

97. Ismael Tereno

    University of Lisbon · Institute of Astrophysics and Space Sciences

    Affiliation as printed

    Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal

    Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal