A

Euclid preparation

Astronomy and Astrophysics, vol. 713, pp. A256

Abstract

We present CosmoPostProcess , a simulation-based forward model algorithm calibrated to reproduce optical cluster observables in line with measurements taken with the Euclid space telescope. The main deliverable of CosmoPostProcess is a correction for stacked surface-density profiles, binned in terms of richness and redshift, that accounts for selection-related systematic effects. These corrections take into account the modification to the stacked weak lensing signal from richness-selected samples of clusters identified in the photometric Euclid survey compared with an unbiased reference sample. In this work, we focus on the Euclid richness definition currently foreseen for the cosmological analysis, which does not apply a colour selection. Euclid also provides an alternative richness estimate based on a red-sequence galaxy selection, which is not considered here. The algorithm processes N -body simulations by painting galaxies with a halo-occupation model and emulating the survey’s detection and richness-assignment algorithms. We implemented a novel algorithm to estimate the optical cluster centres from galaxy-projected densities and validated it against the official Euclid pipelines. The effect of baryonic physics on the halo density profiles is incorporated through a correction calibrated on hydrodynamical simulations, yielding total-matter profiles consistent with those measured in the reference hydrodynamical simulations. In validation against hydrodynamical simulations, the baryon-corrected excess surface density is in agreement to within 2% for cluster-centric radii, r ∈ [0.1, 5] h −1 Mpc. To assess the impact of the different contributions to the selection bias, we performed dedicated tests that included variations of both cosmological parameters and the parameters of the mass–richness relation. Across all these tests, the selection bias induced by projection alone follows a robust pattern: a large-scale structure that is physically correlated with the main halo and projected along the line of sight enhances the stacked surface density profile near the transition from one-halo to two-halo dominance, with a peak radius of about 1 h −1 Mpc and an amplitude of about 20–40%, with a dependence on richness and redshift. This behaviour is mild at low and intermediate redshifts ( z ≲ 0.7), where the impact remains at the level of a few per cent, but it becomes increasingly relevant at higher redshift ( z ≳ 0.7), with a more pronounced enhancement of the transition-scale peak. Finally, baryonic modifications remain sub-dominant outside the core, with an impact of about 2% beyond r ≳ 0.3 h −1 Mpc. As an outcome of this analysis, the CosmoPostProcess framework delivers radial profile corrections with associated uncertainties, combining the selection bias from projection effects with the impact of baryonic physics and miscentring. These corrections will be a key ingredient to ensure controlled systematics in the Euclid DR1 galaxy cluster cosmological analysis.

Authors 100

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

    Affiliation as printed

    Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  2. University of Trieste · Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

  3. Universidade de São Paulo · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · Fondazione ICSC Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing · National Institute for Astrophysics

    Affiliation as printed

    Department of Mathematical Physics, Institute of Physics, University of São Paulo

    ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  4. University of Trieste · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · Fondazione ICSC Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste

    ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  5. University of Trieste · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · Fondazione ICSC Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste

    ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  6. University of Trieste · Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

  7. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  8. Centre National de la Recherche Scientifique · Université Paris Cité

    Affiliation as printed

    Université Paris Cité, CNRS, Astroparticule et Cosmologie

  9. Centre National de la Recherche Scientifique · Université Côte d'Azur · Observatoire de la Côte d’Azur

    Affiliation as printed

    Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS

  10. Universität Innsbruck

    Affiliation as printed

    Universität Innsbruck, Institut für Astro- und Teilchenphysik

  11. Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

  12. European Space Agency · European Space Astronomy Centre

    Affiliation as printed

    ESAC/ESA

  13. Brera Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Brera

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  15. Scuola Internazionale Superiore di Studi Avanzati · Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

    SISSA, International School for Advanced Studies

  16. 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, Università di Bologna

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  19. Trieste Astronomical Observatory · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

  20. Brera Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Genova · University of Genoa · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università di Genova

    INAF-Osservatorio Astronomico di Brera

    INFN-Sezione di Genova

  21. Astronomical Observatory of Capodimonte · University of Naples Federico II · National Institute for Astrophysics

    Affiliation as printed

    Department of Physics “E. Pancini”, University Federico II

    INAF-Osservatorio Astronomico di Capodimonte

  22. Istituto Nazionale di Fisica Nucleare, Sezione di Torino · Osservatorio Astrofisico di Torino · University of Turin · National Institute for Astrophysics

    Affiliation as printed

    Dipartimento di Fisica, Università degli Studi di Torino

    INAF-Osservatorio Astrofisico di Torino

    INFN-Sezione di Torino

  23. Osservatorio Astrofisico di Torino · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino

  24. National Institute for Astrophysics

    Affiliation as printed

    INAF-IASF Milano

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

    Affiliation as printed

    Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT)

    Port d’Informació Científica

  26. Astronomical Observatory of Rome · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  28. Istituto Nazionale di Fisica Nucleare · Astronomical Observatory of Capodimonte · Istituto Nazionale di Fisica Nucleare, Sezione di Napoli · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Capodimonte

    INFN section of Naples

  29. University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna

  30. Instituto de Astrofísica de Canarias

    Affiliation as printed

    Instituto de Astrofísica de Canarias

  31. Royal Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory

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

    Affiliation as printed

    ESAC/ESA

    European Space Agency/ESRIN

  33. Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822

  34. Institució Catalana de Recerca i Estudis Avançats · Institute of Space Sciences · Consejo Superior de Investigaciones Científicas · Institut de Ciències del Cosmos · Universitat de Barcelona

    Affiliation as printed

    Institució Catalana de Recerca i Estudis Avançats (ICREA)

    Institut de Ciencies de l’Espai (IEEC-CSIC), Campus UAB

    Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB)

  35. Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon

  36. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

  37. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  38. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

  39. European Space Agency · European Space Astronomy Centre

    Affiliation as printed

    ESAC/ESA

  40. 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

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  41. Institute for Space Astrophysics and Planetology · National Institute for Astrophysics

    Affiliation as printed

    INAF-Istituto di Astrofisica e Planetologia Spaziali

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  43. 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

    Affiliation as printed

    Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM

  44. Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Bologna

  46. Institute of Space Sciences · Institut d'Estudis Espacials de Catalunya · Universitat Politècnica de Catalunya

    Affiliation as printed

    Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC

    Institute of Space Sciences (ICE, CSIC), Campus UAB

  47. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  49. National Institute for Astrophysics

    Affiliation as printed

    INAF-IASF Milano

  50. Ludwig-Maximilians-Universität München

    Affiliation as printed

    University Observatory, LMU Faculty of Physics

  51. Royal Observatory · University of Edinburgh

    Affiliation as printed

    Institute for Astronomy, University of Edinburgh, Royal Observatory

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  53. Max Planck Institute for Extraterrestrial Physics

    Affiliation as printed

    Max Planck Institute for Extraterrestrial Physics

  54. Osservatorio Astronomico di Padova · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Padova

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

    Affiliation as printed

    Max Planck Institute for Extraterrestrial Physics

    Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München

  56. University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo

  57. California Institute of Technology · Infrared Processing and Analysis Center

    Affiliation as printed

    Caltech/IPAC

  58. Leiden University · Leiden Observatory

    Affiliation as printed

    Leiden Observatory, Leiden University

  59. Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology

  60. Affiliation as printed

    Felix Hormuth Engineering

  61. Technical University of Denmark

    Affiliation as printed

    Cosmic Dawn Center (DAWN)

    Technical University of Denmark

  62. Max Planck Institute for Astronomy

    Affiliation as printed

    Max-Planck-Institut für Astronomie

  63. Goddard Space Flight Center

    Affiliation as printed

    NASA Goddard Space Flight Center

  64. University College London

    Affiliation as printed

    Department of Physics and Astronomy, University College London

  65. 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

    Affiliation as printed

    Aix-Marseille Université, CNRS/IN2P3, CPPM

  66. Jet Propulsion Laboratory

    Affiliation as printed

    Jet Propulsion Laboratory, California Institute of Technology

  67. Lyon 1 Université · Centre National de la Recherche Scientifique · Institut National de Physique Nucléaire et de Physique des Particules · Institut de Physique des 2 Infinis de Lyon

    Affiliation as printed

    Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822

  68. Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics

    Helsinki Institute of Physics

  69. Centre National de la Recherche Scientifique · Université Paris Sciences et Lettres · Observatoire de Paris · Sorbonne Université · Laboratoire d'Étude de l'Univers et des Phénomènes Extrêmes

    Affiliation as printed

    Laboratoire d’etude de l’Univers et des phenomenes eXtremes, Observatoire de Paris, Université PSL, Sorbonne Université, CNRS

  70. Osservatorio Astrofisico di Torino · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astrofisico di Torino

  71. University of Oslo

    Affiliation as printed

    Institute of Theoretical Astrophysics, University of Oslo

  72. Helsinki Institute of Physics

    Affiliation as printed

    Department of Physics

    Helsinki Institute of Physics

  73. SKA Observatory

    Affiliation as printed

    SKAO

  74. Institute for Space Astrophysics and Planetology · National Institute for Astrophysics

    Affiliation as printed

    INAF-Istituto di Astrofisica e Planetologia Spaziali

  75. Centre National de la Recherche Scientifique · Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules

    Affiliation as printed

    Centre de Calcul de l’IN2P3/CNRS

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  77. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

  78. University of Bonn

    Affiliation as printed

    Universität Bonn, Argelander-Institut für Astronomie

  79. Astronomical Observatory of Rome · Istituto Nazionale di Fisica Nucleare, Sezione di Roma I · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Roma

    INFN-Sezione di Roma

  80. Centre National de la Recherche Scientifique · Aix-Marseille Université

    Affiliation as printed

    Aix-Marseille Université, CNRS, CNES, LAM

  81. 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

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  82. Durham University

    Affiliation as printed

    Department of Physics, Institute for Computational Cosmology, Durham University

  83. Istituto Nazionale di Fisica Nucleare, Sezione di Bologna · University of Bologna

    Affiliation as printed

    Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna

    INFN-Sezione di Bologna

  84. Centre National de la Recherche Scientifique · Université Côte d'Azur · Observatoire de la Côte d’Azur

    Affiliation as printed

    Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  86. Centre National de la Recherche Scientifique · Université Paris Cité · Centre Pierre Binétruy · University of California, Berkeley

    Affiliation as printed

    CNRS-UCB International Research Laboratory, Centre Pierre Binétruy, IRL2007

    Université Paris Cité, CNRS, Astroparticule et Cosmologie

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

    Affiliation as printed

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  88. Osservatorio Astronomico di Padova · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Padova

  89. École Polytechnique Fédérale de Lausanne

    Affiliation as printed

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

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

    Affiliation as printed

    Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  91. European Space Agency

    Affiliation as printed

    Telespazio UK S.L. for European Space Agency (ESA)

  92. 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

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

  93. Trieste Astronomical Observatory · Istituto Nazionale di Fisica Nucleare, Sezione di Trieste · Institute for Fundamental Physics of the Universe · National Institute for Astrophysics

    Affiliation as printed

    IFPU, Institute for Fundamental Physics of the Universe

    INAF-Osservatorio Astronomico di Trieste

    INFN, Sezione di Trieste

  94. 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

    INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna

    INFN-Sezione di Bologna

  95. Goddard Space Flight Center

    Affiliation as printed

    NASA Goddard Space Flight Center

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

    Affiliation as printed

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

    Port d’Informació Científica

  97. European Space Agency · European Space Research and Technology Centre

    Affiliation as printed

    European Space Agency/ESTEC

  98. Institute for High Energy Physics · Barcelona Institute of Science and Technology

    Affiliation as printed

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

  99. University of Geneva

    Affiliation as printed

    Department of Astronomy, University of Geneva

  100. Trieste Astronomical Observatory · National Institute for Astrophysics

    Affiliation as printed

    INAF-Osservatorio Astronomico di Trieste

Cited by 0 stored of 0

No patents citing this paper on Lens.org (checked 2026-10-11).

References 99