11institutetext: Universität Innsbruck, Institut für Astro- und
Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria 22institutetext:
Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121
Bonn, Germany 33institutetext: Ruhr University Bochum, Faculty of Physics and
Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological
Lensing (GCCL), 44780 Bochum, Germany 44institutetext: School of Mathematics,
Statistics and Physics, Newcastle University, Herschel Building, Newcastle-
upon-Tyne, NE1 7RU, UK 55institutetext: E. A. Milne Centre, University of
Hull, Cottingham Road, Hull, HU6 7RX, UK 66institutetext: Astronomisches
Institut, Ruhr-Universität Bochum, Universitätsstr. 150, 44801 Bochum, Germany
77institutetext: Leiden Observatory, Leiden University, Einsteinweg 55, 2333
CC Leiden, The Netherlands 88institutetext: Department of Physics and
Astronomy, University College London, Gower Street, London WC1E 6BT, UK
99institutetext: Université Paris-Saclay, CNRS, Institut d’astrophysique
spatiale, 91405, Orsay, France 1010institutetext: ESAC/ESA, Camino Bajo del
Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada,
Madrid, Spain 1111institutetext: School of Mathematics and Physics, University
of Surrey, Guildford, Surrey, GU2 7XH, UK 1212institutetext: INAF-Osservatorio
Astronomico di Brera, Via Brera 28, 20122 Milano, Italy 1313institutetext:
INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero
Gobetti 93/3, 40129 Bologna, Italy 1414institutetext: IFPU, Institute for
Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy
1515institutetext: INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo
11, 34143 Trieste, Italy 1616institutetext: INFN, Sezione di Trieste, Via
Valerio 2, 34127 Trieste TS, Italy 1717institutetext: SISSA, International
School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy
1818institutetext: Dipartimento di Fisica e Astronomia, Università di Bologna,
Via Gobetti 93/2, 40129 Bologna, Italy 1919institutetext: INFN-Sezione di
Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy 2020institutetext: INAF-
Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese
(TO), Italy 2121institutetext: Dipartimento di Fisica, Università di Genova,
Via Dodecaneso 33, 16146, Genova, Italy 2222institutetext: INFN-Sezione di
Genova, Via Dodecaneso 33, 16146, Genova, Italy 2323institutetext: Department
of Physics ”E. Pancini”, University Federico II, Via Cinthia 6, 80126, Napoli,
Italy 2424institutetext: INAF-Osservatorio Astronomico di Capodimonte, Via
Moiariello 16, 80131 Napoli, Italy 2525institutetext: INFN section of Naples,
Via Cinthia 6, 80126, Napoli, Italy 2626institutetext: Instituto de
Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das
Estrelas, PT4150-762 Porto, Portugal 2727institutetext: Faculdade de Ciências
da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal
2828institutetext: Dipartimento di Fisica, Università degli Studi di Torino,
Via P. Giuria 1, 10125 Torino, Italy 2929institutetext: INFN-Sezione di
Torino, Via P. Giuria 1, 10125 Torino, Italy 3030institutetext: INAF-IASF
Milano, Via Alfonso Corti 12, 20133 Milano, Italy 3131institutetext: INAF-
Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone,
Italy 3232institutetext: INFN-Sezione di Roma, Piazzale Aldo Moro, 2 - c/o
Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy
3333institutetext: Centro de Investigaciones Energéticas, Medioambientales y
Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
3434institutetext: Port d’Informació Científica, Campus UAB, C. Albareda s/n,
08193 Bellaterra (Barcelona), Spain 3535institutetext: Institute for
Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University,
52056 Aachen, Germany 3636institutetext: Institute of Space Sciences (ICE,
CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
3737institutetext: Institut d’Estudis Espacials de Catalunya (IEEC), Edifici
RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain 3838institutetext:
Dipartimento di Fisica e Astronomia ”Augusto Righi” - Alma Mater Studiorum
Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
3939institutetext: Institute for Astronomy, University of Edinburgh, Royal
Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK 4040institutetext: Jodrell
Bank Centre for Astrophysics, Department of Physics and Astronomy, University
of Manchester, Oxford Road, Manchester M13 9PL, UK 4141institutetext: European
Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
4242institutetext: Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon,
UMR 5822, Villeurbanne, F-69100, France 4343institutetext: Institute of
Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne
(EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland 4444institutetext:
UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622
Villeurbanne, France 4545institutetext: Departamento de Física, Faculdade de
Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, PT1749-016
Lisboa, Portugal 4646institutetext: Instituto de Astrofísica e Ciências do
Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016
Lisboa, Portugal 4747institutetext: Department of Astronomy, University of
Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland 4848institutetext: INFN-
Padova, Via Marzolo 8, 35131 Padova, Italy 4949institutetext: INAF-Istituto di
Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100
Roma, Italy 5050institutetext: Université Paris-Saclay, Université Paris Cité,
CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France 5151institutetext: Institut de
Ciencies de l’Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n
Cerdanyola del Vallés, 08193 Barcelona, Spain 5252institutetext: Istituto
Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126
Bologna, Italy 5353institutetext: INAF-Osservatorio Astronomico di Padova, Via
dell’Osservatorio 5, 35122 Padova, Italy 5454institutetext: Max Planck
Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching,
Germany 5555institutetext: Universitäts-Sternwarte München, Fakultät für
Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679
München, Germany 5656institutetext: Dipartimento di Fisica ”Aldo Pontremoli”,
Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
5757institutetext: Institute of Theoretical Astrophysics, University of Oslo,
P.O. Box 1029 Blindern, 0315 Oslo, Norway 5858institutetext: Jet Propulsion
Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA, 91109, USA 5959institutetext: Department of Physics, Lancaster
University, Lancaster, LA1 4YB, UK 6060institutetext: Felix Hormuth
Engineering, Goethestr. 17, 69181 Leimen, Germany 6161institutetext: Technical
University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark
6262institutetext: Cosmic Dawn Center (DAWN), Denmark 6363institutetext:
Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98
bis boulevard Arago, 75014 Paris, France 6464institutetext: Max-Planck-
Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
6565institutetext: Department of Physics and Helsinki Institute of Physics,
Gustaf Hällströmin katu 2, 00014 University of Helsinki, Finland
6666institutetext: Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille,
France 6767institutetext: Mullard Space Science Laboratory, University College
London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK 6868institutetext:
Université de Genève, Département de Physique Théorique and Centre for
Astroparticle Physics, 24 quai Ernest-Ansermet, CH-1211 Genève 4, Switzerland
6969institutetext: Department of Physics, P.O. Box 64, 00014 University of
Helsinki, Finland 7070institutetext: Helsinki Institute of Physics, Gustaf
Hällströmin katu 2, University of Helsinki, Helsinki, Finland
7171institutetext: NOVA optical infrared instrumentation group at ASTRON, Oude
Hoogeveensedijk 4, 7991PD, Dwingeloo, The Netherlands 7272institutetext: INFN-
Sezione di Milano, Via Celoria 16, 20133 Milano, Italy 7373institutetext: Aix-
Marseille Université, CNRS, CNES, LAM, Marseille, France 7474institutetext:
Dipartimento di Fisica e Astronomia ”Augusto Righi” - Alma Mater Studiorum
Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
7575institutetext: Department of Physics, Centre for Extragalactic Astronomy,
Durham University, South Road, DH1 3LE, UK 7676institutetext: Université Paris
Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
7777institutetext: Institut d’Astrophysique de Paris, 98bis Boulevard Arago,
75014, Paris, France 7878institutetext: European Space Agency/ESTEC,
Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands 7979institutetext: Department
of Physics, Institute for Computational Cosmology, Durham University, South
Road, DH1 3LE, UK 8080institutetext: Institut de Física d’Altes Energies
(IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193
Bellaterra (Barcelona), Spain 8181institutetext: Department of Physics and
Astronomy, University of Aarhus, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
8282institutetext: Space Science Data Center, Italian Space Agency, via del
Politecnico snc, 00133 Roma, Italy 8383institutetext: Centre National d’Etudes
Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401
Toulouse Cedex 9, France 8484institutetext: Institute of Space Science, Str.
Atomistilor, nr. 409 Măgurele, Ilfov, 077125, Romania 8585institutetext:
Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204, San
Cristóbal de La Laguna, Tenerife, Spain 8686institutetext: Departamento de
Astrofísica, Universidad de La Laguna, 38206, La Laguna, Tenerife, Spain
8787institutetext: Dipartimento di Fisica e Astronomia ”G. Galilei”,
Università di Padova, Via Marzolo 8, 35131 Padova, Italy 8888institutetext:
Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16,
69120 Heidelberg, Germany 8989institutetext: Institut de Recherche en
Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES,
14 Av. Edouard Belin, 31400 Toulouse, France 9090institutetext: Université St
Joseph; Faculty of Sciences, Beirut, Lebanon 9191institutetext: Departamento
de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
9292institutetext: Satlantis, University Science Park, Sede Bld 48940, Leioa-
Bilbao, Spain 9393institutetext: Instituto de Astrofísica e Ciências do
Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda,
1349-018 Lisboa, Portugal 9494institutetext: Universidad Politécnica de
Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del
Hospital 1, 30202 Cartagena, Spain 9595institutetext: INFN-Bologna, Via
Irnerio 46, 40126 Bologna, Italy 9696institutetext: Kapteyn Astronomical
Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The
Netherlands 9797institutetext: Dipartimento di Fisica, Università degli studi
di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146, Genova, Italy
9898institutetext: Infrared Processing and Analysis Center, California
Institute of Technology, Pasadena, CA 91125, USA 9999institutetext: INAF,
Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy
100100institutetext: Junia, EPA department, 41 Bd Vauban, 59800 Lille, France
101101institutetext: ICSC - Centro Nazionale di Ricerca in High Performance
Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy
102102institutetext: Laboratoire Univers et Théorie, Observatoire de Paris,
Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France

#  Euclid and KiDS-1000: Quantifying the impact of source-lens clustering on
cosmic shear analyses††thanks: This paper is published on behalf of the Euclid
Consortium.

L. Linke<EMAIL_ADDRESS>Euclid and KiDS-1000: Quantifying the impact
of source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. S. Unruh Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. A. Wittje Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. T. Schrabback Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Grandis Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. M. Asgari Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. A. Dvornik Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. H. Hildebrandt Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
H. Hoekstra Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. B. Joachimi Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. R. Reischke Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. J. L. van den Busch Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. A. H. Wright Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
P. Schneider Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. N. Aghanim Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. B. Altieri Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
A. Amara Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Andreon Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. N. Auricchio Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
C. Baccigalupi Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
M. Baldi Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Bardelli Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. D. Bonino Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
E. Branchini Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. M. Brescia Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. J. Brinchmann Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Camera Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. V. Capobianco Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
C. Carbone Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. V. F. Cardone Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. J. Carretero Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. S. Casas Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. F. J. Castander Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. M. Castellano Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. S. Cavuoti Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. A. Cimatti Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. G. Congedo Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
C. J. Conselice Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. L. Conversi Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. Y. Copin Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. F. Courbin Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
H. M. Courtois Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. A. Da Silva Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. H. Degaudenzi Euclid
and KiDS-1000: Quantifying the impact of source-lens clustering on cosmic
shear analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. J. Dinis Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. M. Douspis Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. F. Dubath Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
X. Dupac Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Dusini Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. M. Farina Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
S. Farrens Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Ferriol Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. P. Fosalba Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. M. Frailis Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. E. Franceschi Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
M. Fumana Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Galeotta Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. B. Gillis Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
C. Giocoli Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
A. Grazian Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. F. Grupp Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. L. Guzzo Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. S. V. H. Haugan Euclid
and KiDS-1000: Quantifying the impact of source-lens clustering on cosmic
shear analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. W. Holmes Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
I. Hook Euclid and KiDS-1000: Quantifying the impact of source-lens clustering
on cosmic shear analyses††thanks: This paper is published on behalf of the
Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. F. Hormuth Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
A. Hornstrup Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
P. Hudelot Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. K. Jahnke Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. E. Keihänen Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
S. Kermiche Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. A. Kiessling Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. M. Kilbinger Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
T. Kitching Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. B. Kubik Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. K. Kuijken Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
M. Kümmel Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. M. Kunz Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. H. Kurki-Suonio Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. S. Ligori Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. P. B. Lilje Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
V. Lindholm Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
I. Lloro Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. D. Maino Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. E. Maiorano Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
O. Mansutti Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. O. Marggraf Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. K. Markovic Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
N. Martinet Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. F. Marulli Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. R. Massey Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
H. J. McCracken Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. E. Medinaceli Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. S. Mei Euclid and KiDS-1000: Quantifying the impact
of source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. Y. Mellier Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. M. Meneghetti Euclid
and KiDS-1000: Quantifying the impact of source-lens clustering on cosmic
shear analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. E. Merlin Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. G. Meylan Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
M. Moresco Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
L. Moscardini Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. E. Munari Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. R. Nakajima Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. R. C. Nichol Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
S.-M. Niemi Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. J. W. Nightingale Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. C. Padilla Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. S. Paltani Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
F. Pasian Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. K. Pedersen Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. V. Pettorino Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
S. Pires Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. G. Polenta Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. M. Poncet Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
L. A. Popa Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. F. Raison Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. R. Rebolo Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. A. Renzi Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. J. Rhodes Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. G. Riccio Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
E. Romelli Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. M. Roncarelli Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. R. Saglia Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. Z. Sakr Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. D. Sapone Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
B. Sartoris Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
M. Schirmer Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. A. Secroun Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. G. Seidel Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
S. Serrano Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. C. Sirignano Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. G. Sirri Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. L. Stanco Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
J.-L. Starck Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. P. Tallada-Crespí Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. A. N. Taylor Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. I. Tereno Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. R. Toledo-Moreo Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. F. Torradeflot Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. I. Tutusaus Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. L. Valenziano Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. T. Vassallo Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium. G. Verdoes Kleijn
Euclid and KiDS-1000: Quantifying the impact of source-lens clustering on
cosmic shear analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. A. Veropalumbo Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
Y. Wang Euclid and KiDS-1000: Quantifying the impact of source-lens clustering
on cosmic shear analyses††thanks: This paper is published on behalf of the
Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. J. Weller Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. G. Zamorani Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. E. Zucca Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
C. Burigana Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.
A. Pezzotta Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. C. Porciani Euclid and
KiDS-1000: Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. V. Scottez Euclid and KiDS-1000: Quantifying the
impact of source-lens clustering on cosmic shear analyses††thanks: This paper
is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium. M. Viel Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium.Euclid and KiDS-1000: Quantifying the impact of
source-lens clustering on cosmic shear analyses††thanks: This paper is
published on behalf of the Euclid Consortium.Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid
Consortium.Euclid and KiDS-1000: Quantifying the impact of source-lens
clustering on cosmic shear analyses††thanks: This paper is published on behalf
of the Euclid Consortium. A. M. C. Le Brun Euclid and KiDS-1000: Quantifying
the impact of source-lens clustering on cosmic shear analyses††thanks: This
paper is published on behalf of the Euclid Consortium.Euclid and KiDS-1000:
Quantifying the impact of source-lens clustering on cosmic shear
analyses††thanks: This paper is published on behalf of the Euclid Consortium.

Cosmic shear is a powerful probe of cosmological models and the transition
from current Stage-III surveys like the Kilo-Degree Survey (KiDS) to the
increased area and redshift range of Stage IV-surveys such as Euclid will
significantly increase the precision of weak lensing analyses. However, with
increasing precision, the accuracy of model assumptions needs to be evaluated.
In this study, we quantify the impact of the correlated clustering of weak
lensing source galaxies with the surrounding large-scale structure, the so-
called source-lens clustering (SLC), which is commonly neglected. We include
the impact of realistic scatter in photometric redshift estimates, which
impacts the assignment of galaxies to tomographic bins and increases the SLC.
For this, we use simulated cosmological datasets with realistically
distributed galaxies and measure shear correlation functions for both
clustered and uniformly distributed source galaxies. Cosmological analyses are
performed for both scenarios to quantify the impact of SLC on parameter
inference for a KiDS-like and a Euclid-like setting. We find for Stage III
surveys like KiDS, SLC has a minor impact when accounting for nuisance
parameters for intrinsic alignments and shifts of tomographic bins, as these
nuisance parameters absorb the effect of SLC, thus changing their original
meaning. For KiDS (Euclid), the inferred intrinsic alignment amplitude
$A_{\mathrm{IA}}$ changes from $0.11_{-0.46}^{+0.44}$
($-0.009_{-0.080}^{+0.079}$) for data without SLC to $0.28_{-0.44}^{+0.42}$
($0.022_{-0.082}^{+0.081}$) with SLC. However, fixed nuisance parameters lead
to shifts in $S_{8}$ and $\Omega_{\mathrm{m}}$, emphasizing the need for
including SLC in the modelling. For Euclid we find that $S_{8}$ and
$\Omega_{\mathrm{m}}$ are shifted by 0.14 and 0.12 $\sigma$, respectively,
when including free nuisance parameters. Consequently, SLC on its own has only
a small impact on the inferred parameter inference. However, SLC might
conspire with the breakdown of other modelling assumptions, such as
magnification bias or source obscuration, which could collectively exert a
more pronounced effect on inferred parameters.

###### Key Words.:

Gravitational lensing: weak, large-scale structure of Universe, Cosmology:
observations

##  1 Introduction

Weak gravitational lensing has emerged as a powerful tool in the field of
cosmology, providing valuable insights into the nature of our Universe. In
particular, the second-order correlation functions of weak lensing shear have
become widely employed for precision cosmological measurements. These
correlation functions rely on the matter power spectrum and are especially
effective in determining the combined parameter
$S_{8}=\sigma_{8}(\Omega_{\mathrm{m}}/0.3)^{0.5}$, which represents a
combination of the matter density parameter $\Omega_{\mathrm{m}}$ and the
clustering parameter $\sigma_{8}$. Recent Stage III surveys, including the
Hyper Suprime-Cam (HSC) survey (Aihara et al. 2018), Kilo-Degree Survey (KiDS,
Kuijken et al. 2015) and Dark Energy Survey (DES, Abbott et al. 2016; Becker
et al. 2016), have successfully measured $S_{8}$ with remarkable precision,
thereby establishing cosmic shear as a reliable cosmological tool (Asgari et
al. 2021; Amon et al. 2022; Dalal et al. 2023; Li et al. 2023; DES and KiDS
Collaboration: Abbott et al. 2023).

However, intriguing trends have been observed in the results obtained from
cosmic shear experiments. These surveys consistently yield lower values of
$S_{8}$ compared to what would be expected based on measurements of the cosmic
microwave background (CMB) using the Planck satellite under the framework of
the cosmological standard model. Referred to as the $S_{8}$-tension, this
discrepancy has a significance of $2-3\sigma$ and raises the possibility of
issues either in the standard model of cosmology or in the analyses of cosmic
shear or the CMB (Di Valentino et al. 2021; Abdalla et al. 2022).

Several effects have been identified as potential sources for the tension
observed in $S_{8}$ measurements. First, ill-understood astrophysical effects,
such as the impact of baryonic matter or intrinsic alignments of galaxies,
might bias the measurements from cosmic shear (Semboloni et al. 2011; Troxel &
Ishak 2015; Chisari et al. 2019). Second, deviations from the cosmological
standard model, such as modified gravity or exotic dark matter, could play a
role (Planck Collaboration et al. 2016; Di Valentino et al. 2016; Heimersheim
et al. 2020). Third, observational systematics, such as the calibration of
photometric redshift estimates and galaxy shape measurements can bias the
measured cosmic shear signal (Huterer et al. 2006, Euclid Collaboration:
Congedo et al. 2024. Lastly, the apparent tension could be caused by
simplifying assumptions made in the modelling of the cosmic shear signal.
Examples of such assumptions include neglecting magnification bias (Unruh et
al. 2020; von Wietersheim-Kramsta et al. 2021; Duncan et al. 2022), source
obscuration (Hartlap et al. 2011), spatially varying survey depth (Heydenreich
et al. 2020) or the intrinsically clustered positions of source galaxies (Yu
et al. 2015). Understanding these factors is crucial for comprehending the
nature of the $S_{8}$-tension, as well as for assessing the implications for
Stage IV-surveys like Euclid (Laureijs et al. 2011; Euclid Collaboration:
Mellier et al. 2024) or the Vera C. Rubin Legacy Survey of Space and Time
(LSST Ivezić et al. 2019). In this study, we focus specifically on the
clustering of source galaxies with the lensing matter structures, which we
refer to as source-lens clustering (SLC).

Conventionally, cosmic shear analyses assume that source galaxies are
spatially uniformly distributed within the survey footprint, allowing the
cosmic shear field to be sampled randomly across the sky. However, this
assumption does not hold in reality. Source galaxies, like all galaxies, trace
the underlying density field, meaning their positions correlate with the local
matter structures. If the sources are divided into broad redshift bins, some
sources in a bin will be at the same redshift as the matter causing a shear
signal for other sources in the same bin. Therefore, the lensing signal of the
farther sources is correlated to the positions of the closer sources. This
correlation contributes to the measured shear correlation functions and, if
not taken into account, can, in principle, bias cosmological parameter
inference (Bernardeau 1998).

However, the magnitude of this effect is currently unclear. By considering a
simple model that incorporates linear galaxy biases and an analytic form of
the source redshift distribution, Euclid Collaboration: Deshpande et al.
(2024) predicted that the effect of source-lens clustering would be
significant for Stage IV surveys like Euclid and bias constraints on
$\Omega_{\mathrm{m}}$ by more than $1\,\sigma$. However, based on analytical
calculations, Krause et al. (2021) expect the effect to be dependent on
fourth-order correlations and, therefore, negligible, at least for Stage III
surveys. Yu et al. (2015) quantified the effect with $N$-body simulations and
found a 1–10% effect on the lensing power spectrum. However, they considered
only two Gaussian tomographic bins, assumed a linear galaxy bias and did not
include realistic photometric redshift errors in their study. Thus, the
magnitude of SLC for galaxies with realistic redshift distributions is not yet
determined. This paper aims to address this gap in knowledge.

A confounding factor in the discussion of SLC is that the non-uniform
distribution of source galaxies causes several partially counteracting
effects. Firstly, the intrinsic clustering of sources in regions of higher
density means that we sample the cosmic shear field predominantly in regions
with higher shear signals. This effect, considered, e.g. in Krause et al.
(2021), increases the measured cosmic shear signal compared to the theoretical
expectation for unclustered sources. Secondly, the clustering causes a bias on
the standard estimator for cosmic shear correlation functions. This estimator
is only unbiased for uniformly distributed galaxies. Finally, a third effect
occurs due to the noise in photometric redshift estimates. Due to the
uncertainty of photometric redshifts, galaxies at low true redshifts might be
assigned to higher tomographic bins. These galaxies carry less cosmic shear
signal and, therefore, lower the overall signal of a tomographic bin. This
decrease in signal is stronger in regions with high foreground matter
densities since there are also more galaxies that can be assigned to higher
tomographic bins. The correlation between the decrease in signal and the
foreground matter distribution causes a decrease in the measured cosmic shear
signal. Our goal here is to simultaneously constrain the impact of all these
SLC effects on cosmological parameter estimation with cosmic shear.

To achieve this goal, we measure the shear correlation functions for clustered
and uniformly distributed source galaxies in cosmological simulations with
realistically distributed galaxies and Stage III- and Stage IV-like redshift
distributions. We then perform cosmological analyses for the clustered and
unclustered cases to assess the effect of source-lens clustering.

The structure of this paper is as follows: in Sect. 2, we review the basics of
weak gravitational lensing and cosmic shear and give a theoretical description
of the source-lens clustering effect. Section 3 describes the cosmological
simulations used and our steps to obtain clustered and unclustered source
galaxies. We describe our correlation function measurement and cosmological
parameter inference in Sect. 4 and give the resulting parameter estimates in
Sect. 5. We conclude with a discussion in Sect. 6.

##  2  Theoretical background

###  2.1 Second-order cosmic shear statistics

Cosmological analyses of cosmic shear operate in the weak regime of
gravitational lensing (for a review on weak lensing, see, for example,
Bartelmann & Schneider 2001). They mostly analyse second-order statistics of
the shear $\gamma$. The conceptually easiest of these statistics are the shear
correlation functions $\xi_{+}$ and $\xi_{-}$, defined by

$\xi_{\pm}(\theta)=\expectationvalue{\gamma_{\mathrm{t}}\gamma_{\mathrm{t}}}(\theta)\pm\expectationvalue{\gamma_{\times}\gamma_{\times}}(\theta)\;,$
(1)

where $\gamma_{\mathrm{t}}$ and $\gamma_{\times}$ are the tangential and
cross-component of the shear for a galaxy pair with angular separation
$\theta$ and the brackets denote an ensemble average. Assuming a flat sky, the
shear $\gamma$ is related to the convergence $\kappa$ by the Kaiser-Squires
relation (Kaiser & Squires 1993)

$\tilde{\gamma}(\boldsymbol{\ell})=\mathrm{e}^{2\mathrm{i}\,\phi_{\ell}}\tilde{\kappa}(\boldsymbol{\ell})\;,$
(2)

where the tilde denotes Fourier transforms and $\phi_{\ell}$ is the polar
angle of the wavevector $\boldsymbol{\ell}$. Therefore, using the lensing
power spectrum $C(\ell)$, defined with the Dirac delta-‘function’
$\delta_{\mathrm{D}}$, by

$(2\pi)^{2}\delta_{\mathrm{D}}(\boldsymbol{\ell}+\boldsymbol{\ell}^{\prime})\,C(\ell)=\expectationvalue{\hat{\kappa}(\boldsymbol{\ell}^{\prime})\,\hat{\kappa}(\boldsymbol{\ell})}\;,$
(3)

the shear correlation functions can be modelled as

$\xi_{\pm}(\theta)=\int_{0}^{\infty}\frac{\differential{\ell}\,\ell}{2\pi}J_{0,4}(\ell\,\theta)\,C(\ell)\;,$
(4)

where $J_{i}$ is the $i$-th order Bessel function. Consequently, the impact of
any modelling effect on the shear correlation function can be estimated
equivalently on the lensing power spectrum.

The convergence $\kappa$ is a normalized surface mass density and thus related
to the matter density contrast $\delta(\chi\boldsymbol{\theta},\chi)$ at
angular position $\boldsymbol{\theta}$ and comoving distance $\chi$ via

$\kappa(\boldsymbol{\theta})=\int_{0}^{\infty}\differential{\chi}\,\delta(\chi\boldsymbol{\theta},\chi)\,\int_{\chi}^{\infty}\differential{\chi^{\prime}}W(\chi,\chi^{\prime})\,p(\chi^{\prime};\boldsymbol{\theta})$
(5)

where $p(\chi;\boldsymbol{\theta})$ is the probability density of source
galaxies at angular position $\boldsymbol{\theta}$ and comoving distance
$\chi$ and $W$ is the lensing efficiency kernel, which is, assuming a flat
Universe,

$W(\chi,\chi^{\prime})=\frac{3\Omega_{\mathrm{m}}H_{0}^{2}}{2c^{2}}\frac{\chi}{a(\chi)}\frac{\chi^{\prime}-\chi}{\chi^{\prime}}\;.$
(6)

The probability density $p$ is related to the number density $n$ of source
galaxies by

$p(\chi;\boldsymbol{\theta})=\frac{n(\chi\,\boldsymbol{\theta},\chi)}{\int\differential\chi
n(\chi\,\boldsymbol{\theta},\chi)}\;.$ (7)

Usually, one assumes that source galaxies are distributed uniformly across the
survey area. Then, $p$ is only a function of the comoving distance $\chi$, and
the convergence $\kappa_{0}(\boldsymbol{\theta})$ is given by

$\kappa_{0}(\boldsymbol{\theta})=\int_{0}^{\infty}\differential{\chi}\delta(\chi\boldsymbol{\theta},\chi)\int_{\chi}^{\infty}\differential{\chi^{\prime}}W(\chi,\chi^{\prime})\,p(\chi^{\prime})\;.$
(8)

Under the extended Limber approximation (Limber 1953; Kaiser 1998; LoVerde &
Afshordi 2008), the lensing power spectrum then becomes

$C(\ell)=\int_{0}^{\infty}\differential{\chi}\frac{1}{\chi^{2}}\left[\int_{\chi}^{\infty}\differential{\chi^{\prime}}p(\chi^{\prime})\,W(\chi,\chi^{\prime})\right]^{2}\,P\left(\frac{\ell+1/2}{\chi},\chi\right)\;,$
(9)

where $P(k,\chi)$ is the matter power spectrum. This form of the lensing power
spectrum is usually assumed in cosmic shear analyses.

###  2.2 The source-lens clustering effect

However, the assumption of uniformly distributed source galaxies is not
correct. Like any other galaxy population, the sources are tracers of the
matter distribution and, therefore, spatially clustered. This clustering
invalidates Eq. (8), as the source density $n_{\mathrm{s}}$ now depends on
angular position $\boldsymbol{\theta}$. Instead, Eq. (5) needs to be used,
which leads to different effects outlined in this section.

####  2.2.1 Estimator bias (EB)

As noted by Yu et al. (2015), SLC depends on the estimator used for the shear
correlation functions. Different estimators incur different SLC-induced
estimator biases. For example, when using an estimator based on pixelized
shear maps, the noise in each pixel depends on the number of source galaxies
in the pixel. The correlation between this number and the shear signal then
leads to a correlation between the signal estimate and the noise (Gatti et al.
2024). Here, though, we consider a catalogue-based estimator for the shear
correlation functions which does not require pixelisation. This estimator
$\hat{\xi}_{\pm}$ is

$\hat{\xi}_{\pm}(\theta)=\frac{\sum_{i}\sum_{j}(\gamma_{\mathrm{t}}^{i}\gamma_{\mathrm{t}}^{j}\pm\gamma_{\times}^{i}\gamma_{\times}^{j})\triangle(|\boldsymbol{\vartheta}_{i}-\boldsymbol{\vartheta}_{j}|;\theta)}{\sum_{i}\sum_{j}\triangle(|\boldsymbol{\vartheta}_{i}-\boldsymbol{\vartheta}_{j}|;\theta)}\;,$
(10)

where the sums go over all source galaxies, $\gamma_{\mathrm{t}}^{i}$ and
$\gamma_{\times}^{i}$ are the tangential and cross shear of the $i$-th galaxy
and $\triangle(\vartheta;\theta)$ is one if $\vartheta$ lies in the
$\theta$-bin and zero otherwise. Using
$\gamma_{\mathrm{t}/\times}(\boldsymbol{\vartheta},\chi)$ for the tangential
(cross) shear of a hypothetical source at angular position
$\boldsymbol{\vartheta}$ and distance $\chi$, the expectation value of this
estimator is

$\displaystyle\langle\hat{\xi}_{\pm}\rangle(|\boldsymbol{\vartheta}-\boldsymbol{\vartheta}^{\prime}|)$
$\displaystyle=\Bigg{\langle}\Bigg{\\{}\int\differential{\chi_{1}}\int\differential{\chi_{2}}\int\differential[2]{\vartheta}p(\chi_{1};\boldsymbol{\vartheta})\,p(\chi_{2};\boldsymbol{\vartheta}^{\prime})\,$
(11)
$\displaystyle\quad\quad\times\left[\gamma_{\mathrm{t}}(\boldsymbol{\vartheta},\chi_{1})\,\gamma_{\mathrm{t}}(\boldsymbol{\vartheta}^{\prime},\chi_{2})\pm\gamma_{\times}(\boldsymbol{\vartheta},\chi_{1})\,\gamma_{\times}(\boldsymbol{\vartheta}^{\prime},\chi_{2})\right]\Bigg{\\}}$
$\displaystyle\quad\times\left[\int\differential{\chi_{1}}\int\differential{\chi_{2}}\int\differential[2]{\vartheta}p(\chi_{1};\boldsymbol{\vartheta})\,p(\chi_{2},\boldsymbol{\vartheta}^{\prime})\right]^{-1}\Bigg{\rangle}\,.$

If we neglect for the moment the correlation between the source density
$n_{\mathrm{s}}$ and the shear (which we treat in the next two subsections),
we can swap the averaging and the integrations such that the expectation value
becomes

$\displaystyle\langle\hat{\xi}_{\pm}\rangle(|\boldsymbol{\vartheta}-\boldsymbol{\vartheta}^{\prime}|)$
$\displaystyle=\Bigg{[}\int\differential{\chi_{1}}\int\differential{\chi_{2}}\int\differential[2]{\vartheta}\langle
p(\chi_{1},\boldsymbol{\vartheta})\,p(\chi_{2},\boldsymbol{\vartheta}^{\prime})\rangle$
(12)
$\displaystyle\quad\quad\times\langle\gamma_{\mathrm{t}}(\boldsymbol{\vartheta},\chi_{1})\,\gamma_{\mathrm{t}}(\boldsymbol{\vartheta}^{\prime},\chi_{2})\pm\gamma_{\times}(\boldsymbol{\vartheta},\chi_{1})\,\gamma_{\times}(\boldsymbol{\vartheta}^{\prime},\chi_{2})\rangle\Bigg{]}$
$\displaystyle\quad\times\left[\int\differential{\chi_{1}}\int\differential{\chi_{2}}\int\differential[2]{\vartheta}\langle
p(\chi_{1},\boldsymbol{\vartheta})\,p(\chi_{2},\boldsymbol{\vartheta}^{\prime})\rangle\right]^{-1}\,.$

For unclustered sources, $p(\chi,\boldsymbol{\vartheta})$ reduces to $p(\chi)$
and the expectation value in Eq. (12) becomes exactly $\xi_{\pm}$. This occurs
even for clustered sources in the limit of infinitely narrow redshift
distributions, i.e.,
$p(\chi,\boldsymbol{\vartheta})\propto\delta_{\mathrm{D}}(\chi-\chi^{\prime})$,
since then the $p$-correlations in numerator and denominator cancel. In
reality, the shear correlation functions can only be measured for finitely
broad $p(\chi)$, so in general, $\hat{\xi}_{\pm}$ is biased. We refer to this
bias as estimator bias (EB).

The estimator bias is also affected by shear weights. Usually, the measured
galaxy ellipticities have an assigned weight that depends on the statistical
error or bias of the shape measurement. This weight depends on properties of
the considered galaxy, such as magnitude and size, but also on the environment
of the galaxy, e.g, whether it is blended with another object. Consequently,
the shear weight is correlated with the source number density, causing further
bias to the estimator.

####  2.2.2 Intrinsic clustering (IC)

For the EB effect we neglected that the shear signal itself is correlated with
the source galaxy density. This correlation occurs, because due to source
clustering the source redshift distribution is not uniform across the sky but
depends on the local matter density contrast. Therefore, the number density
$n$ needs to be replaced by

$n(\chi)\rightarrow
n(\chi)\left[1+\delta_{\mathrm{g}}(\chi\,\boldsymbol{\theta},\chi)\right]\;,$
(13)

where $\delta_{\mathrm{g}}$ is the (three-dimensional) galaxy number density
contrast. This relation differs from the ‘projected’ SLC ansatz (e.g. Schmidt
et al. 2009; Euclid Collaboration: Deshpande et al. 2024), where
$\delta_{\mathrm{g}}(\chi\,\theta,\chi)$ is replaced by a projected density
contrast $\delta_{\mathrm{g}}^{\mathrm{p}}(\theta)$ which no longer depends on
$\chi$. However, the projected ansatz only agrees with Eq. (13) for very
narrow bins, since then
$\delta_{\mathrm{g}}^{\mathrm{p}}(\theta)\simeq\delta_{\mathrm{g}}(\bar{\chi}\,\theta,\bar{\chi})$,
where $\bar{\chi}$ is the average distance for galaxies in the redshift bin
(Krause et al. 2021).

Under the assumption of a linear galaxy bias $b$,

$n(\chi)\rightarrow
n(\chi)\left[1+b\,\delta(\chi\,\boldsymbol{\theta},\chi)\right]\;.$ (14)

Applying this change to Eq. (8) means that the true convergence $\kappa$ is
given by

$\kappa(\boldsymbol{\theta})=\kappa_{0}(\boldsymbol{\theta})+\Delta\kappa(\boldsymbol{\theta})\;,$
(15)

with

$\Delta\kappa(\boldsymbol{\theta})=b\,\int_{0}^{\infty}\differential{\chi}\delta(\chi\boldsymbol{\theta},\chi)\int_{\chi}^{\infty}\differential{\chi^{\prime}}W(\chi,\chi^{\prime})\,p(\chi^{\prime})\,\delta(\chi^{\prime}\boldsymbol{\theta},\chi^{\prime})\;.$
(16)

The additional term depends on both the density contrast
$\delta(\chi\boldsymbol{\theta},\chi)$ in front of the source galaxies, i.e.
the ‘lens planes’, and the density contrast
$\delta(\chi^{\prime}\boldsymbol{\theta},\chi^{\prime})$ surrounding the
source galaxies, i.e., in the ‘source planes’, which gives the effect its
name: source-lens clustering.

As we show in Appendix A, the $\Delta\kappa$ induces an additional term
$\Delta C$ to the lensing power spectrum 111The contribution to the power
spectrum we derive here follows the same form as the contribution to the shear
power spectrum derived by Krause et al. (2021). It deviates from the
contribution by SLC found by Euclid Collaboration: Deshpande et al. (2024),
since they use the projected SLC ansatz., given by

$\displaystyle\Delta C(\boldsymbol{\ell})$
$\displaystyle=b^{2}\int_{0}^{\infty}\differential{\chi}\int_{\chi}^{\infty}\differential{\chi^{\prime}}\frac{p^{2}(\chi^{\prime})}{\chi^{\prime
2}}\,\frac{W^{2}(\chi,\chi^{\prime})}{\chi^{2}}\,$ (17)
$\displaystyle\quad\times\int\frac{\differential[2]{L}}{(2\pi)^{2}}\,P\left(\frac{L}{\chi},\chi\right)\,P\left(\frac{|\boldsymbol{\ell}-\boldsymbol{L}|}{\chi^{\prime}},\chi^{\prime}\right)\,.$

We note that this expression relies on the assumption of a linear galaxy bias,
which might not be fulfilled at small scales. Therefore, instead of simply
using Eq. (17) to predict the effect, we measure it in the following using
cosmological simulations with realistic galaxy distributions.

####  2.2.3 Tomographic bin contamination (TC)

Another effect occurs when cosmic shear analyses are performed in tomographic
bins divided by photometric redshift estimates. Photometric redshifts of
individual galaxies are typically noisy. Therefore, a galaxy associated with a
tomographic bin between $z_{1}$ and $z_{2}$ might have a true redshift well
outside of this range. On average, this photometric redshift scatter is taken
care of by using a $p(\chi)$ for each tomographic bin, which was calibrated
with spectroscopic redshift estimates (see e.g. Wright et al. 2020). However,
the deviation from the estimated $p(\chi)$ along each line-of-sight correlates
with the galaxy number density. Along a line-of-sight with an overdensity in
the front, there are more galaxies which can potentially be assigned to a
higher tomographic bin, thus ‘contaminating’ this bin. These contaminating
galaxies carry a lower lensing signal. Consequently, in denser regions, the
cosmic shear signal is suppressed. This effect also impacts weak lensing
estimates of galaxy cluster masses (Köhlinger et al. 2015). Due to photometric
redshift scatter, cluster member galaxies can be erroneously treated as
background source galaxies. They carry no lensing signal due to the galaxy
cluster, thus bias the mass estimate low.

All SLC effects are expected to be much smaller than the cosmic shear signal
itself. For example, since Eq. (17) depends on the fourth-order moment of the
matter distribution, one could assume that this effect is negligible in a
realistic weak lensing survey, where shape measurement uncertainties or the
distribution of intrinsic galaxy shapes cause significant noise contributions.
However, while this argument was made for stage III surveys (Krause et al.
2021), it does not necessarily hold for Euclid. As illustration, we compare in
Fig. 1 the shear correlation function $\xi_{+}$ for auto-correlations of
tomographic bins as measured by the stage III surveys KiDS (from Asgari et al.
2021), DES (from Amon et al. 2022), and HSC (from Hamana et al. 2020) with
their reported error bars, to the expectation for Euclid. Due to its greater
depth, Euclid will observe more tomographic bins at higher redshift, which
carry larger cosmic shear signals. Due to its larger area and higher number
density, the noise of the cosmic shear measurements will be significantly
reduced, leading to an order of magnitude increase in S/N. This high precision
requires us to have at least equally accurate models. The first step to these
is understanding how model assumptions impact the cosmological inference.

Figure 1: Upper panel: Shear auto-correlations $\xi_{+}$ for the stage III
surveys KiDS (from Asgari et al. 2021), DES (from Amon et al. 2022), and HSC
(from Hamana et al. 2020) with their reported errorbars and the expectation
for Euclid. Error bars for Euclid are the square root of the covariance matrix
diagonal, calculated as described in Sect. 4.1. The color indicates the median
redshift of the tomographic bins, with darker colors corresponding to higher
redshifts. Lower panel: S/N of $\xi_{+}$, given by dividing the measurement /
prediction by the error bars.

##  3  Simulated datasets

We used two sets of simulated data to estimate the impact of source-lens
clustering on cosmological analyses. One of these datasets, based on the
Marenostrum Institut de Ciències de l’Espai (MICE) simulations, mimics the
redshift distribution and tomographic setup of the KiDS-1000, while the other,
based on the Euclid Flagship2 (FS2) simulation, mimics the expected redshift
distribution and tomographic setup of the Euclid wide survey. We describe
their creation and properties in the following. Simulated galaxy catalogues
with galaxy properties and weak lensing information from both MICE and the FS2
are accessible on CosmoHub222https://cosmohub.pic.es (Carretero et al. 2017;
Tallada et al. 2020).

###  3.1 The Marenostrum Institut de Ciències de l’Espai (MICE) simulations

We created a KiDS-like data set based on the MICE simulation (Fosalba et al.
2015a), a dark-matter-only N-body simulation. The simulation used a flat
$\Lambda$CDM cosmology with $\Omega_{\mathrm{m}}=0.25$,
$\Omega_{\Lambda}=0.75$, $\Omega_{\mathrm{b}}=0.044$, $n_{\mathrm{s}}=0.95$,
$\sigma_{8}=0.8$, $h=0.7$. It evolved $4096^{3}$ particles with a mass of
$2.93\times 10^{10}h^{-1}M_{\odot}$ inside a box with side length
$3072\,h^{-1}\,\mathrm{Mpc}$ from an initial redshift of $z=100$ to today. In
the dark matter particle distribution, halos were identified using a friends-
of-friends halo finder (Crocce et al. 2015). The halos were then populated up
to redshift $z=1.4$ with galaxies, following a mixture of halo abundance
matching and a halo occupation distribution model to match both the spatial
and luminosity distribution of observed galaxies (Carretero et al. 2015). We
used the second version of this galaxy catalogue, called MICE2.

The MICE2 galaxies have assigned fluxes in many photometric bands. To generate
KiDS-like photometry, we used the noiseless simulated photometry from MICE,
similar to the approach presented in van den Busch et al. (2020). We chose the
filters which are most similar to the KiDS-1000 filter set-up, which consists
of the VST OmegaCAM $ugri$ bands and the VISTA VIRCAM $ZYJHK_{\rm s}$ bands
(Kuijken et al. 2019). For the $ugriZ$ bands, we found the SDSS $ugriz$
filters provided in MICE to be most similar to the ones used in KiDS-1000. For
the near-infrared imaging in the $Y$ band, the DES $y$ filter is used as a
reasonable approximation. The filters of the VISTA $JHK_{\rm s}$ bands are
readily available in MICE. As presented in Fosalba et al. (2015b), we applied
a redshift-dependent evolution correction to the MICE magnitudes resulting in
a set of magnitudes $m^{\rm evo}$. To estimate the observed magnitudes, we
approximated the flux noise of KiDS-1000 (Kuijken et al. 2019).

An effective projected galaxy radius size $r_{\rm eff}$ is estimated taking
into account the half-light radius of a galaxy’s bulge and disk and the bulge-
to-total emitted flux fraction given in MICE. The estimated projected galaxy
size translates into a simulated aperture which mimics the Gaussian Aperture
and Point Spread Function (GAaP) apertures used in KiDS (Kuijken 2008). The
aperture major and minor axis $A_{i,x}$ and $B_{i,x}$, respectively, are
calculated per galaxy $i$ and per photometric filter $x$ through

$\displaystyle A_{i,x}$
$\displaystyle=\min\left(\sqrt{r_{\mathrm{eff},i}^{2}+\sigma_{\mathrm{PSF},x}^{2}+r_{\mathrm{min}}^{2}},$$\right)\;,$
(18) $\displaystyle B_{i,x}$
$\displaystyle=\min\left(\sqrt{\left(\left[\frac{b}{a}\right]_{i}r_{\mathrm{eff},i}\right)^{2}+\sigma_{\mathrm{PSF},x}^{2}+r_{\mathrm{min}}^{2}},$$\right)\;,$
(19)

with the mean seeing $\sigma_{\mathrm{PSF},x}$ and the projected axis ratio of
the bulge $\left[\frac{b}{a}\right]_{i}$ with the semi-minor and semi-major
axis $b$ and $a$, respectively, which is given for all the MICE sources. The
minimum radius $r_{\mathrm{min}}$ for the mocks was set to $None$, which is
the maximum difference in PSF size of the KiDS-1000 data between the different
photometric bands. The maximum aperture axis is set to be $None$, as for the
KiDS-1000 data.

Considering the limiting magnitudes $m_{\mathrm{lim},x}$ of the KiDS
observations, we calculated the flux error

$\displaystyle\Delta
f_{i,x}=10^{-0.4(m_{\mathrm{lim},x}-48.6)}\sqrt{\frac{A_{i,x}B_{i,x}}{\sigma_{\mathrm{PSF},x}^{2}}}\;,$
(20)

where we included the mock apertures $\pi A_{i,x}B_{i,x}$ to increase the
noise for larger apertures compared to the PSF
$\pi\sigma_{\mathrm{PSF},x}^{2}$. Given the estimated noise and the evolution-
corrected model fluxes $f^{\rm evo}$, a flux realisation was computed from
$f^{\rm obs}_{i,x}\sim\mathcal{N}(f^{\rm evo}_{i,x},\Delta f_{i,x})$.
Converting to magnitudes $m^{\rm obs}_{i,x}$ and their errors $\Delta
m_{i,x}$, photometric redshift can be computed with the template fitting
photo-$z$ algorithm BPZ (Benitez 2000). We excluded all objects with a signal-
to-noise ratio of less than 1 in the $r$ band since we label these galaxies as
undetected, and they, therefore, would have no shape measurement. Lastly, we
performed a $k$ Nearest Neighbours (kNN) matching between the mock catalogue
and the KiDS data based on the 9 magnitudes $ugrizYJHK_{\rm s}$ to assign a
mock shape weight `recal_weight` from the real galaxies to the mock ones. This
is then used to select the objects with non-zero shape weights, which were
used as the source sample in KiDS.

The MICE simulations were designed for application to gravitational lensing
surveys, and thus the lensing observables shear and convergence were computed
for the simulation as described in Fosalba et al. (2015b) using the approach
by Fosalba et al. (2008) under the Born approximation. From this, one obtains
full sky maps of the lensing convergence for sources at 265 different
redshifts between 0 and 1.4. These $\kappa$-maps were converted to maps of the
weak lensing shear $\gamma$, using first their decomposition in harmonic
space,

$\displaystyle\kappa(\boldsymbol{\vartheta})$
$\displaystyle=\sum_{\ell=0}^{\infty}\sum_{m=-\ell}^{\ell}\hat{\kappa}_{\ell
m}\,Y_{\ell m}(\boldsymbol{\vartheta})\;,$ (21)
$\displaystyle\gamma(\boldsymbol{\vartheta})$
$\displaystyle=\sum_{\ell=2}^{\infty}\sum_{m=-\ell}^{\ell}\hat{\gamma}_{\ell
m}\,{}_{2}Y_{\ell m}(\boldsymbol{\vartheta})\;,$ (22)

where we neglect $B$-modes and use the Laplace spherical harmonics $Y_{\ell
m}$ and the spin-$s$-weighted spherical harmonics ${}_{s}Y_{\ell m}$. Then, we
apply the inverse Kaiser–Squires relation (Kaiser & Squires 1993),

$\hat{\gamma}_{\ell
m}=-\sqrt{\frac{(\ell+2)(\ell-1)}{\ell(\ell+1)}}\hat{\kappa}_{\ell m}\;.$ (23)

Each galaxy at angular position $\boldsymbol{\vartheta}$ and redshift $z$ in
the MICE2 catalogue was then assigned the shear at position
$\boldsymbol{\vartheta}$ of the weak lensing map for redshift $z$. The
galaxies were also assigned deflected positions, arising from magnification of
the sources by the density field. As we are not interested in magnification
effects on the cosmic shear signal, we use throughout the original,
unmagnified positions of the galaxies.

In the following, we use both the MICE2 catalogue and the shear maps to create
clustered and unclustered source galaxy samples, as detailed in Sect. 3.3. For
this, it is sufficient for us to use a rather small area, namely the
rectangular region with right ascension $\alpha\in($$,$$)$ and declination
$\delta\in($$,$$)$.

Figure 2: Redshift distribution of KiDS-1000-like galaxies in the MICE (top)
and Euclid-like galaxies in the FS2 (bottom).

###  3.2 The Euclid flagship simulation 2

Since the MICE galaxies are limited to $z<1.4$, it is not possible to
construct a Euclid-like sample from them, as Euclid will observe a significant
number of galaxies at higher redshifts. Therefore, we used the Euclid flagship
simulations 2 (FS2, Euclid Collaboration: Castander et al. 2024) to create a
Euclid-like sample.

The FS2 used $16\,000^{3}$ particles with a mass of
$10^{9}\,h^{-1}\,M_{\odot}$ and evolved them in a simulation box with side
length $3600\,h^{-1}$ Mpc with the PKDGRAV3 code (Potter & Stadel 2016). This
larger box size allows for ray tracing and galaxy distribution up to $z=3.0$.
The simulation assumed a flat $\Lambda$CDM cosmology with
$\Omega_{\mathrm{m}}=0.319$, $\Omega_{\mathrm{b}}=0.049$,
$\Omega_{\Lambda}=0.681-\Omega_{\gamma}-\Omega_{\nu}$, with a photon density
parameter $\Omega_{\gamma}=0.00005509$, and a neutrino density parameter
$\Omega_{\nu}=0.00140343$. The reduced Hubble constant is $h=0.67$, the scalar
spectral index of the initial fluctuations $n_{\mathrm{s}}=0.96$, and its
amplitude $A_{\mathrm{s}}=2.1\times 10^{-9}$, which corresponds to
$\sigma_{8}\simeq 0.813$.

Dark matter halos were found using the friends-of-friends halo finder ROCKSTAR
(Behroozi et al. 2013). These halos were populated with central and satellite
galaxies according to a halo occupation distribution. Central galaxies were
placed at the halo centres, while satellite galaxies are distributed inside
the halo following a triaxial Navarro-Frenk-White profile. The galaxies were
assigned luminosities with an abundance-matching approach.

The galaxies were assigned photometric redshifts using the nearest-neighbor
photometric redshift (NNPZ) pipeline, which estimates redshift probability
distributions for each galaxy (see Euclid Collaboration: Desprez et al. 2020,
for a comparison of this and other redshift estimation algorithms). We used
the mode of these probability distributions as photometric redshift estimate.
The pipeline used a reference sample of two million objects simulated at the
depth of the Euclid calibration fields. Since the full depth of these
calibration fields will only be available towards the end of Euclid’s
observing run, the accuracy of the derived photometric redshifts is optimistic
for the first Euclid data release. However, it is realistic for the final
Euclid data releases, which have the highest statistical power and are,
therefore, the strongest affected by subtle effects like SLC.

Similarly to the MICE, full-sky shear and convergence maps were computed for
the FS2 with the ray-tracing approach by Fosalba et al. (2008). This approach
produced shear and convergence maps at 115 source redshifts between $z=2.3$
and today, given as healpix maps with $N_{\mathrm{side}}=8192$, which
corresponds to an angular resolution of $\simeq$$$. While the shear maps were
computed for the full-sky, galaxy catalogues are (at time of writing) only
available for an octant, stretching for right ascensions between $None$ and
$None$ and declinations between $None$ and $None$. Therefore, our analysis is
limited to this area.

###  3.3 Creating clustered and unclustered galaxy samples

Both the MICE and the FS2 contain realistically clustered source galaxies. We
divide these galaxies into different tomographic bins based on their
photometric redshifts. For the KiDS-like setup, we use the five bins defined
by Hildebrandt et al. (2021) and also used by Asgari et al. (2021), while for
the Euclid-like setup, we use the 13 tomographic bins defined by Euclid
Collaboration: Pocino et al. (2021), shown in Table 1. We show the
distributions of true redshifts for these bins in Fig. 2.

We create two new galaxy catalogues for each tomographic bin based on the
shear maps and the original catalogue. The first of these, which we refer to
as the ‘clustered’ catalogue, is used purely for validation purposes. To
create it, we take the angular positions $\boldsymbol{\theta}$ and redshift
$z$ of each galaxy in the original catalogue and assign it the shear $\gamma$
at position $\boldsymbol{\theta}$ on the shear map closest in redshift to $z$.

The second catalogue we create, which we refer to as ‘unclustered’, is created
similarly as the clustered catalogue but crucially without using the galaxies
angular positions. Instead, for each galaxy in the catalogue we draw a random
angular position from a uniform distribution and assign the shear at this new
position and the galaxies’ redshift to the galaxy. In this way, the galaxies
in the unclustered catalogue have the same average number density and redshift
distribution as those in the clustered and original catalogue but uniformly
distributed positions. The SLC effect is thus present only in the clustered
catalogue.

Table 1: Photometric redshift ranges of tomographic bins for the KiDS-like and the Euclid-like sample Bin | KiDS-like |  Euclid-like
---|---|---
1 | (0.1,0.3] | (0,0.15]
2 | (0.3, 0.5] | (0.15, 0.31]
3 | (0.5,0.7] | (0.31, 0.46]
4 | (0.7,0.9] | (0.46, 0.63]
5 | (0.9,1.2] | (0.63, 0.77]
6 |  | (0.77, 0.92]
7 |  | (0.92, 1.08]
8 |  | (1.08, 1.23]
9 |  | (1.23, 1.38]
10 |  | (1.38, 1.54]
11 |  | (1.54, 1.69]
12 |  | (1.69, 1.85]
13 |  | (1.85, 2.0]

To test the impact of the individual SLC effects (see Sect. 2.2), we create
two more catalogues from MICE. The first of these consists of taking the true
galaxy positions on the sky and assigning to them the shear at positions
rotated $90^{\circ}$ away with respect to the survey patch center. In this
way, the clustering of the source galaxies is no longer correlated to the
shear signal. This eliminates the IC and TC effects but retains the EB since
the sources still have a non-zero angular correlation function $\omega$.

The last catalogue we create is designed to include the EB and the IC effects
but not the TC. For each tomographic bin, we randomly subselect galaxies from
the full MICE catalogue such that their true redshifts follow the redshift
distribution of the bin but without using the photometric redshifts. In that
way, the selection of galaxies in a tomographic bin is no longer dependent on
the photometric redshift scatter, eliminating the TC effect.

##  4  Cosmological analysis

###  4.1 COSEBI estimation, modelling and covariance

To match the fiducial cosmological analysis of Asgari et al. (2021), we
perform our cosmological inference using the Complete Orthogonal Sets of
E/B-Integrals (COSEBIs, Schneider et al. 2010). These consist of the $E$-modes
$E_{n}$ and the $B$-modes $B_{n}$, where, to first order, only $E$-modes can
be generated by weak lensing. They can be obtained as weighted integrals over
the shear correlation functions $\xi_{+}$ and $\xi_{-}$ with

$\displaystyle E_{n}$
$\displaystyle=\frac{1}{2}\int_{\theta_{\mathrm{min}}}^{\theta_{\mathrm{max}}}\differential\theta\,\theta\left[T_{+n}(\theta)\xi_{+}(\theta)+T_{-n}(\theta)\xi_{-}(\theta)\right]\,,$
(24) $\displaystyle B_{n}$
$\displaystyle=\frac{1}{2}\int_{\theta_{\mathrm{min}}}^{\theta_{\mathrm{max}}}\differential\theta\,\theta\left[T_{+n}(\theta)\xi_{+}(\theta)-T_{-n}(\theta)\xi_{-}(\theta)\right]\,,$
(25)

where $T_{\pm n}(\theta)$ are filter functions defined such that $\theta$ is
bounded by $\theta_{\mathrm{min}}$ and $\theta_{\mathrm{max}}$ (Schneider et
al. 2010).

To obtain the COSEBIs, we first measure the shear correlation functions
$\xi_{+}$ and $\xi_{-}$ for each combination of the tomographic bins. We use
$4000$ radial bins spaced between $None$ and $None$ logarithmically for both
the KiDS and Euclid-like case. The measurements are conducted with `treecorr`
(Jarvis et al. 2004). The correlation functions are then converted to the
first 5 COSEBIs. We choose this number $n_{\mathrm{max}}$ of COSEBIs for two
reasons. First, the information content as a function of $n_{\mathrm{max}}$
saturates between $n_{\mathrm{max}}=5$ and $n_{\mathrm{max}}=10$ (Asgari et
al. 2012). Second, the signal-to-noise ratio diminishes with higher $n$ and
even for the Euclid-like case, the signal-to-noise ratio for $E_{6}$ is lower
than 3.8 for all redshift bins. Thus, we do not expect a significant
improvement when including more COSEBIs. Nevertheless, determining the optimal
choice of $n_{\mathrm{max}}$, along with the considered angular scales is an
important goal for future work. We model $E_{n}$ using

$\displaystyle E_{n}$
$\displaystyle=\int_{0}^{\infty}\frac{\differential\ell\,\ell}{2\pi}C(\ell)\,W_{n}(\ell)\,,$
(26)

where the $W_{n}$ are Hankel transforms of the $T_{\pm n}$ and given in Asgari
et al. (2012). The lensing power spectrum $C(\ell)$ is modelled as in Joachimi
et al. (2021) from Eq. (9). We use the redshift distributions $p_{z}(z)$
displayed in Fig. 2, but include free parameters $\delta z$ for shifts in the
$p_{z}(z)$. This $\delta z$ are the difference between the mean of the
estimated $p_{z}(z)$ of each tomographic bin and the true redshift
distribution. We use the linear power spectrum model from CAMB (Lewis et al.
2000; Howlett et al. 2012).

We model the non-linear matter power spectrum $P(k)$ using HMCode-2020 (Mead
et al. 2021) for the KiDS-like analysis. We fix the baryon feedback parameters
$\eta$ and $A_{\mathrm{b}}$ to 0 and 3.13, respectively, corresponding to the
dark-matter-only case. However, we cannot use the same prescription for the
Euclid-like case. As shown in Fig. 3, the measured shear correlation functions
for the KiDS-like case show a deviation of up to 2% to the HMCode-based
prediction for the simulation cosmology for sources at redshifts between 0.9
and 1.2, which is well within the measurement uncertainty of KiDS-1000. For
Euclid, though, this deviation is of the order of the measurement uncertainty,
indicating that the model is not accurate enough. Instead, for the Euclid-
setup, we use the non-linear matter power spectrum predicted by the
EuclidEmulator2 (Euclid Collaboration: Knabenhans et al. 2021), which agrees
with the measurements within 1%, which is within the uncertainty.

Figure 3: Fractional difference between $\xi_{+}$ modelled with HMCode-2020
(red, dashed) and the EuclidEmulator (black, dash-dotted) to the measurements
in the FS2 for sources at $0.9<z<1.2$. The blue area corresponds to the