11institutetext:  Università di Salerno, Dipartimento di Fisica ”E.R.
Caianiello”, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy
22institutetext: INAF – Osservatorio Astronomico di Capodimonte, Via
Moiariello 16, I-80131 Napoli, Italy 33institutetext: INFN – Gruppo Collegato
di Salerno - Sezione di Napoli, Dipartimento di Fisica ”E.R. Caianiello”,
Università di Salerno, via Giovanni Paolo II, 132 - I-84084 Fisciano (SA),
Italy. 44institutetext: INAF – OAS, Osservatorio di Astrofisica e Scienza
dello Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy
55institutetext: Dipartimento di Fisica e Scienze della Terra, Università
degli Studi di Ferrara, via Saragat 1, I-44122 Ferrara, Italy 66institutetext:
Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16,
I-20133 Milano, Italy 77institutetext: INAF - IASF Milano, via Corti 12,
I-20133 Milano, Italy 88institutetext: Technical University of Munich, TUM
School of Natural Sciences, Department of Physics, James-Franck-Str 1, 85748
Garching, Germany 99institutetext: Max-Planck-Institut für Astrophysik, Karl-
Schwarzschild-Str. 1, 85748 Garching, Germany 1010institutetext: Centro de
Astrobiología, Instituto Nacional de Técnica Aeroespacial, Ctra de Torrejón a
Ajalvir, km 4, 28850 Torrejón de Ardoz, Madrid, Spain 1111institutetext:
Instituto de Física, Pontificia Universidad Católica de Valparaiso, Avda.
Universidad 330, Placilla, Valparaíso, Chile 1212institutetext: INAF – OAA,
Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Firenze,
Italy 1313institutetext: Università degli Studi di Trieste, Dipartimento di
Fisica - Sezione di Astronomia, via Tiepolo 11, I-34143 Trieste, Italy
1414institutetext: INAF - Osservatorio Astronomico di Trieste, via Tiepolo 11,
I-34143 Trieste, Italy 1515institutetext: Faculty of Physics, University
Observatory, Ludwig-Maximilians-Universität München, Munich, Germany
1616institutetext: Institute for Particle Physics and Astrophysics, ETH
Zürich, Zürich, Switzerland

# The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/

Redshift catalog and new lens model using MUSE observations

M. D’Addona The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ A. Mercurio The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ P. Rosati The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ C. Grillo The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ G. Caminha The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ A. Acebron The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ G. Angora The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ P. Bergamini The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ V. Bozza The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ G. Granata The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ M. Annunziatella The powerful lens galaxy cluster PLCK
G287.0+32.9 ($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1
and E.1 are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ A. Gargiulo The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ R. Gobat The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ P. Tozzi The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ M. Girardi The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ M. Lombardi The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ M. Meneghetti The powerful lens galaxy cluster PLCK
G287.0+32.9 ($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1
and E.1 are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ P. Schipani The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ L. Tortorelli The powerful lens galaxy cluster PLCK
G287.0+32.9 ($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1
and E.1 are only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/ E. Vanzella The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/The powerful lens galaxy cluster PLCK G287.0+32.9
($\theta_{\rm{E}}\sim\qty{43}{\arcsec}$)††thanks: Tables C.1, D.1 and E.1 are
only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/

(Received 21 December 2023; accepted 28 January 2024)

###### Abstract

Aims. We present a new high-precision strong-lensing model of PLCK
G287.0$+$32.9, a massive lens galaxy cluster at $z=0.383$, with the aim of
obtaining an accurate estimation of its effective Einstein radius and total
mass distribution. We also present a spectroscopic catalog containing accurate
redshift measurements for close to 500 objects up to redshift $z=6$, including
multiply lensed sources and cluster member galaxies.

Methods. We exploited high-quality spectroscopic data from the Multi Unit
Spectroscopic Explorer (MUSE), covering a central $3\leavevmode\nobreak\
\rm{arcmin}^{2}$ region of the cluster. We supplemented the spectroscopic
catalog by including redshift measurements from VIsible MultiObject
Spectrograph (VIMOS) and DEep Imaging Multi-Object Spectrograph (DEIMOS). We
identified 129 spectroscopic cluster member galaxies with redshift values of
$0.360\leq z\leq 0.405$, and $m_{\rm{F160W}}\leq 21$. We complemented this
galaxy cluster member sample with 24 photometric members identified with a
convolutional neural network (CNN) approach. We also identified 114 multiple
images from 28 background sources, of which 84 images from 16 sources are new
and the remaining ones have already been identified in previous works. From
these, we extracted a ”golden sample” of 47 secure multiple images and used
them, together with the selected cluster member, to build and optimize several
strong-lensing models with the software lenstool.

Results. The best-fitting lens model shows a root mean square (RMS) separation
value between the predicted and observed positions of the multiple images of
$None$. Using its predictive power, we found three new multiple images and we
confirm the configuration of three systems of multiple images that were not
used for the optimization of the model. For a source at a redshift of
$z_{s}=2$, we found a cluster with an Einstein radius of
$\theta_{\rm{E}}=43.4\arcsec\pm 0.1\arcsec$. This value is in agreement with
previous estimates and corresponds to a total mass enclosed in the critical
curve of $\rm{M_{E}}={3.33}_{-0.07}^{+0.02}\times{10^{14}\rm{M}_{\odot}}$.

Conclusions. The combined application of ancillary Hubble Space Telescope
(HST) imaging, VIMOS and DEIMOS data, and the new MUSE spectroscopic
observations allowed us to build a new lens model of the galaxy cluster PLCK
G287.0+32.9, with an improvement in terms of reconstructing the observed
positions of the multiple images of a factor of $2.5$ with respect to previous
models. The derived total mass distribution confirms this cluster to be a very
prominent gravitational lens, with an effective Einstein radius of
$\theta_{\rm{E}}\sim{$$}$. We were also able to construct an extensive
spectroscopic catalog containing 490 objects, of which 153 are bright cluster
members with $m_{\rm{F160W}}\leq 21$, and 114 are multiple images.

###### Key Words.:

galaxies: clusters: general – galaxies: clusters: individual: PLCK G287.0+32.9
– gravitational lensing: strong – dark matter

##  1 Introduction

Galaxy clusters are the largest gravitationally bound structures known in the
Universe. They are not only valuable laboratories in the investigation of
galaxy formation and evolution processes, but given they can act as giant
gravitational lenses, they also are precious tools for investigating distant
and faint objects (Vanzella et al. 2016, 2017). For example, Vanzella et al.
(2021) was able to peer into the internal structure of galaxies at high-
redshift lensed galaxies and unveil star-forming complexes matching the scales
of bound star clusters. The outcome of the strong-lensing models can be used
to constrain cosmological models, such as the standard lambda cold dark matter
cosmology (-CDM, Spergel et al. 2003; Komatsu et al. 2011; Ade et al. 2016;
Aghanim et al. 2020), and validate their predictions: for example, the
analysis of the time delays between the multiple images of variable strongly
lensed sources (Refsdal 1966), such as supernovae (Kelly et al. 2015; Rodney
et al. 2021; Goobar et al. 2017) or quasars (Inada et al. 2012; Oguri et al.
2013; Sharon et al. 2017; Courbin et al. 2018; Bonvin et al. 2018; Acebron et
al. 2022a), has been used to measure the value of the Hubble constant,
$\rm{H}_{0}$ (Suyu et al. 2017; Tewes et al. 2013; Grillo et al. 2018; Birrer
et al. 2019; Sluse et al. 2019; Wong et al. 2020); statistical analyses of the
total mass distributions derived from lens models and the predictions of
cosmological simulations have indicated that the hierarchical formation of the
large-scale structure may not be compatible with the -CDM model (Giocoli et
al. 2008, 2010; Wang et al. 2020; Meneghetti et al. 2020, 2022, 2023);
analyses of the distribution of the effective Einstein radius,
$\theta_{\rm{E}}$, the radius of the area enclosed within the critical curve
of infinite magnification if it were a circle, has in recent years led to a
tension between observations (Zitrin et al. 2012) and theoretical predictions
based on -CDM (Oguri & Blandford 2009; Hennawi et al. 2007).

Even if this tension has been partially scaled down, the study of the observed
distribution of Einstein radii plays an important role in testing the validity
of cosmological models (Waizmann et al. 2012). In fact, since the Einstein
radius is strictly linked to the lens total mass, due to the shape of the
universal mass function (Tinker et al. 2008), $\theta_{\rm{E}}$ is expected to
be on the order of tens of arcseconds (for a lensed source at a redshift of
$z_{\rm{s}}\sim 2$), with clusters with larger Einstein radii becoming rarer
and rarer (Richard et al. 2010; Oguri et al. 2012; Zitrin et al. 2015; Sharon
et al. 2020). To date, only a handful of clusters characterized by
$\theta_{\rm{E}}\geq\qty{40}{\arcsec}$ are known to date (Zitrin et al. 2009a;
Acebron et al. 2020; Broadhurst et al. 2005; Cerny et al. 2018). Therefore,
the number of these massive clusters can enforce strong constraints on
structure formation and evolution models.

Our study focuses on one of these rare gems: the galaxy cluster PLCK
G287.0+32.9 (PLCK-G287 hereafter), a powerful gravitational lens at a redshift
of $z_{c}=0.383$ and the second-most significant Sunyaev-Zel’dovich detection
from the Planck catalog (Ade et al. 2011). Using radio observations from the
Karl Guthe Jansky Very Large Array (VLA) and the Giant Metrewave Radio
Telescope (GMRT), along with X-ray observations from XMM-Newton, Bagchi et al.
(2011) found corroborating evidence for PLCK-G287 to be defined as a massive
post-merger system ($\rm{M}_{\rm{500}}=1.5\times 10^{15}\leavevmode\nobreak\
\rm{M}_{\odot}$) with a very complex structure. This has also been confirmed
by weak-lensing analyses carried out by Gruen et al. (2014) and Finner et al.
(2017) and a study from Bonafede et al. (2014) that is also based on GMRT
observations. More recently, Zitrin et al. (2017) built the first strong-
lensing model for this cluster by using the light-traces-mass method (LTM,
Zitrin et al. 2009b), estimating an effective Einstein radius of
$\theta_{\rm{E}}=\qty{42}{\arcsec}$ with a total uncertainty of $\sim 10\%$.
At the highly non-linear tail of the probability distribution of Einstein
radii, this large uncertainty can make the difference between a mild outlier
and a peculiar object that can be used to challenge the predictions of the
-CDM model. Zitrin et al. (2017) also identified $60$ candidate multiple
images of $20$ background systems using the values of their photometric
redshift estimates, but none of them was spectroscopically confirmed. Of these
multiple images, only $35$ of them, from $10$ background sources, were
confirmed by the model.

Observations from instruments such as the Multi-Unit Spectroscopic Explorer
(MUSE) spectrograph (Bacon et al. 2010) of the European Southern Observatory
(ESO) Very Large Telescope (VLT) have been shown to be a real game-changer
that allowed the identification of large samples of secure multiple images and
cluster members with accurate redshift measurements (e.g., Cerny et al. 2018;
Mahler et al. 2018; Lagattuta et al. 2019; Mercurio et al. 2021; Bergamini et
al. 2023b; Granata et al. 2023), and leading to the flourishing of high-
precision strong-lensing models of galaxy clusters. In this context, we
present a new strong-lensing model and a catalog of redshifts for the galaxy
cluster PLCK-G287.

The structure of this paper is as follows: in Sect. 2, we briefly describe the
data and data analysis used to identify multiple images and cluster members
used for the strong-lensing modeling described in Sect. 3. In Sect. 4, we
present our results, followed by a discussion and a comparison with the
findings of previous works from the literature in Sect. 5. In Appendices C, D,
and E we report the identified multiple images, the identified cluster
members, and the spectroscopic catalog furnished with a list of most prominent
emission and absorption features identified for each object. In this work, we
assume a -CDM cosmology with $\Omega_{m0}=0.3$, $\Omega_{\Lambda 0}=0.7$ and
$\rm{H}_{\rm{0}}=70\leavevmode\nobreak\ \text{km}\leavevmode\nobreak\
\text{s}^{-1}\leavevmode\nobreak\ \text{Mpc}^{-1}$, for which
$\qty{1}{\arcsec}\simeq 5.23\leavevmode\nobreak\ \text{kpc}$ at the redshift
of the cluster PLCK-G287 ($z_{c}=0.383$).

Figure 1: RGB image of the galaxy cluster PLCK-G287 obtained by combining the
HST images with the software fits2rgb 222fits2rgb:
https://github.com/mauritiusdadd/fits2rgb. This is a simple python3 script,
based on the astropy python package (The Astropy Collaboration et al. 2022),
that can merge several monochromatic FITS images into an RGB one.(Red: F105W,
F110W F125W, F140W F160W. Green: F814W. Blue: F435W, F475W, F606W). The yellow
dashed line indicates the footprint of the MUSE spectral data cubes. The cyan
circles and green squares indicate the spectroscopic and CNN-identified
cluster members, respectively (see Sect. 3.1), while the orange and blue
diamonds indicate, respectively, the spectroscopic foreground and background
objects. The two BCGs that have been modeled independently of the other
members are indicated by the red and cyan stars. The redshift estimates for
the objects outside the MUSE footprint come from VIMOS and DEIMOS observations
(see Sect. 2.2). Histograms show the redshift distribution of objects in the
HST footprint: the one on the right is a zooming that shows the redshift of
the BCG ($z=0.383$, solid red line) and the thresholds used to select cluster
members ($0.360\leq z\leq 0.405$, dashed lines). The solid black line shows
the distribution of members with F160W Kron magnitude values equal or lower
than 21.

##  2 Data

###  2.1 Photometric data

PLCK-G287 has been observed by the Hubble Space Telescope (HST) in the
framework of the Reionization Lensing Cluster Survey (RELICS) survey (P.I.:
Dan Coe, Coe et al. 2019, program ID 14096) using both the Advanced Camera for
Surveys (ACS) and the Wide Field Camera 3 (WFC3). Previous observations made
with HST in cycle 23 (P.I.: Seitz, program ID 14165, Seitz 2016) were also
integrated into the RELICS data, for a total of three orbits for the ACS
filters group and two orbits for the WFC3 one. We used publicly available
images in the two resolutions of $\qty{0.03}{\arcsec}$ (30 mas) and
$\qty{0.06}{\arcsec}$ (60 mas) per pixel. They cover an area, centered on the
brightest cluster galaxy (BCG), with a radius of $\sim\qty{1.7}{\arcmin}$ in
the optical bands F435W, F475W, F606W, and F814W; and of
$\sim\qty{1.0}{\arcmin}$ in the infrared bands (IR) F105W, F110W, F125W,
F140W, and F160W. Each science image is also supplemented with a weightmap
image. For the first group of filters, the total exposure time varies from a
minimum of $711\leavevmode\nobreak\ \rm{s}$ for band F125W to a maximum of
$11447\leavevmode\nobreak\ \rm{s}$ for band F110W, while for the second group
it ranges from a minimum of $2125\leavevmode\nobreak\ \rm{s}$ for band F435W
to a maximum of $4680\leavevmode\nobreak\ \rm{s}$ for band F814W. Using a
subset of 28 non-saturated stars, we measured the full width at half maximum
(FWHM) of the point spread function (PSF) as a range that goes from a minimum
of $$$\pm$$$ in the band F814W to a maximum of $$$\pm$$$ in the band F160W
(see Table 1).

Table 1: PSF FWHM measured from the HST images.

FILTER | PSF FWHM $[\arcsec]$ | FILTER | PSF FWHM $[\arcsec]$
---|---|---|---
F435W | $0.12\pm 0.02$ | F105W | $0.20\pm 0.02$
F475W | $0.13\pm 0.03$ | F110W | $0.21\pm 0.03$
F606W | $0.12\pm 0.02$ | F125W | $0.21\pm 0.03$
F814W | $0.11\pm 0.02$ | F140W | $0.21\pm 0.02$
|  | F160W | $0.22\pm 0.02$

333PSF FWHM measured from the HST images taken by the two instruments ACS
(left) and WFC3 (right) with different filters (see Sect. 2)

We used the 60 mas HST images and their corresponding weightmaps to extract
sources and compute the photometry. For each band, we ran Sextractor (Bertinl
1996) in dual-image mode, using the F814W image as the detection image. We
used this band for the detection because of the lower PSF FWHM and higher
exposure time and, secondly, because a large portion of the emission from the
continuum of the spectrum of member galaxies falls in this filter (from $\sim
5000\leavevmode\nobreak\ \text{\AA}$ to $\sim 7000\leavevmode\nobreak\
\text{\AA}$ at the redshift of the cluster). We obtained a catalog that
contains the ICRS R.A. and Dec. and pixel coordinates of the detected sources
(indicated respectively with ALPHA_J2000, DELTA_J2000, X_IMAGE and Y_IMAGE);
their isophotal semi-major and semi-minor axis and rotation angle (A_IMAGE,
B_IMAGE and THETA_IMAGE); the peak surface brightness (MU_MAX); the stellarity
index (CLASS_STAR); the isophotal flux and magnitude (FLUX_ISO and MAG_ISO);
and the fluxes and magnitudes computed at 14 fixed apertures ranging from 2 to
160 pixels (FLUX_APERX_n and MAG_APER_n), corresponding to a range between
$None$ and $None$.

We tuned the extraction parameters to minimize the spurious detections due to
noise and we use a semi-automated procedure to mask star spikes and identify
potential spurious detection, which is described in Appendix A. After this
cleaning process, the photometric catalog contains a total of 3168 objects.
Note that for some extended objects (i.e., lensed galaxies and arcs) single
bright features, such as star formation clumps, appear as distinct objects.

###  2.2 Spectroscopic data and redshift estimation

This study exploits new, extensive, and high-quality spectroscopic data
derived from observations made with MUSE and the Adaptive Optics Facility
(AOF) working in wide field mode (Ströbele et al. 2012; Arsenault et al. 2008)
on three nights in 2019 March-May (P.I.: Amata Mercurio, ESO program
0102.A-0640(A)). These observations produced three spectral data cubes
corresponding to three pointings covering the center of the galaxy cluster
(see Fig. 2) for a total area of $\sim 3\leavevmode\nobreak\ \rm{arcmin}^{2}$
with a spatial resolution of $None$ and with a spectral resolution of
$1.25\leavevmode\nobreak\ \text{\AA}\leavevmode\nobreak\ \text{pixel}^{-1}$ in
the vacuum wavelength range from $4700\leavevmode\nobreak\ \text{\AA}$ to
$9350\leavevmode\nobreak\ \text{\AA}$, with a gap between
$5805\leavevmode\nobreak\ \text{\AA}$ and $5967\leavevmode\nobreak\
\text{\AA}$ due to the emission generated by the guiding laser of the AOF. All
the wavelengths in this work are referred to vacuum. We process and merge the
spectral data cubes following the prescriptions of Caminha et al. (2019),
using the reduction pipeline version 2.8.3 (Weilbacher et al. 2020). The final
data cube has an exposure time on target of 3.1 hours in two pointings and 3.8
hours in the westernmost pointing. The PSF measured from stars on the pseudo-
white images, obtained by staking the data cube along the spectral axis,
exhibits $\rm{FWHM}\approx$$-$$$ across all pointings.

For each object in the photometric catalog that falls into the data cube
footprint, we extract the spectrum with the program python-specex444python-
specex: a python package and a set of programs we developed to handle
spectroscopic data-cubes and to extract 1D spectra from them. More information
can be found at https://github.com/mauritiusdadd/python-specex (D’Addona
2022). using a circular aperture of radius $\qty{0.4}{\arcsec}$. We visually
inspect and determine the redshift ($z$) of each spectrum using the program EZ
(Garilli et al. 2010). A quality flag QF is assigned to each spectrum, that
indicates the reliability of the redshift estimation (Balestra et al. 2016;
Caminha et al. 2016): 1=insecure; 2=likely; 3=secure; 9=based on one emission
line. We were able to determine the redshift for 531 objects, of which 432
have $\rm{QF}\geq 3$. This reliable spectroscopic sample contains 31 stars, 42
foreground objects ($z<0.360$), 213 cluster members ($0.360\leq z\leq 0.405$;
see Sect. 3.1) and 146 background objects ($z>0.405$). Note that, as for the
photometric catalog, clumps of extended objects are considered as distinct
objects since this is useful for the identification of multiple images. For
objects that are outside the MUSE field of view, we use redshift measurements
from observations made with the VIsible MultiObject Spectrograph (VIMOS) on
the VLT UT3 Telescope in service mode on four nights in 2015 February–March
(P.I.: Mario Nonino, period 094.A-0529(B), 11 objects). We completed the
spectroscopic catalog with redshifts measurements (47 objects) by Golovich et
al. (2019b, a), using observations made with the DEep Imaging Multi-Object
Spectrograph (DEIMOS) on the Keck II telescope at the W. M. Keck Observatory
on Maunakea (KECK) over the nights: 2013 January 26, 2014 July 14, 2014
September 5, 2013 December 3–5 (half nights), 2014 June 22–23, 2015 February
15, and 2015 December 13. With these redshift measurements, in the region
covered by HST, we identified: 9 and 35 cluster member galaxies, 1 and 5
foreground objects, and 1 and 7 background objects from VIMOS and DEIMOS,
respectively (see Table 2). The spectroscopic catalog is available at the CDS
(see E).

Table 2: Distribution of the objects in the reliable spectroscopic sample.

$\rm{QF}\geq 3$ | MUSE | VIMOS | DEIMOS | CNN
---|---|---|---|---
Total | 432 | 11 | 47 | –
Stars | 31 | 0 | 0 | –
Foreground | 42 | 1 | 5 | –
Background | 146 | 1 | 7 | –
Cluster Members | 213 | 9 | 35 | 110
C.M. $m_{\rm{F160W}}\leq 21$ | 85 | 9 | 35 | 24

555For completeness, photometric cluster members identified by a CNN are also
reported (see Sect. 3.1).

##  3 Strong-lensing model

In this section, we describe the selection of cluster members and multiple
images used to optimize the lens model. We used the software
lenstool666lenstool: https://projets.lam.fr/projects/lenstool(Kneib et al.
1996; Jullo et al. 2007; Jullo & Kneib 2009) to model the total mass
distribution of the lens cluster following the prescriptions of previous
works, such as Caminha et al. (2019), Bergamini et al. (2021), Acebron et al.
(2022a), and Granata et al. (2023). This pipeline takes advantage of Markov
chain Monte Carlo (MCMC) to retrieve the best-fitting values of the parameters
$\boldsymbol{\xi}$ of a parametric mass model, and their errors, by minimizing
the chi-square function defined by Eq. (1)

$\chi^{2}(\boldsymbol{\xi})\coloneqq\sum_{j=1}^{N_{fam}}\sum_{i=1}^{N^{j}_{img}}\left(\frac{\left\|\boldsymbol{x}^{obs}_{i,j}-\boldsymbol{x}^{pred}_{i,j}(\boldsymbol{\xi})\right\|}{\Delta
x_{i,j}}\right)^{2},$ (1)

where $\boldsymbol{x}^{obs}_{i,j}$ and $\boldsymbol{x}^{pred}_{i,j}$ are the
observed and predicted positions respectively, on the lens plane, of the i-th
counter-image of the j-th family and $\Delta x_{i,j}$ is the corresponding
uncertainty.

###  3.1 Selection of cluster members

Guided by the distribution of the redshifts around the brightest cluster
galaxy (BCG) with ID 237 (see Fig. 2), we identify 257 spectroscopically
confirmed members in the redshift range [$0.360$, $0.405$]. This corresponds
to a peculiar velocity range of [$-5000$,$\leavevmode\nobreak\ +4700$]
$\rm{km}\leavevmode\nobreak\ \rm{s}^{-1}$ in the cluster rest frame centered
at $z_{c}=0.383$. To maximize the completeness of the sample, we also include
110 photometric members that have been identified using the convolutional
neural network developed by Angora et al. (2020): for each object, this CNN
takes in input a set of cut-outs extracted from the ACS and WCF3 images and
returns a probability of the object being a cluster member. To test its
performance on this cluster, we use the CNN to predict the cluster membership
of all the MUSE spectroscopy members, resulting in a purity of $89\%$, a
completeness of $88\%$, and an f1-score of $89\%$. Members that had a missing
magnitude measurement in the band F160W have been inferred using a set of
linear regressors (Appendix B). Furthermore, for two bright members with IDs
3266 and 3266, that are near the very bright star in the western MUSE pointing
and for which Sextractor was not able to reliably measure their photometry, we
estimated their $m_{\rm{F106W}}$ values using astropy/photutils v1.8.0
(Bradley et al. 2023).

Figure 2: Histogram and cumulative distribution of the cluster members as a
function of the Kron magnitudem,$m_{\rm{F106W}}$. The dashed line indicates
the threshold used to select the members utilized in the strong-lensing model.

Finally, to construct the cluster member sample for the lens model, we
selected 129 spectroscopic members and 24 photometric ones for which
$m_{\rm{F160W}}\leq 21$ (Fig. 2, Table 2), for a total of $N_{cm}=153$
selected cluster members. We use this magnitude threshold to reduce the number
of faint members and thus the computation time, after checking that it does
not affect the goodness of our strong-lens modeling. This choice is also
justified by the results by Bergamini et al. (2023b), which shows that using a
magnitude limit of 21 in the band F160W for the cluster member selection does
not produce significant variation in the lens model metric. A similar study by
Raney et al. (2021) also shows a similar behavior for different magnitude
thresholds between 21 and 26 in the F814W band.

###  3.2 Multiple images

We identified multiple images by first searching for objects in the
spectroscopic catalog having a similar redshift and then visually inspecting
both the data-cube and the high-resolution 30 mas HST images. They are labeled
using the format X.Yk, where X is an integer that identifies the background
source system, Y is an integer that indicates any clearly identifiable
substructure, such as star formation clumps, and k is a letter that
differentiates among the different multiple images. A single background system
may, in fact, have multiple clumps and substructures that can be used as
lensed sources themselves. For this reason, we use the term ”family” to
indicate a set of multiple images of the same substructure.

We also checked the multiple images reported in Zitrin et al. (2017) and
spectroscopically confirmed 30 of them from 12 background sources, while
others are too faint to be spectroscopically confirmed or they are outside the
MUSE footprint. When possible, for confirmed multiple images, we used the same
family number used in Zitrin et al. (2017); namely, an image with the ID 7.1a
in this work and one with the ID 7.2 in Zitrin’s work are multiple images of
the same background source. We were able to identify 114 multiple images of 28
background sources, of which 16 are newly identified multiply lensed sources,
corresponding to 38 families in the redshift range $0.60-5.98$ (see Appendix
C). The position of each clump was refined by super-sampling a square cutout
from the F814W image of size $\qty{1}{\arcsec}\times\qty{1}{\arcsec}$,
centered at its initial position, and then taking the position of the peak
nearest to cutout center. For HST-dark objects (mostly Lyman- emitters), the
cutout was extracted from a thin slice of the spectral data-cube, centered on
the wavelength of the strongest emission line, which was stacked along the
spectral axis. We used $None$ as positional error for the multiple images
identified in HST and $None$ for those only visible in the MUSE data.

In order to reduce potential biases in the strong-lensing model optimization
caused by uncertain or incorrect constraints (Grillo et al. 2015), we selected
a reliable subset of multiple images that have a spectroscopic quality flag
$\rm{QF}\geq 3$, for which there is no ambiguity in the identification of the
clumps and that are not a galaxy-galaxy strong-lensing event (GGSL). This
choice is due to the fact that the multiple images generated by these kinds of
events could result in a very strong constraint on the mass of the galaxy that
acts as a lens and could therefore introduce a possible unwanted bias in the
scaling relations for the cluster members. This ”golden sample” contains
$N_{im}^{tot}=47$ multiple images of $N_{fam}=17$ families from 12 background
sources, of which 15 multiple images of 6 background sources were previously
identified in Zitrin et al. (2017). This corresponds to a total number of
observables of $N_{obs}=2\times(N_{im}^{tot}-N_{fam})=60$. It spans a wide
range of redshift, from $z=1.17$ to $z=5.39$ (as shown in Fig. 3), and covers
a large portion of the cluster core (see Fig. 4 and Table C.1). The properties
of the identified multiple images are summarized in Appendix C.

Figure 3: Redshift distribution of the multiple images (in blue) and of the
corresponding background sources (in red) in the golden sample used in the
strong-lensing model optimization.

###  3.3 Lens model

Following the path traced by other works to model the total mass distribution
of galaxy clusters (see e.g., Grillo et al. 2016; Caminha et al. 2017;
Bergamini et al. 2021; Granata et al. 2022; Acebron et al. 2022b), we
decompose the total mass (or equivalently) the total gravitational potential,
$\phi_{tot}$, into several components, as follows (2):

$\phi_{tot}=\sum_{i=1}^{N_{cm}}\phi^{(cm)}_{i}+\sum_{j=1}^{N_{BCG}}\phi^{(BCG)}_{j}+\sum_{k=1}^{N_{h}}\phi^{(h)}_{k}+\phi_{\kappa,\gamma},$
(2)

where the first term takes into account the contribution of the $N_{cm}$
cluster members, the second one is for the two BCGs (IDs 273 and 867, see Fig.
2), which are parameterized separately from the other members, the third one
describes the contribution of the $N_{h}$ cluster-scale halos and the last one
refers to a constant convergence or shear introduced by possible unaccounted
lensing effects (Acebron et al. 2022a).

Each cluster-scale halo potential, $\phi^{(h)}_{k}$, is represented by a dual
pseudo-isothermal elliptical mass density (dPIE, Limousin et al. 2005) with
seven free parameters: position $(x,y)$; position angle ($\theta$);
ellipticity ($e$); central velocity dispersion ($\sigma_{0}$ or, as
equivalently adopted by lenstool, $\sigma_{LT}=\sqrt{2/3}\sigma_{0}$); core
radius ($r_{\rm{core}})$; truncation radius ($r_{\rm{cut}}$). In order to
reduce the number of free parameters (Bergamini et al. 2023a), the value of
the latter has been fixed to $\qty{2000}{\arcsec}$, a value that is large
enough to be considered as infinite compared to the priors assumed for
$r_{\rm{core}}$. We used singular dPIE profiles also for the potentials of the
BCGs, $\phi^{(BCG)}_{j}$ (but fixing their central position), thereby
introducing only four additional free parameters for each BCG. Cluster
members, $\phi^{(cm)}_{i}$, are described with singular, circular dPIE
profiles. In order to reduce the number of free parameters, the following
scaling relations are used:

$\displaystyle\sigma^{(cm)}_{LT,i}$
$\displaystyle=\sigma^{(ref)}_{LT}\left(\frac{L_{i}}{L_{ref}}\right)^{\alpha},$
(3) $\displaystyle r^{(cm)}_{cut,i}$
$\displaystyle=r^{(ref)}_{cut}\left(\frac{L_{i}}{L_{ref}}\right)^{\beta_{cut}},$
(4) $\displaystyle\frac{M_{i}}{L_{i}}$ $\displaystyle\propto L^{\gamma}_{i},$
(5)

We measure the luminosities of the members with their Kron magnitude in band
F160W, using as reference the magnitude $m^{(ref)}_{\rm{F160W}}=16.563$ of the
BCG-273. Following Bergamini et al. (2019), we use $\gamma=0.2$, which is
consistent with the canonical fundamental plane (Faber 1989; Bender et al.
1992), $\alpha=0.35$ and $\beta_{cut}=\gamma-2\alpha+1=0.5$ . The two
remaining free parameters $\sigma^{(ref)}_{LT}$ and $r^{(ref)}_{cut}$ are then
computed for the reference luminosity, $L_{ref}$. Finally, the external
convergence-shear potential has three parameters: convergence, shear, and
position angle. The total number of free parameters of the model is thus:
$N_{par}=6N_{h}+4N_{BCG}+5,$ which is then reduced to
$N_{par}=6N_{h}+4N_{BCG}+2$ if we do not include the shear component. The
corresponding degrees of freedom is $N_{dof}=N_{con}-N_{par}$.

Table 3: Model configurations with the associated reduced $\chi^{2}$ and
$\Delta_{RMS}$ values.

$\phi_{\kappa,\gamma}$ | $N_{h}$ | $N_{BCG}$ | red. $\chi^{2}$ | $\Delta_{RMS}[\arcsec]$
---|---|---|---|---
N | 1 | 2 | 151.11 | 3.44
N | 2 | 2 | 32.90 | 1.74
Y | 2 | 2 | 50.58 | 2.14
N | 2 | 0 | 81.90 | 2.53
N | 3 | 0 | 10.38 | 1.05
N | 3 | 2 | 4.23 | 0.75
N | 4 | 2 | 5.65 | 0.95
777The column $\phi_{\kappa,\gamma}$ indicates whether the model configuration
includes (Y) or does not include (N) an external shear or convergence
component; $N_{h}$ indicates the number of cluster scale halos; $N_{BCG}$
indicates the number of BCGs that are parameterized separately from the other
cluster members; red. $\chi^{2}$ is the reduced $\chi^{2}$ of the optimized
model; $\Delta_{RMS}$ is the quantity defined by Eq. (6).

We tested several models with different numbers of cluster-scale halos ($1\leq
N_{h}\leq 4$), with or without the shear term, and/or the two BCGs in the
scaling relations. For each configuration, we computed the reduced $\chi^{2}$
and the $\Delta_{RMS}$ values, the latter is defined by (6) as the RMS of the
separation between the observed position, $\boldsymbol{x}_{i}^{obs}$, and
predicted one $\boldsymbol{x}_{i}^{pred}$ of the $N_{im}^{tot}$ multiple
images:

$\Delta_{RMS}=\sqrt{\frac{1}{N_{im}^{tot}}\sum_{i=1}^{N_{im}^{tot}}{\lVert\boldsymbol{x}_{i}^{pred}-\boldsymbol{x}_{i}^{obs}\rVert}^{2}}.$
(6)

We find that the model that best reproduces the positions of the observed
multiple images of the golden sample (and for which we describe the resulting
properties in the following section) is the one featuring three cluster-scale
halos ($N_{h}=3$), with the two BCGs out of the scaling relations
($N_{BCG}=2$) and without the external convergence-shear component (see Table
7).

##  4 Results

Table 4:  Input and optimized parameter values and assumed priors for the lens
model.

| Input parameter and assumed priors for the lens model
---|---
|  x $\mathbf{[\arcsec]}$ |  y $\mathbf{[\arcsec]}$ | $\boldsymbol{e}$ |  $\boldsymbol{\theta}$ [°] | $\boldsymbol{\sigma}\leavevmode\nobreak\ \mathbf{[km\leavevmode\nobreak\ s^{-1}]}$ | $\boldsymbol{r_{\rm{core}}}\leavevmode\nobreak\ [\arcsec]$ | $\boldsymbol{r_{\rm{cut}}}\leavevmode\nobreak\ [\arcsec]$
Cluster-scale |  $\boldsymbol{1^{st}}$ Cluster halo | $-30.0\div\leavevmode\nobreak\ 30.0$ | $-30.0\div\leavevmode\nobreak\ 30.0$ | $0.0\div\leavevmode\nobreak\ 0.9$ | $0.0\div\leavevmode\nobreak\ 180.0$ | $400\div 2000$ | $0.5\div 120.0$ | $2000.0$
$\boldsymbol{2^{nd}}$ Cluster halo | $-60.0\div\leavevmode\nobreak\ 80.0$ | $-60.0\div\leavevmode\nobreak\ 50.0$ | $0.0\div\leavevmode\nobreak\ 0.9$ | $0.0\div\leavevmode\nobreak\ 180.0$ | $200\div 2000$ | $0.5\div 120.0$ | $2000.0$
$\boldsymbol{3^{rd}}$ Cluster halo | $-60.0\div\leavevmode\nobreak\ 50.0$ | $-60.0\div\leavevmode\nobreak\ 50.0$ | $0.0\div\leavevmode\nobreak\ 0.9$ | $0.0\div\leavevmode\nobreak\ 180.0$ | $200\div 2000$ | $0.5\div 120.0$ | $2000.0$
Subhalos | BCG-273 | $0.0$ | $0.0$ | $0.0\div\leavevmode\nobreak\ 0.9$ | $0.0\div\leavevmode\nobreak\ 180.0$ | $150\div 450$ | $0.001$ | $0.0\div 120$
BCG-867 | $-16.7$ | $7.0$ | $0.0\div\leavevmode\nobreak\ 0.9$ | $0.0\div\leavevmode\nobreak\ 180.0$ | $150\div 450$ | $0.001$ | $0.0\div 120$
Scaling relations | $\boldsymbol{N_{gal}}=151$ | $\boldsymbol{m^{(ref)}_{\rm{F160W}}}=16.563$ | $\boldsymbol{\alpha}=0.35$ | $\boldsymbol{\sigma^{(ref)}_{LT}}=50\div 400$ | $\boldsymbol{\beta_{cut}}=0.5$ | $\boldsymbol{r^{(ref)}_{cut}}=1.0\div 50.0$ | $\boldsymbol{\gamma}=0.2$

| Optimized output parameters for the lens model
---|---
|  x $\mathbf{[\arcsec]}$ |  y $\mathbf{[\arcsec]}$ | $\boldsymbol{e}$ |  $\boldsymbol{\theta}$ [°] | $\boldsymbol{\sigma}\leavevmode\nobreak\ \mathbf{[km\leavevmode\nobreak\ s^{-1}]}$ | $\boldsymbol{r_{\rm{core}}}\leavevmode\nobreak\ [\arcsec]$ | $\boldsymbol{r_{\rm{cut}}}\leavevmode\nobreak\ [\arcsec]$
Cluster-scale |  $\boldsymbol{1^{st}}$ Cluster halo | ${0.0}\leavevmode\nobreak\ _{-0.4}^{+0.5}$ | ${5.1}\leavevmode\nobreak\ _{-0.3}^{+0.5}$ | ${0.546}\leavevmode\nobreak\ _{-0.014}^{+0.009}$ | ${61.7}\leavevmode\nobreak\ _{-0.6}^{+1.3}$ | ${1330}\leavevmode\nobreak\ _{-20}^{+20}$ | ${29.1}\leavevmode\nobreak\ _{-0.7}^{+0.6}$ | $2000.0$
$\boldsymbol{2^{nd}}$ Cluster halo | ${61.0}\leavevmode\nobreak\ _{-2.0}^{+4.0}$ | ${-20.8}\leavevmode\nobreak\ _{-0.8}^{+1.4}$ | ${0.71}\leavevmode\nobreak\ _{-0.08}^{+0.09}$ | ${24.0}\leavevmode\nobreak\ _{-2.0}^{+2.0}$ | ${580}\leavevmode\nobreak\ _{-30}^{+40}$ | ${15.0}\leavevmode\nobreak\ _{-2.0}^{+3.0}$ | $2000.0$
$\boldsymbol{3^{rd}}$ Cluster halo | ${-51.0}\leavevmode\nobreak\ _{-1.0}^{+1.0}$ | ${-58.9}\leavevmode\nobreak\ _{-0.8}^{+1.7}$ | ${0.7}\leavevmode\nobreak\ _{-0.1}^{+0.1}$ | ${114.0}\leavevmode\nobreak\ _{-7.0}^{+8.0}$ | ${480}\leavevmode\nobreak\ _{-40}^{+60}$ | ${15.0}\leavevmode\nobreak\ _{-3.0}^{+3.0}$ | $2000.0$
Subhalos | BCG-273 | 0 | 0 | ${0.73}\leavevmode\nobreak\ _{-0.03}^{+0.03}$ | ${119.0}\leavevmode\nobreak\ _{-5.0}^{+12.0}$ | ${334}\leavevmode\nobreak\ _{-8}^{+11}$ | $0.001$ | ${90.0}\leavevmode\nobreak\ _{-30.0}^{+20.0}$
BCG-867 | $-16.7$ | $7.0$ | ${0.79}\leavevmode\nobreak\ _{-0.04}^{+0.03}$ | ${171.0}\leavevmode\nobreak\ _{-2.0}^{+1.0}$ | ${435}\leavevmode\nobreak\ _{-14}^{+6}$ | $0.001$ | ${100.0}\leavevmode\nobreak\ _{-20.0}^{+10.0}$
Scaling relations | $\boldsymbol{N_{gal}}=151$ | $\boldsymbol{m^{(ref)}_{\rm{F160W}}}=16.563$ | $\boldsymbol{\alpha}=0.35$ | $\boldsymbol{\sigma^{(ref)}_{LT}}={310.0}\leavevmode\nobreak\ _{-10.0}^{+10.0}$ | $\boldsymbol{\beta_{cut}}=0.5$ | $\boldsymbol{r^{(ref)}_{cut}}={16.0}\leavevmode\nobreak\ _{-2.0}^{+3.0}$ | $\boldsymbol{\gamma}=0.2$

888Input parameter values and assumed uniform priors (top panel) and median
optimized parameter values with their 16th and 84th percentiles from the
marginalized posterior distribution (bottom panel). Boundaries of uniform
priors are separated by the $\div$ symbol; $N_{gal}$ is the number of cluster
member galaxies optimized using the scaling relations (see Eqs. 3, 4, and 5);
$m^{(ref)}_{\rm{F160W}}$ is the magnitude in band F160W of BCG-273 and it has
been used as reference for the scaling relations. We use the coordinates of
the center of BCG-273 (ICRS $177.7090129,-28.0821343$) as the reference
coordinates for the strong-lensing model. Note: for lenstool to compute the
relative positions, the x and y coordinates are expressed in arcseconds with
the x-axis directed toward the west (decreasing direction of R.A.) and the
y-axis toward the north (increasing direction of Dec.).

Figure 4: Absolute magnification, $\mid\mu\mid,$ map for images of a source at
redshift of $z_{s}=3.4$, overlaid onto the F814W image. The red circles
indicate the position of the observed multiple images in the golden sample and
pink crosses are the multiple images predicted with the optimized lens model.
Figure 5: Distribution of the displacement in the image plane, in arcseconds,
along the x and y axes between the observed and model-predicted positions of
multiple images in the golden sample. The color of the points indicates the
redshift of the objects. The histograms are the marginal distributions of the
displacements, computed using ten bins of width $\qty{0.25}{\arcsec}$, and the
solid black lines are their kernel density estimates. The displacement root
mean square (RMS) is $\Delta_{RMS}=\qty{0.75}{\arcsec}$.

Figure 6: Total projected mass distribution in units of
$10^{9}\leavevmode\nobreak\ \rm{M}_{\odot}\leavevmode\nobreak\
/\leavevmode\nobreak\ \rm{kpc}^{2}$ and the central position of the three
cluster halos (black + markers), overlaid onto an F814W image (upper panel)
and cumulative total median mass profile as a function of the distance $R$
from the BCG 273 (middle panel). Vertical lines mark the radial distance of
the multiple images: the golden sample used to optimize the lens model is
indicated in gold and other multiple images are indicated by the gray dashed
lines. Cumulative mass profiles for the cluster members, including the two
BCGs, (in blue), and for the cluster halos (in red) are also shown, along with
their ratio with the total mass profile (lower panel). The shaded area
indicates, for each mass component, the $\pm 1\sigma$ interval. Magenta dashed
lines indicate the cluster Einstein radius ($\theta_{\rm{E}}$) and the total
mass enclosed by the corresponding critical curve ($\rm{M_{E}}$) for a source
at a redshift of $z_{s}=2$.

Figure 7: Critical curves, overlaid onto the F814W image, for various redshift
values, $z_{s}$, of the source plane in the range $1\leq z_{s}\leq 5$ (upper
panel) and the corresponding effective Einstein radii, $\theta_{\rm{E}}$,
(lower panel). Error bars in the Einstein radii plot indicate the 16th and
84th percentiles. The values are reported in Table 5. The color maps the
redshift of the source, $z_{s}$.

In the top panel of Table 4, we report the input parameter values and the
assumed uniform priors. In the bottom panel, we report the median values for
the parameters of the optimized strong-lensing model, along with the 16th and
84th percentiles from their marginalized posterior distributions. All the
percentiles and uncertainties for the quantities reported in this section have
been computed using a sample of 150 random realizations of the model extracted
from the MCMC chain. For the Einstein radii estimates, we also used a
bootstrapping technique (Efron 1979) to reduce as much as possible the
potential biases caused by a non-normal distribution of the values. The best-
fit model is characterized by $\Delta_{RMS}=$$$, which corresponds to an
increase in the accuracy by a factor of $\sim 2.5,$ compared to value of
$None$ of the model presented by Zitrin et al. (2017). The goodness of the
model in reproducing the observed positions of the multiple images of the
golden sample is also illustrated in Fig. 4, where both the observed and
model-predicted positions of the multiple images are plotted. Moreover, Fig. 5
shows no correlation between the displacements of the positions of the
multiple images and the redshift of the sources.

Figure 6 shows (in the upper panel) the total projected mass distribution
overlaid onto the F814W HST image. In the lower panels, the cumulative total
mass profile and its different mass components, within
$500\leavevmode\nobreak\ \text{kpc}$ from BCG-273, are illustrated. In Fig. 7,
we show the critical lines, overlaid onto the F814W HST image, for a source at
different redshift values in the range $1\leq z_{s}\leq 5$ and a scatter plot
of the median effective Einstein radius, $\theta_{\rm{E}}=\sqrt{A/\pi}$, where
$A$ is the area enclosed within the critical curve. For each value of $z_{s}$
we considered only the biggest critical curve (i.e., the critical curves
generated by isolated cluster members were ignored) and the calculation of the
value of $\theta_{\rm{E}}$ was made in the image pixel-space and then the
resulting radius is converted into physical angular values. Our lens modeling
of this cluster reveals a mass distribution that is slightly elongated along
the NW-SE direction, corroborating the evidence of a post-merger scenario
suggested by the previous X-ray and radio observations of Bagchi et al. (2011)
and Bonafede et al. (2014), as well as the weak-lensing analysis of Finner et
al. (2017) based on Subaru and HST telescopes observations. In particular, we
note that the positions of the cluster-scale halos 1, 2, and 3 of our
optimized lens model are consistent with the positions of the halos NWc, SEc,
and Wc detected by Finner et al. (2017), respectively

In Table 5, we report the median values of $\theta_{\rm{E}}$ and total mass,
$\rm{M_{E}}$, enclosed within the critical curve (with the 16th and 84th
percentiles) for several values of $z_{s}$. For a source at $z_{s}=2$, we find
that this galaxy cluster has an effective Einstein radius of
$\theta_{\rm{E}}=43.4\arcsec\pm 0.1\arcsec$, which corresponds to a total mass
enclosed within the critical curve of $3.33_{-0.07}^{+0.02}\times
10^{14}\rm{M}_{\odot}$. These results are also in agreement with the previous
measurements by Zitrin et al. (2017), who found $\theta_{E}=(42\pm 4)"$ and an
enclosed mass of $(3.1\pm 0.5)\times 10^{14}M_{\odot}$. There are currently
only four clusters with a confirmed $\theta_{\rm{E}}\geq\qty{40}{\arcsec}$ and
our modeling of PLCK-G287 confirms it to be the third largest after MACS
J0717.5$+$3745 ($\theta_{\rm{E}}\sim\qty{55}{\arcsec}$, Zitrin et al. 2009a)
and Abell 1689 ($\theta_{\rm{E}}\sim\qty{45}{\arcsec}$, Broadhurst et al.
2005), and coming just before RXC J2211.7$-$0349
($\theta_{\rm{E}}\sim\qty{41}{\arcsec}$, Cerny et al. 2018). Clusters like
this are of particular interest when comparing Einstein radius distributions
from observations to those from theoretical expectations; for example, the
semi-analytic analysis of Oguri & Blandford (2009), based on the -CDM model
and cosmological parameters from Wilkinson Microwave Anisotropy Probe five-
year data (WMAP5, Spergel et al. 2003), predicts an all-sky total of $\sim
15\pm 5$ galaxy clusters with $\theta_{\rm{E}}\geq\qty{40}{\arcsec}$ for a
source at $z_{s}=3$. Since the Einstein radius increases with the redshift of
the lensed source, for a source at $z_{s}=2,$ the all-sky total number of
galaxy clusters with $\theta_{\rm{E}}\geq\qty{40}{\arcsec}$ should be lower
than this quantity. In fact, Zitrin et al. (2012) reported the result of the
same analysis, but done using WMAP seven-year data (WMAP7, Komatsu et al.
2011) and for a source at $z_{s}=2$, from which we would get a total all-sky
count of only $\sim 8\pm 3$ galaxy clusters.

We also computed the probability of galaxy-galaxy strong-lensing (GGSL) events
using the same methodologies described in Meneghetti et al. (2023). We find a
median GGSL probability of $P_{\rm{GGLS}}=\left(1.7_{-0.2}^{+0.5}\right)\times
10^{-2}$, for a source at $z_{s}=6$ . This value is approximately one order of
magnitude larger than the probabilities reported by Meneghetti et al. (2023)
for the other galaxy clusters at similar redshift. According to this study,
there is a significant discrepancy with the results of cosmological
simulations. However, we point out that at the moment, there is no simulated
cluster with an Einstein radius as large as that of PLCK-G287. Therefore, the
implications of this intriguing result will be discussed in detail in a future
work

Using the positions of the multiple images predicted by the best-fitting
model, we also discovered the new multiple images 49.1c, 5.1e, and 5.2e that
were not previously identified (see Fig. 8). These observed new multiple
images are a few arcseconds off the predicted position, but this is expected
since they are not considered in the model optimization. We also tried to
predict the position of the counter-images for systems 3, 18, and 19 (see Fig.
9, Fig. 10, and Fig. 11). These systems are not part of the golden sample due
to the uncertainty on the quality of the redshift estimation caused by the low
signal-to-noise ratio (S/N) of their extracted spectra. Therefore, we used the
strong-lensing model to predict the positions of the multiple images of 3.1a,
3.2a, 18.1a, and 19.1e for various redshift values and then selecting (for
each system) the one that produced the lowest value for the $\Delta_{RMS}$. We
repeated the process also using 150 random realizations of the model built by
randomly extracting the configurations from the MCMC chain. In this way, we
were able to compute the probability density functions (PDF) of the redshifts
for these two systems. This gives us a median value of the redshift of
$z_{s3}=2.11\pm 0.05,$ with $\Delta_{RMS}=$$\pm$$$ for system 3,
$z_{s50}=1.70_{-0.15}^{+0.13}$ with $\Delta_{RMS}=$$\pm$$$ for system 18, and
$z_{s19}=5.79\pm 0.17$ with $\Delta_{RMS}=$$\pm$$$ for system 19. It is worth
noting that the redshifts predicted for systems 3 and 18 are compatible with
the spectroscopic ones within $2\sigma$ and $1\sigma$, respectively, while the
redshift predicted for system 19 is compatible within $2\sigma$ with the
photometric redshift from Zitrin et al. (2017). System 19 was also identified
in by Salmon et al. (2020) during their search for high-redshift objects in
the RELICS survey. The prediction of our model is compatible within $3\sigma$
with their photometric redshift estimation of $6.8_{-0.2}^{+0.4}$.

Table 5:  Effective Einstein radii and masses enclosed in the critical curves.

$z_{s}$ |  $\theta_{\rm{E}}\leavevmode\nobreak\ [\arcsec]$ |  $\rm{M_{E}}\leavevmode\nobreak\ [10^{14}\leavevmode\nobreak\ \rm{M}_{\odot}]$ | $z_{s}$ |  $\theta_{\rm{E}}\leavevmode\nobreak\ [\arcsec]$ |  $\rm{M_{E}}\leavevmode\nobreak\ [10^{14}\leavevmode\nobreak\ \rm{M}_{\odot}]$ | $z_{s}$ |  $\theta_{\rm{E}}\leavevmode\nobreak\ [\arcsec]$ |  $\rm{M_{E}}\leavevmode\nobreak\ [10^{14}\leavevmode\nobreak\ \rm{M}_{\odot}]$
---|---|---|---|---|---|---|---|---
1.0 | ${22.82}\leavevmode\nobreak\ _{-0.04}^{+0.09}\leavevmode\nobreak\ $ | ${1.19}\leavevmode\nobreak\ _{-0.02}^{+0.01}\leavevmode\nobreak\ $ | 2.4 | ${46.82}\leavevmode\nobreak\ _{-0.04}^{+0.05}\leavevmode\nobreak\ $ | ${3.76}\leavevmode\nobreak\ _{-0.08}^{+0.03}\leavevmode\nobreak\ $ | 3.8 | ${51.89}\leavevmode\nobreak\ _{-0.11}^{+0.06}\leavevmode\nobreak\ $ | ${4.38}\leavevmode\nobreak\ _{-0.09}^{+0.04}\leavevmode\nobreak\ $
1.2 | ${28.16}\leavevmode\nobreak\ _{-0.03}^{+0.03}\leavevmode\nobreak\ $ | ${1.67}\leavevmode\nobreak\ _{-0.03}^{+0.01}\leavevmode\nobreak\ $ | 2.6 | ${47.81}\leavevmode\nobreak\ _{-0.04}^{+0.02}\leavevmode\nobreak\ $ | ${3.88}\leavevmode\nobreak\ _{-0.08}^{+0.03}\leavevmode\nobreak\ $ | 4.0 | ${52.40}\leavevmode\nobreak\ _{-0.11}^{+0.09}\leavevmode\nobreak\ $ | ${4.46}\leavevmode\nobreak\ _{-0.09}^{+0.04}\leavevmode\nobreak\ $
1.4 | ${34.19}\leavevmode\nobreak\ _{-0.04}^{+0.10}\leavevmode\nobreak\ $ | ${2.26}\leavevmode\nobreak\ _{-0.05}^{+0.01}\leavevmode\nobreak\ $ | 2.8 | ${48.68}\leavevmode\nobreak\ _{-0.03}^{+0.06}\leavevmode\nobreak\ $ | ${4.00}\leavevmode\nobreak\ _{-0.08}^{+0.03}\leavevmode\nobreak\ $ | 4.2 | ${52.79}\leavevmode\nobreak\ _{-0.06}^{+0.08}\leavevmode\nobreak\ $ | ${4.51}\leavevmode\nobreak\ _{-0.09}^{+0.04}\leavevmode\nobreak\ $
1.6 | ${39.35}\leavevmode\nobreak\ _{-0.04}^{+0.04}\leavevmode\nobreak\ $ | ${2.85}\leavevmode\nobreak\ _{-0.06}^{+0.02}\leavevmode\nobreak\ $ | 3.0 | ${49.48}\leavevmode\nobreak\ _{-0.06}^{+0.05}\leavevmode\nobreak\ $ | ${4.08}\leavevmode\nobreak\ _{-0.08}^{+0.03}\leavevmode\nobreak\ $ | 4.4 | ${53.13}\leavevmode\nobreak\ _{-0.06}^{+0.06}\leavevmode\nobreak\ $ | ${4.55}\leavevmode\nobreak\ _{-0.09}^{+0.04}\leavevmode\nobreak\ $
1.8 | ${41.59}\leavevmode\nobreak\ _{-0.02}^{+0.04}\leavevmode\nobreak\ $ | ${3.12}\leavevmode\nobreak\ _{-0.06}^{+0.02}\leavevmode\nobreak\ $ | 3.2 | ${50.19}\leavevmode\nobreak\ _{-0.03}^{+0.06}\leavevmode\nobreak\ $ | ${4.16}\leavevmode\nobreak\ _{-0.08}^{+0.04}\leavevmode\nobreak\ $ | 4.6 | ${53.43}\leavevmode\nobreak\ _{-0.06}^{+0.10}\leavevmode\nobreak\ $ | ${4.58}\leavevmode\nobreak\ _{-0.09}^{+0.04}\leavevmode\nobreak\ $
2.0 | ${43.41}\leavevmode\nobreak\ _{-0.06}^{+0.05}\leavevmode\nobreak\ $ | ${3.33}\leavevmode\nobreak\ _{-0.07}^{+0.02}\leavevmode\nobreak\ $ | 3.4 | ${50.87}\leavevmode\nobreak\ _{-0.05}^{+0.05}\leavevmode\nobreak\ $ | ${4.24}\leavevmode\nobreak\ _{-0.08}^{+0.04}\leavevmode\nobreak\ $ | 4.8 | ${53.76}\leavevmode\nobreak\ _{-0.08}^{+0.12}\leavevmode\nobreak\ $ | ${4.62}\leavevmode\nobreak\ _{-0.09}^{+0.04}\leavevmode\nobreak\ $
2.2 | ${45.43}\leavevmode\nobreak\ _{-0.07}^{+0.05}\leavevmode\nobreak\ $ | ${3.59}\leavevmode\nobreak\ _{-0.07}^{+0.03}\leavevmode\nobreak\ $ | 3.6 | ${51.38}\leavevmode\nobreak\ _{-0.03}^{+0.06}\leavevmode\nobreak\ $ | ${4.33}\leavevmode\nobreak\ _{-0.08}^{+0.04}\leavevmode\nobreak\ $ | 5.0 | ${53.98}\leavevmode\nobreak\ _{-0.07}^{+0.08}\leavevmode\nobreak\ $ | ${4.65}\leavevmode\nobreak\ _{-0.09}^{+0.05}\leavevmode\nobreak\ $

999Median values of effective Einstein radius ($\theta_{\rm{E}}$) for several
redshifts of the source ($z_{s}$) and corresponding median total mass enclosed
in the critical curve ($\rm{M_{E}}$) from the best-fit model. We also quote
also the 16th - 84th percentiles.

Figure 8: Predicted (green arrows) and observed (cyan dashed circles)
positions for multiple lensed images 5.1e, 5.2e (left panel), and 49.1c (right
panel). These multiple images were not detected originally and have been found
by visually inspecting the data-cube around the positions predicted by the
strong-lensing model. Note: System 49 is a Lyman- emitter that is too faint to
be visible in the RGB cutout, but it is clearly visible in the spectral data-
cube (see the spectrum plots for system 49 in Fig. 44 in Appendix C).

Figure 9: Predicted (green arrows) and observed (cyan dashed circles)
positions for multiple lensed images of system 3 (left panel) and the PDF of
the redshift obtained from the strong-lensing model (right panel). From the
redshift PDF we get a median value of $z_{s3}=2.11\pm 0.05$ with a
$\Delta_{RMS}=$$\pm$$$. The critical line for a source at this redshift is
also shown in the right panel.

Figure 10: Predicted (green arrows) and observed (cyan dashed circles)
positions for multiple lensed images of system 18 (left panel) and the PDF of
the redshift obtained from the strong-lensing model (right panel). From the
redshift PDF we get a median value of $z_{s18}=1.70\pm 0.15$ with a
$\Delta_{RMS}=$$\pm$$$. The critical line for a source at this redshift is
also shown in the right panel.

Figure 11: Predicted (green arrows) and observed (cyan dashed circles)
positions for multiple lensed images of system 19 (left panel) and the PDF of
the redshift obtained from the strong-lensing model (right panel). From the
redshift PDF we get a median value of $z_{s19}=5.79\pm 0.17$ with a
$\Delta_{RMS}=$$\pm$$$. The critical line for a source at this redshift is
also shown in the images.

##  5 Summary

We present a new high-precision strong-lensing model for the galaxy cluster
PLCK G287.0+32.9, including a catalog of spectroscopic redshift containing 490
objects with a quality flag $\rm{QF}\geq 3$. The combined use of HST ACS and
WFC3 images, as well as spectroscopic data from VLT MUSE and VIMOS and from
KECK DEIMOS allow us to confirm 30 multiple images of 12 background sources
previously identified by Zitrin et al. (2017) and to identify 16 new multiply
lensed background sources, resulting in a total sample of 114 multiple images
of 28 multiply lensed sources. Of these, a golden sample of 47 multiple images
of 12 multiply lensed sources is used to optimize our best-fitting strong-
lensing model. To date, this is the largest spectroscopic sample of multiple
images available for this cluster.

The final $\Delta_{RMS}$ is equal to $None$, which corresponds to an
improvement of a factor of $\sim 2.5$ compared to the previous lens model by
Zitrin et al. (2017) in terms of the accuracy in reconstructing the position
of the multiple images. The derived total mass distribution and Einstein
radius confirm this cluster to be a very prominent gravitational lens with an
effective $\theta_{\rm{E}}=43.4\arcsec\pm 0.1\arcsec$, for a source at
redshift of $z_{s}=2$, and a corresponding total mass enclosed in the critical
curve $\rm{M_{E}}={3.33}_{-0.07}^{+0.02}\times{10^{14}\rm{M}_{\odot}}$.

We also validated the lens model by searching for possible new multiple images
that had not previously been identified and, subsequently, we also checked its
ability to reproduce the multiple images of three systems not used in the
optimization process. The predictions of the model lead us to the
identification of three new multiple images (5.1e, 5.2e, and 49.1c) and allow
us to reproduce the complex configurations of the systems 3 and 18, with a low
value of their $\Delta_{RMS}$, while also producing redshift estimates that
are compatible with the spectroscopic ones. The model is also able to
reproduce the geometry of system 19 and provides a redshift that is compatible
with the photometric estimates of previous studies, thus confirming that this
is a high-redshift object at $z\sim 6$.

###### Acknowledgements.

This work is based on observations taken by the RELICS Treasury Program (GO
14096) with the NASA/ESA HST, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
Based on observations collected at the European Southern Observatory under ESO
programme(s) 0102.A-0640(A) and/or data obtained from the ESO Science Archive
Facility with DOI(s) under https://doi.org/10.18727/archive/41. We acknowledge
financial support through grants PRIN-MIUR 2017WSCC32 and 2020SKSTHZ. AM
acknowledges financial support through grant NextGenerationEU” RFF M4C2 1.1
PRIN 2022 project 2022ZSL4BL INSIGHT. AA has received funding from the
European Union’s Horizon 2020 research and innovation programme under the
Marie Skłodowska-Curie grant agreement No 101024195 — ROSEAU. The data
published in this paper have been obtained using the pandora.ez software
developed by INAF IASF-Milano. This research made use of Photutils, an Astropy
package for the detection and photometry of astronomical sources (Bradley et
al. 2023).

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##  Appendix A Masking star diffraction spikes

Even if we have a single detection image, we test a semi-automatic procedure
that requires only a minimum of human intervention and that can be easily
reused in other cases. The procedure starts by identifying the brightest stars
in the plane MU_MAX vs. MAG_AUTO for the detection image. In this plane,
bright stars form a sequence made by two intersecting lines (Fig. 12):
saturated stars form a horizontal line at low values of MU_MAX, this indicates
that their peak surface brightness does not change even if the Kron magnitude
does and this is, in fact, due to saturated pixels. At some point, when the
brightness is low enough so that there are no more saturated pixels, MU_MAX
increases almost linearly with MAG_AUTO. Using the subsample of objects with
the stellarity index $\rm{CLASS\\_STAR}\geq 0.9$, we fit a simple two-segment
linear model defined by (7) with a Levenberg-Marquardt minimizer (The Astropy
Collaboration et al. 2022). Because the quality of the fit is sensitive to the
initial values, we used the Hough transform (Hough 1962) to get an approximate
estimate of the slope of the linear part of the star sequence.

$f(x)=\begin{cases}A+B\cdot x&\text{if{}}\,x>x_{sat}\\\ A+B\cdot
x_{sat}&\text{if{}}\,x\leq x_{sat}\end{cases}.\\\ $ (7)

Figure 12: Objects distribution in the plane MU_MAX vs. MAG_AUTO for the F814W
band. Color maps to Sextractor stellarity index CLASS_STAR, where yellow
indicates a star and blue indicates not a star. The magenta solid line is the
fitted model of the star sequence, while the red dashed line indicates the
thresholds used to select the brightest stars that may contain diffraction
spikes. Objects circled in red are the actually selected stars.

We then fixed an upper threshold for Kron magnitude equal to $x_{sat}+2$. This
value has been chosen to include most of the brightest stars that may show
spikes, while minimizing the total number of stars that would require further
checking. For all objects in the star subsample with
$x_{sat}<\rm{MAG\\_AUTO}<x_{sat}+2$, we computed the distance from the fitted
model and the standard deviation, $\sigma_{d}$, of these distances is used to
compute the offset $\Delta_{mu}=5\sigma_{d}$. Finally, we identified a
selection region in the MU_MAX - MAG_AUTO plane defined by Eq. (8):

$y\leq\begin{cases}f(x)+\Delta_{mu}&\text{if{}}x<x_{sat}+2\\\
f(x_{sat}+2)+\Delta_{mu}&\text{if{}}x>=x_{sat}+2\\\ \end{cases}.\\\ $ (8)

All objects within this region, independently of their value of the stellarity
index, were checked for the presence of diffraction spikes as follows. For
each object, a cutout $C(x,y)$ of size $W=60$ pixels is extracted from the
detection image, converted from fluxes to magnitudes, so that the object is in
the center (Fig. 13a). The cutout is transformed to a log-polar representation
$C(r,\theta),$ where $\theta\in[0,2\pi]$ with an angular resolution of $None$
and $r\in[0,W/2]$. It is then divided into $N$ stripes of equal height
$C_{k}(r,\theta^{\prime})$ with
$\theta^{\prime}\in\left[\frac{2\pi}{N}k,\frac{2\pi}{N}(k+1)\right]$ and
$k\in\\{0,...,N-1\\}$ (Fig. 13b). The number of stripes $N$ is equal to the
number of spikes that are expected to be produced (four in this case) and it
is known beforehand since it depends only on the optics of the telescope. The
stripes are then median-stacked to reduce the noise and the influence of any
nearby object, obtaining a median stripe
$\overline{C}(r,\theta^{\prime\prime})$ with
$\theta^{\prime\prime}\in\left[0,\frac{2\pi}{N}\right]$ (Fig. 13c). This
median stripe is further stacked along the polar axis to get a median radial
profile of the star
$\overline{I}(r)={med}_{\theta}(\overline{C}(r,\theta^{\prime\prime}))$ (Fig.
13d). The radial profile is used to make a 2D model of the star
$S(r,\theta^{\prime\prime})=\overline{I}(r)\forall\theta^{\prime\prime}$ that
is then subtracted from the median stripe and the result is weighted by the
inverse of the radial profile, leaving
$R(r,\theta^{\prime\prime})=[\overline{C}(r,\theta^{\prime\prime})-S(r,\theta^{\prime\prime})]/S(r,\theta^{\prime\prime})$
only the noise and the diffraction spike in the residual image, if it is
bright enough to be detected (Fig. 13e). The angular profile
$I(\theta^{\prime\prime})=med_{r}(\overline{C}(r,\theta^{\prime\prime}))$,
obtained by computing median along the radial axis of this residual image
(Fig. 13f), can be used to detect the presence of a diffraction spike, as well
as its angular position, by applying a simple peak finding algorithm like
find_peaks from the scipy python library (Virtanen et al. 2020). If other than
one prominent peak is detected, it means that there are no bright diffraction
spikes; otherwise, the position of the peak indicates the angular position of
the diffraction spikes. It is worth pointing out that since a spike has
usually a small angular extension and therefore should have a low, but still
non-vanishing influence on the radial profile, making it slightly biased.
However, this bias will: a) make the generated circular masks slightly bigger
with respect to the ones computed with unbiased radial profiles; b) affect the
spike detection only for faint stars. Both these issues should not negatively
affect the masking of bright stars, which are the ones that generate most of
the spurious detections.

Figure 13: Flowchart of the spike detection algorithm: a) original cutout of
the star; b) log-Polar transformed cutout. The dashed magenta lines indicate
the division into four stripes of same size; c) median stacking of the
stripes; d) radial profile of the median stripe; e) residual image obtained by
first subtracting the radial profile from the median stripe and then dividing
the result by the same radial profile; f) angular profile of the residual
image, obtained by computing the median value along the radial axis. The
magenta dashed line indicates the angular position of the spike.

For each star that presents a diffraction spike, a masking region is
constructed by generating a series of N rectangular masks centered on the
object itself and rotated using the angular position of the spike that has
been found previously. The length of the rectangular regions is computed using
the function in Eq. (9):

$S_{len}(m)=a+(b\cdot m)^{\gamma},$ (9)

where $S_{len}$ is the length in pixels, $m$ is the value of MAG_AUTO and $a$,
$b,$ and $\gamma$ are parameters that depend on the instrumentation and the
photometric setup used. In our case, for the 60 mas F814W band, we used
$a=100$, $b=4.7\cdot 10^{13}$, and $\gamma=-9.37$. Our goal is not to have a
precise estimation of the length of the spikes but to make a masking region
long enough to contain at least the bright visible part of the spikes. To
check that the values we have chosen satisfy this requirement, from our
detection images, we selected a sample of seven stars of different magnitudes
and manually measured the length of the diffraction spikes. From Fig. 14, we
can see that in every case, the length $S_{len}$ is always slightly bigger
than the true length. We also construct a circular mask for the central bright
part of the star and its radius, $r_{c}$, is derived from the radial profile,
$\overline{I}(r),$ so that the difference between the maximum of
$\overline{I}$ and $\overline{I}(r_{c})$ is the 97% of the range of
$\overline{I}$ (10):

$r_{c}{}:{}\frac{max(\overline{I}(r))-\overline{I}(r_{c})}{max(\overline{I}(r))-min(\overline{I(r)}}=0.97.$
(10)

In each masked region, we mark any object with an ellipticity of
$e=1-\rm{A\\_IMAGE}/\rm{B\\_IMAGE}\geq 0.5$ as a spurious detection. We also
marked as spurious detection objects with an unrealistic value of
$\rm{MAG\\_AUTO}>40$ (Fig. 15), where this threshold is chosen to be as
conservative as possible.

Figure 14: Comparison between the length of the diffraction spikes of a random
sample of stars in the 60 mas detection image (band F814W) and the estimated
length of the mask, $S_{len}$, as a function of the magnitude, MAG_AUTO

(a)

(b)

Figure 15: Two examples of masks used to remove spurious detections near
bright stars in the band F814W: removed objects are highlighted in red. Note:
in (b) a bright galaxy is not marked as a spurious detection, despite being in
the masked region, because its ellipticity is lower than the threshold value
of $0.5$.

##  Appendix B Extrapolation of the missing magnitudes in band F160W

Cluster members that have missing data for the magnitude in band F160W are
inferred using a set of linear regressors: using all objects in the
photometric catalog, we first compute the Pearson correlation coefficient
(PCC) between the Kron magnitudes, $m_{\rm{F160W}}$, in band F160W and the
ones in any other photometric band, $m_{x}$. We then used the photometric band
with the greatest value of the PCC to train a linear regressor that is used to
impute the missing data in the cluster member sample. We repeat the process
using the remaining photometric bands sorted according to their value of the
PCC with the condition that $PCC\geq 0.5$. With this procedure, 55 objects
were imputed using the band F110W and 14 using the band F814W, for a total of
69 objects

To assess the goodness of the imputation process, we use the two regressors
that are trained on $m_{\rm{F110W}}$ and $m_{\rm{F814W}}$ to predict the
$m_{\rm{F160W}}$ of 222 spectroscopic members that have no missing value in
any of the previous three features and the statistical indicators computed on
the residuals. Fig. 16 seems to confirm the reliability of the regressors,
especially for magnitudes lower than the threshold used to select the cluster
members sample.

Figure 16: True versus predicted Kron magnitudes $m_{\rm{F160W}}$ plots (upper
panel) and residuals (lower panel) for 222 spectroscopic cluster members. The
predicted values were obtained using two linear regressors trained using Kron
magnitudes, $m_{\rm{F110W}}$ and $m_{\rm{F814W}}$, (red and blue points,
respectively). The brown dash-dotted line indicates the magnitude threshold
used to select the cluster members sample used for the strong-lensing model.
The table shows various statistical indicators for the best and worst
regressor, considering all the values (first and third column) or only the
objects for which $m_{\rm{F160W}}\leq 21$ (second and last column).

##  Appendix C Multiple Images

In Table C.1, only available in electronic form at the CDS, we summarize the
properties of the identified multiple images, reporting also the eventual
photometric redshift estimations from Zitrin et al. (2017). The first column
(name) reports the name of the images in the format X.Yk, where X indicates
the background source, Y indicates the clump and substructure, and k
differentiates among the various counter-images. A leading c in the name
indicates a candidate counter-image that is difficult to confirm owing to the
low quality of the redshift estimation and/or the complex geometry of the
system; the second column (ID) reports the corresponding ID in the
spectroscopic and photometric catalogs; the fourth and fifth columns show the
J2000 ICRS right ascension and declination (R.A and Dec.); the sixth and
seventh columns ($z_{\rm{spec}}$ and QF) report the measured spectroscopic
redshift and its estimation quality flag (1=insecure, 2=likely, 3=secure, and
9=based on one emission line); the eighth column (Gold) indicates whether an
image belongs to the golden sample used to optimize the lens model; The ninth
column ($z_{\rm{model}}$) reports the median redshift estimated using the best
fitting lens model along with the 16th and 84th percentiles; the last two
columns (Arc ID and $z_{\rm{phot}}$) are the original ID from Zitrin et al.
(2017) and the photometric redshift estimation from Zitrin et al. (2017),
along with the associated $95\%$ confidence interval.

The figures from Fig. 17 to Fig. 44 show, for each system of multiple images,
a portion of the spectrum centered on the most prominent emission line (if
any) used to determine the redshift, along with two $\qty{5}{\arcsec}$ cut-
outs, centered on the position of each multiple source. These cut-outs are
taken from the HST RGB image (in the upper-left panel), and from the white-
light image obtained by stacking a slice of the spectral data cube
corresponding to the wavelengths range shown in the plot of the spectrum (in
the upper right corner)

Figure 17: System 1

Figure 18:  System 2

Figure 19: System 3

Figure 20: System 5

Figure 21: System 6

Figure 22: System 7

Figure 23: System 8

Figure 24: System 10

Figure 25: System 11

Figure 26: System 12

Figure 27: System 17

Figure 28: System 18

Figure 29: System 22

Figure 30: System 24

Figure 31: System 35

Figure 32: System 36

Figure 33: System 37

Figure 34: System 38

Figure 35: System 39

Figure 36: System 40

Figure 37: System 41

Figure 38: System 42

Figure 39: System 43

Figure 40: System 44

Figure 41: System 45

Figure 42: System 47

Figure 43: System 48

Figure 44: System 49

##  Appendix D Cluster members

Table D.1 (only available in electronic form at the CDS) presents the selected
cluster members used in the lens model, sorted by their increasing magnitude
values in the band F160W. The first column (ID) reports the ID in the
spectroscopic and photometric catalogs; the second and third columns show the
J2000 ICRS right ascension and declination (R.A and Dec.); the fourth one
(Source) reports the source of the redshift estimation for the spectroscopic
members (m = MUSE; v = VIMOS; d = DEIMOS), while photometric members
identified by the CNN are indicated by a c (see Sect. 3.1); the fifth column
($z_{\rm{spec}}$) reports the measured spectroscopic redshift; the last column
($m_{\rm{F160W}}$ show the Kron magnitudes in the band F160W);

##  Appendix E Spectroscopic catalog

Table E.1 (only available in electronic form at the CDS) presents the full
spectroscopic catalog. The first column (ID) reports an increasing unique
identification number; the second and third columns show the J2000 ICRS right
ascension and declination (R.A and Dec.); the fourth one (Source) reports the
source of the redshift estimation (m = MUSE; v = VIMOS; d = DEIMOS); the fifth
and sixth columns ($z_{\rm{spec}}$ and QF) reports the measured spectroscopic
redshift and its estimation quality flag (1=insecure, 2=likely, 3=secure, and
9=based on one emission line); the last column (Comments) provides comments on
the redshift estimation and/or the most prominent spectral features detected.