11institutetext: Instituto de Astrofísica de Andalucía – Consejo Superior de
Investigaciones Científicas, Glorieta de la Astronomía S/N, E-18008 Granada,
Spain 22institutetext: LESIA, Observatoire de Paris, Université PSL, Sorbonne
Université, Université de Paris, CNRS, 92190 Meudon, France 33institutetext:
Laboratório Interinstitucional de e-Astronomia - LIneA & INCT do e-Universo,
Rua Gal. José Cristino 77, Bairro Imperial de São Cristóvão, Rio de Janeiro
(RJ), Brazil 44institutetext: UNESP - São Paulo State University, Grupo de
Dinâmica Orbital e Planetologia, Guaratinguetá, SP, 12516-410, Brazil
55institutetext: Astronomical Institute of the Romanian Academy, 5 Cuţitul de
Argint, 040557 Bucharest, Romania 66institutetext: Instituto de Astrofísica de
Canarias (IAC), C/Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain
77institutetext: Observatório Nacional/MCTI, Rio de Janeiro (RJ), Brazil, Rua
Gal. José Cristino 77, Bairro Imperial de São Cristóvão, Rio de Janeiro (RJ),
Brazil 88institutetext: Florida Space Institute, UCF, 12354 Research Parkway,
Partnership 1 building, Room 211, Orlado, USA 99institutetext: naXys,
University of Namur, 8 Rempart de la Vierge, Namur, B-5000, Belgium
1010institutetext: Department of astronomy, Faculty of Mathematics, University
of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia 1111institutetext:
Humboldt Research Fellow, Hamburger Sternwarte, Universität Hamburg,
Gojenbergsweg 112, 21029 Hamburg, Germany 1212institutetext: Astronomical
Observatory, Volgina 7, 11000 Belgrade, Serbia 1313institutetext: Institute of
Astronomy and National Astronomical Observatory, Bulgarian Academy of
Sciences, Sofia, Bulgaria 1414institutetext: ROASTERR-1 Observatory, L04, Cluj
Napoca, Romania 1515institutetext: Stardust Observatory, L13, Brasov, Romania
1616institutetext: Astroclubul Bucureşti, Romania 1717institutetext:
Stardreams Observatory, L16, Vălenii de Monte, Romania 1818institutetext:
Romanian Academy - Cluj-Napoca Branch, Astronomical Observatory Cluj-Napoca,
Romania 1919institutetext: University of Craiova, Craiova, Romania
2020institutetext: Institutul de Stiinte Spatiale (ISS), Atomistilor 409,
C.P.: MG-23 Magurele 077125, Ilfov, Romania 2121institutetext: Societatea
Română pentru Astronomie Culturală (SRPAC), Timisoara, Romania
2222institutetext: Federal University of Technology - Paraná (UTFPR / DAFIS),
Curitiba, Brazil 2323institutetext: Institut Polytechnique des Sciences
Avancées IPSA, 63 boulevard de Brandebourg, F-94200 Ivry-sur-Seine, France.
2424institutetext: Institut de Mécanique Céleste et de Calcul des Éphémérides,
IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne
Universités, UPMC Univ Paris 06, Univ. Lille, 77 Av. Denfert-Rochereau,
F-75014 Paris, France. 2525institutetext: Universidade Federal do Rio de
Janeiro, Observatório do Valongo, Rio de Janeiro, Brazil 2626institutetext:
Astronomical Institute of the Slovak Academy of Sciences, 059 60 Tatranska
Lomnica, Slovakia, 2727institutetext: Konkoly Observatory, Research Centre for
Astronomy and Earth Sciences, H-1121 Budapest, Konkoly Thege Miklos ut 15-17,
Hungary 2828institutetext: Osservatorio Astrofisico di Catania (OACt-INAF),
Via S. Sofia 78, 95123 Catania, Italy 2929institutetext: ELTE Eötvös Loránd
University, Gothard Astrophysical Observatory, Szombathely, Hungary
3030institutetext: MTA-ELTE Exoplanet Research Group, 9700 Szombathely, Szent
Imre h. u. 112, Hungary 3131institutetext: Mt. Suhora Observatory, Pedagogical
University of Cracow 3232institutetext: Isaac Newton Group of Telescopes,
Santa Cruz de La Palma, Spain 3333institutetext: Osservatorio Astronomico di
Monte Agliale, Via Cune Motrone, Borgo a Mozzano, Italy 3434institutetext:
PDlink Observatory, Cadca, Slovakia 3535institutetext: INAF – Osservatorio
Astronomico di Trieste, Via Tiepolo 11, I-34143 Trieste, Italy
3636institutetext: Gruppo Astrofili Massesi, EAON, Massa, Italy
3737institutetext: International Occultation Timing Association - European
Section (IOTA/ES) 3838institutetext: Ia cu Stele, Bucharest, Romania
3939institutetext: Crni Vrh Observatory, Crni Vrh nad Idrijo, Slovenia
4040institutetext: Faculty of Mathematics and Physics, University of
Ljubljana, Slovenia 4141institutetext: Dark Sky Slovenia, Savlje 89, 1000
Ljubljana, Slovenia

# The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2

M. Vara-Lubiano The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on
2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 G. Benedetti-
Rossi The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 P. Santos-Sanz The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2
J. L. Ortiz The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on
2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 B. Sicardy The
multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2 M. Popescu The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 N. Morales The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 F. L. Rommel
The multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 B. Morgado The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2 C. L. Pereira The
multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 A. Álvarez-Candal The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 E. Fernández-Valenzuela The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 D. Souami The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2 D. Ilic The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 O. Vince The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 R. Bachev
The multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2 E. Semkov The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 D. A. Nedelcu The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 A. Şonka The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2 L. Hudin The multi-chord stellar occultation on 2019 October
22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2
M. Boaca DeceasedThe multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on
2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 V. Inceu The
multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2 L. Curelaru The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 R. Gherase The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 V. Turcu The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 D. Moldovan
The multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2 L. Mircea The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 M. Predatu The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 M. Teodorescu The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 L. Stoian The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 A. Juravle The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 F. Braga-Ribas The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 J. Desmars The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 R. Duffard The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 J. Lecacheux
The multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2 J.I.B. Camargo The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 M. Assafin The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2 R. Vieira-Martins The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2 T. Pribulla The
multi-chord stellar occultation on 2019 October 22 by the trans-Neptunian
object (84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22
by the trans-Neptunian object (84922) 2003 VS2 M. Husárik The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 P. Sivanič The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 A. Pal The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2 R. Szakats The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 C. Kiss The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on
2019 October 22 by the trans-Neptunian object (84922) 2003 VS2 J. Alonso-
Santiago The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2 A. Frasca The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2 G. M. Szabó The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 A. Derekas The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2 L. Szigeti The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 M. Drozdz The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 W. Ogloza The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 J. Skvarc̆ The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 F. Ciabattari The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 P. Delincak The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 P. Di Marcantonio The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 G. Iafrate The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 I. Coretti The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 V. Baldini The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 P. Baruffetti The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2 O. Klös The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2 V. Dumitrescu The multi-chord stellar occultation on 2019
October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-chord
stellar occultation on 2019 October 22 by the trans-Neptunian object (84922)
2003 VS2 H. Mikuz̆ The multi-chord stellar occultation on 2019 October 22 by
the trans-Neptunian object (84922) 2003 VS2The multi-chord stellar occultation
on 2019 October 22 by the trans-Neptunian object (84922) 2003 VS2The multi-
chord stellar occultation on 2019 October 22 by the trans-Neptunian object
(84922) 2003 VS2The multi-chord stellar occultation on 2019 October 22 by the
trans-Neptunian object (84922) 2003 VS2 A. Mohar The multi-chord stellar
occultation on 2019 October 22 by the trans-Neptunian object (84922) 2003
VS2The multi-chord stellar occultation on 2019 October 22 by the trans-
Neptunian object (84922) 2003 VS2

(Received date / Accepted date)

###### Abstract

Context. Stellar occultations have become one of the best techniques to gather
information about the physical properties of trans-Neptunian objects (TNOs),
which are critical objects for understanding the origin and evolution of our
Solar System.

Aims. The purpose of this work is to determine with better accuracy the
physical characteristics of the TNO (84922) 2003 VS2 through the analysis of
the multi-chord stellar occultation on 2019 October 22 and photometric data
collected afterward.

Methods. We predicted, observed, and analyzed the multi-chord stellar
occultation of the Gaia DR2 source 3449076721168026624 (mv = 14.1 mag) by the
plutino object 2003 VS2 on 2019 October 22. We performed aperture photometry
on the images collected and derived the times when the star disappeared and
reappeared from the observing sites that reported a positive detection. We
fitted the extremities of such positive chords to an ellipse using a Monte
Carlo method. We also carried out photometric observations to derive the
rotational light curve amplitude and rotational phase of 2003 VS2 during the
stellar occultation. Combining the results and assuming a triaxial shape, we
derived the 3D shape of 2003 VS2.

Results. Out of the 39 observatories involved in the observational campaign,
12 sites, located in Bulgaria (one), Romania (ten), and Serbia (one), reported
a positive detection; this makes it one of the best observed stellar
occultations by a TNO so far. Considering the rotational phase of 2003 VS2
during the stellar occultation and the rotational light curve amplitude
derived ($\Delta m$ = 0.264 $\pm$ 0.017 mag), we obtained a mean area-
equivalent diameter of $D_{\mathrm{A_{eq}}}$ = 545 $\pm$ 13 $\mathrm{km}$ and
a geometric albedo of 0.134 $\pm$ 0.010. By combining the rotational light
curve information with the stellar occultation results, we derived the best
triaxial shape for 2003 VS2, which has semi-axes a = 339 $\pm$ 5
$\mathrm{km}$, b = 235 $\pm$ 6 $\mathrm{km}$, and c = 226 $\pm$ 8
$\mathrm{km}$. The derived aspect angle of 2003 VS2 is $\theta$ = 59° $\pm$
2°or its supplementary $\theta$ = 121° $\pm$ 2°, depending on the north-pole
position of the TNO. The spherical-volume equivalent diameter is
$D_{\mathrm{V_{eq}}}$ = 524 $\pm$ 7 $\mathrm{km}$. If we consider large albedo
patches on its surface, the semi-major axis of the ellipsoid could be $\sim$
10 km smaller. These results are compatible with the previous ones determined
from the single-chord 2013 and four-chord 2014 stellar occultations and with
the effective diameter and albedo derived from Herschel and Spitzer data. They
evidence that 2003 VS2’s 3D shape is not compatible with a homogeneous
triaxial body in hydrostatic equilibrium, but it might be a differentiated
body and/or might be sustaining some stress. No secondary features related to
rings or material orbiting around 2003 VS2 were detected.

###### Key Words.:

Kuiper belt objects: individual: 2003 VS2 – Methods: observational –
Techniques: photometric

##  1 Introduction

Trans-Neptunian objects (TNOs) offer a unique opportunity to better understand
the origins and the chemical, dynamical, and collisional evolution of the
outer Solar System. Possibly dispatched to further distances from the Sun than
Neptune’s due to gravitational perturbations after their formation (Gomes et
al. 2005; Levison et al. 2008), their global composition has been virtually
unaffected by solar irradiation, keeping it very similar to that of the
primitive nebula (Morbidelli et al. 2008).

In the last decade, stellar occultations by TNOs have proved to be one of the
best techniques to determine the size and shape of these objects, show
features such as satellites (Sickafoose et al. 2019) or rings (Braga-Ribas et
al. 2014; Ortiz et al. 2015, 2017), and reveal possible atmospheres (Hubbard
et al. 1988; Stern & Trafton 2008; Meza et al. 2019). If we combine this
technique with light-reflection measurements, we can also derive their
geometric albedo. Furthermore, we can calculate their density if we assume
hydrostatic equilibrium or if the body is part of a binary system or has a
satellite, in which case we can obtain its mass.

Although this technique has been increasingly used in the past few years, it
is still challenging to predict and obtain positive results from multi-chord
stellar occultations (Ortiz et al. 2020), mainly due to the uncertainties in
the orbits of TNOs. The Second Gaia Data Release (Gaia DR2; Gaia Collaboration
et al. 2016b, a, 2018) eases the process by providing peerless accurate
positions and proper motions of more than one billion sources. However, the
large orbital periods of TNOs and the short time span of the observations
result in non-negligible uncertainties in their orbital elements, making
astrometric observations close to the stellar occultation date indispensable
for a successful event prediction.

The object (84922) 2003 VS2 orbits in the 3:2 mean motion resonance (MMR) with
Neptune, which makes it a plutino. This TNO presents a double-peaked
rotational light curve with an accurately determined rotation period of
7.41753 $\pm$ 0.00001 $\mathrm{h}$ (Santos-Sanz et al. 2017). No satellites
nor secondary features have been discovered so far around 2003 VS2. Its near-
infrared spectrum reveals the presence of exposed water ice (Barkume et al.
2008) which, according to Mommert et al. (2012), might explain the increase in
2003 VS2’s albedo from the typical value of 0.07 for the plutinos. The orbital
elements and most relevant physical characteristics of 2003 VS2 can be found
in Table 1.

Table 1: Orbital elements and physical characteristics of 2003 VS2.

$a$ | $q$ | $e$ | $i$ | $H_{V}$ | $P$ | $\Delta m$ |  $D_{area,eq}$aa$a$Mommert et al. (2012) obtained an area-equivalent diameter of $D\leavevmode\nobreak\ =\leavevmode\nobreak\ 523^{+35.1}_{-34.4}$ km | $D_{vol,eq}$ |  $p_{V}$bb$b$an albedo of $p_{\mathrm{V}}\leavevmode\nobreak\ =\leavevmode\nobreak\ 0.147^{+0.063}_{-0.043}$
---|---|---|---|---|---|---|---|---|---
(au) | (au) |  | (°) |  | ($\mathrm{h}$) | (mag) | ($\mathrm{km}$) | ($\mathrm{km}$) |
39.249 | 36.386 | 0.073 | 14.83 | 4.14$\pm$0.07 | 7.41753$\pm$0.00001 | 0.141$\pm$0.009 | 553${}^{+36}_{-33}$ | 548.3${}^{+29.5}_{-44.6}$ | 0.131${}^{+0.024}_{-0.013}$

111Orbital elements of 2003 VS2 from Jet Propulsion Laboratory (JPL) Small-
Body Database Browser (https://ssd.jpl.nasa.gov/sbdb.cgi): $a$, semi-major
axis; $q$, perihelion distance; $e$, eccentricity; $i$, inclination. Absolute
magnitude $H_{V}$ from Alvarez-Candal et al. (2016) and priv. comm.. Rotation
period $P$ is the preferred value from Santos-Sanz et al. (2017). Rotational
light curve amplitude ($\Delta m$), spherical volume-equivalent diameter
($D_{vol,eq}$), and albedo ($p_{\mathrm{V}}$) from Benedetti-Rossi et al.
(2019). Mean area-equivalent diameter ($D_{area,eq}$) calculated from the
values given in Benedetti-Rossi et al. (2019) and taking into account the
rotational phase using Eq. 1.
and .

A recent work was published with results from a four-chord and two single-
chord stellar occultations by 2003 VS2 in 2013 and 2014 (Benedetti-Rossi et
al. 2019). In that work, they reconstructed the 3D shape of 2003 VS2 by
combining the data from the multi-chord stellar occultation and the rotational
light curve obtained. The principal semi-axes that provided the best fit had
values of a = 313.8 $\pm$ 7.1 $\mathrm{km}$, b = 265.5${}^{+8.8}_{-9.8}$
$\mathrm{km}$, and c = 247.3${}^{+26.6}_{-43.6}$ $\mathrm{km}$, being these
measurements inconsistent with a Jacobi ellipsoid (Chandrasekhar 1987). This
solution was highly affected by the rotational light curve amplitude derived
in the paper, which was 0.141 $\pm$ 0.009 mag, significantly smaller than the
previously moderately large ones reported by Ortiz et al. (2006), Sheppard
(2007), and Thirouin et al. (2010). In this work we show that such a
rotational light curve amplitude cannot be correct based on new data and other
reasoning. Benedetti-Rossi et al. (2019) also reported the presence of a
putative secondary feature detected from one of the observing stations but,
without further data, they could not discard if it was due to a companion star
or instrumental effects.

In this work we present the results of the multi-chord stellar occultation by
2003 VS2 in 2019 October 22. A total of thirty-nine observatories were
involved in the campaign, from which 12 positive chords were obtained, a
considerable improvement with respect to the previous occultations by this
TNO. Combining the collected data from the stellar occultation and ensuing
photometric measurements we derived the 3D shape of 2003 VS2.

##  2 Observations

This section presents the observations carried out to improve the prediction
of the stellar occultation, the observations of the actual event, and the
observations performed shortly afterward to obtain the rotational light curve
of 2003 VS2.

###  2.1 Occultation predictions

The stellar occultation on 2019 October 22 was singled out from the systematic
searches for TNOs occultation candidate stars carried out by the European
Research Council (ERC) Lucky Star222https://lesia.obspm.fr/lucky-
star/index.php project collaboration (Desmars et al. 2015, 2018). The Lucky
Star’s NIMA333Numerical Integration of the Motion of an Asteroid. ephemeris
thus gave the initial prediction444https://lesia.obspm.fr/lucky-
star/occ.php?p=32895 for the 2019 October 22 stellar occultation, and the
candidate star was identified in the Gaia DR2 catalog (source ID:
3449076721168026496; UCAC4555The fourth U.S. Naval Observatory CCD Astrograph
Catalog. identifier 616-023624). Relevant information about the star, such as
its coordinates, proper motions, parallax, and their uncertainties, as well as
the star’s $G$, $B$, $V$, and $K$ magnitudes, can be found in Table $a$.

Table 2: Main information of the occulted star (Gaia DR2
3449076721168026496aa$a$From Vizier: https://bit.ly/3vUjwkZ; UCAC4 identifier
616-023624aa$a$From Vizier: https://bit.ly/3vUjwkZ).

RA (ICRFbb$b$International Celestial Reference System.) | errRA |  Dec (ICRFbb$b$International Celestial Reference System.) | errDec | pmRA | pmDec | Plx | $G$ | $B$ | $V$ | $K$
---|---|---|---|---|---|---|---|---|---|---
| (mas) |  | (mas) |  (mas yr-1) |  (mas yr-1) | (mas) | (mag) | (mag) | (mag) | (mag)
05h 30m 38.0442s | 0.0401 |  \+ 33° 07′ 01$\aas@@fstack{\prime\prime}$748 | 0.0330 |  -0.34$\pm$0.06 |  -1.76$\pm$0.05 |  0.2084$\pm$0.0533 | 14.1625 | 15.030 | 14.150 | 10.968
666Star Coordinates in RA and Dec propagated to the occultation epoch
(2458779.35870) and respective errors (errRA, errDec), proper motion in RA and
Dec and respective errors, absolute stellar parallax with error, and magnitude
$G$ from Gaia DR2 (Gaia Collaboration et al. 2016b, a, 2018). Magnitudes $B$,
$V$, and $K$ from the Naval Observatory Merged Astrometric Dataset (NOMAD)
catalog (Zacharias et al. 2004).

To reduce the uncertainty on 2003 VS2’s orbit and narrow down the predicted
location of the shadow path, we performed two observing runs with two
different telescopes a few days before the event.

The first observing run was carried out on 2019 October 5, with the charge-
coupled device (CCD) Andor ikon-L camera of the 1.5-m telescope at the Sierra
Nevada Observatory (OSN) in Granada, Spain. This camera provides a field of
view (FOV) of 7$\aas@@fstack{\prime}$92 $\times$ 7$\aas@@fstack{\prime}$92,
with an image scale of 0$\aas@@fstack{\prime\prime}$232 pixel-1. The 15 images
of this set were acquired in 2$\times$2 binning mode, with no filter and an
integration time of 400 s. The average seeing was
1$\aas@@fstack{\prime\prime}$84\. Bias and flat-field frames were taken for
standard calibration, which was done afterward following the steps in
Fernández-Valenzuela et al. (2016).

The second run was taken on 2019 October 8, with the IO:O camera of the
Liverpool 2-m Telescope at the Roque de los Muchachos Observatory in La Palma,
Spain. This instrument has a FOV of 10′$\times$10′and an image scale of
0$\aas@@fstack{\prime\prime}$15 pixel-1. The ten images of this set were
acquired in 2$\times$2 binning mode, with the Sloan R-filter and 300 s of
integration time. The average seeing was 1$\aas@@fstack{\prime\prime}$2\. Bias
and flat-field frames were also taken for standard calibration.

With the OSN data, the obtained offsets with respect to the Jet Propulsion
Laboratory (JPL) #30 orbit were ($-$360 $\pm$ 36) mas in right ascension (RA)
and (+4 $\pm$ 25) mas in declination (Dec). The Liverpool data yielded offsets
of ($-$368 $\pm$ 12) mas in RA and (+24 $\pm$ 11) mas in Dec.

We made two different predictions using the OSN and the Liverpool data,
although the result was roughly identical (the Liverpool prediction being
$\sim$ 20 mas north of the OSN). We used the predicted shadow path obtained by
updating 2003 VS2’s ephemeris from JPL with the Liverpool data (shown in Fig.
1), as it was taken closer to the event date and with better seeing.

Figure 1: Predicted (solid lines) and observed (dashed lines) shadow paths for
the 2003 VS2 stellar occultation on 2019 October 22 through the Gaia DR2
source 3449076721168026496. The prediction was made updating JPL #30 ephemeris
with the offsets obtained with data from the Liverpool 2-m Telescope in the
Roque de los Muchachos Observatory (La Palma, Spain). The green line
represents the middle of the shadow path and the blue lines indicate the
limits of the shadow (width of the shadow path is 479 $\mathrm{km}$, from Jet
Propulsion Laboratory). The observing sites involved in the event are also
marked: in green, the ones that reported a positive detection; in red, those
that reported a negative detection; and, in blue, those that could not observe
due to bad weather or technical problems, see Tables 3, 4, and 8.

###  2.2 Stellar occultation observations

On 2019 October 22, 39 observational stations spread across 11 countries
(including both professional telescopes and amateur observers, Fig. 1) were
all set to observe the Gaia DR2 source 3449076721168026496 around the
predicted occultation time. Out of the total participating stations, 12
reported a positive detection, 14 reported a negative detection (among which
two were very close to the shadow path and provide constraints to the shape
fitting), and 13 could not observe due to bad weather or technical
difficulties. Detailed information about all the participant observatories,
divided between positive detections, negative detections, and observations
with technical problems or overcast, can be respectively found in Tables 3, 4,
and 8. The detailed instrumental settings at the sites with positive
detections are also given in Table 3. All the teams that could observe
collected series of Flexible Image Transport System (FITS) images, except for
one site in Romania that took data in Tagged Image File Format (TIFF) format
and required a different analysis, as explained in Sect. 3.1. The time span of
the collected images includes several minutes before and after the stellar
occultation.

In this kind of event, it is crucial to save within the images’ header the
individual acquisition time and all participating stations must be
synchronized. Clock synchronizations were used to accomplish it: all the
observing teams used Internet Network Time Protocol servers (NTP), except for
two negative sites that used Global Positioning System Video Time Inserters
(GPS-VTI). Three positive sites had synchronization issues that are addressed
in Sect. 3.1.

We performed synthetic aperture photometry of the occulted star and nearby
comparison stars to correct for seeing effects and atmospheric transparency
fluctuations. The synthetic aperture photometry was done using our own
DAOPHOT-based routines coded in Interactive Data Language (IDL), following the
procedures described in Fernández-Valenzuela et al. (2016). In this case,
though, we fixed the centroid relative to the non-occulted stars in the FOV so
that it did not change when the TNO occults the star. We used several
apertures and annuli and chose those that resulted in the least scatter in the
photometry. In Fig. 2 we show the resulting normalized flux (the blended flux
of the occulted star + TNO divided by its mean value outside the occultation
moment) vs. time from the positive sites, which show deep drops in flux around
the predicted occultation time. We note that 2003 VS2 is too faint to be seen
with the available equipment, so the star’s flux drops to zero during the
occultation. We derived the error bars in Fig. 2 from Poisson noise
calculations, but the results are scaled so that their standard deviation
matches that of the data outside the main drop of the occultation (Col. seven
in Table 5). We do not see secondary flux drops other than the one
corresponding to the main body, which could indicate that there is not a
sufficiently wide and dense ring orbiting around 2003 VS2 that could have
produced detectable flux drops, but due to the small signal-to-noise ratio
(S/N) we cannot discard it. We put special care doing the photometry of the
data from the places that missed the occultation but were very close to the
shadow path, as they put constraints to 2003 VS2’s final shape.

Figure 2: Normalized light curves from the positive detections of the stellar
occultation by 2003 VS2 on 2019 October 22 and the two closest negatives. The
relative flux of the occulted star with respect to the comparison chosen stars
is plotted against time, given in seconds after 2019 October 22 20:40:00 UT.
The uncertainty bars of the flux are plotted for all the chords, although some
have the size of the points and are not visible. The light curves have been
displaced in flux for better visualization and follow the same order as in
Table 3. Chords 0 and 13 (top and bottom chords, in gray) correspond to the
negative detections from observers H. Mikuz̆ and V. Dumitrescu, respectively
(see Table 4.) Light curves plotted in blue required a special consideration
regarding the time synchronization, see Sect. 3.1. Chord 3’ is the result of
merging chords 3 and 4, see the text for details. Table 3: Details of the
observing stations of the 2003 VS2 multi-chord stellar occultation on 2019
October 22 with positive detection.

Chord | Site name | Latitude (N) | Telescope Aperture | Exposure Time | Observers
---|---|---|---|---|---
number | Location | Longitude (E) | (cm) | Cycle Timebb$b$Cycle time is the sum of exposure time plus dead time. |
| MPC Code | Altitude (m) | Detector/Instrument | (s) |
| ROASTERR-1 Observatory (1) | 46° 49′ 15$\aas@@fstack{\prime\prime}$6 | 30 | 3 |
1 | Romania | 23° 35′ 47″ | KAF8300 | 5.18 | L. Hudin
| L04 | 391aa$a$Altitudes from Google Earth. |  |  |
| ROASTERR-1 Observatory (2) | 46° 49′ 15$\aas@@fstack{\prime\prime}$6 | 28 | 2 |
2 | Romania | 23° 35′ 47″ | ATIK-414ex | 3.01 | M. Boaca
| L04 | 391aa$a$Altitudes from Google Earth. |  |  | V. Inceu
|  | 46° 42′ 37$\aas@@fstack{\prime\prime}$557 | 30.5 | 2 | V. Turcu
3 | Romania | 23° 35′ 35$\aas@@fstack{\prime\prime}$647 | SBIG STT-1603ME | 3 | D. Moldovan
| – | 783.405 |  |  | L. Mircea
|  | 46° 42′ 37$\aas@@fstack{\prime\prime}$452 | 40.6 | 2 | V. Turcu
4 | Romania | 23° 35′ 36$\aas@@fstack{\prime\prime}$94 | SBIG STT-1603ME | 3 | D. Moldovan
| – | 787.56 |  |  | L. Mircea
|  | 45° 42′ 11$\aas@@fstack{\prime\prime}$94 | 27.94 | 5 | L. Stoian
5 | Romania | 21° 26′ 12$\aas@@fstack{\prime\prime}$78 | ZWO ASI 224 CMOS | 5.14 | A. Juravle
| – | 92aa$a$Altitudes from Google Earth. |  |  |
| Berthelot Observatory | 45° 36′ 59$\aas@@fstack{\prime\prime}$4 | 36.83 | 2.5 | D. A. Nedelcu
6 | Romania | 22° 53′ 19$\aas@@fstack{\prime\prime}$7 | SBIG | 8.64 | A. Sonka
| L54 | 400 | STL11000M CCD |  |
| Stardust Observatory | 45° 38′ 30″ | 20.32 | 8.5 |
7 | Romania | 25° 37′ 19″ | CCD Atik 383L | 10.28 | L. Curelaru
| L13 | 597 |  |  |
|  | 44° 19′ 24$\aas@@fstack{\prime\prime}$5 | 35.6 | 3.01 |
8 | Romania | 23° 47′ 19$\aas@@fstack{\prime\prime}$0 | ASI 1600 | 3.34 | M. Predatu
| – | 109aa$a$Altitudes from Google Earth. |  |  |
| Stardreams Observatory | 45° 12′ 13$\aas@@fstack{\prime\prime}$3 | 20 | 4 |
9 | Romania | 26° 02′ 44$\aas@@fstack{\prime\prime}$2 | ATIK 460ex | 5.52 | R. Gherase
| L16 | 382aa$a$Altitudes from Google Earth. |  |  |
| Astronomical Station Vidojevica | 43° 08′ 24$\aas@@fstack{\prime\prime}$6 | 140 | 0.8 | D. Ilic
10 | Serbia | 21° 33′ 20$\aas@@fstack{\prime\prime}$4 | Andor ikonL | 1.55 | O. Vince
| C89 | 1150 |  |  |
| Belogradchik Observatory | 43° 37′ 22″ | 60 | 6 | R. Bachev
11 | Bulgaria | 22° 40′ 30″ | FLI PL9000 | 6.86 | E. Semkov
| – | 650 |  |  |
|  | 44° 19′ 19$\aas@@fstack{\prime\prime}$14 | 35.5 | 2 |
12 | Romania | 25° 59′ 8$\aas@@fstack{\prime\prime}$69 | ASI 1600 | 2.50 | M. Teodorescu
| – | 70aa$a$Altitudes from Google Earth. |  |  |

777The sites are sorted by their distance to the center of the predicted
shadow path.

Table 4: Details of the observing stations of the 2003 VS2 multi-chord stellar
occultation on 2019 October 22 with negative detection.

Site name | Latitude (N) | Telescope | Observers
---|---|---|---
Location | Longitude (E) | aperture |
MPC Code | Altitude (m) | ($\mathrm{cm}$) |
Bremthal | 50° 08′ 17$\aas@@fstack{\prime\prime}$4 |  |
Germany | 08° 21′ 50$\aas@@fstack{\prime\prime}$4 | 25.4 | O. Klös
– | 256 |  |
PDlink Observatory | 49° 24′ 15$\aas@@fstack{\prime\prime}$20 |  |
Cadca, Slovakia | 18° 42′ 09$\aas@@fstack{\prime\prime}$47 | 40 | P. Delincak
– | 680 |  |
Mt. Suhora Observatory | 49° 34′ 09″ |  | M. Drozdz
Poland | 20° 04′ 03″ | 60 | W. Ogloza
– | 1009 |  |
Skalnate Pleso | 49° 11′ 21$\aas@@fstack{\prime\prime}$8 |  | T. Pribulla
Slovakia | 20° 14′ 02$\aas@@fstack{\prime\prime}$1 | 130 | M. Husárik
056 | 1786 |  | P. Sivanič
| 44° 01′ 16$\aas@@fstack{\prime\prime}$96 |  |
Massa, Italy | 10° 07′ 56$\aas@@fstack{\prime\prime}$65 | 30 | P. Baruffetti
– | 30 |  |
Gothard Observatory | 47° 15′ 29$\aas@@fstack{\prime\prime}$83 |  | G. M. Szabó
Szombathely, Hungary | 16° 36′ 15$\aas@@fstack{\prime\prime}$67 | 80 | A. Derekas
– | 220aa$a$Altitudes from Google Earth. |  | L. Szigeti
C̆rni Vrh Observatory | 45° 56′ 45$\aas@@fstack{\prime\prime}$1 |  |
Slovenia | 14° 04′ 16$\aas@@fstack{\prime\prime}$4 | 60 | J. Skvarc̆
– | 726 |  |
Monte Agliale Observatory | 43° 59′ 43$\aas@@fstack{\prime\prime}$0 |  |
Borgo a Mozzano, Italy | 10° 30′ 53$\aas@@fstack{\prime\prime}$7 | 50 | F. Ciabattari
159 | 756 |  |
Stazione Osservativa di Basovizza | 45° 38′ 33″ |  | P. Di Marcantonio
Osservatorio Astronomico di Trieste, Italy | 13° 52′ 23″ | 35 | G. Iafrate
038 | 400 |  | I. Coretti, V. Baldini
Piszkéstető Station | 47° 55′ 6$\aas@@fstack{\prime\prime}$0 |  | A. Pal
Konkoly Obs., Hungary | 19° 53′ 41$\aas@@fstack{\prime\prime}$7 | 100 | R. Szakats
561 | 924aa$a$Altitudes from Google Earth. |  | C. Kiss
Konkoly Observatory | 47° 29′ 59$\aas@@fstack{\prime\prime}$28 |  | A. Pal
Normafa, Hungary | 18° 57′ 51$\aas@@fstack{\prime\prime}$12 | 60 | R. Szakats
053 | 468aa$a$Altitudes from Google Earth. |  | C. Kiss
| 49° 24′ 15$\aas@@fstack{\prime\prime}$20 |  |
Vratnik, Croatia | 18° 42′ 09$\aas@@fstack{\prime\prime}$47 | 20 | H. Mikuz̆
– | 775 |  | A. Mohar
| 44° 07′ 56$\aas@@fstack{\prime\prime}$8 |  |
Romania | 26° 13′ 04$\aas@@fstack{\prime\prime}$3 | 20 | V. Dumitrescu
– | 88aa$a$Altitudes from Google Earth. |  |
Mount Etna Observatory | 37° 41′ 05″ |  | J. Alonso-Santiago
Osservatorio Astrofisico di Catania, Italy | 14° 58′ 04″ | 91 | A. Frasca
156 | 1735 |  |

888The sites are sorted by their distance to the center of the predicted
shadow path.

###  2.3 Rotational light curve observations

Given that 2003 VS2 has a double-peaked rotational light curve and is large
enough to allow a hydrostatic equilibrium shape (see a detailed explanation in
Benedetti-Rossi et al. 2019), we can assume that the body is a triaxial
ellipsoid (Chandrasekhar 1987). If this were the case, one would need at least
three body projections at different rotational phases to correctly derive the
actual 3D shape of 2003 VS2.

However, we can overcome this by combining the occultation information with
time-series photometric data, taken closer to the occultation date. To do so,
we observed 2003 VS2 on two consecutive nights, two days after the event (2019
October 24 and 25), with the 1.23-m telescope at the Calar Alto Observatory in
Almería (Spain). This telescope is equipped with a 4k x 4k CCD DLR-MKIII
camera, which provides a FOV of
21$\aas@@fstack{\prime}$5$\times$21$\aas@@fstack{\prime}$5 with an image scale
of 0$\aas@@fstack{\prime\prime}$32 pixel-1. This wide FOV allowed us to keep
the same stellar field both nights, making it possible to choose the same
reference stars during the run to minimize systematic photometric errors.

A total of 143 images were acquired in 2$\times$2 binning mode and with an
integration time of 400$\mathrm{s}$, using no filter to maximize the S/N. The
moonshine was 14% for the first night and 7% for the second night. The average
seeing at Calar Alto from the Differential Image Motion monitor was
1$\aas@@fstack{\prime\prime}$6 for the second night; unfortunately, the Calar
Alto seeing tracker did not work for the first night. The average measured
full width at half maximum (FWHM) was $\sim$ 2.5 pixels ($\sim$
1$\aas@@fstack{\prime\prime}$6) for the first night and $\sim$ 2.3 pixels
($\sim$ 1$\aas@@fstack{\prime\prime}$5) for the second. The S/N was between 30
and 70 during the first night and between 20 and 80 during the second night.
We also took bias and flat-field frames each night for standard calibration,
which was performed using our own specific routines written in IDL.

##  3 Data reduction

###  3.1 Time synchronization and extraction

Robust clock synchronization is essential to have the absolute acquisition
time written on each frame header to obtain the actual star dis- and re-
appearance times from each site and, hence, the projected chords’ relative
position. In this regard, some of the images collected required a different
treatment to obtain their absolute acquisition time:

  * •

Chords 3 and 4: there was an intentionally applied 1 $\mathrm{s}$ difference
between the images acquired from the two telescopes at this site, aiming to
cover the whole event avoiding the dead time of the CCDs. Since the two
telescopes used the same instrument and took FITS images with the same
exposure time, we merged the data from these two telescopes to obtain one
single chord. By doing this, we doubled the sampling of the light curve and,
therefore, we obtained the immersion and emersion times from this site with a
smaller uncertainty. Hereafter we will refer to this as a single chord (chord
3’).

  * •

Chord 8: although this chord was nearly overlapping chord 9, its center was
shifted by more than 12 $\mathrm{s}$ with respect to the linear fit of the
rest of the centers (see Fig. 2 and Table 5). Later tests performed a month
after the occultation event showed a difference of more than one minute
between the acquisition system and a synchronized clock, but we were not able
to find out the exact time offset during the occultation event. All of this
suggested that the time synchronization at this site was not correctly
applied, so we could only use the chord length but not the absolute time of
the chord.

  * •

Chord 12: the images from this site were recorded in a data cube in TIFF
format. We converted them to FITS format using the Planetary Imaging
PreProcessor (PIPP), but then all the images had the same time written on the
header. The observer provided us with the acquisition times of the images, but
their accuracy only reached the order of seconds (as this is the accuracy
reached by the software used to save the images). We used the mid-integration
times for the light curve and then increased the uncertainties of the
immersion and emersion times by the exposure time (two seconds) since it was
not possible to know if the acquisition times we have corresponded to the
beginning, middle, or end of the images’ integration.

We saw no evidence for wrong time synchronization for the remaining positive
chords, given their relative positions (see Fig. 5a).

###  3.2 Occultation times and chord lengths

From every site that reported a positive detection, the stellar occultation
starting and ending times (disappearance and reappearance of the star,
respectively) were determined by fitting each light curve to a sharp-edge
square-well model convolved by: (1) Fresnel diffraction by a point-like source
at the distance of 2003 VS2 from the observer, (2) the CCD bandwidth, (3) the
finite stellar diameter projected at the object’s distance, in kilometers, and
(4) the finite integration time (see, e.g., Widemann et al. 2009; Braga-Ribas
et al. 2013).

During the stellar occultation, 2003 VS2 was at a geocentric distance of
$\Delta$ = 36.1 au=5.40$\times 10^{9}$ $\mathrm{km}$; this implies that for a
typical wavelength of $\lambda$=0.65 $\mathrm{\SIUnitSymbolMicro m}$, the
Fresnel scale F$=\sqrt{\lambda D/2}$ has a value of 1.33 $\mathrm{km}$.

We estimated the projected stellar diameter using the formulae from van Belle
(1999) and its $B$, $V$, and $K$ apparent magnitudes, obtained from the NOMAD
catalog (Zacharias et al. 2004, Table $a$). The diameters obtained are 0.86
$\mathrm{km}$ if considering a Super Giant or 0.91 $\mathrm{km}$ if
considering a Main Sequence star.

Finally, we converted the shortest integration time among the positive
observations (0.8 $\mathrm{s}$, chord 10) into the distance in the sky-plane
traveled by 2003 VS2 between two adjacent data points; since the velocity of
2003 VS2’s shadow-path was 13.01 $\mathrm{km}\text{\,}{\mathrm{s}}^{-1}$, that
distance was 10.41 $\mathrm{km}$. As a result, our light curves are dominated
mainly by the integration times and not by Fresnel diffraction nor the stellar
diameter.

The fitting procedure then searches for the times of disappearance and
reappearance of the star that minimize a classical $\chi^{2}$ function, as
explained in Sicardy et al. (2011, suppl. inf.). The uncertainty bars are
estimated by varying the occultation times to increase $\chi^{2}$ to
$\chi^{2}+1$. Since these uncertainty bars depend on the fit of the photometry
and the typical errors in the photometry are very small, the uncertainty in
the derived time of ingress and egress is also small, a small fraction of the
integration time. Figure 3 shows an example of the best fit to one of the
stellar occultation light curves (chord 2). All the derived disappearance and
reappearance times and chord lengths are listed in Table 5.

Figure 3: Best fit of the data from ROASTERR-1 Obs.(2) to the convolved
square-well model. The flux from the occulted star + 2003 VS2 is plotted with
black dots, normalized to the flux of the star while unocculted. Time is in
seconds after 2019 October 22 - 20:40:00 UT. The dashed gray line represents
the initial square-well model; the solid blue line represents the final fit,
after convolving the square-well model by Fresnel diffraction, the exposure
time, and the stellar diameter, see Sect. 3.2 for details. The open blue
circles show the expected flux from such model. The stellar occultation
starting and ending times derived are plotted in red, with their
uncertainties. For all the positive chords, the star dis- and re-appearance
times and chord lengths derived are listed in Table 5. Table 5: Star dis- and
re-appearance UT times on 2019 October 22, chord lengths, time shifts, and
dispersion ($\sigma$) of the light curves outside the occultation.

Chord number | Disappearance (s) | Reappearance (s) | Chord size (s) | Chord Size (km) | Shift (s)aa$a$A positive shift means a shift toward the east, a negative one indicates a shift toward the west. | $\sigma$
---|---|---|---|---|---|---
1 | 20:41:34.800 $\pm$ 1.155 | 20:42:14.995 $\pm$ 0.225 | 40.2 $\pm$ 1.2 | 523 $\pm$ 16 | +0.7 | 0.06
2 | 20:41:35.54 $\pm$ 0.46 | 20:42:14.47 $\pm$ 0.55 | 38.9 $\pm$ 0.7 | 506 $\pm$ 9 | +0.6 | 0.06
3’bb$b$Chord 3’ is the result of merging chords 3 and 4 in Table 3, see Sect. 3.1 for details. | 20:41:35.609 $\pm$ 0.109 | 20:42:16.585 $\pm$ 0.077 | 40.98 $\pm$ 0.13 | 533.1 $\pm$ 1.7 | +0.03 | 0.06
5 | 20:41:44.375 $\pm$ 0.525 | 20:42:24.95 $\pm$ 0.40 | 40.6 $\pm$ 0.7 | 528 $\pm$ 9 | -0.06 | 0.11
6 | 20:41:37.325 $\pm$ 1.100 | 20:42:24.062 $\pm$ 1.287 | 46.7 $\pm$ 1.7 | 608 $\pm$ 22 | +1.6 | 0.08
7 | 20:41:35.420 $\pm$ 0.425 | 20:42:17.411 $\pm$ 0.382 | 42.0 $\pm$ 0.6 | 546 $\pm$ 8 | +0.07 | 0.05
8 | 20:42:02.05 $\pm$ 0.73 | 20:42:37.76 $\pm$ 0.76 | 35.7$\pm$ 1.1 | 464 $\pm$ 14 | -14 | 0.23
9 | 20:41:37.491 $\pm$ 0.590 | 20:42:14.897 $\pm$ 0.160 | 37.4 $\pm$ 0.6 | 487 $\pm$ 8 | +1.1 | 0.06
10 | 20:41:57.914 $\pm$ 0.110 | 20:42:31.944 $\pm$ 0.136 | 34.03 $\pm$ 0.17 | 443 $\pm$ 2 | +0.3 | 0.02
11 | 20:41:54.60 $\pm$ 0.15 | 20:42:28.76 $\pm$ 0.12 | 34.16 $\pm$ 0.19 | 444 $\pm$ 2 | -0.7 | 0.02
12 | 20:41:53.551 $\pm$ 2.186cc$c$We have added two seconds to the uncertainty bar given by the square-well fit for chord 12, as explained in Sect. 3.1. | 20:42:12.949 $\pm$ 2.387cc$c$We have added two seconds to the uncertainty bar given by the square-well fit for chord 12, as explained in Sect. 3.1. | 19 $\pm$ 3 | 247 $\pm$ 39 | -2 | 0.12

999Chords’ shifts are explained in Sect. 4.1.

###  3.3 Rotational light curve

We performed aperture photometry on 2003 VS2 and 16 reference stars with good
photometric behavior using the routines and procedures mentioned in Fernández-
Valenzuela et al. (2016). We tested different synthetic aperture radii and sky
annuli to maximize the S/N of the object while minimizing the dispersion of
the residuals to the rotational light curve fit. We chose different aperture
parameters for each observing day but selecting the same reference stars and
then combined the best photometry results.

The obtained rotational light curve is shown in Fig. 4 and the data used is
available online. We folded the relative flux of 2003 VS2 vs. time using its
well-known rotation period of 7.41753 $\pm$ 0.00001 $\mathrm{h}$ (Santos-Sanz
et al. 2017) and used a fourth-order Fourier function to fit the folded data.
The obtained peak-to-peak amplitude of the rotational light curve was $\Delta
m$ = 0.264 $\pm$ 0.017 mag; the nominal value is the one that best fits the
data in terms of minimization of the sum of squared residuals and the
uncertainty is given as the standard deviation of a Monte Carlo distribution.
This amplitude is larger than other values found in the literature (0.23 $\pm$
0.07 mag, 0.21 $\pm$ 0.02 mag, 0.21 $\pm$ 0.03 mag; Ortiz et al. 2006;
Sheppard 2007; Thirouin et al. 2010, respectively), although it is consistent
within their error bars, but the greatest disagreement appears when comparing
this work’s amplitude with the last 0.141 $\pm$ 0.009 mag value found in
Benedetti-Rossi et al. (2019), which was obtained with data from 2014. Our
confidence is stronger for this work’s rotational light curve since the
dispersion of the residuals to the fit is lower than the one in Benedetti-
Rossi et al. (2019) and the obtained amplitude is more compatible with the
ones previously published in the literature. The slight increase in the
rotational light curve amplitude along the years may be explained by a change
in the object’s aspect angle, as found in the case of the TNO Varuna
(Fernández-Valenzuela et al. 2019).

We calculated the rotational phase of 2003 VS2 at the time of the stellar
occultation101010To do this, we considered 2458779.36248264 to be the Julian
date of the occultation event, as it was the closest recorded date to the
average value of the mid-occultation times from all sites. However, choosing a
different Julian date close to the stellar occultation would not change the
results, given the object’s rotation period., which was 0.32 with respect to
the absolute brightness maximum (see the vertical black dashed line in Fig.
4). We did not correct the Julian dates from light travel time since this
source of error is negligible due to the closeness in time of all data. The
rotational phase obtained implies that the apparent surface area of 2003 VS2
was near its minimum during the occultation event. We note that the rotational
phase at the time of the occultation is not influenced by the amplitude of the
rotational light curve but by the rotation period. Given the precision of the
rotation period and the time-span between the data taken for the occultation
event and the rotational light curve, the error calculating the rotational
phase is negligible.

Figure 4: On top, rotational light curve of 2003 VS2 from data collected in
2019 October 24 (black triangles) and 25 (blue squares). The data were folded
using the rotation period of 7.41753 $\mathrm{h}$ (Santos-Sanz et al. 2017).
The fourth-order Fourier fit is shown in a solid red line. The vertical black-
dashed line indicates the rotational phase of 2003 VS2 at the time of the
stellar occultation. The plot has been arbitrarily shifted to make the minimum
of the fit (maximum brightness) correspond to rotational phase 0. On the
bottom, differences between the observational data and the fit. Julian dates
are not corrected from light travel time.

##  4 Results analysis

###  4.1 Limb fitting

The generally considered shape for a TNO’s limb fitting is an ellipse (see,
e.g., Ortiz et al. 2017; Benedetti-Rossi et al. 2019), even though the object
might not project a perfect regular elliptical shape. In this work we do not
have enough positive chords to account for topographic features or deviations
from a true elliptical shape, so we can only use the simplest and most general
model for the limb fitting.

Five adjustable parameters characterize the considered ellipse: the body’s
center coordinates relative to the star in the sky plane ($f_{\mathrm{c}}$,
$g_{\mathrm{c}}$), the apparent semi-major axis a’, the apparent semi-minor
axis b’, and the tilt angle of the ellipse PA, which is the position angle of
the semi-minor axis from celestial north, positive to the west. If we assume
the Gaia DR2 star position to be correct, the coordinates ($f_{\mathrm{c}}$,
$g_{\mathrm{c}}$) respectively give the offsets in RA and Dec to apply to the
object’s adopted ephemeris.

We considered two configurations of the positive chords for the limb fitting.
For the first configuration, we kept the relative positions of the original
chords but had to correct the absolute time of chord 8 (see Sect. 3.1). In
this regard, we performed a weighted111111The weights of the chords’ centers
were calculated as the inverse of
$\frac{1}{2}\sqrt{\sigma_{ingress}^{2}+\sigma_{egress}^{2}}$. least-squares
polynomial fit of degree one to the centers of the chords in Table 5, not
using chord 8 for that fit. We then shifted chord 8 until its center lay on
said linear regression and thus performed the elliptical fitting to the
chords’ extremities (Fig. 5a). For the second configuration, we aligned the
centers of all the chords using the aforementioned linear regression and then
performed the elliptical limb fitting to the chords’ extremities (see Fig.
5b).

The alignment of the centers is a condition for the parallel chords of an
ellipse, and the needed shifts are not within the centers’ uncertainties.
Although synchronization via NTP servers provides theoretical accuracies of
0.01 $\mathrm{s}$, uncertainties of up to tenths of a second have been
reported to arise from using different operating systems (Barry et al. 2015),
camera software, or even due to delays in the shutter opening. However, adding
a nominal average error to all the extremities would be unwise since such
error should be the same for the ingress and egress of each chord, and we
would be overestimating the error. On the other hand, the necessity of
correcting unexplained time shifts has also been reported (Elliot et al. 2010;
Braga-Ribas et al. 2013). So by aligning the chords, we account for possible
systematic timing errors and small topography that could have decentered the
chords.

We obtained the best elliptical fit to the extremities of the chords via
minimization of the sum of squared residuals
$\sum_{i}(d_{i,\mathrm{obs}}-d_{i,\mathrm{fit}})^{2}$, being $d_{i}$ the
shortest distance between the $i$-extremity and the evaluated ellipse
following the direction of the chord. The uncertainties of the elliptical
parameters were determined using a Monte Carlo method. To do this, we
generated 10 000 random sets of extremities of the chords for each
configuration, sampled from within the uncertainty bars, and then searched for
the ellipse that minimizes the aforementioned equation. The Monte Carlo
distributions obtained for each of the ellipse parameters are included in
Appendix B. In Table 6 we show the nominal value and the standard deviation of
each distribution.

Table 6: Results of the elliptical limb fitting.

Parameter | Original chordsaa$a$Chord 8 is the only chord that has been shifted for this case, see Sect. 4.1. | Aligned chords
---|---|---
Semi-major axis a’ (km) | 292 $\pm$ 3 | 293 $\pm$ 3
Semi-minor axis b’ (km) | 231 $\pm$ 6 | 230 $\pm$ 6
Oblateness $\epsilon^{\prime}=(a^{\prime}-b^{\prime})/a^{\prime}$ | 0.21 $\pm$ 0.03 | 0.21 $\pm$ 0.03
Tilt angle (°) | -11 $\pm$ 2 | -6 $\pm$ 2
($f_{\mathrm{c}}$, $g_{\mathrm{c}}$) (km)bb$b$Offsets with respect to the JPL #33 orbit. | (-1010 $\pm$ 2, 770 $\pm$ 5) | (-1007 $\pm$ 2, 769 $\pm$ 5)
($f_{\mathrm{c}}$, $g_{\mathrm{c}}$) (mas)bb$b$Offsets with respect to the JPL #33 orbit. | (-38.57 $\pm$ 0.09, 29.40 $\pm$ 0.19) | (-38.43 $\pm$ 0.09, 29.37 $\pm$ 0.17)
Area-equivalent diameter (km) | 519 $\pm$ 10 | 519 $\pm$ 10
Mean area-equivalent diameter (km) | 545 $\pm$ 13 | 545 $\pm$ 13
Geometric albedo $p_{\mathrm{V}}$ | 0.134 $\pm$ 0.010 | 0.134 $\pm$ 0.010

121212The nominal values are obtained by minimization of a least squares
function and the uncertainties are the standard deviation of the Monte Carlo
distributions, see Sect. 4.1. The corresponding distributions can be seen in
appendix B. The uncertainty bars of the equivalent diameters and albedo are
obtained analytically from their respective mathematical expressions.

The instantaneous area-equivalent diameter of 2003 VS2 is also given in Table
6. Given that the rotational phase of 2003 VS2 was near its brightness minimum
during the stellar occultation (see Fig. 4), the projected area was also near
its minimum, and thus this diameter is a lower limit for the real equivalent
diameter of 2003 VS2. If we take the rotational phase and the rotational light
curve amplitude into account, we can derive the mean area-equivalent diameter
as:

$D_{\mathrm{mean}}=D_{\mathrm{occ}}\times 10^{(m_{occ}-m_{mean})/5},$ (1)

where $m_{occ}$ is the relative magnitude of 2003 VS2 during the stellar
occultation ($m_{occ}\leavevmode\nobreak\ =\leavevmode\nobreak\
0.104\leavevmode\nobreak\ \pm\leavevmode\nobreak\ 0.010$ and
$m_{mean}\leavevmode\nobreak\ =\leavevmode\nobreak\ 0$, see Fig. 4), and
$D_{occ}$ is its instantaneous area-equivalent diameter.

The derived mean area-equivalent diameter of 545 $\pm$ 13 $\mathrm{km}$ is
slightly greater than the value obtained from Herschel radiometric data
($D=523^{+35.1}_{-34.4}$\mathrm{km}$$, Mommert et al. 2012) but in agreement
within the error bars. It is, however, slightly smaller than the area-
equivalent diameter of 553${}^{+36}_{-33}$ $\mathrm{km}$ calculated with the
data from Benedetti-Rossi et al. (2019) and applying Eq. 1 to take into
account the rotational phase at the occultation time, but still compatible
within the uncertainty.

Figure 5: Elliptical fit to the chords of the stellar occultation, for the two
considered configurations: (a) original distribution of the chords, with chord
8 (dashed line) already shifted, and (b) final distribution of the chords
after aligning their centers using a least squares linear fit. In both plots:
the positive chords are shown in solid blue, negative chords in dotted blue;
uncertainties of the star’s disappearance time are shown in green and those of
the reappearance time in red; the black dots show the center of the chords.
From top to bottom, the chords follow the same order as in Table 3. The
limiting negative chord on the north corresponds to observer H. Mikuz̆ and the
chord limiting on the south corresponds to observer V. Dumitrescu, see Table
4. The black arrows on the top-left of each plot show the direction of the
shadow motion. The best elliptical fit to the extremities of the chords is
shown in black and all the ellipses from the Monte Carlo distribution are
plotted in gray, see Sect. 4.1 for details.

###  4.2 Geometric albedo

The geometric albedo at $V$-band of 2003 VS2 at the time of the stellar
occultation can be derived from:

$p_{V}=10^{0.4(m_{V,\mathrm{Sun}}-H_{V,\mathrm{occ}})}/(A/\pi)$ (2)

being $m_{\mathrm{V,Sun}}$ the $V$-magnitude of the Sun
($m_{\mathrm{V,Sun}}$=-26.74 mag), $H_{\mathrm{V,occ}}$ the instantaneous
absolute magnitude of 2003 VS2 in $V$-band at the time of the stellar
occultation, and A the projected area of 2003 VS2 during the event in
astronomical units squared.

To obtain $H_{\mathrm{V,occ}}$ we corrected 2003 VS2’s rotationally averaged
$H_{\rm V}$ (4.14 $\pm$ 0.07 mag; Alvarez-Candal et al. (2016) and priv.
comm.) by adding the theoretical relative magnitude of 2003 VS2 during the
stellar occultation, which is given by the Fourier fit to the rotational light
curve and has a value of 0.104 $\pm$ 0.010 mag at the $1\sigma$-level.

The obtained geometric albedo of 0.134 $\pm$ 0.010 (Table 6) is slightly
smaller but compatible with the one derived from the combination of Herschel
thermal measurements and Spitzer data ($0.147^{+0.063}_{-0.043}$, Lellouch et
al. 2013), and is also in agreement with the last derived albedo from
Benedetti-Rossi et al. (2019) (0.131 ${}^{+0.024}_{-0.013}$), see Table 1.

If we use the same absolute magnitude as Lellouch et al. (2013) ($H_{\rm V}=$
4.11 $\pm$ 0.38 mag) to calculate the albedo, it has a value of 0.14 $\pm$
0.05, which is still smaller but compatible within the error bars.

###  4.3 Size and shape

The double-peaked rotational light curve of 2003 VS2 suggests that it is
either a rotating triaxial ellipsoid or an oblate spheroid with a significant
irregularity or a large albedo variation along its surface; this second case
is unlikely, especially considering 2003 VS2’s large light curve amplitude.
Besides, the two maxima and minima per rotation cycle are different, which
usually indicates a triaxial shape with some albedo spots or small topographic
features, since we do not expect a perfectly symmetrical and homogeneous body
orbiting in space. This is the case for many observed TNOs with large
rotational light curve amplitudes, such as Haumea (Lacerda 2010), Varuna
(Fernández-Valenzuela et al. 2019), and 2008 OG19 (Fernández-Valenzuela et al.
2016). On the other hand, if not triaxial, the rotation period of 2003 VS2
would be 3.6 $\mathrm{h}$, which is probably too fast for a TNO (no TNO is
known to rotate that fast). Hence, assuming a triaxial ellipsoidal shape for
2003 VS2, we searched for the axes $a>b>c$ of a triaxial body, rotating around
its $c$-axis, that would give the observed elliptical projection during the
stellar occultation (Fig. 5) while also showing an amplitude of $\Delta m$ =
0.264 $\pm$ 0.017 mag on its rotational light curve.

To do this, we used the procedures described in Gendzwill & Stauffer (1981) to
generate ellipsoids characterized by three semi-major axes and three
orientation angles with respect to the Cartesian system, and then project
these ellipsoids into a plane perpendicular to the line of sight, in order to
compare that projection with the instantaneous limb of 2003 VS2 during the
stellar occultation (Fig. 5).

An additional constraint to the model is the observed rotational light curve
amplitude of 2003 VS2 (Fig. 4). To include it, we implemented the well-known
relation between the peak-to-peak variation of the rotational light curve of a
small body and its three principal semi-axes (Binzel et al. 1989):

$\Delta
m=2.5\log\left(\frac{a}{b}\right)-1.25\log\left(\frac{a^{2}\cos^{2}(\theta)+c^{2}\sin^{2}(\theta)}{b^{2}\cos^{2}(\theta)+c^{2}\sin^{2}(\theta)}\right)$
(3)

where $\theta$ is the polar aspect viewing angle, that is, the angle between
the rotation axis (c, in this case) and the line of sight.

For each of the ellipses obtained via Monte Carlo for the limb-fitting (Sect.
4.1, Fig. 5), we searched for the ellipsoid that would give the most similar
projection in terms of least squares minimization. Although the limb fit
obtained in Sect. 4.1 has virtually the same values for both considered chord
configurations, we decided to search for the corresponding ellipsoid of both
solutions to see if the slight difference in the tilt angle would give
different 3D shapes. The obtained distributions for the ellipsoid’s semi-axes,
aspect angle, and the corresponding rotational light curve amplitude derived
from Eq. 3 are shown in appendix B. In Table 7 we show the best 3D fit (which
is the one corresponding to the best limb fit in Table 6), and the uncertainty
bars are given as the standard deviation of the Monte Carlo distributions.
According to the results, the obtained triaxial ellipsoid would produce a
variation of 0.24 mag during its rotation so, as stated before, the remaining
observed rotational light curve amplitude might be due to albedo spots or
topographic features that cannot be studied with the available data; we would
either need more chords from the stellar occultation to study topographic
features, or rotational light curves obtained with different filters to study
albedo variations. The differences in the rotational light curve amplitude due
to albedo spots would be on the order of a few cents of a magnitude (this is
the range of variability due to albedo variegations observed in large TNOs
such as Varuna, Haumea, 2008 OG19) Considering this and given that a model of
a triaxial body without albedo spots to explain the light curve amplitude is a
simplification, we also computed the ellipsoid accepting solutions that give a
rotational light curve amplitude 0.06 mag less than the observed value, to
allow for large albedo spots. These results are also included in Table 7 and
appendix B. Finally, the spherical volume equivalent diameter
($D_{\mathrm{V_{eq}}}$) derived from these parameters is also presented in
Table 7.

Table 7: Results of the 3D-fit of 2003 VS2.

Parameter | Observed $\Delta m$ |  $\Delta m_{min}$ = 0.18 mag
---|---|---
Original chordsaa$a$Chord 8 is the only chord that has been shifted for this case, see Sect. 4.1. | Shifted chord | Original chordsaa$a$Chord 8 is the only chord that has been shifted for this case, see Sect. 4.1. | Shifted chords
Semiaxis a (km) | 339 $\pm$ 5 | 338 $\pm$ 5 | 327 $\pm$ 5 | 330 $\pm$ 5
Semiaxis b (km) | 235 $\pm$ 6 | 233 $\pm$ 7 | 233 $\pm$ 6 | 235 $\pm$ 9
Semiaxis c (km) | 226 $\pm$ 8 | 227 $\pm$ 7 | 228 $\pm$ 8 | 222 $\pm$ 8
Aspect angle $\theta$ (°) | 59 $\pm$ 2 | 57 $\pm$ 3 | 51 $\pm$ 2 | 51 $\pm$ 6
Rotational light curve amplitude (mag) | 0.2497 $\pm$ 0.0008 | 0.2489 $\pm$ 0.0009 | 0.187 $\pm$ 0.003 | 0.184 $\pm$ 0.003
$a/b$ | 1.44 $\pm$ 0.06 | 1.45 $\pm$ 0.06 | 1.41 $\pm$ 0.06 | 1.40 $\pm$ 0.07
$b/c$ | 1.040 $\pm$ 0.017 | 1.022 $\pm$ 0.018 | 1.02 $\pm$ 0.02 | 1.06 $\pm$ 0.03
Spherical volume equivalent diameter (km) | 524 $\pm$ 7 | 523 $\pm$ 7 | 517 $\pm$ 7 | 516 $\pm$ 8

131313We present the ellipsoids obtained using the observed rotational light
curve amplitude ($\Delta m$ = 0.264 $\pm$ 0.017 mag) and the ones allowing for
bigger albedo spots, see Sect. 4.3. The nominal values of the parameters are
the ones obtained from the optimal ellipses in Table 6. The uncertainties are
given as the standard deviation of the Monte Carlo distributions shown in
appendix B, for the two chords’ configurations considered for the limb-
fitting.

Both obtained solutions are almost compatible with the one presented in
Benedetti-Rossi et al. (2019) within the errors. The differences might arise
from the fact that, in the previous work, the calculations were simplified by
considering that 2003 VS2 was on its brightness maximum during the 2014
occultation, when the actual rotational phase at the time of the occultation
was +0.07 with respect to the brightness maximum. Moreover, the rotational
light curve amplitude they used was smaller than the one used in this work.
However, we checked that the two amplitudes cannot be explained simultaneously
by a change of the aspect angle.

We derived the ecliptic coordinates of the pole $(\lambda_{p},\beta_{p})$ by
simultaneously minimizing the difference between the observed rotational light
curve amplitude and the one derived using Eq. 3, and the difference between
the aspect angle $\delta$ derived in Sect. 4.3 and the one derived via:

$\delta=\frac{\pi}{2}-\arcsin\left[\sin{\beta_{e}}\sin{\beta_{p}}+\cos{\beta_{e}}\cos{\beta_{p}}\cos{(\lambda_{e}-\lambda_{p})}\right]$
(4)

being $(\lambda_{e},\beta_{e})$ the ecliptic coordinates of the sub-Earth
point in the object-centered reference frame at the time of this work’s
stellar occultation. The pole’s ecliptic coordinates $(\lambda_{p},\beta_{p})$
derived are (228°, 39°) (for a more detailed explanation see Fernández-
Valenzuela (2022) and references therein). Combining the pole’s coordinates,
2003 VS2’s ephemeris, and the three-dimensional axes obtained in Sect. 4.3, we
obtained the theoretical variation of the rotational light curve amplitude
through the years and compared it to the values in the literature. The results
are plotted in Fig. 6. It can be seen that the previously published results
were obtained during the minimum of the rotational light curve amplitude, but
it has been increasing since 2005. The published value found in Benedetti-
Rossi et al. (2019) is much lower than theoretically expected, but the
remaining measurements do agree with the model. We suspect that the rotational
light curve in Benedetti-Rossi et al. (2019) may have been contaminated by a
background star or had some yet unidentified technical problem or reduction
artifact because there are no physical scenarios that can explain a sudden
decrease in the amplitude except perhaps a sudden brightening due to dust
release through sublimation activity or through a collision, but this is very
unlikely.

Figure 6: Theoretical long-term variability of 2003 VS2’s rotational light
curve amplitude and observational results found in the literature.

The projection of the ellipsoids obtained from the original-chords
configuration at the rotational phase in which the stellar occultation in
Benedetti-Rossi et al. (2019) happened (+0.07 with respect to the brightness
maximum) gives ellipses with semi-axes $a\leavevmode\nobreak\
\times\leavevmode\nobreak\ b=305\pm 4\leavevmode\nobreak\
\times\leavevmode\nobreak\ 230\pm 6$ km (for the observed rotational light
curve amplitude) and $a\leavevmode\nobreak\ \times\leavevmode\nobreak\
b=302\pm 4\leavevmode\nobreak\ \times\leavevmode\nobreak\ 230\pm 6$ km (for a
minimum rotational light curve amplitude of 0.18 mag), which are in agreement
with the limb fit reported in Benedetti-Rossi et al. (2019).

To conclude, we can compare these results with the theoretical axes-ratios of
a triaxial ellipsoid with the rotation period of 2003 VS2 and a homogeneous
density, to see if the derived shape is compatible with a hydrostatic-
equilibrium figure. Using the formalism from Chandrasekhar (1987), we searched
for the theoretical values of the axes-ratios a/b and b/c (solid and dashed
lines in Fig. 7, respectively) of a triaxial ellipsoid with a rotation period
of 7.41753 $\pm$ 0.00001 $\mathrm{h}$ and homogeneous densities between 600
and 1000 $\mathrm{kg}\text{\,}{\mathrm{m}}^{-3}$. We also plotted in Fig. 7
the axes-ratios bands derived from the stellar occultation (their values are
presented in Table 7). In the figure, one can see that there is an overlapping
region between the theoretical and observed axes-ratio a/b, but that is not
the case for the axes-ratio b/c. Therefore, we can conclude that the derived
shape of 2003 VS2 is not consistent with the hydrostatic-equilibrium figure of
a homogeneous body with the rotation period of 2003 VS2 for any density value.
This result suggests that, similar to the case of Haumea (Ortiz et al. 2017),
we might need to consider granular physics to explain the body’s shape,
because in this case, a differentiated body is less plausible due to 2003
VS2’s smaller size. Actually, the differentiation obtained by Loveless et al.
(2022) for icy bodies with radii larger than 200 km, although not negligible,
is so small that it would probably not produce a significant deviation from
the equilibrium shape for a homogeneous body of the size of 2003 VS2. However,
that model excludes or simplifies some of the physical and chemical processes
and considers pure spherical bodies, so we cannot discard some
differentiation. The possibility that 2003 VS2 might be sustaining some stress
seems more plausible but, in reality, we can only speculate that the deviation
of its shape from that of pure hydrostatic equilibrium could be due to one or
a combination of both scenarios.

Figure 7: Theoretical axes-ratios $a/b$ (solid blue line) and $b/c$ (dashed
red line) of a three-dimensional body in hydrostatic equilibrium, rotating
with a period of 7.41753 $\pm$ 0.00001 $\mathrm{h}$, for different densities
(Chandrasekhar 1987). The axes-ratios from the observed data are plotted as
colored bands, for the both considered cases. The theoretical $b/c$ ratios
from hydrostatic equilibrium do not agree with the observations for any
possible density of a homogeneous body because there is no intersection of the
dashed red line with the pink band.

##  5 Conclusions

On 2019 October 22, we observed the stellar occultation of the GAIA source
3449076721168026496 (mV = 14.1 mag) caused by the plutino (84922) 2003 VS2.
Out of the 39 participant observing sites, 12 reported a positive detection,
located in Bulgaria, Romania, and Serbia. Two positive chords were combined
into a single one, giving 11 effective positive chords. This is one of the
best observed stellar occultations by a TNO so far.

The projected shape of 2003 VS2 was fitted to an ellipse considering two
configurations of the positive chords: for the first one, we fitted the
extremities of the original chords obtained from the stellar occultation after
shifting only one chord due to a problem with its absolute time; for the
second case we shifted all the positive chords to align their centers. The
best solution for the instantaneous limb of 2003 VS2 was obtained by
minimization of the sum of squared residuals, and the uncertainties were
derived via a Monte Carlo method and correspond to the standard deviation of
the obtained distributions. The result has virtually the same value for both
configurations as can be seen in Table 6; for the original configuration it
has semi-axes a’1 = 292 $\pm$ 3 $\mathrm{km}$ and b’1 = 231 $\pm$ 6
$\mathrm{km}$, and a tilt angle of $-$11° $\pm$ 2°.

We carried out photometric observations of 2003 VS2 two days after the stellar
occultation and derived an amplitude of $\Delta m$ = 0.264 $\pm$ 0.017 mag
from the obtained rotational light curve. This value is slightly greater than
the ones previously published for this object, but can be explained through a
change in the aspect angle of the body. Taking this and the rotational phase
during the stellar occultation into account, the mean area-equivalent diameter
of 2003 VS2 is $D_{\mathrm{A_{eq}}}$ = 545 $\pm$ 13 $\mathrm{km}$. The derived
geometric albedo during the stellar occultation is $p_{\mathrm{V}}$ = 0.134
$\pm$ 0.010. These values are in agreement with the ones published in
Benedetti-Rossi et al. (2019), and with the diameter derived from thermal
models and the radiometric albedo obtained with Herschel and Spitzer data
within the error bars ($D=523^{+35.1}_{-34.4}$km and $p_{\mathrm{V}}$ =
0.147${}^{+0.063}_{-0.043}$, Mommert et al. 2012).

We derived the 3D shape of 2003 VS2 by combining its rotational light curve
and the instantaneous projection and assuming a triaxial ellipsoidal shape.
The obtained ellipsoid has principal semi-axes a = 339 $\pm$ 5 $\mathrm{km}$,
b = 235 $\pm$ 6 $\mathrm{km}$, and c = 226 $\pm$ 8 $\mathrm{km}$, with an
aspect angle of either $\theta_{1}$ = 59° $\pm$ 2°or its supplementary
$\theta_{2}$ = 121° $\pm$ 2°, depending on the considered sense of rotation.
If we allow for a 0.1 mag variability due to albedo spots in the 3D model, the
resulting ellipsoid has a semi-major axis $\sim$ 10 km smaller and fully
compatible with the projected shape in Benedetti-Rossi et al. (2019). These
values give a spherical-volume equivalent diameter of $D_{\mathrm{V_{eq}}}$ =
524 $\pm$ 7 $\mathrm{km}$. This solution is not compatible with a homogeneous
body in hydrostatic equilibrium rotating with the known period of 2003 VS2,
requiring differentiation or, most likely, an internal structure that can
sustain stress to some degree.

We found no evidence of a dense ring or debris material orbiting around 2003
VS2, of the type seen in Chariklo (Braga-Ribas et al. 2014).

###### Acknowledgements.

We acknowledge financial support from the State Agency for Research of the
Spanish MCIU through the ”Center of Excellence Severo Ochoa” award to the
Instituto de Astrofísica de Andalucía (SEV-2017-0709). Funding from Spanish
projects PID2020-112789GB-I00 from AEI and Proyecto de Excelencia de la Junta
de Andalucía PY20-01309 is acknowledged. Part of the research leading to these
results has received funding from the European Research Council under the
European Community’s H2020 (2014-2020/ERC Grant Agreement no. 669416 “LUCKY
STAR”). M.V-L. acknowledges funding from Spanish project AYA2017-89637-R
(FEDER/MICINN). P.S-S. acknowledges financial support by the Spanish grant
AYA-RTI2018-098657-J-I00 “LEO-SBNAF”. Part of the work of M.P. was financed by
a grant of the Romanian National Authority for Scientific Research and
Innovation, CNCS - UEFISCDI, PN-III-P1-1.1-TE-2019-1504. E.F.-V. acknowledges
financial support from the Florida Space Institute and the Space Research
Initiative. The following authors acknowledge the respective CNPq grants:
F.B-R 309578/2017-5; B.E.M. 150612/2020-6; RV-M 304544/2017-5, 401903/2016-8;
J.I.B.C. 308150/2016-3 and 305917/2019-6; M.A 427700/2018-3, 310683/2017-3 and
473002/2013-2. D.I. and O.V. acknowledge funding provided by the Ministry of
Education, Science, and Technological Development of the Republic of Serbia
(contracts 451-03-9/2021-14/200104, 451-03-9/2021-14/200002). D.I.
acknowledges the support of the Alexander von Humboldt Foundation. M.H. thanks
the Slovak Academy of Sciences (VEGA No. 2/0059/22) and the Slovak Research
and Development Agency under the Contract No. APVV-19-0072. This work has also
been supported by the VEGA grant of the Slovak Academy of Sciences No.
2/0031/18. A.P., R.S. and C.K. acknowledge the grant of K-138962 of National
Research, Development and Innovation Office (Hungary). This study was financed
in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -
Brasil (CAPES) - Finance Code 001 and the National Institute of Science and
Technology of the e-Universe project (INCT do e-Universo, CNPq grant
465376/2014-2). This work has made use of data from the European Space Agency
(ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia
Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This research is partially
based on observations collected at the Centro Astronómico Hispano-Alemán
(CAHA) at Calar Alto, operated jointly by Junta de Andalucía and Consejo
Superior de Investigaciones Científicas (IAA-CSIC). This research is also
partially based on observations carried out at the Observatorio de Sierra
Nevada (OSN) operated by Instituto de Astrofísica de Andalucía (CSIC). This
article is also based on observations made in the Observatorios de Canarias
del IAC with the Liverpool Telescope operated on the island of La Palma by the
Instituto de Astrofísica de Canarias in the Roque de los Muchachos
Observatory.

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##  Appendix A Observing sites involved in the occultation campaign that could
not observe

In this appendix we include the list of contacted observing sites that could
not observe due to bad weather or technical problems.

Table 8: Details of the observing sites involved in the 2003 VS2 2019 October 22 occultation that could not observe. Site name | Latitude (N) | Telescope |  |
---|---|---|---|---
Location | Longitude (E) | aperture | Observers | Problem
MPC Code |  | (cm) |  |
Galaţi Observatory ($\times$2) | 45° 25′ 7$\aas@@fstack{\prime\prime}$9 | 40 | O. Tercu |
Romania | 28° 1′ 57″ | 20 | A. M. Stoian | Bad Weather
C73 |  |  | G. Neagu |
|  |  | D.Zlat |
Astroclubul Bucureşti ($\times$2) | – | 40 | D. Berteşteanu |
Romania (mobile telescope) |  | 20 | M. H. Naiman | Technical problems
– |  |  | Z. Deak |
| – |  |  |
Romania (mobile telescope) |  | 20 | B. Dumitru | Technical problems
– |  |  |  |
Bârlad Observatory | 46° 13′ 54$\aas@@fstack{\prime\prime}$1 |  |  |
Romania | 27° 40′ 10$\aas@@fstack{\prime\prime}$2 | 20 | C. Vantdevara | Bad weather
L22 |  |  |  |
G.V.Schiaparelli Observatory | 45° 52′ 04″ |  |  |
Varese, Italy |  $-$08° 46′ 15″ | 84 | L. Buzzi | Bad weather
204 |  |  |  |
San Marcello Pistoiese | 44° 3′ 46$\aas@@fstack{\prime\prime}$9 |  |  |
Italy | 10° 48′ 15$\aas@@fstack{\prime\prime}$1 | 60 | P. Bacci | Technical problems
104 |  |  |  |
ISON Uzhgorod Observatory | 48° 33′ 48$\aas@@fstack{\prime\prime}$2 |  |  |
Derenivka, Ukraine | 22° 27′ 12$\aas@@fstack{\prime\prime}$6 | 40 | V. Kudak | Technical problems
K99 |  |  |  |
Odessa-Mayaki | 46° 23′ 50$\aas@@fstack{\prime\prime}$2 |  | Y. Krugly |
Ukraine | 30° 16′ 18$\aas@@fstack{\prime\prime}$1 | 80 | I. Belskaya | Bad weather
583 |  |  |  |
Zalistci | 48° 50′ 53$\aas@@fstack{\prime\prime}$9 |  | Y. Krugly |
Ukraine | 26° 43′ 5$\aas@@fstack{\prime\prime}$9 | 30 | I. Belskaya | Bad weather
L18 |  |  |  |
Uzhgorod-Derenivka, | 48° 33′ 48$\aas@@fstack{\prime\prime}$2 |  | Y. Krugly |
Ukraine | 22° 27′ 12$\aas@@fstack{\prime\prime}$599 | 40 | I. Belskaya | Bad weather
K99 |  |  |  |
Kyiv-Comet Station | 50° 17′ 52$\aas@@fstack{\prime\prime}$8 |  | Y. Krugly |
Ukraine | 30° 31′ 28$\aas@@fstack{\prime\prime}$6 | 70 | I. Belskaya | Bad weather
585 |  |  |  |
Kharkiv-Chuguev Station | 49° 38′ 34$\aas@@fstack{\prime\prime}$6 |  | Y. Krugly |
Ukraine | 36° 56′ 12$\aas@@fstack{\prime\prime}$8 | 70 | I. Belskaya | Bad weather
121 |  |  |  |
Hvar Observatory | 43° 10′ 42″ |  | D. Ruzdjak |
Hvar, Croatia | 16° 26′ 54″ | 106 | S. Cikota | Bad weather
– |  |  |  |

##  Appendix B Monte Carlo distributions

In this appendix we present the obtained Monte Carlo distributions for the
limb-fitting and the 3D-fitting of 2003 VS2, respectively discussed in Sects.
4.1 and 4.3, for the two considered distributions of the positive chords.

Figure 8: Monte Carlo distributions for the semi-axes a and b (in
$\mathrm{km}$), the tilt angle (in degrees) and the coordinates (x,y) of the
center of the ellipse, from the elliptical fit to the unshifted chords (with
only chord 8 shifted) in Fig. 5a, see Sect. 4.1. The vertical red lines show
the value of the parameters for the best elliptical fit via minimization of
the sum of squared residuals, see Table 6. Figure 9: Monte Carlo distributions
for the semi-axes a and b (in $\mathrm{km}$), the tilt angle (in degrees) and
the coordinates (x,y) of the center of the ellipse, from the elliptical fit to
the aligned chords in Fig. 5b, see Sect. 4.1. The vertical red lines show the
value of the parameters for the best elliptical fit via minimization of the
sum of squared residuals, see Table 6. Figure 10: Monte Carlo distributions
for the semi-axes a, b, and c (in $\mathrm{km}$) of a triaxial ellipsoid
compatible with the occultation observation and observed rotational light
curve amplitude, as well as distributions of the aspect angle and derived
rotational light curve amplitude obtained via Eq. 3, for the case of the
original chords with only chord 8 shifted, see Sects. 4.1 and 4.3. The
vertical red lines show the ellipsoidal values corresponding to the best
elliptical fit, see Table 7. Figure 11: Monte Carlo distributions for the
semi-axes a, b, and c (in $\mathrm{km}$) of a triaxial ellipsoid compatible
with the occultation observation and observed rotational light curve of 2003
VS2, as well as distributions of the aspect angle and derived rotational light
curve amplitude obtained via Eq. 3, for the case of all the chords shifted,
see Sects. 4.1 and 4.3. The vertical red lines show the ellipsoidal values
corresponding to the best elliptical fit, see Table 7.

(a)

(b)

Figure 12: Monte Carlo distributions of the axes-ratios $a/b$ and $b/c$ of the
fitted ellipsoid for the considered case of (a) the chords unshifted with only
chord 8 shifted, and (b) the aligned chords, for the observed rotational light
curve amplitude. The vertical red lines show the axes-ratios derived from the
best elliptical fit, see Table 7. Figure 13: Monte Carlo distributions for the
semi-axes a, b, and c (in $\mathrm{km}$) of a triaxial ellipsoid compatible
with the occultation observation and allowing a minimum rotational light curve
amplitude of 0.18 mag, as well as distributions of the aspect angle and
derived rotational light curve amplitude obtained via Eq. 3, for the case of
the original chords with only chord 8 shifted, see Sects. 4.1 and 4.3. The
vertical red lines show the ellipsoidal values corresponding to the best
elliptical fit, see Table 7. Figure 14: Monte Carlo distributions for the
semi-axes a, b, and c (in $\mathrm{km}$) of a triaxial ellipsoid compatible
with the occultation observation and allowing a minimum rotational light curve
amplitude of 0.18 mag, as well as distributions of the aspect angle and
derived rotational light curve amplitude obtained via Eq. 3, for the case of
all the chords shifted, see Sects. 4.1 and 4.3. The vertical red lines show
the ellipsoidal values corresponding to the best elliptical fit, see Table 7.

(a)

(b)

Figure 15: Monte Carlo distributions of the axes-ratios $a/b$ and $b/c$ of the
fitted ellipsoid for the considered case of (a) the chords unshifted with only
chord 8 shifted, and (b) the aligned chords, if we allow a minimum rotational
light curve amplitude of 0.18 mag. The vertical red lines show the axes-ratios
derived from the best elliptical fit, see Table 7.