# Erratum: Gaia Early Data Release 3

A. Brown, A. Vallenari, T. Prusti, J. de Bruijne, C. Babusiaux, M. Biermann, O. Creevey, D. Evans, L. Eyer, A. Hutton, et al.

► To cite this version:

A. Brown, A. Vallenari, T. Prusti, J. de Bruijne, C. Babusiaux, et al. Erratum: Gaia Early Data Release 3. Astronomy and Astrophysics - A&A, 2021, 650, pp.C3. 10.1051/0004-6361/202039657e . hal-03385137

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Submitted on 16 Nov 2021

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<figure><img src="image_1.png" /></figure>
# Gaia Early Data Release 3

## Summary of the contents and survey properties

## (Corrigendum)

Gaia Collaboration: A. G. A. Brown¹,*, A. Vallenari², T. Prusti³, J. H. J. de Bruijne³, C. Babusiaux⁴,⁵, M. Biermann⁶, O. L. Creevey⁷, D. W. Evans⁸, L. Eyer⁹, A. Hutton¹⁰, F. Jansen³, C. Jordi¹¹, S. A. Klioner¹², U. Lammers¹³, L. Lindegren¹⁴, X. Luri¹¹, F. Mignard⁷, C. Panem¹⁵, D. Pourbaix¹⁶,¹⁷, S. Randich¹⁸, P. Sartoretti⁵, C. Soubiran¹⁹, N. A. Walton⁸, F. Arenou⁵, C. A. L. Bailer-Jones²⁰, U. Bastian⁶, M. Cropper²¹, R. Drimmel²², D. Katz⁵, M. G. Lattanzi²²,²³, F. van Leeuwen⁸, J. Bakker¹³, C. Cacciari²⁴, J. Castañeda²⁵, F. De Angeli⁸, C. Ducourant¹⁹, C. Fabricius¹¹, M. Fouesneau²⁰, Y. Frémat²⁶, R. Guerra¹³, A. Guerrier¹⁵, J. Guiraud¹⁵, A. Jean-Antoine Piccolo¹⁵, E. Masana¹¹, R. Messineo²⁷, N. Mowlavi⁹, C. Nicolas¹⁵, K. Nienartowicz²⁸,²⁹, F. Pailler¹⁵, P. Panuzzo⁵, F. Riclet¹⁵, W. Roux¹⁵, G. M. Seabroke²¹, R. Sordo², P. Tanga⁷, F. Thévenin⁷, G. Gracia-Abril³⁰,⁶, J. Portell¹¹, D. Teyssier³¹, M. Altmann⁶,³², R. Andrae²⁰, I. Bellas-Velidis³³, K. Benson²¹, J. Berthier³⁴, R. Blomme²⁶, E. Brugaletta³⁵, P. W. Burgess⁸, G. Busso⁸, B. Carry⁷, A. Cellino²², N. Cheek³⁶, G. Clementini²⁴, Y. Damerdji³⁷,³⁸, M. Davidson³⁹, L. Delchambre³⁷, A. Dell'Oro¹⁸, J. Fernández-Hernández⁴⁰, L. Galluccio⁷, P. García-Lario¹³, M. Garcia-Reinaldos¹³, J. González-Núñez³⁶,⁴¹, E. Gosset³⁷,¹⁷, R. Haigron⁵, J.-L. Halbwachs⁴², N. C. Hambly³⁹, D. L. Harrison⁸,⁴³, D. Hatzidimitriou⁴⁴, U. Heiter⁴⁵, J. Hernández¹³, D. Hestroffer³⁴, S. T. Hodgkin⁸, B. Holl⁹,²⁸, K. Janßen⁴⁶, G. Jevardat de Fombelle⁹, S. Jordan⁶, A. Krone-Martins⁴⁷,⁴⁸, A. C. Lanzafame³⁵,⁴⁹, W. Löffler⁶, A. Lorca¹⁰, M. Manteiga⁵⁰, O. Marchal⁴², P. M. Marrese⁵¹,⁵², A. Moitinho⁴⁷, A. Mora¹⁰, K. Muinonen⁵³,⁵⁴, P. Osborne⁸, E. Pancino¹⁸,⁵², T. Pauwels²⁶, J.-M. Petit⁵⁵, A. Recio-Blanco⁷, P. J. Richards⁵⁶, M. Riello⁸, L. Rimoldini²⁸, A. C. Robin⁵⁵, T. Roegiers⁵⁷, J. Rybizki²⁰, L. M. Sarro⁵⁸, C. Siopis¹⁶, M. Smith²¹, A. Sozzetti²², A. Ulla⁵⁹, E. Utrilla¹⁰, M. van Leeuwen⁸, W. van Reeven¹⁰, U. Abbas²², A. Abreu Aramburu⁴⁰, S. Accart⁶⁰, C. Aerts⁶¹,⁶²,²⁰, J. J. Aguado⁵⁸, M. Ajaj⁵, G. Altavilla⁵¹,⁵², M. A. Álvarez⁶³, J. Álvarez Cid-Fuentes⁶⁴, J. Alves⁶⁵, R. I. Anderson⁶⁶, E. Anglada Varela⁴⁰, T. Antoja¹¹, M. Audard²⁸, D. Baines³¹, S. G. Baker²¹, L. Balaguer-Núñez¹¹, E. Balbinot⁶⁷, Z. Balog⁶,²⁰, C. Barache³², D. Barbato⁹,²², M. Barros⁴⁷, M. A. Barstow⁶⁸, S. Bartolomé¹¹, J.-L. Bassilana⁶⁰, N. Bauchet³⁴, A. Baudesson-Stella⁶⁰, U. Becciani³⁵, M. Bellazzini²⁴, M. Bernet¹¹, S. Bertone⁶⁹,⁷⁰,²², L. Bianchi⁷¹, S. Blanco-Cuaresma⁷², T. Boch⁴², A. Bombrun⁷³, D. Bossini⁷⁴, S. Bouquillon³², A. Bragaglia²⁴, L. Bramante²⁷, E. Breedt⁸, A. Bressan⁷⁵, N. Brouillet¹⁹, B. Bucciarelli²², A. Burlacu⁷⁶, D. Busonero²², A. G. Butkevich²², R. Buzzi²², E. Caffau⁵, R. Cancelliere⁷⁷, H. Cánovas¹⁰, T. Cantat-Gaudin¹¹, R. Carballo⁷⁸, T. Carlucci³², M. I. Carnerero²², J. M. Carrasco¹¹, L. Casamiquela¹⁹, M. Castellani⁵¹, A. Castro-Ginard¹¹, P. Castro Sampol¹¹, L. Chaoul¹⁵, P. Charlot¹⁹, L. Chemin⁷⁹, A. Chiavassa⁷, M.-R. L. Cioni⁴⁶, G. Comoretto⁸⁰, W. J. Cooper⁸¹,²², T. Cornez⁶⁰, S. Cowell⁸, F. Crifo⁵, M. Crosta²², C. Crowley⁷³, C. Dafonte⁶³, A. Dapergolas³³, M. David⁸², P. David³⁴, P. de Laverny⁷, F. De Luise⁸³, R. De March²⁷, J. De Ridder⁶¹, R. de Souza⁸⁴, P. de Teodoro¹³, A. de Torres⁷³, E. F. del Peloso⁶, E. del Pozo¹⁰, M. Delbo⁷, A. Delgado⁸, H. E. Delgado⁵⁸, J.-B. Delisle⁹, P. Di Matteo⁵, S. Diakite⁸⁵, C. Diener⁸, E. Distefano³⁵, C. Dolding²¹, D. Eappachen⁸⁶,⁶², B. Edvardsson⁸⁷, H. Enke⁴⁶, P. Esquej⁸⁸, C. Fabre⁸⁹, M. Fabrizio⁵¹,⁵², S. Faigler⁹⁰, G. Fedorets⁵³,⁹¹, P. Fernique⁴²,⁹², A. Fienga⁹³,³⁴, F. Figueras¹¹, C. Fouron⁷⁶, F. Fragkoudi⁹⁴, E. Fraile⁸⁸, F. Franke⁹⁵, M. Gai²², D. Garabato⁶³, A. Garcia-Gutierrez¹¹, M. García-Torres⁹⁶, A. Garofalo²⁴, P. Gavras⁸⁸, E. Gerlach¹², R. Geyer¹², P. Giacobbe²², G. Gilmore⁸, S. Girona⁶⁴, G. Giuffrida⁵¹, R. Gomel⁹⁰, A. Gomez⁶³, I. Gonzalez-Santamaria⁶³, J. J. González-Vidal¹¹, M. Granvik⁵³,⁹⁷, R. Gutiérrez-Sánchez³¹, L. P. Guy²⁸,⁸⁰, M. Hauser²⁰,⁹⁸, M. Haywood⁵, A. Helmi⁶⁷, S. L. Hidalgo⁹⁹,¹⁰⁰, T. Hilger¹², N. Hladczuk¹³, D. Hobbs¹⁴, G. Holland⁸, H. E. Huckle²¹, G. Jasniewicz¹⁰¹, P. G. Jonker⁶²,⁸⁶, J. Juaristi Campillo⁶, F. Julbe¹¹, L. Karbevska⁹, P. Kervella¹⁰²

<footnote>* Corresponding author: e-mail: brown@strw.leidenuniv.nl</footnote>
S. Khanna<sup>67</sup>, A. Kochoska<sup>103</sup>, M. Kontizas<sup>44</sup>, G. Kordopatis<sup>7</sup>, A. J. Korn<sup>45</sup>, Z. Kostrzewa-Rutkowska<sup>1,86</sup>, K. Kruszyńska<sup>104</sup>, S. Lambert<sup>32</sup>, A. F. Lanza<sup>35</sup>, Y. Lasne<sup>60</sup>, J.-F. Le Campion<sup>105</sup>, Y. Le Fustec<sup>76</sup>, Y. Lebreton<sup>102,106</sup>, T. Lebzelter<sup>65</sup>, S. Leccia<sup>107</sup>, N. Leclerc<sup>5</sup>, I. Lecoeur-Taibi<sup>28</sup>, S. Liao<sup>22</sup>, E. Licata<sup>22</sup>, H. E. P. Lindstrøm<sup>22,108</sup>, T. A. Lister<sup>109</sup>, E. Livanou<sup>44</sup>, A. Lobel<sup>26</sup>, P. Madrero Pardo<sup>11</sup>, S. Managau<sup>60</sup>, R. G. Mann<sup>39</sup>, J. M. Marchant<sup>110</sup>, M. Marconi<sup>107</sup>, M. M. S. Marcos Santos<sup>36</sup>, S. Marinoni<sup>51,52</sup>, F. Marocco<sup>111,112</sup>, D. J. Marshall<sup>113</sup>, L. Martin Polo<sup>36</sup>, J. M. Martín-Fleitas<sup>10</sup>, A. Masip<sup>11</sup>, D. Massari<sup>24</sup>, A. Mastrobuono-Battisti<sup>14</sup>, T. Mazeh<sup>90</sup>, P. J. McMillan<sup>14</sup>, S. Messina<sup>35</sup>, D. Michalik<sup>3</sup>, N. R. Millar<sup>8</sup>, A. Mints<sup>46</sup>, D. Molina<sup>11</sup>, R. Molinaro<sup>107</sup>, L. Molnár<sup>114,115,116</sup>, P. Montegriffo<sup>24</sup>, R. Mor<sup>11</sup>, R. Morbidelli<sup>22</sup>, T. Morel<sup>37</sup>, D. Morris<sup>39</sup>, A. F. Mulone<sup>27</sup>, D. Munoz<sup>60</sup>, T. Muraveva<sup>24</sup>, C. P. Murphy<sup>13</sup>, I. Musella<sup>107</sup>, L. Noval<sup>60</sup>, C. Ordénovic<sup>7</sup>, G. Orrù,<sup>27</sup>, J. Osinde<sup>88</sup>, C. Pagani<sup>68</sup>, I. Pagano<sup>35</sup>, L. Palaversa<sup>117,8</sup>, P. A. Palicio<sup>7</sup>, A. Panahi<sup>90</sup>, M. Pawlak<sup>118,104</sup>, X. Peñalosa Esteller<sup>11</sup>, A. Penttilä,<sup>53</sup>, A. M. Piersimoni<sup>83</sup>, F.-X. Pineau<sup>42</sup>, E. Plachy<sup>114,115,116</sup>, G. Plum<sup>5</sup>, E. Poggio<sup>22</sup>, E. Poretti<sup>119</sup>, E. Poujoulet<sup>120</sup>, A. Prša<sup>103</sup>, L. Pulone<sup>51</sup>, E. Racero<sup>36,121</sup>, S. Ragaini<sup>24</sup>, M. Rainer<sup>18</sup>, C. M. Raiteri<sup>22</sup>, N. Rambaux<sup>34</sup>, P. Ramos<sup>11</sup>, M. Ramos-Lerate<sup>122</sup>, P. Re Fiorentin<sup>22</sup>, S. Regibo<sup>61</sup>, C. Reylé,<sup>55</sup>, V. Ripepi<sup>107</sup>, A. Riva<sup>22</sup>, G. Rixon<sup>8</sup>, N. Robichon<sup>5</sup>, C. Robin<sup>60</sup>, M. Roelens<sup>9</sup>, L. Rohrbasser<sup>28</sup>, M. Romero-Gómez<sup>11</sup>, N. Rowell<sup>39</sup>, F. Royer<sup>5</sup>, K. A. Rybicki<sup>104</sup>, G. Sadowski<sup>16</sup>, A. Sagristà Sellés<sup>6</sup>, J. Sahlmann<sup>88</sup>, J. Salgado<sup>31</sup>, E. Salguero<sup>40</sup>, N. Samaras<sup>26</sup>, V. Sanchez Gimenez<sup>11</sup>, N. Sanna<sup>18</sup>, R. Santoveña<sup>63</sup>, M. Sarasso<sup>22</sup>, M. Schultheis<sup>7</sup>, E. Sciacca<sup>35</sup>, M. Segol<sup>95</sup>, J. C. Segovia<sup>36</sup>, D. Ségransan<sup>9</sup>, D. Semeux<sup>89</sup>, S. Shahaf<sup>90</sup>, H. I. Siddiqui<sup>123</sup>, A. Siebert<sup>42,92</sup>, L. Siltala<sup>53</sup>, E. Slezak<sup>7</sup>, R. L. Smart<sup>22</sup>, E. Solano<sup>124</sup>, F. Solitro<sup>27</sup>, D. Souami<sup>102,125</sup>, J. Souchay<sup>32</sup>, A. Spagna<sup>22</sup>, F. Spoto<sup>72</sup>, I. A. Steele<sup>110</sup>, H. Steidelmüller<sup>12</sup>, C. A. Stephenson<sup>31</sup>, M. Süveges<sup>28,126,20</sup>, L. Szabados<sup>114</sup>, E. Szegedi-Elek<sup>114</sup>, F. Taris<sup>32</sup>, G. Tauran<sup>60</sup>, M. B. Taylor<sup>127</sup>, R. Teixeira<sup>84</sup>, W. Thuillot<sup>34</sup>, N. Tonello<sup>64</sup>, F. Torra<sup>25</sup>, J. Torra<sup>†11</sup>, C. Turon<sup>5</sup>, N. Unger<sup>9</sup>, M. Vaillant<sup>60</sup>, E. van Dillen<sup>95</sup>, O. Vanel<sup>5</sup>, A. Vecchiato<sup>22</sup>, Y. Viala<sup>5</sup>, D. Vicente<sup>64</sup>, S. Voutsinas<sup>39</sup>, M. Weiler<sup>11</sup>, T. Wevers<sup>8</sup>, Ł. Wyrzykowski<sup>104</sup>, A. Yoldas<sup>8</sup>, P. Yvard<sup>95</sup>, H. Zhao<sup>7</sup>, J. Zorec<sup>128</sup>, S. Zucker<sup>129</sup>, C. Zurbach<sup>130</sup>, and T. Zwitter<sup>131</sup>

*(Affiliations can be found after the references)*

A&A, 649, A1 (2021), https://doi.org/10.1051/0004-6361/202039657

**Key words.** catalogs – astrometry – parallaxes – proper motions – techniques: photometric – errata, addenda

This is a corrigendum for Gaia Collaboration (2021). It corrects errors in Sects. 6.3.2 and 7.2 and Appendix A, which erroneously state that the correction to the G-band fluxes and magnitudes presented in Riello et al. (2021) (their Table 5) should be applied to sources in Gaia EDR3 with six-parameter astrometric solutions. In fact, the corrections should be applied to sources with two-parameter or six-parameter astrometric solutions. The corrected Astronomical Data Query Language (ADQL) query and Python source code from Appendix A are presented in the new version of Appendix A below.

Following the discovery of the above error, a more detailed investigation was done for the sources with two-parameter (2-p) astrometric solutions. Out of the 344 million 2-p sources present in Gaia EDR3, about 20 million have an astrometric solution in which the actual source colour was used instead of a default colour. This means that for these 20 million 2-p sources the G-band correction should actually not be applied. These sources are mostly faint, with 96% at magnitudes G > 20, and for 75% of these 20 million sources the correction that is (wrongly) applied amounts to less than 4 milli-magnitudes. It was thus decided

not to make a special effort to exclude these sources from the correction. Should a user of the Gaia EDR3 data wish to undo the wrong correction for one or more of these 20 million sources, the list of source IDs and applied corrections can be provided on request.

## Appendix A: G-band corrections for sources with two-parameter or six-parameter astrometric solutions

Figure A.1 shows how to formulate an ADQL query, to be executed in the Gaia EDR3 archive, that contains an on-the-fly calculation of the corrected G-band fluxes or magnitudes. These queries are somewhat complex and create a performance overhead. Hence downloading the requisite Gaia EDR3 fields and calculating the corrections a posteriori may be more efficient. Example Python code to do this is included in Fig. A.2. The Python code is also available as a Jupyter notebook<fnref n="1" />.

<footnote n="1">¹ https://github.com/agabrown/gaiaedr3-6p-gband-correction</footnote>
Query that includes a calculation of the G-band flux correction. The condition `bp RP > -20` ensures that no correction is attempted in case the ($G_{BP} - G_{RP}$) colour is not available ('bp RP is not null' does not work). The condition on `random_index` is included to retrieve example data for a random sample of sources.

```sql
select source_id, astrometric_params_solved, bp RP, phot_g_mean_mag, phot_g_meanaim flux,
ifThenElse(
    bp RP > -20,
    case Condition(
        phot_g_meanAIM flux * (1.00525 - 0.02323 * greatest(0.25, least(bp RP, 3)))
            + 0.01740 * power(greatest(0.25, least(bp RP, 3)), 2)
            - 0.00253 * power(greatest(0.25, least(bp RP, 3)), 3)),
        astrometric_params_solved = 31,
        phot_g_meanAIM flux,
        phot_g_meanAIM mag < 13,
        phot_g_meanAIM flux,
        phot_g_meanAIM mag < 16,
        phot_g_meanAIM flux * (1.00876 - 0.02540 * greatest(0.25, least(bp RP, 3)))
            + 0.01747 * power(greatest(0.25, least(bp RP, 3)), 2)
            - 0.00277 * power(greatest(0.25, least(bp RP, 3)), 3))
    ),
    phot_g_meanAIM flux
) as phot_g_meanAIM flux corr
from gaiaedr3.gaia_source
where random_index between 1000000 and 1999999
```

Query that includes a calculation of the G-band magnitude correction. We note the type-cast `to_real()` of the return value of the conditional part of the query.

```sql
select source_id, astrometric_params_solved, bp RP, phot_g_mean_mag, phot_g_meanAIMflux,
ifThenElse(
    bp RP > -20,
    to Real (case Condition(
        phot_g_meanAIM mag - 2.5 * log10((1.00525 - 0.02323 * greatest(0.25, least(bp RP, 3)))
            + 0.01740 * power(greatest(0.25, least(bp RP, 3)), 2)
            - 0.00253 * power(greatest(0.25, least(bp RP, 3)), 3))),
        astrometric_params_solved = 31,
        phot_g_meanAIM mag,
        phot_g_meanAIM mag < 13,
        phot_g_meanAIM mag,
        phot_g_meanAIM mag < 16,
        phot_g_meanAIM mag - 2.5 * log10((1.00876 - 0.02540 * greatest(0.25, least(bp RP, 3)))
            + 0.01747 * power(greatest(0.25, least(bp RP, 3)), 2)
            - 0.00277 * power(greatest(0.25, least(bp RP, 3)), 3)))
    ))
    ,
    phot_g_meanAIM mag
) as phot_g_meanAIM mag corr
from gaiaedr3.gaia_source
where random_index between 5000000 and 5999999
```

<caption>**Fig. A.1.** Example queries that can be submitted to the Gaia archive in ADQL to retrieve corrected G-band photometry.</caption>
import numpy as np

def correct_gband(bp RP, astrometric_params_solved, phot_g_mean_mag, phot_g_mean_flux):

Correct the G-band fluxes and magnitudes for the input list of Gaia EDR3 data.

Parameters

----------

bp RP: float, array_like

The (BP-RP) colour listed in the Gaia EDR3 archive.

astrometric_params_solved: int, array_like

The astrometric solution type listed in the Gaia EDR3 archive.

phot_g_mean_mag: float, array_like

The G-band magnitude as listed in the Gaia EDR3 archive.

phot_g_mean_flux: float, array_like

The G-band flux as listed in the Gaia EDR3 archive.

Returns

-------

The corrected G-band magnitudes and fluxes. The corrections are only applied to
sources with a 2-parameter or 6-parameter astrometric solution fainter than G=13,
for which a (BP-RP) colour is available.

Example

gmag_corr, gflux_corr = correct_gband(bp RP, astrometric_params_solved,
                                     phot_g_mean_mag, phot_g_mean_flux)
"""

if np.isscalar(bp RP) or np.isscalar(astrometric_params_solved) or \
             np.isscalar(phot_g_mean_mag) or np.isscalar(phot_g_mean_flux):
    bp RP = np.float64(bp RP)
    astrometric_params_solved = np.int64(astrometric_params_solved)
    phot_g_mean_mag = np.float64(phot_g_mean_mag)
    phot_g_mean_flux = np.float64(phot_g_mean_flux)

if not (bp RP.shape == astrometric_params_solved.shape \
       == phot_g_mean_mag.shape == phot_g_mean_flux.shape):
    raise ValueError('Function parameters must be of the same shape!')

do_notCorrect = np.isnan(bp RP) | (phot_g_mean_mag < 13) | \
                 (astrometric_params_solved == 31)
brightCorrect = np(logical_not(do_notCorrect) & (phot_g_mean_mag >= 13) & \
                   (phot_g_mean_mag <= 16))
faintCorrect = np(logical_not(do_notCorrect) & (phot_g_mean_mag > 16))
bp RP_c = np.Clip(bp RP, 0.25, 3.0)

correction_factor = np.ones_like(phot_g_mean_mag)
correction_factor[faintCorrect] = 1.00525 - 0.02323*bp RP_c[faintCorrect] + \
    0.01740*np.power(bp RP_c[faintCorrect],2) - \
    0.00253*np.power(bp RP_c[faintCorrect],3)
correction_factor[brightCorrect] = 1.00876 - 0.02540*bp RP_c[brightCorrect] + \
    0.01747*np.power(bp RP_c[brightCorrect],2) - \
    0.00277*np.power(bp RP_c[brightCorrect],3)

gmag_corrected = phot_g_mean_mag - 2.5*np.log10 correc

gflux_corrected = phot_g_mean_flux * correction_factor

return gmag_corrected, gflux_corrected

**Fig. A.2.** Python code for calculating the corrections to the G-band photometry for sources with two-parameter or six-parameter astrometric solutions.
## References

Gaia Collaboration (Brown, A. G. A., et al.) 2021, A&A, 649, A1
Riello, M., De Angeli, F., Evans, D. W., et al. 2021, A&A, 649, A3

<footnote n="1">¹ Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands</footnote>

<footnote n="2">² INAF – Osservatorio astronomico di Padova, Vicolo Osservatorio 5, 35122 Padova, Italy</footnote>

<footnote n="3">³ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands</footnote>

<footnote n="4">⁴ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France</footnote>

<footnote n="5">⁵ GEPI, Observatoire de Paris, Université PSL, CNRS, 5 Place Jules Janssen, 92190 Meudon, France</footnote>

<footnote n="6">⁶ Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg, Mönchhofstr. 12-14, 69120 Heidelberg, Germany</footnote>

<footnote n="7">⁷ Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France</footnote>

<footnote n="8">⁸ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK</footnote>

<footnote n="9">⁹ Department of Astronomy, University of Geneva, Chemin des Mail-lettres 51, 1290 Versoy, Switzerland</footnote>

<footnote n="10">¹⁰ Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain</footnote>

<footnote n="11">¹¹ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain</footnote>

<footnote n="12">¹² Lohrmann Observatory, Technische Universität Dresden, Mommsenstraße 13, 01062 Dresden, Germany</footnote>

<footnote n="13">¹³ European Space Agency (ESA), European Space Astronomy Centre (ESAC), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain</footnote>

<footnote n="14">¹⁴ Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, 22100 Lund, Sweden</footnote>

<footnote n="15">¹⁵ CNES Centre Spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France</footnote>

<footnote n="16">¹⁶ Institut d'Astronomie et d'Astrophysique, Université Libre de Bruxelles CP 226, Boulevard du Triomphe, 1050 Brussels, Belgium</footnote>

<footnote n="17">¹⁷ F.R.S.-FNRS, Rue d'Egmont 5, 1000 Brussels, Belgium</footnote>

<footnote n="18">¹⁸ INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy</footnote>

<footnote n="19">¹⁹ Laboratoire d'astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France</footnote>

<footnote n="20">²⁰ Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany</footnote>

<footnote n="21">²¹ Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK</footnote>

<footnote n="22">²² INAF – Osservatorio Astrofisico di Torino, via Osservatorio 20, 10025 Pino Torinese (TO), Italy</footnote>

<footnote n="23">²³ University of Turin, Department of Physics, Via Pietro Giuria 1, 10125 Torino, Italy</footnote>

<footnote n="24">²⁴ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via Piero Gobetti 93/3, 40129 Bologna, Italy</footnote>

<footnote n="25">²⁵ DAPCOM for Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain</footnote>

<footnote n="26">²⁶ Royal Observatory of Belgium, Ringlaan 3, 1180 Brussels, Belgium</footnote>

<footnote n="27">²⁷ ALTEC S.p.a, Corso Marche, 79, 10146 Torino, Italy</footnote>

<footnote n="28">²⁸ Department of Astronomy, University of Geneva, Chemin d'Ecogia 16, 1290 Versoy, Switzerland</footnote>

<footnote n="29">²⁹ Sednai Sàrl, Geneva, Switzerland</footnote>

<footnote n="30">³⁰ Gaia DPAC Project Office, ESAC, Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain</footnote>

<footnote n="31">³¹ Telespazio Vega UK Ltd for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain</footnote>

<footnote n="32">³² SYRTE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, LNE, 61 avenue de l'Observatoire 75014 Paris, France</footnote>

<footnote n="33">³³ National Observatory of Athens, I. Metaxa and Vas. Pavlou, Palaia Penteli, 15236 Athens, Greece</footnote>

<footnote n="34">³⁴ IMCCE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Univ. Lille, 77 av. Denfert-Rochereau, 75014 Paris, France</footnote>

<footnote n="35">³⁵ INAF – Osservatorio Astrofisico di Catania, via S. Sofia 78, 95123 Catania, Italy</footnote>

<footnote n="36">³⁶ Serco Gestión de Negocios for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain</footnote>

<footnote n="37">³⁷ Institut d'Astrophysique et de Géophysique, Université de Liège, 19c, Allée du 6 Août, 4000 Liège, Belgium</footnote>

<footnote n="38">³⁸ CRAAG – Centre de Recherche en Astronomie, Astrophysique et Géophysique, Route de l'Observatoire Bp 63 Bouzareah 16340 Algiers, Algeria</footnote>

<footnote n="39">³⁹ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK</footnote>

<footnote n="40">⁴⁰ ATG Europe for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain</footnote>

<footnote n="41">⁴¹ ETSE Telecomunicación, Universidade de Vigo, Campus Lagoas-Marcosende, 36310 Vigo, Galicia, Spain</footnote>

<footnote n="42">⁴² Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 11 rue de l'Université, 67000 Strasbourg, France</footnote>

<footnote n="43">⁴³ Kavli Institute for Cosmology Cambridge, Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA</footnote>

<footnote n="44">⁴⁴ Department of Astrophysics, Astronomy and Mechanics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, 15783 Athens, Greece</footnote>

<footnote n="45">⁴⁵ Observational Astrophysics, Division of Astronomy and Space Physics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden</footnote>

<footnote n="46">⁴⁶ Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany</footnote>

<footnote n="47">⁴⁷ CENTRA, Faculdade de Ciências, Universidade de Lisboa, Edif. C8, Campo Grande, 1749-016 Lisboa, Portugal</footnote>

<footnote n="48">⁴⁸ Department of Informatics, Donald Bren School of Information and Computer Sciences, University of California, 5019 Donald Bren Hall, 92697-3440 CA Irvine, USA</footnote>

<footnote n="49">⁴⁹ Dipartimento di Fisica e Astronomia “Ettore Majorana”, Università di Catania, Via S. Sofia 64, 95123 Catania, Italy</footnote>

<footnote n="50">⁵⁰ CITIC, Department of Nautical Sciences and Marine Engineering, University of A Coruña, Campus de Elviña s/n, 15071, A Coruña, Spain</footnote>

<footnote n="51">⁵¹ INAF – Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monte Porzio Catone (Roma), Italy</footnote>

<footnote n="52">⁵² Space Science Data Center - ASI, Via del Politecnico SNC, 00133 Roma, Italy</footnote>

<footnote n="53">⁵³ Department of Physics, University of Helsinki, PO Box 64, 00014 Helsinki, Finland</footnote>

<footnote n="54">⁵⁴ Finnish Geospatial Research Institute FGI, Geodeetinrininne 2, 02430 Masala, Finland</footnote>

<footnote n="55">⁵⁵ Institut UTINAM CNRS UMR6213, Université Bourgogne Franche-Comté, OSU THETA Franche-Comté Bourgogne, Observatoire de Besançon, BP1615, 25010 Besançon Cedex, France</footnote>

<footnote n="56">⁵⁶ STFC, Rutherford Appleton Laboratory, Harwell, Didcot, OX11 0QX, UK</footnote>

<footnote n="57">⁵⁷ HE Space Operations BV for European Space Agency (ESA), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands</footnote>

<footnote n="58">⁵⁸ Dpto. de Inteligencia Artificial, UNED, c/ Juan del Rosal 16, 28040 Madrid, Spain</footnote>

<footnote n="59">⁵⁹ Applied Physics Department, Universidade de Vigo, 36310 Vigo, Spain</footnote>
60 Thales Services for CNES Centre Spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

61 Instituut voor Sterrenkunde, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium

62 Department of Astrophysics/IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The Netherlands

63 CITIC – Department of Computer Science and Information Technologies, University of A Coruña, Campus de Elviña s/n, 15071, A Coruña, Spain

64 Barcelona Supercomputing Center (BSC) - Centro Nacional de Supercomputación, c/ Jordi Girona 29, Ed. Nexus II, 08034 Barcelona, Spain

65 University of Vienna, Department of Astrophysics, Türkenschanzstraße 17, A1180 Vienna, Austria

66 European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany

67 Kapteyn Astronomical Institute, University of Groningen, Landleven 12, 9747 AD Groningen, The Netherlands

68 School of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK

69 Center for Research and Exploration in Space Science and Technology, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore MD, USA

70 GSFC – Goddard Space Flight Center, Code 698, 8800 Greenbelt Rd, 20771 MD Greenbelt, USA

71 EURIX S.r.l., Corso Vittorio Emanuele II 61, 10128 Torino, Italy

72 Harvard-Smithsonian Center for Astrophysics, 60 Garden St., MS 15, Cambridge, MA 02138, USA

73 HE Space Operations BV for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

74 CAUP - Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, Porto, Portugal

75 SISSA - Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136 Trieste, Italy

76 Telespazio for CNES Centre Spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

77 University of Turin, Department of Computer Sciences, Corso Svizzera 185, 10149 Torino, Italy

78 Dpto. de Matemática Aplicada y Ciencias de la Computación, Univ. de Cantabria, ETS Ingenieros de Caminos, Canales y Puertos, Avda. de los Castros s/n, 39005 Santander, Spain

79 Centro de Astronomía - CITEVA, Universidad de Antofagasta, Avenida Angamos 601, Antofagasta 1270300, Chile

80 Vera C Rubin Observatory, 950 N. Cherry Avenue, Tucson, AZ 85719, USA

81 Centre for Astrophysics Research, University of Hertfordshire, College Lane, AL10 9AB, Hatfield, UK

82 University of Antwerp, Onderzoeksgroep Toegepaste Wiskunde, Middelheimlaan 1, 2020 Antwerp, Belgium

83 INAF – Osservatorio Astronomico d’Abruzzo, Via Mentore Magini, 64100 Teramo, Italy

84 Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão, 1226, Cidade Universitaria, 05508-900 São Paulo, SP, Brazil

85 Mésocentre de calcul de Franche-Comté, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, France

86 SRON, Netherlands Institute for Space Research, Sorbonnelaan 2, 3584CA Utrecht, The Netherlands

87 Theoretical Astrophysics, Division of Astronomy and Space Physics, Department of Physics and Astronomy, Uppsala University, Box 516, 751 20 Uppsala, Sweden

88 RHEA for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

89 ATOS for CNES Centre Spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

90 School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel

91 Astrophysics Research Centre, School of Mathematics and Physics, Queen's University Belfast, Belfast BT7 1NN, UK

92 Centre de Données Astronomique de Strasbourg, Strasbourg, France

93 Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Géoazur, Bd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France

94 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany

95 APAVE SUDEUROPE SAS for CNES Centre Spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

96 Área de Lenguajes y Sistemas Informáticos, Universidad Pablo de Olavide, Ctra. de Utrera, km 1. 41013 Sevilla, Spain

97 Onboard Space Systems, Luleå University of Technology, Box 848, 981 28 Kiruna, Sweden

98 TRUMPF Photonic Components GmbH, Lise-Meitner-Straße 13, 89081 Ulm, Germany

99 IAC – Instituto de Astrofísica de Canarias, Via Láctea s/n, 38200 La Laguna S.C., Tenerife, Spain

100 Department of Astrophysics, University of La Laguna, Via Láctea s/n, 38200 La Laguna S.C., Tenerife, Spain

101 Laboratoire Univers et Particules de Montpellier, CNRS Université Montpellier, Place Eugène Bataillon, CC72, 34095 Montpellier Cedex 05, France

102 LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 Place Jules Janssen, 92190 Meudon, France

103 Villanova University, Department of Astrophysics and Planetary Science, 800 E Lancaster Avenue, Villanova PA 19085, USA

104 Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

105 Laboratoire d'astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France

106 Université Rennes, CNRS, IPR (Institut de Physique de Rennes) - UMR 6251, 35000 Rennes, France

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

108 Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen Ø, Denmark

109 Las Cumbres Observatory, 6740 Cortona Drive Suite 102, Goleta, CA 93117, USA

110 Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK

111 IPAC, Mail Code 100-22, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA

112 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, M/S 169-327, Pasadena, CA 91109, USA

113 IRAP, Université de Toulouse, CNRS, UPS, CNES, 9 Av. colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France

114 Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, MTA Centre of Excellence, Konkoly Thege Miklós út 15-17, 1121 Budapest, Hungary

115 MTA CSFK Lendület Near-Field Cosmology Research Group, Konkoly Thege Miklós út 15-17, 1121 Budapest, Hungary

116 ELTE Eötvös Loránd University, Institute of Physics, 1117, Pázmány Péter sétány 1A, Budapest, Hungary

117 Ruđer Bošković Institute, Bijenička cesta 54, 10000 Zagreb, Croatia

118 Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic

119 INAF – Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate (LC), Italy

120 AKKA for CNES Centre Spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

121 Departmento de Física de la Tierra y Astrofísica, Universidad Complutense de Madrid, 28040 Madrid, Spain

122 Vitrociset Belgium for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

123 Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton NJ 08544, USA
124 Departamento de Astrofísica, Centro de Astrobiología (CSIC-INTA), ESA-ESAC. Camino Bajo del Castillo s/n 28692 Villanueva de la Cañada, Madrid, Spain

125 naXys, University of Namur, Rempart de la Vierge, 5000 Namur, Belgium

126 EPFL – Ecole Polytechnique fédérale de Lausanne, Institute of Mathematics, Station 8 EPFL SB MATH SDS, Lausanne, Switzerland

127 H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK

128 Sorbonne Université, CNRS, UMR7095, Institut d'Astrophysique de Paris, 98bis bd. Arago, 75014 Paris, France

129 Porter School of the Environment and Earth Sciences, Tel Aviv University, Tel Aviv 6997801, Israel

130 Laboratoire Univers et Particules de Montpellier, Université Montpellier, Place Eugène Bataillon, CC72, 34095 Montpellier Cedex 05, France

131 Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia