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# Gaia Data Release 3: Stellar multiplicity, a teaser for the hidden treasure

F. Arenou, C. Babusiaux, M. A. Barstow, S. Faigler, A. Jorissen, P. Kervella, T. Mazeh, N. Mowlavi, P. Panuzzo, J. Sahlmann, et al.

► To cite this version:

F. Arenou, C. Babusiaux, M. A. Barstow, S. Faigler, A. Jorissen, et al. Gaia Data Release 3: Stellar multiplicity, a teaser for the hidden treasure. Astronomy and Astrophysics - A&A, 2023, 674, pp.A34. 10.1051/0004-6361/202243782. hal-03857442

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# Gaia Data Release 3
## Stellar multiplicity, a teaser for the hidden treasure

Gaia Collaboration: F. Arenou¹,*, C. Babusiaux²,¹, M. A. Barstow³, S. Faigler⁴, A. Jorissen⁵, P. Kervella⁶, T. Mazeh⁴, N. Mowlavi⁷, P. Panuzzo¹, J. Sahlmann⁸, S. Shahaf⁹, A. Sozzetti¹⁰, N. Bauchet¹, Y. Damerdji¹²,¹¹, P. Gavras⁸, P. Giacobbe¹⁰, E. Gosset¹¹,¹³, J.-L. Halbwachs¹⁴, B. Holl⁷,¹⁵, M. G. Lattanzi¹⁰,¹⁶, N. Leclerc¹, T. Morel¹¹, D. Pourbaix⁵,¹³,†, P. Re Fiorentin¹⁰, G. Sadowski⁵, D. Ségransan⁷, C. Siopis⁵, D. Teyssier¹⁷, T. Zwitter¹⁸, L. Planquart⁵, A. G. A. Brown¹⁹, A. Vallenari²⁰, T. Prusti²¹, J. H. J. de Bruijne²¹, M. Biermann²², O. L. Creevey²³, C. Ducourant²⁴, D. W. Evans²⁵, L. Eyer⁷, R. Guerra²⁶, A. Hutton²⁷, C. Jordi²⁸, S. A. Klioner²⁹, U. L. Lammers²⁶, L. Lindegren³⁰, X. Luri²⁸, F. Mignard²³, C. Panem³¹, S. Randich³², P. Sartoretti¹, C. Soubiran²⁴, P. Tanga²³, N. A. Walton²⁵, C. A. L. Bailer-Jones³³, U. Bastian²², R. Drimmel¹⁰, F. Jansen³⁴,**, D. Katz¹, F. van Leeuwen²⁵, J. Bakker²⁶, C. Cacciari³⁵, J. Castañeda³⁶, F. De Angeli²⁵, C. Fabricius²⁸, M. Fouesneau³³, Y. Frémat³⁷, L. Galluccio²³, A. Guerrier³¹, U. Heiter³⁸, E. Masana²⁸, R. Messineo³⁹, C. Nicolas³¹, K. Nienartowicz⁴⁰,¹⁵, F. Pailler³¹, F. Riclet³¹, W. Roux³¹, G. M. Seabroke⁴¹, R. Sordo²⁰, F. Thévenin²³, G. Gracia-Abril⁴²,²², J. Portell²⁸, M. Altmann²²,⁴³, R. Andrae³³, M. Audard⁷,¹⁵, I. Bellas-Velidis⁴⁴, K. Benson⁴¹, J. Berthier⁴⁵, R. Blomme³⁷, P. W. Burgess²⁵, D. Busonero¹⁰, G. Busso²⁵, H. Cánovas¹⁷, B. Carry²³, A. Cellino¹⁰, N. Cheek⁴⁶, G. Clementini³⁵, M. Davidson⁴⁷, P. de Teodoro²⁶, M. Nuñez Campos²⁷, L. Delchambre¹¹, A. Dell'Oro³², P. Esquej⁸, J. Fernández-Hernández⁴⁸, E. Fraile⁸, D. Garabato⁴⁹, P. García-Lario²⁶, R. Haigron¹, N. C. Hambly⁴⁷, D. L. Harrison²⁵,⁵⁰, J. Hernández²⁶, D. Hestroffer⁴⁵, S. T. Hodgkin²⁵, K. Janßen⁵¹, G. Jevardat de Fombelle⁷, S. Jordan²², A. Krone-Martins⁵²,⁵³, A. C. Lanzafame⁵⁴,⁵⁵, W. Löffler²², O. Marchal¹⁴, P. M. Marrese⁵⁶,⁵⁷, A. Moitinho⁵², K. Muinonen⁵⁸,⁵⁹, P. Osborne²⁵, E. Pancino³²,⁵⁷, T. Pauwels³⁷, A. Recio-Blanco²³, C. Reylé⁶⁰, M. Riello²⁵, L. Rimoldini¹⁵, T. Roegiers⁶¹, J. Rybizki³³, L. M. Sarro⁶², M. Smith⁴¹, E. Utrilla²⁷, M. van Leeuwen²⁵, U. Abbas¹⁰, P. Ábrahám⁶³,⁶⁴, A. Abreu Aramburu⁴⁸, C. Aerts⁶⁵,⁶⁶,³³, J. J. Aguado⁶², M. Ajaj¹, F. Aldea-Montero²⁶, G. Altavilla⁵⁶,⁵⁷, M. A. Álvarez⁴⁹, J. Alves⁶⁷, F. Anders²⁸, R. I. Anderson⁶⁸, E. Anglada Varela⁴⁸, T. Antoja²⁸, D. Baines¹⁷, S. G. Baker⁴¹, L. Balaguer-Núñez²⁸, E. Balbinot⁶⁹, Z. Balog²²,³³, C. Barache⁴³, D. Barbato⁷,¹⁰, M. Barros⁵², S. Bartolomé²⁸, J.-L. Bassilana⁷⁰, U. Becciani⁵⁴, M. Bellazzini³⁵, A. Berihuete⁷¹, M. Bernet²⁸, S. Bertone⁷²,⁷³,¹⁰, L. Bianchi⁷⁴, A. Binnenfeld⁷⁵, S. Blanco-Cuaresma⁷⁶, A. Blazere⁷⁷, T. Boch¹⁴, A. Bombrun⁷⁸, D. Bossini⁷⁹, S. Bouquillon⁴³,⁸⁰, A. Bragaglia³⁵, L. Bramante³⁹, E. Breedt²⁵, A. Bressan⁸¹, N. Brouillet²⁴, E. Brugaletta⁵⁴, B. Bucciarelli¹⁰,¹⁶, A. Burlacu⁸², A. G. Butkevich¹⁰, R. Buzzi¹⁰, E. Caffau¹, R. Cancelliere⁸³, T. Cantat-Gaudin²⁸,³³, R. Carballo⁸⁴, T. Carlucci⁴³, M. I. Carnerero¹⁰, J. M. Carrasco²⁸, L. Casamiquela²⁴,¹, M. Castellani⁵⁶, A. Castro-Ginard¹⁹, L. Chaoul³¹, P. Charlot²⁴, L. Chemin⁸⁵, V. Chiaramida³⁹, A. Chiavassa²³, N. Chornay²⁵, G. Comoretto¹⁷,⁸⁶, G. Contursi²³, W. J. Cooper⁸⁷,¹⁰, T. Cornez⁷⁰, S. Cowell²⁵, F. Crifo¹, M. Cropper⁴¹, M. Crosta¹⁰,⁸⁸, C. Crowley⁷⁸, C. Dafonte⁴⁹, A. Dapergolas⁴⁴, P. David⁴⁵, P. de Laverny²³, F. De Luise⁸⁹, R. De March³⁹, J. De Ridder⁶⁵, R. de Souza⁹⁰, A. de Torres⁷⁸, E. F. del Peloso²², E. del Pozo²⁷, M. Delbo²³, A. Delgado⁸, J.-B. Delisle⁷, C. Demouchy⁹¹, T. E. Dharmawardena³³, S. Diakite⁹², C. Diener²⁵, E. Distefano⁵⁴, C. Dolding⁴¹, H. Enke⁵¹, C. Fabre⁷⁷, M. Fabrizio⁵⁶,⁵⁷, G. Fedorets⁵⁸,⁹³, P. Fernique¹⁴,⁹⁴, F. Figueras²⁸, Y. Fournier⁵¹, C. Fouron⁸², F. Fragkoudi⁹⁵,⁹⁶,⁹⁷, M. Gai¹⁰, A. Garcia-Gutierrez²⁸, M. Garcia-Reinaldos²⁶, M. García-Torres⁹⁸, A. Garofalo³⁵, A. Gavel³⁸, E. Gerlach²⁹, R. Geyer²⁹, G. Gilmore²⁵, S. Girona⁹⁹, G. Giuffrida⁵⁶, R. Gomel⁴, A. Gomez⁴⁹, J. González-Núñez⁴⁶,¹⁰⁰, I. González-Santamaría⁴⁹, J. J. González-Vidal²⁸, M. Granvik⁵⁸,¹⁰¹, P. Guillout¹⁴, J. Guiraud³¹, R. Gutiérrez-Sánchez¹⁷, L. P. Guy¹⁵,¹⁰², D. Hatzidimitriou¹⁰³,⁴⁴, M. Hauser³³,¹⁰⁴, M. Haywood¹, A. Helmer⁷⁰, A. Helmi⁶⁹, M. H. Sarmiento²⁷, S. L. Hidalgo¹⁰⁵,¹⁰⁶, T. Hilger²⁹, N. Hladczuk²⁶,¹⁰⁷, D. Hobbs³⁰, G. Holland²⁵, H. E. Huckle⁴¹, K. Jardine¹⁰⁸, G. Jasniewicz¹⁰⁹, A. Jean-Antoine Piccolo³¹, Ó. Jiménez-Arranz²⁸, J. Juaristi Campillo²², F. Julbe²⁸, L. Karbevska¹⁵,¹¹⁰,

<footnote>* Corresponding author: F. Arenou, e-mail: Frederic.arenou@obspm.fr</footnote>

<footnote>** Retired from ESA.</footnote>

<footnote>† Deceased.</footnote>
S. Khanna<sup>69,10</sup>, G. Kordopatis<sup>23</sup>, A. J. Korn<sup>38</sup>, Á. Kóspál<sup>63,33,64</sup>, Z. Kostrzewa-Rutkowska<sup>19,111</sup>, K. Kruszyńska<sup>112</sup>, M. Kun<sup>63</sup>, P. Laizeau<sup>113</sup>, S. Lambert<sup>43</sup>, A. F. Lanza<sup>54</sup>, Y. Lasne<sup>70</sup>, J.-F. Le Campion<sup>24</sup>, Y. Lebreton<sup>6,114</sup>, T. Lebzelter<sup>67</sup>, S. Leccia<sup>115</sup>, I. Lecoeur-Taibi<sup>15</sup>, S. Liao<sup>116,10,117</sup>, E. L. Licata<sup>10</sup>, H. E. P. Lindstrøm<sup>10,118,119</sup>, T. A. Lister<sup>120</sup>, E. Livanou<sup>103</sup>, A. Lobel<sup>37</sup>, A. Lorca<sup>27</sup>, C. Loup<sup>14</sup>, P. Madrero Pardo<sup>28</sup>, A. Magdaleno Romeo<sup>82</sup>, S. Managau<sup>70</sup>, R. G. Mann<sup>47</sup>, M. Manteiga<sup>121</sup>, J. M. Marchant<sup>122</sup>, M. Marconi<sup>115</sup>, J. Marcos<sup>17</sup>, M. M. S. Marcos Santos<sup>46</sup>, D. Marín Pina<sup>28</sup>, S. Marinoni<sup>56,57</sup>, F. Marocco<sup>123</sup>, D. J. Marshall<sup>124</sup>, L. Martin Polo<sup>46</sup>, J. M. Martín-Fleitas<sup>27</sup>, G. Marton<sup>63</sup>, N. Mary<sup>70</sup>, A. Masip<sup>28</sup>, D. Massari<sup>35</sup>, A. Mastrobuono-Battisti<sup>1</sup>, P. J. McMillan<sup>30</sup>, S. Messina<sup>54</sup>, D. Michalik<sup>21</sup>, N. R. Millar<sup>25</sup>, A. Mints<sup>51</sup>, D. Molina<sup>28</sup>, R. Molinaro<sup>115</sup>, L. Molnár<sup>63,125,64</sup>, G. Monari<sup>14</sup>, M. Monguió<sup>28</sup>, P. Montegriffo<sup>35</sup>, A. Montero<sup>27</sup>, R. Mor<sup>28</sup>, A. Mora<sup>27</sup>, R. Morbidelli<sup>10</sup>, D. Morris<sup>47</sup>, T. Muraveva<sup>35</sup>, C. P. Murphy<sup>26</sup>, I. Musella<sup>115</sup>, Z. Nagy<sup>63</sup>, L. Noval<sup>70</sup>, F. Ocaña<sup>17,126</sup>, A. Ogden<sup>25</sup>, C. Ordenovic<sup>23</sup>, J. O. Osinde<sup>8</sup>, C. Pagani<sup>3</sup>, I. Pagano<sup>54</sup>, L. Palaversa<sup>127,25</sup>, P. A. Palicio<sup>23</sup>, L. Pallas-Quintela<sup>49</sup>, A. Panahi<sup>4</sup>, S. Payne-Wardenaar<sup>22</sup>, X. Peñalosa Esteller<sup>28</sup>, A. Penttilä<sup>58</sup>, B. Pichon<sup>23</sup>, A. M. Piersimoni<sup>89</sup>, F.-X. Pineau<sup>14</sup>, E. Plachy<sup>63,125,64</sup>, G. Plum<sup>1</sup>, E. Poggio<sup>23,10</sup>, A. Prša<sup>128</sup>, L. Pulone<sup>56</sup>, E. Racero<sup>46,126</sup>, S. Ragaini<sup>35</sup>, M. Rainer<sup>32,129</sup>, C. M. Raiteri<sup>10</sup>, P. Ramos<sup>28,14</sup>, M. Ramos-Lerate<sup>17</sup>, S. Regibo<sup>65</sup>, P. J. Richards<sup>130</sup>, C. Rios Diaz<sup>8</sup>, V. Ripepi<sup>115</sup>, A. Riva<sup>10</sup>, H.-W. Rix<sup>33</sup>, G. Rixon<sup>25</sup>, N. Robichon<sup>1</sup>, A. C. Robin<sup>60</sup>, C. Robin<sup>70</sup>, M. Roelens<sup>7</sup>, H. R. O. Rogues<sup>91</sup>, L. Rohrbasser<sup>15</sup>, M. Romero-Gómez<sup>28</sup>, N. Rowell<sup>47</sup>, F. Royer<sup>1</sup>, D. Ruz Mieres<sup>25</sup>, K. A. Rybicki<sup>112</sup>, A. Sáez Núñez<sup>28</sup>, A. Sagristà Sellés<sup>22</sup>, E. Salguero<sup>48</sup>, N. Samaras<sup>37,131</sup>, V. Sanchez Gimenez<sup>28</sup>, N. Sanna<sup>32</sup>, R. Santoveña<sup>49</sup>, M. Sarasso<sup>10</sup>, M. Schultheis<sup>23</sup>, E. Sciacca<sup>54</sup>, M. Segol<sup>91</sup>, J. C. Segovia<sup>46</sup>, D. Semeux<sup>77</sup>, H. I. Siddiqui<sup>132</sup>, A. Siebert<sup>14,94</sup>, L. Siltala<sup>58</sup>, A. Silvelo<sup>49</sup>, E. Slezak<sup>23</sup>, I. Slezak<sup>23</sup>, R. L. Smart<sup>10</sup>, O. N. Snaith<sup>1</sup>, E. Solano<sup>133</sup>, F. Solitro<sup>39</sup>, D. Souami<sup>6,134</sup>, J. Souchay<sup>43</sup>, A. Spagna<sup>10</sup>, L. Spina<sup>20</sup>, F. Spoto<sup>76</sup>, I. A. Steele<sup>122</sup>, H. Steidelmüller<sup>29</sup>, C. A. Stephenson<sup>17,135</sup>, M. Süveges<sup>136</sup>, J. Surdej<sup>11,137</sup>, L. Szabados<sup>63</sup>, E. Szegedi-Elek<sup>63</sup>, F. Taris<sup>43</sup>, M. B. Taylor<sup>138</sup>, R. Teixeira<sup>90</sup>, L. Tolomei<sup>39</sup>, N. Tonello<sup>99</sup>, F. Torra<sup>36</sup>, J. Torra<sup>28,†</sup>, G. Torralba Elipe<sup>49</sup>, M. Trabucchi<sup>139,7</sup>, A. T. Tsounis<sup>140</sup>, C. Turon<sup>1</sup>, A. Ulla<sup>141</sup>, N. Unger<sup>7</sup>, M. V. Vaillant<sup>70</sup>, E. van Dillen<sup>91</sup>, W. van Reeven<sup>142</sup>, O. Vanel<sup>1</sup>, A. Vecchiato<sup>10</sup>, Y. Viala<sup>1</sup>, D. Vicente<sup>99</sup>, S. Voutsinas<sup>47</sup>, M. Weiler<sup>28</sup>, T. Wevers<sup>25,143</sup>, Ł. Wyrzykowski<sup>112</sup>, A. Yoldas<sup>25</sup>, P. Yvard<sup>91</sup>, H. Zhao<sup>23</sup>, J. Zorec<sup>144</sup>, S. Zucker<sup>75</sup>

(Affiliations can be found after the references)

Received 13 April 2022 / Accepted 9 June 2022

## ABSTRACT

**Context.** The Gaia DR3 catalogue contains, for the first time, about 800 000 solutions with either orbital elements or trend parameters for astrometric, spectroscopic, and eclipsing binaries, and combinations of these three.

**Aims.** With this paper, we aim to illustrate the huge potential of this large non-single-star catalogue.

**Methods.** Using the orbital solutions and models of the binaries, we have built a catalogue of tens of thousands of stellar masses or lower limits thereof, some with consistent flux ratios. Properties concerning the completeness of the binary catalogues are discussed, statistical features of the orbital elements are explained, and a comparison with other catalogues is performed.

**Results.** Illustrative applications are proposed for binaries across the Hertzsprung-Russell Diagram (HRD). Binarity is studied in the giant branch and a search for genuine spectroscopic binaries among long-period variables is performed. The discovery of new EL CVn systems illustrates the potential of combining variability and binarity catalogues. Potential compact object companions are presented, mainly white dwarf companions or double degenerates, but one candidate neutron star is also found. Towards the bottom of the main sequence, the orbits of previously suspected binary ultracool dwarfs are determined and new candidate binaries are discovered. The long awaited contribution of Gaia to the analysis of the substellar regime shows the brown dwarf desert around solar-type stars using true rather than minimum masses, and provides new important constraints on the occurrence rates of substellar companions to M dwarfs. Several dozen new exoplanets are proposed, including two with validated orbital solutions and one super-Jupiter orbiting a white dwarf, all being candidates requiring confirmation. Besides binarity, higher order multiple systems are also found.

**Conclusions.** By increasing the number of known binary orbits by more than one order of magnitude, Gaia DR3 will provide a rich reservoir of dynamical masses and an important contribution to the analysis of stellar multiplicity.

**Key words.** binaries: general – astrometry – planetary systems – stars: fundamental parameters – catalogs – white dwarfs

## 1. Introduction

The success of Gaia (Gaia Collaboration 2016b), with parallaxes for around 1.5 billion sources, could overshadow the difficulties faced in measuring the first stellar distances. The two millenia during which this research was unsuccessfully carried out were littered with unrelated but equally fundamental discoveries. In particular, Herschel, following the suggestion by Ramponi to Galileo in 1611 (Siebert 2005), observed pairs of stars in order to measure their differential parallaxes, but did not succed.

Instead, what he demonstrated for the first time, in 1802, was the existence of orbits for these stars, changing their nature from unrelated double stars to binaries, proving that the law of gravitation was universal.

After Bessel obtained the first convincing parallax measurement in 1838, he also deduced in 1844, from the non-linear proper motion of Sirius and Procyon, that there could exist not only visual binaries but also invisible binaries, nowadays referred to as astrometric binaries. Astrometry and binarity have
therefore been intimately linked from the start. Indeed, it was
not until much later, by observing the periodic Doppler shift
of Algol's lines, that Vogel correctly deduced in 1889 that this
latter was due to its orbital motion, making Algol the first
spectroscopic binary. Furthermore, the periodic eclipse of Algol
was hypothesised by John Goodricke in 1782, making this star
also the first eclipsing binary (Leverington 1995).

Since then, binary stars have been found to be important for
deriving the physical properties of stars but also for their fun-
damental role in stellar evolution; understanding the statistical
properties of binary and multiple stars is therefore of utmost
importance for developing our knowledge of the Galaxy. The
properties of companions down to the substellar regime are also
important for understanding stellar formation. Unfortunately,
until now, small sample sizes, selection effects, and the absence
of the required astrometric precision have complicated the anal-
ysis of the various existing ground-based data.

As a large survey, *Gaia* should be in an ideal place to bring a
new and much broader perspective to these fundamental topics.
What makes *Gaia* so unique is its ability to find, and above all,
to parameterise most types of binaries simultaneously, whether
they be visual, astrometric, spectroscopic, or eclipsing, and even
through stellar parametrisation, with a remarkable homogeneity
of epoch, level of calibration accuracy, data reduction, and pro-
cess organisation.

The Gaia precursor, HIPPARCOS, had already discovered and
measured double stars (Lindegren 1997), mostly resolved ones
but also several categories of unresolved astrometric binaries,
which allowed stellar masses to be determined (Söderhjelm et al.
1997; Martin et al. 1997) albeit for only a small number of
sources.

With the successive Gaia DR1 (Gaia Collaboration 2016a),
DR2 (Gaia Collaboration 2018b), and then EDR3 (Gaia
Collaboration 2021a), multiple stars were still not handled, with
analysing single stars already posing a significant challenge, and
these successive releases represent the improvement of calibrat-
tions and source analysis. This does not mean that non-single
stars were absent. Whether double or binaries, they are indeed
present and processing them as single stars seriously degrades
their results. Nevertheless, several flags in the Gaia catalogue
inform us about the potential duplicity, and the combination of
these first Gaia releases with HIPPARCOS data already allowed
the community to detect long-period binaries (Kervella et al.
2019a, 2022; Brandt 2021).

The advent of Gaia DR3 (Gaia Collaboration 2023b) now
presents impressive new data products among which, to quote
only a few, variability (Eyer et al. 2023), radial velocities (RV,
Katz et al. 2023), and astrophysical parameters (Creevey et al.
2023) determined using either high-resolution (RVS) or low-
resolution data (BP-RP photometers, De Angeli et al. 2023) for
a very large fraction of the catalogue. Gaia DR3 also contains the
first analysis of the unresolved binary star contents, covering the
typical binary classes (astrometric, spectroscopic, photometric)
and presented in several tables: two-body orbits, astrometric or
spectroscopic accelerations, and variable binaries. These tables
contain the orbital or trend parameters of the binaries that have
been discovered. Above all, this offers the prospect of deriv-
ing the physical properties of the individual components. This
should also improve the measurements of these systems in the
main catalogue, with better astrometric parameters or systemic
radial velocity.

Although the maturity of the analysis of *Gaia* data now
makes it possible to obtain, for the first time, a multi-type cat-
alogue of binaries that is much larger than has been compiled –
with difficulty – over the previous centuries, it must be stressed
that only a small fraction of the binary content of the main cata-

logue has been analysed for DR3. This data analysis is described
in the documentation (Pourbaix et al. 2022)<fnref n="1" /> and the articles
accompanying this data release, namely Halbwachs et al. (2023),
Holl et al. (2023b), Gosset et al. (in prep.), Mowlavi et al. (2023)
and Siopis (in prep.).

The purposes of this publication are manifold. It is first
intended to describe the possible use cases of the catalogue, illus-
trating in particular the potential complementarity of the differ-
ent data processing chains. This is essentially an appetiser that
shows the quality of the data, highlighting the basic results that
can be readily obtained, in particular estimating masses which
were not part of the non-single star tables. In addition, this per-
formance verification paper acts as a final validation step before
releasing the data. It is beyond the scope of this publication to
explore the data in detail, and we do not intend to compare them
with models or to confirm candidates of various kinds, as these
will be the goals of scientific exploitation by the community,
but we wish to facilitate this exploitation by describing what has
been learnt from our analysis of the data so far.

We start by describing the data content. Useful statistical
properties are then clarified together with what is known about
the selection function. We then focus on orbits, and not on accel-
eration solutions (for astrometry) or trend solutions (for spectro-
scopic binaries), and instead propose a catalogue of masses for
these orbital solutions. From this, we present an impressionis-
tic panorama of the potential of this catalogue concerning basic
statistical properties and candidate sources of various types; for
example EL CVn, compact companions, white dwarfs and high-
mass dwarfs, and then ultracool dwarfs and substellar compan-
ions. Finally, multiple systems are discussed.

## 2. Data description

### 2.1. Table contents

The non-single star (NSS) tables are presented by type of solu-
tion or period range rather than according to binary type. The
first of the four tables, nss_two_body_orbit, contains the
orbital parameters for all three categories, that is, astromet-
ric, spectroscopic, and eclipsing binary, all being unresolved.
The table nssaccelerationAstro contains accelerations or
derivative of this parameter for sources that have an astrometric
motion better described using a quadratic or cubic rather than a
linear proper motion. Similarly, the nss_non_linearspectro
are trend (long-period) solutions of spectroscopic binaries. The
solutions in the nss_vim_f1 table are different in that the pho-
tocentre displacement due to the photometric variability of one
component of fixed binaries required the correction of the astro-
metric parameters (variable-induced movers fixed, VIMF). A
summary of the solutions is given in Table 1.

The astrometric orbits in the nss_two_body_orbit table
have a nssSolution_type name starting with Orbital* and
the orbital parameters are described in Appendix B.1. The spec-
troscopic binaries with either one component being parametrised
(SB1) or both (SB2) have their parameters described in
Appendix B.2 and short periods may have a circular solu-
tion (nssSolution_type = SB1C). As a source may simul-
taneously be, for example, an astrometric binary and a spec-
troscopic binary, combined solutions have been computed in
some cases (nssSolution_type = AstroSpectroSB1). For
the same reason, the EclipsingSpectro solutions are combi-
nations of eclipsing and spectroscopic solutions. However, when
no combination has been performed, then two solutions for the
same source may be present in the nss_two_body_orbit table;

<footnote n="1">¹ https://gea.esac.esa.int/archive/documentation/GDR3/index.html</footnote>
<table><caption>**Table 1.** Content of the four non-single star tables.</caption><thead><tr><th>Table</th><th>nssSolution_type</th><th>Solutions</th><th>Description</th></tr></thead><tbody><tr><td rowspan="2">nssAcceleration_astro</td><td>Acceleration7</td><td>246947</td><td>Second derivatives of position (acceleration)</td></tr><tr><td>Acceleration9</td><td>91268</td><td>Third derivatives of position (jerk)</td></tr><tr><td rowspan="6">nss_two_body_orbit</td><td>Orbital</td><td>134598</td><td>Orbital astrometric solutions</td></tr><tr><td>OrbitalAlternative*</td><td>629</td><td>Orbital astrometric, alternative solutions</td></tr><tr><td>OrbitalTargetedSearch*</td><td>533</td><td>Orbital astrometric, supplementary external input list</td></tr><tr><td>AstroSpectroSB1</td><td>33467</td><td>Combined orbital astrometric + spectroscopic solutions</td></tr><tr><td>SB1 or SB2</td><td>186905</td><td>Orbital spectroscopic solutions</td></tr><tr><td>EclipsingSpectro</td><td>155</td><td>Combined orbital spectroscopic + eclipsing solutions</td></tr><tr><td rowspan="2">nss_non_linearspectro</td><td>EclipsingBinary</td><td>86918</td><td>Orbits of eclipsing binaries</td></tr><tr><td>FirstDegreeTrendSB1</td><td>24083</td><td>First order derivatives of the radial velocity</td></tr><tr><td rowspan="2">nss_vim_fl</td><td>SecondDegreeTrendSB1</td><td>32725</td><td>Second order derivatives of the radial velocity</td></tr><tr><td>VIMF</td><td>870</td><td>Variable-induced movers fixed</td></tr></tbody></table>

**Notes.** The number of solutions is larger than the number of sources. The type of solution *OrbitalAlternative* indicates solutions that are either *OrbitalAlternative* or *OrbitalAlternativeValidated*.

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Magnitude distribution for each solution type in the nss_two_body_orbit table.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Number of solutions for each solution type in the nss_two_body_orbit table as a function of period.</figcaption></figure>

that is, a query by `source_id` may return several solutions. These multiple solutions may indicate either triple systems, or some inconsistency that users may wish to sort out, and then possibly combine these solutions offline.

For the same reason, some sources may also have solutions in several tables simultaneously. To take an example, there are 160 eclipsing binaries that also have a VIMF solution. As the VIMF model should have improved their astrometric solution, and the distance of eclipsing binaries is of interest, this solution should in principle be preferred over the one given in the `gaia_source` table. This potential multiplicity of solutions for a given source explains why the total number of unique NSS sources is 813 687 while the total number of NSS solutions is larger, 839 098.

The distributions of the various orbital solutions with magnitude are shown Fig. 1. As expected, the brightest are the SB1 and SB2, and consequently also their intersection with astrometric binaries, AstroSpectroSB1, and with eclipsing binaries, EclipsingSpectro. The orbital astrometric binaries (brighter than $G < 19$) peak at $G \approx 14$ while the OrbitalTargetedSearch span the entire magnitude range as the sources were given as input list. The eclipsing binaries are the faintest. We note that the NSS eclipsing binaries are a small subset of the ones detected by photometry (Mowlavi et al. 2023), for which an orbital solution has been computed (Siopis, in prep.); we refer to the much more complete vari_eclipsing_binary table for comparison.

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** $G$ apparent magnitude vs. period in the nss_two_body_orbit table.</figcaption></figure>

The distribution of periods, by construction restricted to the nss_two_body_orbit table, is depicted in Fig. 2. The short-period eclipsing and long-period astrometric binaries are nicely bridged by the SBs. Within a few years, Gaia has covered the impressive 0.28–1500-day period range (99% CI) for thousands of sources, which should prove very valuable for the statistics of binary properties. The coverage in the joint distribution of period and magnitude is qualitatively illustrated in Fig. 3.
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Gaia HRD, uncorrected for extinction, for all NSS solutions with a relative parallax error of better than 20%. No selection is done on the photometric quality. The colour scale represents the square root of the relative density of stars. Top: astrometric binaries, (a): all Orbital* solutions plus AstroSpectroSB1, (b): Acceleration solutions, (c): VIMF; bottom: Spectroscopic binaries with (d): SB* orbits and (e): NonLinearSpectro, (f): eclipsing binaries.</figcaption></figure>

The Hertzsprung-Russell diagrams (HRDs) for the various categories are represented Fig. 4 for sources with a parallax signal-to-noise ratio (S/N) >5. We note that the used parallax is that from the NSS solution for what concerns the putative astrometric binaries, while we use the one from the main catalogue for spectroscopic and eclipsing binaries.

## 2.2. Table construction

Although we refer to the online documentation and the articles accompanying this data release for a detailed understanding of the data processing, it is of interest to describe how the NSS data were obtained, starting with their input data selection, as this is one first key to understanding the NSS selection function.

The basic NSS processing procedure selected its input sources from those that had a poor goodness of fit (GoF) in the upstream results, either in the astrometric or in the spectroscopic processing, or from those that were detected as eclipsing variables; the only exception is the OrbitalTargetedSearch (see Sect. 2.2.2), where a predefined source list was given as input to

the astrometric orbital fit, irrespective of their actual GoF in the single star solution.

### 2.2.1. Astrometric binaries: main processing

As Gaia DR3 is the first publication of NSS solutions, we decided to limit the content to the most significant ones, this criterion being relaxed for further releases, and the motivation for this is explained below. The definition of the input source list started after Gaia DR2, where it was assumed that the sources with $ruwe > 1.4$ represented a reasonable threshold for sources with problematic astrometric solutions<fnref n="2" />. A more recent analysis (e.g. Penoyre et al. 2022) appears to suggest that a lower threshold could have been chosen, but this value also has the advantage that it decreases the processing requirements.

To this $ruwe > 1.4$ criterion, $G < 19$ was added in order to keep the best S/N. The sample defined in this way contains many contaminants, partially resolved rather than unresolved

<footnote n="2">² Cf. Gaia DR2 documentation.</footnote>
sources. In particular, for a double star with a projected sep-
aration between components of between ≈9 mas and ≈0.27"
(Lindegren 2022), depending on the magnitude difference, the
epoch position is not exactly on the photocentre<fnref n="3" />, meaning that
the astrometry of such sources is perturbed and the source is
likely to have been selected.

Consequently, the criterion ipd_frac_multi_peak≤2 was added to avoid double stars with a large separation and ipd_gof_harmonic_amplitude < 0.1 was also added to reject pairs with smaller separations. The visibility periods used > 11 criterion was also added (>12 for orbital solutions) in order to avoid spurious solutions<fnref n="4" />.

However, the sample was still polluted, and so another cri-
teration was added, this time based on photometry, as an attempt
to avoid sources with light being contaminated by a neighbour.
For this purpose, we made use of the corrected BP and RP flux
excess factor C* associated to its uncertainty σC*(G) as defined
by Riello et al. (2021, Eqs. (6) and (18)), selecting sources with
|C*| < 1.645σC* only.

2.2.2. Astrometric binaries: alternative processing

As described by Holl et al. (2023b), alternative orbit deter-
mination algorithms have been run on two different input
lists. The first one is based on astrometric binaries that could
not be successfully modelled by any model in the main pro-
cessing pipeline, for which a more complex handling was
attempted, nssSolution_type = OrbitalAlternative*.
These sources originate from the same list as described
in Sect. 2.2.1. The second one is a sample of sources
with detected companions published in the literature,
nssSolution_type = OrbitalTargetedSearch*, where all
sources have been kept for processing.

2.2.3. Spectroscopic binaries

The selection of the sources that had to be treated by
the spectroscopic binary pipeline was based on sources
with enough measurements, and a large enough disper-
sion of these measurements, rejecting stars not having
rv_renormalised_gof > 4, rv_nb_transits ≥ 10, and
3875 K < rv_template_teff < 8125 K, or detected as SB2.
One may notice that there are more than 6000 sources with
a SB solution that have no average radial velocity in the
gaia_source main catalogue. In that case (as in the other cases
where a SB solution is given), the center_of_massVelocity
gives the systemic velocity. The absence of a mean RV for what
concerns SB2s is normal, as the main spectroscopic processing
did not compute this value. For SB1s, it may be useful to
note that the computation had not been performed for the
sources that were considered either peculiar, potentially SB2,
too hot, or with emission lines. Consequently, when some SB
results appear doubtful, it may then be useful to check whether
gaia_source.radialVelocity is NULL for these sources.
More details are given in Gosset et al. (in prep.).

2.2.4. Eclipsing binaries

The input list for candidate eclipsing binaries contained
about 2.1 million sources that can be found in the
vari_eclipsing_binary Gaia DR3 table. Their selection is
described by Mowlavi et al. (2023); see also the online doc-
umentation. The selection of the subset therein for which an
orbital solution has been computed is described by Siopis
(in prep.).

2.3. Output filtering

Once the first processing results were analysed, it appeared that
the cleaning of the input list had still left a very large frac-
tion of spurious solutions. This is why it was decided to keep
the most significant solutions for Gaia DR3: a general filter
was applied to keep those with goodness of fit smaller than 50
and significance >5 (>2 for OrbitalTargetedSearch*). The
significance is computed as the S/N of the semi-major axis
for astrometric orbits, (a₀/σa₀), as the S/N of the acceleration
module for acceleration solutions, and as the S/N of the semi-
amplitude for spectroscopic binaries, (K₁/σK₁). Supplementary
filtering was applied during the processing or at post-processing
level as described for the various models below.

Astrometric binaries: acceleration solutions. One could
naively hope that the estimated accelerations would allow us to
detect binaries of intermediate period and provide some use-
ful information about the binary, such as the minimum mass
producing the given acceleration on the primary. However, the
situation appears more complex. The acceleration values them-
selves are not discussed, and it can be seen that these solutions
improve the baseline solution; for example, the giant branch
appears slightly thinner for an HRD produced using the paral-
laxes from the acceleration solution compared to those from the
main catalogue.

However, two effects conspire to make the interpretation of
the acceleration term unclear. The first one originates from the
organisation of the NSS processing: acceleration solutions were
attempted before any other solutions, and kept if found to be
sufficiently significant with a reasonable GoF. The (unwanted)
effect is that some solutions that could have received a full orbit
parametrisation were not attempted and appear in the NSS cata-
logue with an acceleration solution instead. The second effect is
that an acceleration term can be significant even for short peri-
ods or very long periods. This is demonstrated by the analysis by
Lindegren (2022).

The following filtering has been applied (see documentation
and Halbwachs et al. 2023, for details): the sources which have
been kept are those with significance *s* > 20 and ϖ/σμ >
1.2 *s*¹.⁰⁵ and GoF < 22 for Acceleration7 and ϖ/σμ >
2.1 *s*¹.⁰⁵ and GoF < 25 for Acceleration9. Despite this, it is
known that a large fraction of the acceleration solutions are not
intermediate-period binaries as one would expect, but are rather
short- or long-period binaries instead.

*Astrometric binaries: Orbital solutions.* The processing of
orbital solutions starts by a period search. Unfortunately, this
may lead to the detection of periods related to the scan law,
rather than due to some true periodic motion: partially resolved
objects with fixed position may give a signal depending on the
scanning angle with respect to the orientation of the pair. This
problem is fully analysed by Holl et al. (2023a). Consequently,
most detected periods below ≈100 days were erroneous, leading
to solutions with huge and incorrect mass functions.

<footnote n="3">³ We coined the word ‘Gaiacenter’ in Kervella et al. (2022) by anal-
ogy with the ‘Hippacenter’ defining the actual pointing of the epoch
HIPPARCOS observations of double stars (Martin et al. 1997).</footnote>

<footnote n="4">⁴ Although the DoF is still large enough as there are about 18 astro-
metric observations per visibility period on average, one may still be
cautious with solutions for which there are a low number of visibility
periods.</footnote>
To circumvent this problem, the following filtering was adopted (Halbwachs et al. 2023): parallax $S/N > 20000/\text{period}$, significance $s = a_0/\sigma_{a_0} > 5$, and $s > 158/\sqrt{\text{period}}$, eccentricity_error $<0.182 * \log_{10}(\text{period}) -0.244$.

**Astrometric binaries: alternative processing.** Aggressive post-processing filtering approaches for both samples produced subsets of solutions that were assigned OrbitalAlternative\* and OrbitalTargetedSearch\* solution types, respectively, in the Gaia DR3 archive. For both cases, subsamples of sources that passed a variety of validation procedures were further assigned OrbitalAlternativeValidated and OrbitalTargetedSearchValidated solution types (see Holl et al. 2023b, for details).

Inspection of the OrbitalAlternative solutions reveals that the caveat of unrealistically large inferred companion masses at short orbital periods is not entirely removed. A few percent of spurious solutions still likely contaminates this sample.

**Spectroscopic binaries.** Only the sources with $GoF < 3$, $|center\_of\_mass\_velocity| < 1000 \text{ km s}^{-1}$, $K_1 < 250 \text{ km s}^{-1}$, and efficiency $> 0.1$ were kept, where efficiency is a measure of the correlation between parameters. One of the most important problems found after processing was the presence of many spurious SB detections with short periods. For this reason, the lower confidence threshold on the period was adapted depending on the period itself: it was set to 0.995 for $P < 1$ d, 0.95 for $P > 10$ d, and $-0.045 \log P + 0.995$ in between. For details on this and other filtering during the spectroscopic processing, see Gosset et al. (in prep.).

Despite all this, the comparison of NSS results with catalogues of known binaries shows that for a few percent of the SB1 solutions, the period may still be incorrect, mainly because of the sparse time sampling. When these sources have both an SB1 and Orbital solution, such cases may be spotted by comparing the respective semi-amplitudes. Short periods with large ruwe (e.g. $>1.4$) are frequently suspect; some may be the inner system of a triple system, but most may instead be some kind of aliases of a longer period.

Inspecting the SB1 solutions, an overdensity of solutions with periods around the precession period (62.97 days) can be noted, in particular by selecting sources with large astrometric excess noise (see Fig. 5). These solutions are spurious and due to some offset in the astrometric coordinates, which generates in turn a spurious variation of the computed epoch radial velocities; as this offset depends on the scanning angle, it occurs with a periodicity linked to the precession of the satellite. The inaccuracy of the astrometric coordinates is most probably due to the fact that they are partially resolved binaries or double stars, which is confirmed by the fact that we also see this overdensity when selecting sources with ipd Frac multi peak $> 20$. Holl et al. (2023a) describe the effect of the scanning law on the NSS solutions in more detail.

Spurious SB1 solutions can also be generated by pulsation of the source, as in RR Lyrae and Cepheids. In many cases, the SB1 solution will have the same period as the pulsation, but in other cases, due to the sparse sampling, the pipeline can find a Keplerian fitting solution at a different, typically shorter period. During the release validation, SB1 solutions of sources identified by Gaia as RR Lyrae or Cepheids were removed from the release.

Another source of spurious SB1 solutions is contamination from a nearby, brighter star. As explained by Seabroke et al.

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** $K_1$ semi-amplitude vs. period diagram of SB1 solutions, colour coded according to their astrometric_excess_noise. The diagram shows the presence of an overdensity of solutions at periods near the precession period (marked with a vertical line) with large astrometric excess noise. The histogram at the top shows the density of solutions with astrometric excess noise larger than 1 mas (blue line) and of those with ipd Frac multi peak $> 20$ (orange line).</figcaption></figure>

(2021), and noted by Boubert et al. (2019), the RVS spectrum of sources extracted at a given transit can be contaminated by a nearby source, producing spurious values of the radial velocity. In Gaia DR3, the RVS pipeline includes a deblending algorithm, which is nevertheless limited to spectra with overlapping windows (see Seabroke et al. 2021, for details).

**Eclipsing binaries.** At post-processing, only the sources with $0.2 < efficiency \le 1$ and $g\_rank \ge 0.6$ were kept, where the rank is a measure of the quality of the fit. See the online documentation (Pourbaix et al. 2022, Sect. 7.6) for details.

## 3. Completeness

The resulting NSS dataset is the result of a selection process in three successive steps: (a) the selection of the input list, discussed Sect. 2.2; (b) the sources for which the orbital motion can be preferentially detected by the processing; (c) the filtering done at post processing, indicated Sect. 2.3.

In this section, we give some indications concerning the second step. One main reason for the expected non-uniformity of orbit detections is the number of observations and their temporal distribution. As this is governed by the scanning law of the Gaia satellite (see e.g. Fig. 7), this should appear clearly on a sky plot, and this is discussed in Sect. 3.1.

However, even with a given set of observations, all orbits are not perfectly equivalent. First, the period distribution of astrometric orbits shows a prominent lack of solutions around one year, which was obviously expected due to the difficulty in decoupling the orbital from the parallactic effect. There are other more subtle biases depending on the orbit itself; these are discussed Sect. 3.2. The distribution of solutions is finally discussed within the 100 pc horizon at Sect. 3.3 and the completeness is also studied for HIPPARCOS stars Sect. 4.2.2.
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Sky density factor (Galactic coordinates, healpix level 4, log scale, see text) illustrating the excess or deficit factors of NSS sources compared to their sky average value. Panel a: SB*, panel b: Acceleration, panel c: EclipsingBinary, panel d: Orbital*.</figcaption></figure>

## 3.1. Sky distribution

Over the sky, the distribution of the various solution types shows the expected higher density along the Galactic plane together with a larger excess at high ecliptic latitudes around $l \pm 100^{\circ}$. The latter is due to a larger number of observations, and therefore to a larger probability of detecting periodically variable motions.

However, this tells us little about whether or not the (in)completeness is uniform over the sky. Although we may have for example more eclipsing binaries among young stars, let us assume for a moment that *F*, the true (unknown) fraction of binaries, is uniform over the sky, and that our NSS samples are roughly complete up to some given magnitude $G_{max}$.

Dividing up the sky in healpix (Górski et al. 2005) level 4 equal-area pixels, we note $N_j$ the number of sources up to $G < G_{max}$ in the full Gaia catalogue in a given healpix cell $j$, and $n_j$ the corresponding number of NSS of a given type up to $G < G_{max}$. With $f = \text{med}(n_j/N_j)$, the empirical median of the ratio over the sky as estimate of *F*, we call ‘sky density factor’ $d_j = n_j / f N_j$. This factor gives the up or down factor of the average NSS fraction and should be a noisy value around 1 if *F* is approximately constant over the sky.

Figure 6 shows the sky density factor for several solution types truncated up to a reasonable $G_{max}$ value in healpix level 4 pixels. As this density factor may be attributed to the number of observations available, Fig. 7 presents the ratio of useful observations over the sky for photometry and astrometry, with the same scale for comparison purposes.

For all types of binaries, the expected deficit of sources near the Galactic centre can be seen because of both high density and poor coverage. The distribution of spectroscopic binaries ($G_{RVS-max}$ = 12, Fig. 6a) is also as expected with a smooth pattern of regions with higher numbers of field-of-view transits. The non-uniformity is less expected for eclipsing binaries ($G_{max}$ = 18, Fig. 6c) with a slight excess at the anticentre and an excess – larger than expected from the number of transits – around $l \pm 100^{\circ}$ towards high ecliptic latitudes. For acceleration solutions ($G_{max}$ = 15, Fig. 6b), there is a deficit in the Galactic plane and an excess at high ecliptic latitudes. This is worse for

Orbital solutions ($G_{max}$ = 15, Fig. 6d), which may be due to the fact that orbital solutions require a greater number of observations than acceleration solutions as there are a greater number of parameters to determine. Again, the sky density factor is relative to the average over the sky, meaning that an excess in some regions may rather indicate a deficit in the rest of the sky. Some or part of the above features of the astrometric solutions likely originate from the input source selection, where sources suspected to be resolved doubles were excluded, which is more frequent in the Galactic plane.

## 3.2. Astrometric orbit detection sensitivity as a function of orbital inclination

Gaia is observing sources with a cadence and scan angle $\psi$ determined by its scanning law. Depending on whether a binary system is seen face-on (inclination $i = 0^{\circ}$ or $i = 180^{\circ}$) or edge-on ($i = 90^{\circ}$), the detection probability of the astrometric orbit varies. An edge-on orbit that is oriented north-south and is being observed only with 1D astrometry along the east-west axis is undetectable. This extreme example does not occur for Gaia, but it illustrates that we can expect continuous variation as a function of inclination angle, with edge-on orbits having the lowest detection probability.

To obtain an empirical estimate of the expected dependency, we simulated 50 000 circular orbits ($e = 0, \omega = 0$) with the following fixed parameters: distance 20 pc; period of 500 days; primary mass $1 M_{\odot}$; companion mass of $1 M_{\text{Jup}}$, and hence a semi-major axis of $a_0 = 0.059$ mas for the orbit of the host. The ascending node $\Omega$ was uniformly distributed. We simulated inclinations such that $\cos i$ is uniformly distributed, as expected for isotropic orbit orientation in space.

To each orbit we assigned a realistic Gaia DR3 time sampling with associated scan angles randomly retrieved from approximately 1000 real sources distributed over the entire sky with the aim of averaging scan-law-dependent effects. We then computed the rms dispersion of the AL signal $w_{kl}$, Eq. (B.6), caused by the astrometric orbit only, that is, neglecting proper and parallactic motion. This dispersion shows a clear
<figure><img src="image_9.png" /><figcaption>Fig. 7. Ratio of the number of photometric observations over their median values for G < 18 (left) and the ratio of the number of visibility periods used in astrometry over their median values for G < 15 (right), with the same colour scale (from 1/4 to 4) as Fig. 6.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. Density histograms of simulated orbit signal dispersion as a function of cos i (top) and Ω (bottom). The black solid curve shows the running median value. Top panel: the empirical and analytic models are shown as dashed grey and black lines, respectively. Edge-on orbits have cos i = 0 and face-on configurations have | cos i | = 1.</figcaption></figure>

dependence on inclination angle (see Fig. 8), with the expected minimum for edge-on orbits. The vertical scatter is caused by the variation in the number of assigned Gaia observations and their scan-angle distribution for a particular time-series realisation. The dependence on ascending node (Fig. 8, bottom) is much weaker but noticeable. Because we limited our simulation to circular orbits, there is no dependence on the argument of periastron.

In Appendix C we analytically derive the following expression, Eq. (C.10), for the rms of $w_{kl}$ as a function of $\cos i$, which is valid for one-dimensional (1D) along-scan (AL) observations as used for DR3 (Lindegren et al. 2021) under the assumption of circular orbits and random scan angles:

$$ \text{rms}(w_{kl})(x) = \frac{a_0}{2} \sqrt{1 + x^2} \quad \text{with} \quad x = \cos i. \qquad (1) $$

This dependency is shown as ‘Analytic model’ in Fig. 8. A fit with a quadratic polynomial is also shown as ‘Empirical model’. The analytic model reproduces the data very well, both in absolute amplitude and shape, except for a small amplitude offset which probably reflects the fact that the Gaia scan angles are not random and are sometimes restricted in range.

Because the amplitude of the orbit signal is the principal factor in deciding whether an orbit can be detected<fnref n="5" />, there is no need to simulate the complete processing chain (Halbwachs et al. 2023; Holl et al. 2023b). Our simulations demonstrate that the signal of a face-on orbit is $\sqrt{2}$ larger than that of an edge-on orbit, which means that the former is more likely to be detected.

### 3.3. The Gaia catalogue of nearby stars

A clean catalogue of 331 312 sources within 100 pc of the Sun (Gaia Collaboration 2021b, GCNS) was published together with Gaia EDR3. This catalogue would represent a useful subset for the completeness analysis.

As the NSS parallaxes of Orbital or acceleration solutions may supersede the EDR3 ones, it is of interest to first analyse their potential impact on the GCNS content. One finds 116 orbital sources that would now enter GCNS using the following query:

```sql
SELECT NSS.source_id, GS.phot_g_mean_mag, NSS.parallax, NSS.parallax_error, GS.parallax as gs_parallax, GS.parallax_error as gs_parallax_error
FROM user_dr3int6.nss_two_body_orbit NSS, user_dr3int6.gaia_source GS
LEFT JOIN external.gaiaedr3_gcns_main_1 GCNS ON NSS.source_id = GCNS.source_id
WHERE GCNS.source_id IS NULL AND NSS.source_id = GS.source_id AND NSS.parallax > 10
```

Using a similar query, 89 sources with an acceleration solution would enter GCNS, giving a total of 205 sources. These numbers would change by 13% only if we were to take a $1\sigma$ margin, and so the random errors have a weak influence on this.

Conversely, one may count sources that should no longer belong to GCNS according to their new parallax:

```sql
SELECT NSS.source_id, GS.phot_g_mean_mag, NSS.parallax, NSS.parallax_error, GS.parallax as gs_parallax, GS.parallax_error as gs_parallax_error
FROM user_dr3int6.nss_two_body_orbit NSS, user_dr3int6.gaia_source gs, external.gaiaedr3_gcns_main_1 GCNS
WHERE NSS.source_id = GS.source_id AND NSS.source_id = GCNS.source_id AND NSS.parallax < 10,
```

<footnote n="5">⁵ This holds when neglecting complications with e.g. periods of around 1 yr due to crosstalk with parallax- or scan-angle-dependent effects (Holl et al. 2023a).</footnote>
amounting to 415 sources for orbital solutions plus 413 sources for acceleration solutions, giving a total of 828 sources.

Having $4723+4523 = 9246$ astrometric NSS sources which are in the GCNS, these 828 sources represent 9% of the orbital plus acceleration solutions which may no longer be in the GCNS while 2% may now enter. This means that any study of the NSS completeness within the GCNS should use the NSS parallax rather than the one from the main catalogue.

One may also note that the balance between the number of NSSs that would be rejected from GCNS and the number that would enter illustrates one long-since recognised adverse effect of the random errors (Eddington 1913; Trumpler & Weaver 1953). The parallaxes of NSS sources managed as single stars in DR3 have a significant error, which should now be much reduced in the NSS tables; this, added to the asymmetric distribution of the parallaxes, means that binary sources preferentially entered GCNS that should not belong to it. As the DR3 NSS catalogue contains only a small fraction of the actual unresolved astrometric binaries, using the GCNS to compute a binarity fraction may produce a small positive bias.

As a clarification of the GCNS content using the NSS parallax is outside the scope of this article, we keep the GCNS for reference in what follows. We show the fraction of NSS sources among $G < 19$ GCNS sources as a function of parallax for all solution types (see right panel of Fig. 9). In these figures and the following, we add the AstroSpectroSB1 counts both to orbital solution counts and SB counts, in addition to counting them independently and, for the comparison to be fair, we restricted the ratios to the typical magnitude ranges used respectively for astrometric, spectroscopic, and eclipsing binaries.

What first appears is the conspicuous increase in the fraction of SBs up to 100 pc. One reason for this may be the transition from the $G_{RVS} < 12$ population of dwarfs to giants, as can be seen in Fig. 4d, with the latter having a better intrinsic RV precision at a given apparent magnitude (Katz et al. 2023), and thus a larger binary detection probability; however, a difference in the binary fraction between dwarfs and giants cannot be excluded. Second, contrary to what might have been expected, the total fraction of orbital and acceleration solutions, about 3%, appears roughly constant with distance in the GCNS, despite all the complex filtering that has been applied. For comparison, the fraction of NSSs among DR3 sources (left panel of Fig. 9) shows a drop in astrometric solutions with distance beyond 100 pc, while the fraction of spectroscopic binaries (SB+NSS_non_linearspectro) does not vary as sharply. From this comparison, we retain the fact that even if the absolute value of the astrometric binary fraction is difficult to extrapolate after all the filtering done, the fact that it appears roughly uniform with distance in a first approximation in the GCNS sample means that this sample could be useful for studying the properties of the astrometric binaries.

Consequently, the fraction of NSSs among GCNS may provide useful insights, and Fig. 10 represents this ratio versus $G$ apparent and absolute magnitude of the pair, respectively. The absolute magnitude mg_gspphot originates from the General Stellar Parametrizer from Photometry (GSP-Phot), which computed the astrophysical parameters of stars from the low-resolution BP/RP spectra and is available in the astrophysical_parameters table.

# 4. Caveats

Many validations have been performed and described in the catalogue documentation (Pourbaix et al. 2022), accompanying

papers (Halbwachs et al. 2023; Holl et al. 2023b; Gosset et al., in prep.; Siopis, in prep.), and the independent validation of all catalogues (Babusiaux et al. 2023). Elsewhere in this article, we also check the distribution tails of some parameters which allowed us to discover undesired aspects and we indicate ways to circumvent them. Here, we describe two supplementary tests that draw attention to some properties of the catalogue, the first analysing the distribution of orbital parameters, the second comparing the results to binaries detected externally.

## 4.1. Distributions and biases of astrometric orbit parameters

Under the assumption that the orbits of binary systems are randomly oriented, we can infer the expected distributions in the geometric elements of the corresponding astrometric orbits, that is, the inclination *i*, the argument of periastron $\omega$, and the longitude of the ascending node $\Omega$<fnref n="6" />. In an ideal experiment, we expect to recover uniform distributions in $\cos i$, $\Omega$, and $\omega$. Here, we inspect the observed distributions of these parameters in DR3.

### 4.1.1. Observed distributions of geometric elements in DR3 solutions

Figure 11 shows the distributions of $\cos i$, $\Omega$, and $\omega$ for the solution types Orbital and AstroSpectroSB1. To mitigate effects related to incomplete orbit coverage, we selected solutions with orbital periods shorter than 1000 days, which roughly corresponds to the DR3 time span.

For Orbital solutions, there is a strong modulation in $\cos i$. Although the expected suppression of edge-on orbits is present, the observed distribution deviates significantly from the empirical model defined in Sect. 3.2. For progressively face-on configurations with increasing $|\cos i|$ there is an excess of solutions compared to the model. Beyond the modes $|\cos i| \gtrsim 0.85$, the number of detected almost-face-on orbits drops sharply and far below the expected level. We also observe a smooth modulation of the $\Omega$ distribution<fnref n="7" /> with a single minimum at $\Omega = 90^\circ$ and a bimodal modulation of the $\omega$ distribution with minima at $\omega = 90^\circ$ and $270^\circ$.

For AstroSpectroSB1 solutions resulting from the combined analysis of Gaia astrometry and RVs, the $\cos i$ distribution shows good agreement with the empirical model for edge-on and intermediate configurations without regions of excess detections. However, there is also a clear lack of face-on orbits compared to the empirical expectation. This is influenced by the decreasing orbital RV signature towards face-on orbits. As AstroSpectroSB1 solutions require independent detections in both astrometry and RV, the lack of face-on orbits can be expected. The modulation in $\Omega$ is similar to Orbital solutions but weaker<fnref n="8" /> and there is no apparent modulation in the $\omega$ distribution.

<footnote n="6">⁶ These Campbell elements were computed from the Thiele-Innes coefficients $(A, B, F, G)$ – which are part of the archive table – using standard formulae (e.g. Halbwachs et al. 2023); software tools are available at https://www.cosmos.esa.int/web/gaia/dr3-software-tools</footnote>

<footnote n="7">⁷ The ascending node extracted from the Thiele-Innes coefficients of astrometric orbits is constrained to $\pm 180^\circ$. By convention, the value between 0 and $180^\circ$ is chosen.</footnote>

<footnote n="8">⁸ The $\Omega$ parameter is only constrained by the astrometry data. When deriving it from the AstroSpectroSB1 Thiele-Innes coefficients we neglected the additional RV information that would have allowed us to compute it unambiguously.</footnote>
<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Fraction of NSS solutions among EDR3 sources vs. parallax (**left**) and fraction of NSS sources in GCNS (**right**). In both figures, we added AstroSpectroSB1 counts to Orbital counts and to SB*=SB1+SB2 counts in addition to counting them individually, and we restrict the ratios to $G_{RVS} < 12$ sources only for SB* and NonLinearSpectro, to $G < 19$ for Orbital and Acceleration solutions, and to $G < 20$ for eclipsing binaries.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Fraction of NSS solutions among GCNS sources vs. $G$ apparent magnitude (**left**) and vs. $G$ GSP-Phot absolute magnitude (**right**). The same constraints as mentioned in Fig. 9 have been applied.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Normalised distributions of $\cos i$ (**left**), $\Omega$ (**middle**), and $\omega$ (**right**) parameters. Orbital (solid lines, 122 989 entries) and AstroSpectroSB1 (dashed lines, 29 770 entries) solutions with $P < 1000$ d are shown. The orb6 solutions from the literature (3405 entries, without filter on period) are shown in grey. Left panel: the dotted line shows the empirical model defined in Sect. 3.2, which was re-scaled on the five central histogram bins. Right panel: we have suppressed the circular solutions with $\omega = 0$.</figcaption></figure>

Figure 12 shows the $\cos i$ distributions for systems within 200 pc, where the S/N is on average higher and the astrometric-orbit detection can be expected to be more complete. This is confirmed by the Orbital solutions that follow the empirical model nicely across most of the inclination range. This validates our model for the inclination-dependent detection efficiency of astrometric surveys (Sect. 3.2). The $\Omega$ and $\omega$ distributions for this subset of solutions are approximately uniform. We inspected other astrometric solution types but do not discuss these here because they have fewer (<1000) entries and are therefore less suitable for distribution analyses.

### 4.1.2. Origins of the geometric element biases

Concentrating on the Orbital solutions, we identify three main deviations from the expected uniform distributions in the low-

$S/N$ regime, which comprise most solutions and therefore dominate the overall distributions in Fig. 11: (a) a pronounced suppression of face-on orbits; (b) a smooth modulation of the $\Omega$ distribution with a single minimum; and (c) a bimodal modulation of the $\omega$ distribution.

In Appendix D.1 we identify the origin of features (a) and (b) in the linear fit of the Thiele-Innes coefficients to noisy data and reproduce these biases qualitatively in simulations. The noise bias in the recovered inclination shifts solutions away from face-on configurations leading to the observed excess at intermediate inclinations<fnref n="9" />. A modulation akin to feature (c) can also be caused by noise biases, albeit with a 90° phase shift. In Appendix D.2,

<footnote n="9">⁹ As the survey is not volume-limited, Gaia's sensitivity variation in principle leads to an expected excess of face-on orbit detections. We believe that such effects are secondary in the context of DR3.</footnote>
<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Normalised distributions of $cos i$ within 200 pc for Orbital (solid line, 9106 entries) and AstroSpectroSB1 (grey-filled, 5735 entries) solutions with $P < 1000$ d and $\bar{\omega} > 5$ mas. The dashed line shows the empirical model defined in Sect. 3.2.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 13.** Normalised distributions of $cos i$ for non-circular Orbital solutions with $P < 1000$ d (121 207 entries). The linearised and Monte Carlo estimates are shown as a solid line and a filled grey area, respectively.</figcaption></figure>

we show that feature (c) is instead explained by the application of a semi-major axis significance threshold when selecting the solutions to be published.

### 4.1.3. Geometric elements from Monte Carlo resampled Thiele-Innes coefficients

Instead of using the linearised formulae (e.g. Halbwachs et al. 2023) for converting A, B, F, and G values and uncertainties to $a_0$, $i$, $\Omega$, and $\omega$, one can use Monte Carlo resampling which accounts more accurately for the parameter correlations (Appendix D.3). As an example of the potential effects that this may have, we computed an alternative estimate of the orbital inclination for individual solutions as the median of the resampled Monte Carlo distribution. The difference between linearised and Monte Carlo estimates on the inclination distribution is shown in Fig. 13, where we see that the apparent depletion of face-on orbits is more pronounced when applying the resampling. We note that the resampled distributions of $a_0$, $i$, $\Omega$, and $\omega$ are seldom Gaussian and the median value is not always a good representation. Whether it is advisable to use the linearised estimate or Monte Carlo resampling depends on the particular problem and individual orbital solution.

### 4.1.4. Comparison with known astrometric orbits

Figure 11 also shows the distributions of geometric elements compiled in the “Sixth Catalog of Orbits of Visual Binary Stars”

(orb6, Hartkopf et al. 2001)<fnref n="10" />. The orb6 inclination distribution is bimodal with modes at $|cos i| \approx 0.5$, which could be interpreted as the same signature of lacking face-on orbits as for Gaia Orbital but setting in earlier. The comparison with the simulated inclination biases in Fig. D.1 would then lead to the interpretation that the average S/N is higher for the Gaia orbits than for the orb6 solutions. However, we caution that the orb6 dataset is of heterogeneous nature and such comparisons have to be made more carefully by accounting for differences in period range, significance, and other factors.

The orb6 $\Omega$ distribution does not seem to exhibit the minimum at $\Omega = 90^\circ$ seen for Gaia Orbital. In contrast, the orb6 $\omega$ distribution shows clear modes at $\omega = 90^\circ$ and $270^\circ$, that is, shifted by $90^\circ$ relative to Gaia Orbital. Our simulations in Fig. D.3 reproduce the peak location for orb6 orbits but not for Orbital solutions.

It is clear that the increase in astrometric orbit solutions by a factor of more than 40 delivered by Gaia DR3 compared to orb6 will facilitate a multitude of population-level studies and push forward our understanding of stellar binary systems.

### 4.1.5. Recommendations

The observed features in the distributions of $i$, $\omega$, and $\Omega$ are the result of variations in the detection sensitivity of the survey, of selection effects, and of biases that are introduced in the astrometric non-single star processing. Their presence is not specific to Gaia and astrometric orbits in the literature show similar features. The geometric elements of DR3 orbits are encoded in the Thiele-Innes coefficients and different conversion methods can be applied depending on the use case and individual solution. Both the distribution features and the conversion aspects have to be considered in scientific analyses of Gaia DR3 orbital parameters and their distributions.

## 4.2. Proper motion anomaly of HIPPARCOS stars of the NSS sample

### 4.2.1. Comparison sample

In this section, we compare the properties of the HIPPARCOS stars based on the proper-motion anomaly (PMa) approach (Kervella et al. 2022; see also Brandt 2021) and the NSS analysis. The PMa approach is described in detail by Kervella et al. (2019a). The general principle is to look for a difference in proper motion (PM) between the long-term PM computed from the HIPPARCOS (epoch 1991.25; van Leeuwen 2007a, see also ESA 1997) and Gaia DR3 (2016.0; Gaia Collaboration 2021a) astrometric ($\alpha$, $\delta$) positions on the one hand and the individual short-term PM vector from the Gaia DR3 catalogue on the other. For a single star, the long-term PM is identical to the short-term PM measured by Gaia, as its space velocity is constant with time. For a binary star, the short-term PM includes in addition the tangential component of the orbital velocity of its photocentre. As the latter is changing with time over the orbital period of the system, a deviation appears between the short-term and long-term PMs of the star which is due to the curvature of its sky trajectory. The PMa, namely, the difference between the short-term and long-term PM, is therefore an efficient and sensitive indicator of non-single stars.

<footnote n="10">¹⁰ We retrieved http://www.astro.gsu.edu/wds/orb6/orb6_orbits.sql on 2022-02-11 and did not remove orbits with two independent solutions or apply any other filters.</footnote>
In order to compare the NSS catalogue with the PMa approach, we cross-matched the NSS catalogue with the PMa catalogue<fnref n="11" /> of Kervella et al. (2022), which covers 116 343 HIPPARCOS stars. This resulted in a list of 2767 common targets with astrometric NSS Acceleration7 or Acceleration9 solutions and 5416 stars with Orbital, AstroSpectroSB1, or OrbitalTargetedSearch* orbital solutions. In addition, 4385 HIPPARCOS targets are listed in the NSS tables with EclipsingBinary (photometric), SB1 or SB2 (radial velocity) solutions. Overall, 12 568 HIPPARCOS/PMa stars have an entry in the NSS catalogue, that is, 10.8% of the HIPPARCOS/PMa catalogue.

### 4.2.2. Completeness of the NSS sample for HIPPARCOS stars

The Gaia stars that are present in the NSS catalogue were selected based on criteria on parameters from their single-star solutions tailored to identify the most probable binaries. For the astrometric solutions based on astrometry, this includes the presence of a ruwe higher than 1.4 in their single-star solution. As pointed out by Belokurov et al. (2020) and Stassun & Torres (2021), this criterion is efficient at identifying the stars that host partially resolved companions. Furthermore, based on the PMa analysis, the binary fraction was found to remain high for ruwe values lower than 1.4 by Kervella et al. (2022) with for example 30% of the stars with ruwe ≈ 1.2 exhibiting a PMa $S/N > 3$ (their Fig. 11). As a consequence, the degree of completeness of the star sample present in the NSS is likely relatively low because of its selection threshold on the ruwe value. To estimate the completeness of the NSS for the HIPPARCOS stars, we first applied to the PMa catalogue the same selection criteria as the NSS input sources (Sect. 2.2.1) – except the condition ruwe > 1.4 – resulting in a subsample of 92 240 stars (79.3%). Within this subsample, 28 111 stars are high-probability astrometric binaries as their PMa $S/N > 3$. Restricting the count to the NSS stars that have an astrometric solution (Acceleration7, Acceleration9, Orbital, AstroSpectroSB1 or OrbitalTargetedSearch*), we obtain a completeness level of the NSS catalogue relative to the PMa catalogue of 8183/28 111 = 29.1%.

However, this high-level estimate based on global target numbers does not directly reflect the actual efficiency of the NSS reduction in detecting that a star is a binary or not compared to the PMa technique. To estimate this efficiency, we consider the same initial sample – following the NSS selection criteria including ruwe > 1.4 – and we derive the fraction of stars with an NSS solution within this common sample. The results are listed in Table 2. Overall, the astrometric solutions provided in the NSS catalogue represent 41% of the potential binaries present in the NSS reference sample, compared to 92% for the PMa catalogue.

In summary, because of the stringent selection of the solutions for the NSS, the catalogue comprises approximately 40% of the binaries from the HIPPARCOS–Gaia PMa catalogue that were potentially detectable from Gaia astrometry alone.

### 4.2.3. Statistics of the proper motion anomaly of NSS targets

The PMa is an efficient tracer of the presence of a massive orbiting companion, but its sensitivity is limited by two factors. Firstly, the time baseline between HIPPARCOS and Gaia (24.75 years), although long, significantly reduces the PMa sig-

<table><caption>**Table 2.** Comparison of the PMa and NSS astrometric detection rate on the common HIPPARCOS star sample.</caption><thead><tr><th></th><th>Number</th><th>Fraction</th></tr></thead><tbody><tr><td>Objects eligible to NSS & PMa</td><td>14 748</td><td>100.0%</td></tr><tr><td>PMa S/N &lt; 3 and absent from NSS</td><td>2254</td><td>15.3%</td></tr><tr><td>PMa S/N &gt; 3 and absent from NSS</td><td>7320</td><td>49.6%</td></tr><tr><td>PMa S/N &lt; 3 and present in NSS</td><td>950</td><td>6.4%</td></tr><tr><td>PMa S/N &gt; 3 and present in NSS</td><td>4224</td><td>28.6%</td></tr><tr><td>Total non-single stars (PMa or NSS)</td><td>12 494</td><td>100.0%</td></tr><tr><td>Non-single stars detected from PMa</td><td>11 544</td><td>92.4%</td></tr><tr><td>Non-single stars present in NSS</td><td>5174</td><td>41.4%</td></tr></tbody></table>

nature of companions with orbital periods longer than approximately three times the HIPPARCOS–Gaia time, that is, 75 yr. Secondly, the fact that the Gaia DR3 proper motions are the result of an averaging over a time window of 34 months strongly smears out the signature of companions with orbital periods shorter than approximately 4 yr. In summary, the PMa technique is most sensitive for companions with orbital periods of between ≈4 and 75 yr. On the other hand, the capacity to determine orbital solutions directly from Gaia astrometry (or radial velocity) time series is significantly higher for binaries with periods of shorter than the Gaia DR3 measurement window. The longer periods remain detectable, mostly up to about twice the measurement window. However, the astrometric displacement of long-period binaries is generally detected only as an acceleration, that is, without a period determination.

Figure 14 shows the histograms of the number of NSSs with different kinds of solutions as a function of their PMa $S/N$. The five histograms that are colour coded in blue correspond to NSS solutions that include the Gaia DR3 astrometry either exclusively (Acceleration7, Acceleration9, Orbital) or in conjunction with spectroscopic radial velocities (AstroSpectroSB1) or previously known substellar orbital parameters (OrbitalTargetedSearch*). The eclipsing binary stars (EclipsingBinary; green colour) are characterised from the Gaia photometric data, and the spectroscopic binaries (SB1, SB2; yellow colour) rely on the spectroscopic radial velocities measured by the Gaia RVS (Cropper et al. 2018; Katz et al. 2019).

### 4.2.4. Orbital periods and sensitivity

Almost all the HIPPARCOS targets with an Acceleration7 or Acceleration9 solution show a significant PMa signal. This behaviour is expected for two reasons: (1) The NSS astrometric solutions were selected among the Gaia sources with a ruwe larger than 1.4. This favours partially resolved binary stars, which often have orbital periods within the sensitivity range of the PMa technique. (2) For orbital periods longer than the Gaia measurement window, the PMa and the acceleration are physically similar quantities, both related to the curvature of the sky trajectory of the star.

The NSS catalogue stars with Orbital or AstroSpectro SB1 solutions generally have shorter orbital periods than the Gaia DR3 time window. Because of the time smearing of the Gaia EDR3 proper motions, this usually prevents the production of a clear signature in PMa. Nevertheless, approximately two-thirds of the stars of these NSS classes exhibit a significant PMa signal with $S/N > 3$ (Fig. 14). As shown in Fig. 15, the

<footnote n="11">¹¹ Available through the CDS/VizieR service as catalogue J/A+A/657/A7/tablea1.</footnote>
<figure><img src="image_16.png" /><figcaption>**Fig. 14.** Histogram of the number of NSS stars with different solution types that are present in the HIPPARCOS catalogue, as a function of the S/N of their Gaia DR3 proper motion anomaly from Kervella et al. (2022). The total number of targets *N* and the fraction of stars with a PMa S/N larger than 3 is displayed in each panel.</figcaption></figure>

longer Gaia EDR3 time window compared to the DR2 results in a decrease of the PMa S/N for the binaries whose orbital period is shorter than ≈1000 days. This is caused by the stronger time smearing of the astrometric signal by the integration window in the Gaia DR3 compared to that of the DR2, which is not compensated by the increase in measurement accuracy in the Gaia DR3. The systems with shorter orbital periods than the Gaia integration window exhibit a median PMa *S/N* ≈ 3. This indicates that despite the smearing, statistically, the mean Gaia PM vector still contains a significant signature of the binarity. The vast majority of Gaia NSS targets with orbital periods longer than the Gaia time window (both for the DR2 and EDR3) exhibit a significant PMa *S/N* > 3.

### 4.2.5. Long-term HIPPARCOS–Gaia proper motion

Here we compare the long-term proper motion deduced from the difference in position between the HIPPARCOS (1991.25) and Gaia DR3 (2016.0) epochs by Kervella et al. (2022; hereafter $\mu_{HG}$) with the short-term proper motion as determined in the NSS catalogue ($\mu_{NSS}$). Figure 16 shows the observed differences $\Delta\mu = \mu_{NSS} - \mu_{HG}$ between these two quantities for the HIPPARCOS catalogue stars with either accelerations (Acceleration7, Acceleration9) or orbital (Orbital, AstroSpectroSB1) solutions in the NSS. There is a significantly larger divergence of the long-term proper motions between the stars with NSS accelerations only for which $\sigma(\Delta\mu) \approx 2.6$ mas a$^{-1}$ than for the stars with an orbital solution for which $\sigma(\Delta\mu) \approx 0.1$ mas a$^{-1}$. The relatively poor agreement for the NSS acceleration stars may be explained by the fact that the measurement of the curvature of the sky trajectory is significantly easier with the longer HIPPARCOS–Gaia temporal baseline. For the full NSS orbital solutions, the agreement between the HIPPARCOS–Gaia PM and the NSS PM is remarkably good, demonstrating that the orbital fit procedure does not introduce systematic biases on the estimation of the mean PM value.

<figure><img src="image_17.png" /><figcaption>**Fig. 15.** Proper motion anomaly S/N as a function of the NSS catalogue orbital period for the DR2 PMa (top panel) from Kervella et al. (2019a); and the EDR3 PMa (bottom panel) from Kervella et al. (2022). The horizontal dashed line indicates the PMa *S/N* = 3 significance limit.</figcaption></figure>

## 5. Catalogue of masses

As the `nss_two_body_orbit` table only gives access to the orbital parameters, it was found desirable to provide an estimate of the masses, the flux ratio, or the lower and upper limits of these, wherever possible. Here, we describe the construction and content of the table `binary_masses` which is made available in the Gaia archive.
<figure><img src="image_18.png" /><figcaption>Fig. 16. Comparison of the long-term proper motions determined from the HIPPARCOS and Gaia DR3 positions $\mu_{HG}$ with the Gaia DR3 proper motions $\mu_{NSS}$ for NSS stars with acceleration solutions (left panel) and orbital solutions (right panel). We highlight the different scales.</figcaption></figure>

## 5.1. Computation of the masses

The astrometric binaries give access to an astrometric mass function which depends on the flux ratio ($F_2/F_1$) of the components:

$$ (M_1 + M_2) \left( \frac{M_2}{M_1 + M_2} - \frac{F_2/F_1}{1 + F_2/F_1} \right)^3 = \frac{(a_0/\bar{\sigma})^3}{(P/365.25)^2}, \quad (2) $$

while the spectroscopic binaries provide a spectroscopic mass function which also depends on the inclination:

$$ f(M) = \frac{M_2^3 \sin^3 i}{(M_1 + M_2)^2} = 1.0385 \times 10^{-7} K_1^3 (1 - e^2)^{3/2} P, \quad (3) $$

with P the period in days and $K_1$ the semi-amplitude of the primary in km s⁻¹. For AstroSpectroSB1, we have access to the Thiele Innes coefficients instead of $K_1$ which leads to the equivalent formula:

$$ \frac{M_2^3 \sin^3 i}{(M_1 + M_2)^2} = \frac{(C^2 + H^2)^{3/2}}{(P/365.25)^2}. \quad (4) $$

The inclination can be provided by an astrometric solution or an eclipsing one. Without the inclination, Eq. (3) only leads to minimum mass function information. When a SB2 solution is provided, we have access to the mass ratio $M_2/M_1 = K_1/K_2$. When a system has a SB2 solution and either an astrometric solution or an eclipsing one, the primary mass can be derived directly from the binary orbital parameters.

Two estimates of $M_1$ are provided in the Gaia DR3 by the FLAME module (Creevey et al. 2023): mass_flame, based on GSP-Phot parameters and available in the astrophysical_parameters table, and mass_flame_spec, based on GSP-Spec parameters and available in the astrophysical_parameters_supp table. However the FLAME masses have three main limitations for our NSS sample: they are based on the parallax from the main catalogue while we now have a more accurate estimate for all astrometric

solutions; these also assume a null flux ratio, which we know is not appropriate for a significant fraction of the NSS solutions, in particular the SB2 ones; these are not available for stars with masses smaller than 0.5 $M_\odot$. We therefore implemented a specific code to derive the mass of the primary that allows us to manipulate the luminosity ratio and is described in detail in Appendix E. These masses are only derived for stars on the main sequence – as estimations for evolved stars are degenerate (e.g. Creevey et al. 2023) – and are referred to hereafter as ‘IsocLum’ masses. For white dwarfs, we simply assumed a fixed mass of 0.65 ± 0.16 $M_\odot$ (Giammichele et al. 2012).

The uncertainties on the masses and flux ratios obtained are derived using a Monte Carlo simulation of 1000 points. We take into account the covariance matrix of the orbital parameters. For $a_0$ as well as for the AstroSpectroSB1 spectroscopic part $a_1 = \sqrt{C^2 + H^2}/\sin i$, we use a Gaussian distribution with a local linearisation error estimation as Monte Carlo techniques are not adapted to the Thiele Innes coefficients (see Babusiaux et al. 2023). Only sources with a significance > 5 are present in NSS solutions, meaning that a Gaussian distribution of the semi-major axis errors is a reasonable assumption. The uncertainties for the SB2 and eclipsing solutions have been re-scaled according to their goodness-of-fit. For the IsocLum masses, we use the full mass distribution function as we have it available. We then compute the 16th and 84th quantiles (corresponding to ±1σ) of the derived parameter distributions to estimate the lower and upper values, respectively. The direct values are provided whenever applicable for m1, m2, and fluxratio.

When combining two NSS solutions, we only use those with periods and eccentricities compatible within 5σ, assuming an uncertainty of 0.1 on the eccentricity for sources with a fixed eccentricity. A weighted mean of the periods and eccentricities of both solutions is then used in Eqs. (2) and (3). For the combination of astrometric and spectroscopic solutions, the primary mass is tested for different flux ratios in steps of 0.01; for each of these, the secondary mass is then derived from Eq. (3) and the flux ratio from Eq. (2), and only solutions that are consistent with
<table><caption>**Table 3.** Content summary of the catalogue of masses.</caption><thead><tr><th>Combination method</th><th>Number</th><th>M<sub>1</sub></th><th>M<sub>2</sub></th><th>F<sub>2</sub>/F<sub>1</sub></th></tr></thead><tbody><tr><td>Orbital+SB2</td><td>23</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td>EclipsingSpectro(SB2)</td><td>3</td><td>✓</td><td>✓</td><td></td></tr><tr><td>Eclipsing+SB2</td><td>53</td><td>✓</td><td>✓</td><td></td></tr><tr><td>AstroSpectroSB1+M1</td><td>17 578</td><td></td><td>✓</td><td>✓</td></tr><tr><td>Orbital+SB1+M1</td><td>1513</td><td></td><td>✓</td><td>✓</td></tr><tr><td>EclipsingSpectro+M1</td><td>71</td><td></td><td>✓</td><td></td></tr><tr><td>Eclipsing+SB1+M1</td><td>155</td><td></td><td>✓</td><td></td></tr><tr><td>SB2+M1</td><td>3856</td><td></td><td>✓</td><td></td></tr><tr><td>Orbital+M1</td><td>111 792</td><td></td><td>Lower/upper</td><td></td></tr><tr><td>SB1+M1</td><td>60 271</td><td></td><td>Lower</td><td></td></tr></tbody></table>

**Notes.** The full table is available in the Gaia table binary_masses.

the tested flux ratio are kept. When no solution is consistent, the closest one is used.

For Orbital solutions, only upper and lower values can be derived as the flux ratio is not known. Different flux ratios are tested in steps of 0.01. The lower (respectively upper) secondary mass value is computed from the mass distribution obtained with the lower flux ratio (respectively upper). The solution with fluxratio = 0 is always kept, as soon as the primary star magnitude is compatible with the isochrones. For the other flux ratios tested, the secondary mass derived is accepted if consistent with a secondary star on the main sequence. In practice, the Monte Carlo masses of the secondary lead to a range of possible absolute magnitudes from the isochrones, which, for the flux ratio tested, are converted into an absolute magnitude of the system which is accepted when it is at less than 3 sigma from the absolute magnitude of the system measured by Gaia. In some cases, this means that no flux ratio is kept. These can be either pre-main sequence stars, in which case our masses are invalid, or triple systems with a primary, which needs a flux ratio, but a secondary mass not consistent with it. To handle this second option, the minimum flux ratio compatible with a primary on the main sequence is used to derive the primary mass but the secondary mass is derived with $F_2/F_1 = 0$. These cases can be isolated with a 'fluxratio_lower is NULL' query. No limit is tested on the maximum flux ratio for white dwarfs. For SB1 solutions, the lowest valid flux ratio is used to derive the primary mass and the lower secondary mass value is derived on the distribution assuming $sin i = 1$. For eclipsing binaries, the flux ratio is fixed by g_luminosity_ratio.

The catalogue of masses we derive is available in the Gaia Archive table binary_masses. A summary of the number of dynamical masses and flux ratio is presented in Table 3. We selected only sources with a S/N higher than 5 on the astrometric semi-major axis and on the spectroscopic primary semi-amplitude, as well as a S/N of higher than 2 for the eclipsing binary and astrometric $sin i$ and the spectroscopic secondary semi-amplitude. For AstroSpectroSB1 solutions, we verify that both the S/N for the spectroscopic part, computed as $\sqrt{C^2 + H^2}$, and for $a_1$ are higher than 5. If not, the AstroSpectroSB1 is treated as an Orbital solution only. OrbitalAlternative solutions with $log_{10}(parallax/parallax_error) < 3.7-1.1$ $log_{10}(period)$ have been excluded. There are 76 sources duplicated, having both an astrometric solution and either an eclipsing binary (6) or a SB2 solution (70), with the astrometric solution period being larger than the other one by

<figure><img src="image_19.png" /><figcaption>**Fig. 17.** Distribution of the secondary mass of astrometric solutions with fluxratio_lower = 0 in Table 3.</figcaption></figure>

more than 10 sigma. For sources with both an SB1 and an Orbital solution, only the Orbital solution has been kept.

A particularly interesting subset of this table are the astrometric solutions with fluxratio_lower = 0. There is only one star (Gaia DR3 4288765058313593856) for which the secondary mass is sufficiently small ($0.57 M_\odot$) compared to the primary ($1.26 M_\odot$), meaning that fluxratio_lower = 0 is compatible with the secondary star being on the main sequence. The others are systems for which the secondary mass solutions for flux ratio > 0 did not have a mass compatible with any of the flux ratios tested. The secondary mass distribution of these is presented in Fig. 17. There are 12 stars with a secondary mass smaller than the minimum mass handled by the isochrones of $0.1 M_\odot$ and a low mass for the primary as well. Three other stars with low-mass secondaries could be either triple or pre-main sequence stars for which the primary mass is not correct. The most predominant peak is that of the white dwarfs at $M_2 = 0.61 M_\odot$ which has a standard deviation of $0.07 M_\odot$. We note that some white dwarf companions should actually have a flux ratio > 0, such as Gaia DR3 6416572288572864512 which is an AstroSpectroSB1 with a significant flux ratio; the primary mass has been estimated as that of a metal-poor star because of its location on the left of the main sequence; if it had been solved as an astrometric solution only, it would have had fluxratio_lower = 0 and an underestimated secondary mass. A long tail of high-mass secondaries is also present. These could be compact objects, but also triple stars for which the single primary star hypothesis was not valid (see Sect. 7.1), primary stars that started to evolve, or metal-poor giants for which the primary mass is not correct.

## 5.2. Masses using external data

In this section, we illustrate how other mass estimates can be obtained thanks to various kinds of combinations with external data.
<figure><img src="image_20.png" /><figcaption>Fig. 18. Eccentricity vs. period for most solutions with orbits.</figcaption></figure>

### 5.2.1. External SB2

Combining astrometric orbits with spectroscopic ones from large surveys is not a recently developed procedure, and was done for example with HIPPARCOS (Arenou et al. 2000). Once the inclination is known from the astrometric orbit, the semi-amplitudes from the spectroscopic orbit allow the masses and luminosities of the two components to be determined simultaneously. Recently, APOGEE DR17 data were used to detect 8105 SB2 or higher order systems (Kounkel et al. 2021). Once the required number of epochs become available, individual masses and magnitude differences will be obtained for the sources with an NSS Orbital* solution. Here, we simply take the example of Gaia DR3 702393458327135360, with $K_1 = 19.53 \pm 0.95$ km s$^{-1}$ and $K_2 = 21 \pm 1.1$ km s$^{-1}$. The masses are found to be $M_1 = 1.14 \pm 0.38$ $M_\odot$ and $M_2 = 1.06 \pm 0.35$ $M_\odot$ with a $0.567 \pm 0.071$ flux ratio.

### 5.2.2. Occultations

Occultations represent a method to constrain the sum of masses of binaries thanks to the measurement of their separation at a given epoch. We illustrate this with Gaia DR3 3162827836766605440 (HIP 36189) which is a $V \approx 6.5^m$ K giant that was discovered to be double thanks to an occultation by (704) Interamnia on 23 March 2003. Its acceleration had been detected in Kervella et al. (2019a, 2022), and Brandt (2021). Satō et al. (2014) indicate a $\rho = 12 \pm 3$ mas separation while a more precise indication is given by Herald et al. (2020): $\rho = 13.0 \pm 0.7$ mas with position angle $\theta = 231.9 \pm 4.0^\circ$. Satō et al. (2014) evaluate the magnitude difference between components to about 1.5, to which we attribute a 0.2 mag uncertainty, accounting in particular for the observation in a band different from the G band. This source received an Orbital solution with a 2.6 yr period. From the combined information, the masses of the components are found to be $M_1 = 3.9 \pm 2.2$ $M_\odot$ and $M_2 = 3.5 \pm 1.6$ $M_\odot$.

### 5.2.3. One SB1 Cepheid

Although it is known that many Cepheids are in binary systems (e.g. Kervella et al. 2019b), not many orbits are present in the NSS catalogue. On the spectroscopic orbit side, the Gaia DR3 data processing does not yet include the simultaneous handling of orbit and Cepheid pulsations, meaning that it is only the latter that were detected. Consequently, these solutions were filtered

<figure><img src="image_21.png" /><figcaption>Fig. 19. Location in the dereddened HRD of the ($G_{BP,0}-G_{RP,0}$) bins used in Fig. 20. Small blue dots correspond to the SB1s not selected by our selection criteria. The radius is the FLAME estimate.</figcaption></figure>

out from the catalogue to avoid any confusion. On the astrometric orbit side, one Cepheid received an Orbital solution.

Gaia DR3 470361114339849472 = RX Cam is known to be a G2Ib+A0V spectroscopic binary from Imbert (1996). The Gaia solution has a period of 999 ± 104 d and an eccentricity of 0.514 ± 0.049, consistent at $1\sigma$ with respectively 1113.8 ± 0.5 d and 0.459 ± 0.007 from Groenewegen (2013). The inclination is $i = 113.5^\circ \pm 1.7^\circ$. We may safely assume that there is no flux contribution (in the G band) from the companion, as confirmed by the difference between the semi-major axis of the primary and that of the photocentre $a_1 - a_0 = 0.04 \pm 0.12$ au. Using the semi-amplitude $K_1 = 14.27 \pm 0.11$ km s$^{-1}$ from Groenewegen (2013) and the estimation of the primary mass from Kervella et al. (2019b), $M_1 = 5.40 \pm 0.81$ $M_\odot$, we obtain $M_2 = 2.87 \pm 0.34$ $M_\odot$.

## 6. Special binaries in the HRD

In this section, we select several illustrative cases where the NSS catalogue can provide useful insights into populations of the HRD. For further reference, Fig. 18 presents the period-eccentricity diagram for the NSS solutions with orbits.

### 6.1. Spectroscopic binaries along the main sequence

In this section, we present and briefly discuss the eccentricity-period (hereafter *e-P*) diagrams of SB1s along the main sequence, defined as $-7.5 + 10(G_{BP,0}-G_{RP,0}) < M_{G,0}$ (Fig. 19), with the photometry being de-reddened in the same way as for the mass derivation (see Appendix E). Stars along the main sequence are divided according to ($G_{BP,0}-G_{RP,0}$) bins, as indicated in Fig. 19.

The *e-P* diagrams along the main sequence are displayed in Fig. 20. Because of the aliasing problems faced by the SB1 processing (see Sect. 2.3), these diagrams are shown for different filtering based on the significance of the RV semi-amplitude, namely $K_1/\sigma_{K_1}$ larger than 10, 20, or 40 (from left to right). This filtering removes both high-eccentricity short-period orbits and long-period orbits. The former filtering is designed to remove possibly spurious solutions, while the disappearance of the long-period solutions is a side effect due to the fact that long periods have on average smaller $K_1$ and thus smaller significances as well. Nevertheless, this filtering has the consequence of revealing the shape expected for any *e-P* diagram, namely short-period orbits being
<figure><img src="image_22.png" /><figcaption>Fig. 20. The e-P diagram for SB1s along the main sequence, filtered according to significance factors larger than 10, 20, or 40 (from left to right), and for different ($G_{BP,0}$-$G_{RP,0}$) spans (top to bottom). Filtering on the significance removes potentially spurious high-eccentricity solutions at small periods with the side effect of removing long period solutions. The drop in the number of systems at P = 0.5 yr due to insufficient sampling at this specific period. The color codes for the FLAME radius estimate.</figcaption></figure>

almost exclusively circular below a given 'transition' period (see e.g. Mazeh 2008, for a detailed discussion).

The e-P diagrams along the main sequence, when ordered according to bins of increasing $G_{BP,0}$-$G_{RP,0}$ and properly filtered on a significance larger than 40 (right panels of Fig. 20), reveal that this transition period does not vary strongly between the various $G_{BP,0}$-$G_{RP,0}$ bins, which is contrary to the situation prevailing along the giant branch, as discussed below (Sect. 6.2). Mazeh (2008) reviewed the processes shaping e-P diagrams, and concluded that the constancy of the transition period along the main sequence would naturally result if the circularisation occurred during the pre-main sequence phase when the stars were large, following a suggestion by Zahn & Bouchet (1989) for F, G, and K stars from 0.25 to 1.25 $M_\odot$. The transition period of these stars indeed remains constant along the main sequence at about 8 d as, although the transition period observed in Fig. 20 appears slightly shorter.

Mazeh (2008) also argues that short-period binaries (i.e. below the transition period) with non-circular orbits could result from a third distant companion pumping eccentricity into the binary orbit. However, at present, because of the confusion caused by possible period aliasing among short-period SB1 systems, this possibility cannot be tested with confidence.

## 6.2. Binaries along the RGB and AGB

The goal of this section is to show that the transition period between circular and non-circular orbits increases with radius and luminosity along the red giant branch (RGB) and asymptotic giant branch (AGB). To select stars on these branches, it is more efficient to use the 2MASS colour-magnitude diagram ($J - K, M_K$) rather than the usual Gaia colour-magnitude diagram. We used the 2MASS cross-match with EDR3 available within the data archive<fnref n="12" /> and used the following criteria to select giants:

$$J - K > 0 \text{ and } M_K < 0, \qquad (5)$$

as illustrated below.

### 6.2.1. Period-radius diagram

The existence of a circularisation threshold period in the e-P diagram was demonstrated by Pourbaix et al. (2004) in their Fig. 4 (see also Zahn & Bouchet 1989; Verbunt & Phinney 1995; Mazeh 2008; Jorissen et al. 2009; Escorza et al. 2019). Its analytic form in a period-radius diagram may be easily obtained from the simple expression of the Roche radius $R_R$ around the star of mass $M_1$ with a companion of mass $M_2$ (Paczyński 1971):

$$R_{R,1} = a \left( 0.38 + 0.2 \log \frac{M_1}{M_2} \right). \qquad (6)$$

Substituting Kepler's third law, and assuming that the period threshold (expressed in days) corresponds to the situation where the star radius is equal to the Roche radius, one finds after some algebra:

$$\log(P_d^{\text{thresh}}/365.25) = (3/2) \log(R_1/216 R_\odot) \\ - (1/2) \log(M_1 + M_2) \\ - (3/2) \log\left(0.38 + 0.2 \log \frac{M_1}{M_2}\right) \qquad (7)$$

$$\equiv (3/2) \log(R_1/216 R_\odot) \\ - (3/2) c_1, \qquad (8)$$

where $c_1$ only depends on the masses. These thresholds are represented in Fig. 21 as dashed lines (corresponding to different choices for the pair $M_1, M_2$). Figure 21 presents all SB1 solutions falling along the RGB and AGB as defined above based on the ($J - K, M_K$) colour-magnitude diagram; however, it reveals that there are many SB1 solutions involving giant stars that do not fulfill the condition $P \ge P^{\text{thresh}}$ expressed by Eqs. (7) and (8), especially when the significance $K_1/\sigma_{K_1}$ is smaller than 40.

<footnote n="12">¹² https://gea.esac.esa.int/archive/documentation/EDR3/Gaia_archive/chap_datamodel/secablCrossmatches/ssecablCrossmass_pscxsc_best_neighbour.html</footnote>
<figure><img src="image_23.png" /><figcaption>**Fig. 21.** Period-radius diagram for all SB1 solutions falling along the RGB and AGB according to criterion (5), and with a radius available from *radius_flame*. The dashed lines correspond to the threshold periods expressed by Eq. (7) for $M_1 = 1.3 M_\odot$ and $M_2 = 1.0 M_\odot$ (red dashed line) and $M_1 = 1.3 M_\odot$ and $M_2 = 0.2 M_\odot$ (cyan dashed line). Left (a): unfiltered, 44 706 SB1 solutions (among which 3056 unphysical, that is, below the cyan dashed line). Middle (b): filtered by significance $K_1/\sigma_{K_1} > 20, 27, 404$ solutions are rejected and 17 302 are kept (among which 214 unphysical). Right (c): filtered by significance >40, 37 850 solutions are rejected and 6856 are kept (among which 21 unphysical).</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>**Fig. 22.** *e-P* diagrams for all SB1 (**left panel**: unfiltered; adequately filtered *e-P* diagrams for SB1 with an RGB and AGB primary are presented in Fig. 24) and astrometric (**right panel**) solutions falling along the RGB and AGB according to criterion (5), and with a radius available from *radius_flame*. We highlight the restricted period scale of the astrometric binaries as compared to the SB1, and the lack of binaries with periods close to 1 yr among astrometric binaries.</figcaption></figure>

### 6.2.2. *e-P*, *P-f(M)* diagrams

Figure 22 presents the *e-P* diagram for the same set of SB1 solutions (left panel) as shown in Fig. 21a, as compared to astrometric binaries along the RGB and AGB (right panel). The difference between the period range covered by SB1 and astrometric solutions is striking. As most astrometric orbits have periods longer than about 200 d, they clearly satisfy the criterion expressed by the dashed line in Fig. 21 and do not overfill their Roche lobe, contrary to the short-period SB1 solutions.

Figure 23a is similar to Fig. 22 but replacing eccentricities by mass functions, and revealing again two populations of SB1 solutions, the short-period ones being characterised by very small mass functions $f(M)$. The origin of this population of short-period SB1 solutions among RGB and AGB stars clearly requires clarification. In the following, we show that they are associated with poorly defined solutions. It appears indeed that almost all unphysical SB1 solutions may be eliminated by using the same purely observational criterion as used in Sect. 6.1, and based on the value of the significance of the SB1 solution (available in Table nss_two_body_orbit from the Gaia archive), that is, $K_1/\sigma_{K_1}$, $K_1$ being the semi-amplitude of the first component.

Almost no outlier remains in the *P-R* (Fig. 21c) and *P-f(M)* (Fig. 23c) diagrams when that significance exceeds 40; a few outliers remain when it exceeds 20 but many more solutions are kept, as may be seen from Table 4. This latter table shows that the gradual disappearance of unphysical SB1 solutions as the significance increases corresponds to a real filtering out of unphysical solutions, because the fraction of remaining unphysical solutions truly diminishes as the significance increases (passing from 6.8% in the absence of any filtering to 0.3% when the significance threshold is set at 40; see Table 4). However, the drawback of a filtering on significance is that it tends to also filter out solutions with long orbital periods, as those have on average smaller $K_1$ values (this was also very clear from Fig. 20). Alternatively, if one does not want to loose the long-period orbits as a result of filtering on significance, filtering is also possible with the physical condition $P \ge P^{\text{thresh}}$ – Eq. (7) – with appropriate mass values; however Fig. 21 reveals that for systems with periods above 10 d, the boundary between physical and unphysical systems does not depend sensitively on the choice of $M_1, M_2$.

Now that the sample of RGB and AGB stars has been adequately cleaned of its unphysical orbits, it is possible to investigate the properties of the *e-P* diagram for giant stars. Figure 24 presents those for bins of increasing radius (as taken from the
<figure><img src="image_25.png" /><figcaption>**Fig. 23.** P-f($\mathcal{M}$) diagrams for SB1 along the RGB/AGB. Left (a): unfiltered. The yellow tail extending down to $f(\mathcal{M}) \sim 10^{-5} \mathcal{M}_{\odot}$ at periods in the range 300–800 d corresponds to pseudo-orbits associated to long-period pulsators (see Sect. 6.2.3). Middle (b): filtered by significance >20 and >40 (right (c)).</figcaption></figure>

<table><caption>**Table 4.** Sizes of the SB1 sample involving RGB and AGB primaries for different filtering on the significance threshold.</caption><thead><tr><th>Significance</th><th>Rejected</th><th>Accepted</th><th>Unphys.</th><th>(%)</th></tr></thead><tbody><tr><td>All</td><td>0</td><td>44 706</td><td>3056</td><td>(6.8%)</td></tr><tr><td>>20</td><td>27 404</td><td>17 302</td><td>214</td><td>(1.2%)</td></tr><tr><td>>40</td><td>37 850</td><td>6856</td><td>21</td><td>(0.3%)</td></tr></tbody></table>

**Notes.** The numbers of rejected and kept sources are given as a function of the significance $K_1/\sigma_{K_1}$. The column labelled ‘unphys.’ lists the number of sources which would have a Roche filling factor of greater than unity (or $P < P^{\text{thresh}}$ in Eq. (7), thus falling below the cyan dashed line on Fig. 21). The column labelled ‘fraction’ gives the ratio ‘unphys.’/‘accepted’ (expressed as %).

corresponding radius_flame field), as indicated in the figure labels. As expected from the dashed lines in Fig. 21, the minimum period increases with increasing radius. In the following discussion, we adopt $M_1 = 1.3 M_{\odot}$ and $M_2 = 1.0 M_{\odot}$ (corresponding to the red dashed line in Fig. 21, and $c_1 = -0.274$ in Eq. (8)), as these values nicely match the observed trend. The above value for $c_1$ combined with the upper bound of the radius range adopted in each panel of Fig. 24 defines the lower bound on the orbital period $P_{\text{min}}$ for $e = 0$. It appears that the upper envelope of the data cloud observed in each panel of Fig. 24 is well fitted by the empirical relation $P = P_{\text{min}}(1 - e)^3$ represented by the solid black lines in Fig. 24, as already found by Pourbaix et al. (2004) in their analysis of the Ninth Catalogue of Spectroscopic Binary Orbits (their Fig. 5). Despite the fact that this curve matches the uppermost data points in almost all panels rather well, it must be stressed that there seems to be no physical justification for this specific analytical form. However, a closer look at each of these panels reveals an interesting sub-structure. At the shortest periods, each panel is dominated by a large number of (nearly) circular orbits caused by circularisation operating in those systems where the giant stars with their convective envelope are close to filling their Roche lobe. As shown above, $P_{\text{min}}$ in each panel actually refers to systems where the giants with the shortest radius in the considered range fill their Roche lobe (see e.g. Verbunt & Phinney 1995; Mazeh 2008, for details).

### 6.2.3. A search for genuine SB1s among giants

The identification of SB1 among highly evolved giants and long-period variables (LPVs) is made difficult by the enve-

<figure><img src="image_26.png" /><figcaption>**Fig. 24.** e-P diagram for SB1 systems along the giant branch, filtered according to significance factors larger than 40, for various radius spans. Top panel: is the full sample. The solid black lines correspond to the loci where $P(1 - e)^3$ is constant (see text). The sample sizes are, from top to bottom, 1960, 2358, 1643, 737, and 40. The location in the HRD of the SB1 systems with $0.7 < \log(R/R_{\odot}) \le 1.0$ (second panel from top), $1.3 < \log(R/R_{\odot}) \le 1.6$ (fourth panel from top) and $1.9 < \log(R/R_{\odot})$ (bottom panel) is shown in Fig. 25.</figcaption></figure>

lope pulsation (Alvarez et al. 2001; Hinkle et al. 2002; Jorissen 2004; Jorissen et al. 2019). Other methods have therefore previously been used (Jorissen & Frankowski 2008; Sahai et al. 2008; Decin et al. 2020; Ortiz & Guerrero 2021) to identify true binaries. Gaia on the other hand, with its survey combining radial velocity and photometry data, offers exquisite prospects to disentangle pulsational from orbital RV variations. In that respect, the bottom panel of Fig. 24 offers an interesting benchmark sample of giant stars with $R > 80 R_{\odot}$ with a SB1-like signature in their RVs. There are 40 such giants if the significance threshold
<table><caption>**Table 5.** Source id and basic parameters for SB1 and acceleration solutions with significance larger than 40 for giants with $R > 80 R_\odot$ (bottom panel of Fig. 24).</caption><thead><tr><th>Source_id</th><th>R (R<sub>☉</sub>)</th><th>Significance</th><th>ΔG (mag)</th><th>G (mag)</th><th>e</th><th>P<sub>nss</sub> (d)</th><th>P<sub>lpv</sub> (d)</th><th>Alt. id</th><th>Rem.</th></tr></thead><tbody><tr><td colspan="11" style="text-align:center; font-weight:bold;">SB1</td></tr><tr><td>1825471125022885760</td><td>111</td><td>62</td><td>0.0006</td><td>11.74</td><td>0.19</td><td>475</td><td></td><td></td><td></td></tr><tr><td>1963830094814564992</td><td>98</td><td>71</td><td>0.0025</td><td>9.48</td><td>0.06</td><td>340</td><td>183</td><td></td><td>Ell. var.</td></tr><tr><td>1972501599433801856</td><td>104</td><td>82</td><td>0.0026</td><td>11.21</td><td>0.04</td><td>286</td><td>143</td><td></td><td>Ell. var.</td></tr><tr><td>1993611806061037824</td><td>91</td><td>45</td><td>0.0011</td><td>11.66</td><td>0.05</td><td>255</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>1996190371286907904</td><td>81</td><td>51</td><td>0.0005</td><td>11.65</td><td>0.10</td><td>368</td><td></td><td></td><td></td></tr><tr><td>2022016864326072832</td><td>81</td><td>53</td><td>0.0002</td><td>12.25</td><td>0.13</td><td>1182</td><td></td><td></td><td></td></tr><tr><td>203396083342181248</td><td>79</td><td>55</td><td>0.0004</td><td>11.48</td><td>0.28</td><td>851</td><td></td><td></td><td></td></tr><tr><td>2072346498024572672</td><td>83</td><td>49</td><td>0.0006</td><td>11.67</td><td>0.40</td><td>805</td><td></td><td></td><td></td></tr><tr><td>2153213619706962304</td><td>85</td><td>97</td><td>0.0008</td><td>8.92</td><td>0.02</td><td>395</td><td></td><td>BD+56 2152 <sup>(a)</sup></td><td></td></tr><tr><td>2179330422489474304</td><td>100</td><td>63</td><td>0.0007</td><td>11.27</td><td>0.40</td><td>1261</td><td></td><td></td><td></td></tr><tr><td>2189793031540178560</td><td>109</td><td>46</td><td>0.0010</td><td>11.33</td><td>0.09</td><td>582</td><td></td><td></td><td></td></tr><tr><td>2190661233409369728</td><td>81</td><td>179</td><td>0.0008</td><td>9.75</td><td>0.26</td><td>538</td><td></td><td></td><td></td></tr><tr><td>2198983058969830272</td><td>91</td><td>148</td><td>0.0019</td><td>10.03</td><td>0.06</td><td>573</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>2203704946009240576</td><td>85</td><td>78</td><td>0.0007</td><td>11.05</td><td>0.15</td><td>663</td><td></td><td></td><td></td></tr><tr><td>3023454391367052928</td><td>79</td><td>52</td><td>0.0023</td><td>11.52</td><td>0.02</td><td>513</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>3385138711262550144</td><td>107</td><td>48</td><td>0.0012</td><td>10.34</td><td>0.20</td><td>1063</td><td></td><td></td><td></td></tr><tr><td>3441375569926160768</td><td>82</td><td>72</td><td>0.0004</td><td>8.58</td><td>0.45</td><td>1115</td><td></td><td>BD+26 935 <sup>(b)</sup></td><td></td></tr><tr><td>4309778580925549312</td><td>86</td><td>78</td><td>0.0024</td><td>11.75</td><td>0.08</td><td>212</td><td>106</td><td></td><td>Ell. var.</td></tr><tr><td>4538064682637397504</td><td>81</td><td>55</td><td>0.0005</td><td>10.47</td><td>0.02</td><td>440</td><td></td><td></td><td></td></tr><tr><td>465787042893453696 <sup>(c)</sup></td><td>87</td><td>58</td><td>0.0107</td><td>11.71</td><td>0.09</td><td>366</td><td>375</td><td>V688 Cas <sup>(d)</sup></td><td>Mira</td></tr><tr><td>468328667095902720</td><td>82</td><td>109</td><td>0.0008</td><td>11.31</td><td>0.01</td><td>374</td><td></td><td></td><td></td></tr><tr><td>4479122750503280512</td><td>100</td><td>64</td><td>0.0009</td><td>10.89</td><td>0.11</td><td>307</td><td></td><td></td><td></td></tr><tr><td>519141188227099776</td><td>89</td><td>46</td><td>0.0004</td><td>11.04</td><td>0.02</td><td>420</td><td></td><td></td><td></td></tr><tr><td>5340777165298298880</td><td>83</td><td>53</td><td>0.0014</td><td>11.57</td><td>0.02</td><td>273</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>5354875859285271936</td><td>89</td><td>50</td><td>0.0003</td><td>9.56</td><td>0.45</td><td>764</td><td></td><td></td><td></td></tr><tr><td>5355550645876247808</td><td>95</td><td>49</td><td>0.0014</td><td>12.44</td><td>0.04</td><td>399</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>5405499126983935872</td><td>83</td><td>40</td><td>0.0018</td><td>13.07</td><td>0.03</td><td>243</td><td>122</td><td></td><td>Ell. var.</td></tr><tr><td>5406434021101010176</td><td>102</td><td>40</td><td>0.0010</td><td>10.28</td><td>0.01</td><td>319</td><td></td><td></td><td></td></tr><tr><td>5604143357268838400</td><td>80</td><td>53</td><td>0.0007</td><td>9.97</td><td>0.04</td><td>327</td><td></td><td></td><td></td></tr><tr><td>5697523299266655104</td><td>81</td><td>108</td><td>0.0007</td><td>10.69</td><td>0.28</td><td>585</td><td></td><td></td><td></td></tr><tr><td>5697806664034217216</td><td>98</td><td>65</td><td>0.0009</td><td>10.59</td><td>0.37</td><td>889</td><td></td><td></td><td></td></tr><tr><td>5796104824632537600</td><td>86</td><td>104</td><td>0.0018</td><td>10.12</td><td>0.17</td><td>556</td><td></td><td></td><td></td></tr><tr><td>5806597567164955776</td><td>88</td><td>55</td><td>0.0018</td><td>10.94</td><td>0.09</td><td>433</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>5835609040544745344</td><td>108</td><td>40</td><td>0.0007</td><td>11.46</td><td>0.09</td><td>315</td><td></td><td></td><td></td></tr><tr><td>5847195453486047616</td><td>105</td><td>56</td><td>0.0009</td><td>9.74</td><td>0.13</td><td>782</td><td></td><td></td><td></td></tr><tr><td>5854104780242997504</td><td>92</td><td>49</td><td>0.0003</td><td>12.22</td><td>0.04</td><td>495</td><td></td><td></td><td></td></tr><tr><td>5878621900997292800</td><td>92</td><td>114</td><td>0.0004</td><td>12.20</td><td>0.02</td><td>534</td><td></td><td></td><td></td></tr><tr><td>5888442292197648000</td><td>115</td><td>40</td><td>0.0018</td><td>12.08</td><td>0.04</td><td>305</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>6012575363926683648</td><td>84</td><td>44</td><td>0.0014</td><td>12.43</td><td>0.04</td><td>439</td><td></td><td></td><td>Ell. var.?</td></tr><tr><td>6056302632126821760</td><td>84</td><td>43</td><td>0.0005</td><td>12.05</td><td>0.39</td><td>1261</td><td></td><td></td><td></td></tr><tr><td>6057537697261452288</td><td>86</td><td>86</td><td>0.0004</td><td>11.02</td><td>0.01</td><td>343</td><td></td><td></td><td></td></tr><tr><td>992206959423861888</td><td>94</td><td>43</td><td>0.0022</td><td>9.72</td><td>0.27</td><td>1152</td><td></td><td></td><td></td></tr><tr><td colspan="11" style="text-align:center; font-weight:bold;">Acceleration solution</td></tr><tr><td>6665511449204071424</td><td>92</td><td>28</td><td>0.0013</td><td>4.19</td><td>-</td><td>-</td><td>-</td><td>HD 190421</td><td></td></tr></tbody></table>

**Notes.** The radius *R* is from FLAME. The column labelled Δ*G* gives a proxy of the variability in the *G* band (see text). The column labelled *P*<sub>lpv</sub> lists the period obtained by the photometric analysis (table *vari_long_period_variable*), whereas *P*<sub>nss</sub> corresponds to the period of the SB1 orbit. <sup>(a)</sup>Limb-darkened diameter of 0.393 mas from Cruzalèbes et al. (2019), or 96 *R*<sub>☉</sub> with parallax *σ* = 0.44 mas. <sup>(b)</sup>Limb-darkened diameter of 0.672 mas from Cruzalèbes et al. (2019), or 106 *R*<sub>☉</sub> with parallax *σ* = 0.68 mas. <sup>(c)</sup>Since *P*<sub>nss</sub> = *P*<sub>lpv</sub>, the RV variations are due to atmospheric pulsations rather than to orbital motion. <sup>(d)</sup>Also CGCS 396 in the General Catalog of Cool Galactic Carbon Stars, flagged as Mira variable.

is set at 40<sup>13</sup>. No Orbital or AstroSpectroSB1 solutions are

present in Gaia DR3 among those giants with large radii (compare with Fig. 22). Table 5 lists their main properties, while their location in the HRD is shown as the yellow crosses in Fig. 25.

As mentioned above, as there is the risk that some of these SB1 solutions may be caused by envelope pulsation mistaken as SB1s, a proxy for the amplitude of the photometric variation

<footnote n="13"><sup>13</sup> Interested readers may set the significance threshold at 20 instead to get more SB1-like solutions (namely approximately 100), especially with long periods for the reasons explained in the text, or use instead the physical filtering *P* ≥ *P*<sub>thresh</sub>.</footnote>
in the G band has been listed as well, namely phot_g_mean_mag_error from the gaia_source table. We also performed a cross-match with table vari_long_period_variable and the photometric period, whenever available, has been listed in the column $P_{\text{lpv}}$. It appears that only one LPV is present in this list (a carbon star also known as V688 Cas), as confirmed by its largest $\Delta G$ value in Table 5. As $P_{\text{lpv}} = P_{\text{nss}}$ for this star, the RV variations are not due to orbital motion but to envelope pulsations. Many other such cases will be discussed below (Table 6). There are only four other stars appearing in the vari_long_period_variable table in common with Table 5, and these four have the unexpected property that $P_{\text{lpv}} = 0.5 P_{\text{nss}}$, with a moderate $\Delta G$ value (on the order of 0.001–0.003 mag). We argue below, in relation to Table 6, that these are ellipsoidal variables and therefore true binaries, where the giant primary is close to filling its Roche lobe. Based on the fact that these ellipsoidal variables identified in table vari_long_period_variable have small eccentricities ($e < 0.1$), we suspect that Table 5 contains many more such ellipsoidal variables, namely those with $e < 0.1$ and $\Delta G > 0.001$ mag, flagged as ‘Ell. var.?’ in the last column of Table 5.

The longest period found in Table 5 is 1261 d, a value that is nicely in line with the Gaia DR3 time span, but short with respect to the periods expected among evolved giants (consider for instance the 17 yr period found by Jorissen et al. 2019 for the carbon Mira V Hya). Such long periods are not detectable at the current stage of the Gaia mission, either as SB1 or as astrometric binaries. Nevertheless, one may look for acceleration solutions (there is only one solution from table nssAccelerationAstro matching the giant criteria defining Table 5; regarding acceleration solutions, we refer to Sect. 4.2.3 and Wielen et al. 1999; Makarov & Kaplan 2005; Frankowski et al. 2007; Kervella et al. 2019a, 2022; Brandt 2021) or for solutions with a trend in the RVs (121 solutions for giants found in nss_non_linearspectro, not listed here).

### 6.2.4. Combining photometry and spectroscopy to diagnose RV variations in giants: pulsation, ellipsoidal variables, and rotational modulation

With the initial aim being to further investigate how many LPVs may be mistaken as SB1, we searched for targets in common between SB1 from the NSS vari_long_period_variable table and LPVs as provided by the variability study in the vari_long_period_variable table. However, this cross-match revealed some surprises. The following query yields 1869 entries, as shown in Fig. 26:

```sql
SELECT * from gaiadr3.nss_two_body_orbit TBO,
       gaiadr3.vari_long_period_variable LPV where
       LPV.source_id = TBO.source_id and
       LPVamedia.frecuencia is
       not null
```

The three panels differ in terms of the level of filtering applied on the SB1 significance parameter, as defined above: >5 (default, top panel), >20 (middle panel), and >40 (bottom panel). Striking are the two straight sequences observed in all three panels. The upper sequence corresponds to $P_{\text{lpv}}/P_{\text{nss}} = 0.5$ (as expected for ellipsoidal variables), whereas the lower sequence corresponds to $P_{\text{lpv}}/P_{\text{nss}} = 1$ (as expected for pulsating stars or rotational modulation in a synchronised system). The lower sequence is further made of two distinct clumps, one at short periods ($P_{\text{lpv}} \le 100$ d; which could be due to starspot modulation on a spin-orbit synchronised star) and the other at long

<figure><img src="image_27.png" /><figcaption>**Fig. 25.** Location in the HRD of three among the samples displayed in Fig. 24, namely $0.7 < \log(R/R_\odot) \le 1.0$ (dots), $1.3 < \log(R/R_\odot) \le 1.6$ (plus symbols), and $1.9 < \log(R/R_\odot)$ (crosses). Small cyan dots correspond to the SB1 not selected by our selection criteria. See Table 5 for a full discussion of the properties of the yellow crosses.</figcaption></figure>

periods ($200 \le P_{\text{lpv}} \le 1000$ d; LPVs). These are discussed in turn below.

#### Ellipsoidal variables

Besides the obvious property of their light-to-RV period ratio equal to 0.5, the ellipsoidal-variable sequence is further confirmed from its following properties: (i) small eccentricities ($e \le 0.1$), (ii) large filling factors ($R_1/R_{R,1} \ge 0.65$ from Eq. (6)), adopting radii from FLAME and the same typical masses as above – $M_1 = 1.3 M_\odot$, $M_2 = 1.0 M_\odot$) whenever available, and (iii) small $G$ amplitudes ($0.01 \le \Delta G \le 0.1$ mag; see Table 6). We confirmed the ellipsoidal nature of these stars by a comparison between the light and RV curves. As expected, the maximum light indeed occurs at the quadratures, when the RV is maximum or minimum. In Fig. 24, at any given radius range, these ellipsoidal variables are located in the nearly circular tail of each panel. The full list of ellipsoidal variables is not provided here as the reader may easily obtain it from the ADQL query mentioned at the beginning of this section and filtering on $P_{\text{lpv}}/P_{\text{nss}}$ around 0.5 (370 stars in the inclusive range 0.45–0.55, most of them having significances in excess of 20). The first part of Table 6 nevertheless lists a few randomly selected examples. Figure 27 shows the position in the 2MASS infrared colour-magnitude diagram ($M_K, J - K$) of the 370 stars with $0.45 \le P_{\text{lpv}}/P_{\text{nss}} \le 0.55$ (dots). These ellipsoidal variables are located from the tip of the RGB<fnref n="14" /> to 3 mag below. We note that some among these stars might be young pre-main sequence stars. Gaia DR3 2162167694508896128 = V1540 Cyg listed in Table 6 is one such case (on Fig. 27, it is located at $M_K = -6.2$ and $J - K = 1.41$).

#### Long-period variables

The transition between dots and crosses in Fig. 27 corresponds to the transition across the RGB tip. Above the RGB tip, most

<footnote n="14">¹⁴ $M_{K,\text{RGB-tip}} = -6.49$ as derived from Lebzelter et al. (2019) who find $K_{\text{RGB-tip}} = 12$ for the LMC and considering its distance modulus 18.49±0.09 mag (de Grijs et al. 2017).</footnote>
<table><caption>**Table 6.** A few illustrative examples of ellipsoidal variables ($P_{\text{lpv}}/P_{\text{nss}} = 0.5$) mistaken as LPVs in the *vari_long_period_variable* table, LPVs with a pseudo SB1 orbit ($P_{\text{lpv}}/P_{\text{nss}} = 1$, $\Delta G > 0.1$ mag, $P_{\text{lpv}} > 180$ d) in the *nss_two_body_orbit* table and short-period ($P_{\text{lpv}} < 100$ d) 'LPVs' with $P_{\text{lpv}}/P_{\text{nss}} = 1$.</caption><thead><tr><th>Gaia DR3 id</th><th>P<sub>lpv</sub><br>(d)</th><th>P<sub>nss</sub><br>(d)</th><th>P<sub>lpv</sub>/P<sub>nss</sub></th><th>Signif.</th><th>K<sub>1</sub><br>(km s<sup>-1</sup>)</th><th>e</th><th>&Delta;G<br>(mag)</th><th>f(M)<br>(M<sub>&odot;</sub>)</th><th>R/R<sub>R</sub></th><th>R<br>(R<sub>&odot;</sub>)</th><th>Alt. id.</th></tr></thead><tbody><tr><td colspan="12" style="text-align:center; font-weight:bold;">Ellipsoidal variables</td></tr><tr><td>2162167694508896128 <sup>(a)</sup></td><td>143 &plusmn; 16</td><td>289 &plusmn; 0.2</td><td>0.49</td><td>249</td><td>34.6</td><td>0.02</td><td>0.02</td><td>1.25</td><td></td><td></td><td>V1540 Cyg</td></tr><tr><td>5871624883899265280</td><td>48 &plusmn; 3</td><td>95.1 &plusmn; 0.1</td><td>0.50</td><td>101</td><td>22.0</td><td>0.03</td><td>0.06</td><td>0.105</td><td>0.92</td><td>43</td><td></td></tr><tr><td>449088171382718848</td><td>178 &plusmn; 50</td><td>356.7 &plusmn; 1.5</td><td>0.50</td><td>73</td><td>12.8</td><td>0.01</td><td>0.09</td><td>0.078</td><td></td><td></td><td></td></tr><tr><td>528840770565380352</td><td>54 &plusmn; 4</td><td>108.6 &plusmn; 0.1</td><td>0.50</td><td>89</td><td>31.7</td><td>0.01</td><td>0.06</td><td>0.358</td><td>0.88</td><td>45</td><td></td></tr><tr><td>1837292073273265920</td><td>58 &plusmn; 3</td><td>116.1 &plusmn; 0.1</td><td>0.50</td><td>86</td><td>34.1</td><td>0.04</td><td>0.06</td><td>0.477</td><td></td><td></td><td></td></tr><tr><td>4305358093199399168</td><td>42 &plusmn; 2</td><td>84.8 &plusmn; 0.1</td><td>0.50</td><td>89</td><td>27.3</td><td>0.03</td><td>0.05</td><td>0.178</td><td>0.74</td><td>32</td><td></td></tr><tr><td>6653811713476525440</td><td>63 &plusmn; 4</td><td>125.4 &plusmn; 0.6</td><td>0.50</td><td>19</td><td>11.4</td><td>0.16</td><td>0.09</td><td>0.019</td><td>0.67</td><td>37</td><td></td></tr><tr><td>5933194270923372288</td><td>10 &plusmn; 17</td><td>219.4 &plusmn; 0.4</td><td>0.50</td><td>63</td><td>21.8</td><td>0.05</td><td>0.05</td><td>0.234</td><td></td><td></td><td></td></tr><tr><td>5998937575770407936</td><td>69 &plusmn; 9</td><td>137.1 &plusmn; 0.2</td><td>0.50</td><td>50</td><td>21.7</td><td>0.05</td><td>0.07</td><td>0.144</td><td>0.75</td><td>45</td><td></td></tr><tr><td colspan="12" style="text-align:center; font-weight:bold;">Large-amplitude (&Delta;G &gt; 0.1 mag) LPVs (Mira or SRa,b) with a pseudo SB1 orbit</td></tr><tr><td>3029929312263388416</td><td>330 &plusmn; 39</td><td>329 &plusmn; 3</td><td>1.002</td><td>27</td><td>5.6</td><td>0.27</td><td>0.27</td><td>0.0057</td><td></td><td></td><td></td></tr><tr><td>5861476288517412096</td><td>351 &plusmn; 29</td><td>350 &plusmn; 4</td><td>1.003</td><td>22</td><td>7.4</td><td>0.14</td><td>0.25</td><td>0.0144</td><td></td><td></td><td></td></tr><tr><td>4498570706006456320</td><td>196 &plusmn; 11</td><td>196 &plusmn; 2</td><td>1.003</td><td>9</td><td>3.5</td><td>0.36</td><td>0.21</td><td>0.0008</td><td></td><td></td><td></td></tr><tr><td>6635121600650977280</td><td>310 &plusmn; 42</td><td>309 &plusmn; 2</td><td>1.003</td><td>18</td><td>2.9</td><td>0.29</td><td>0.13</td><td>0.0007</td><td>-</td><td>75</td><td></td></tr><tr><td>185224454669173120</td><td>491 &plusmn; 114</td><td>490 &plusmn; 9</td><td>1.003</td><td>9</td><td>2.6</td><td>0.34</td><td>0.29</td><td>0.0009</td><td></td><td></td><td></td></tr><tr><td>5522324157261027968</td><td>321 &plusmn; 37</td><td>320 &plusmn; 3</td><td>1.003</td><td>23</td><td>5.3</td><td>0.29</td><td>0.26</td><td>0.0046</td><td></td><td></td><td></td></tr><tr><td>5428546471231540608</td><td>455 &plusmn; 60</td><td>454 &plusmn; 6</td><td>1.003</td><td>7</td><td>2.8</td><td>0.33</td><td>0.24</td><td>0.0009</td><td></td><td></td><td></td></tr><tr><td>463720476424410624</td><td>353 &plusmn; 24</td><td>352 &plusmn; 3</td><td>1.004</td><td>34</td><td>7.5</td><td>0.17</td><td>0.26</td><td>0.0152</td><td></td><td></td><td></td></tr><tr><td>6358622017131465728</td><td>181 &plusmn; 7</td><td>180 &plusmn; 2</td><td>1.004</td><td>10</td><td>6.4</td><td>0.17</td><td>0.54</td><td>0.0048</td><td>-</td><td>138</td><td></td></tr><tr><td>2180493018598279296</td><td>178 &plusmn; 25</td><td>177 &plusmn; 2</td><td>1.004</td><td>11</td><td>2.3</td><td>0.09</td><td>0.12</td><td>0.0002</td><td></td><td></td><td></td></tr><tr><td>5318375436185802368</td><td>262 &plusmn; 32</td><td>260 &plusmn; 2</td><td>1.005</td><td>12</td><td>2.6</td><td>0.33</td><td>0.18</td><td>0.0004</td><td>-</td><td>97</td><td></td></tr><tr><td>5522970154700635392</td><td>412 &plusmn; 37</td><td>410 &plusmn; 8</td><td>1.005</td><td>14</td><td>5.6</td><td>0.04</td><td>0.49</td><td>0.0076</td><td>-</td><td>84</td><td></td></tr><tr><td>1989628623330891904</td><td>419 &plusmn; 18</td><td>[25 &plusmn; 0.02]<sup>(b)</sup></td><td>[16.7]<sup>(b)</sup></td><td>21</td><td>6.6</td><td>0.39</td><td>0.60</td><td>0.0006</td><td></td><td></td><td></td></tr><tr><td colspan="12" style="text-align:center; font-weight:bold;">Genuine binaries among LPVs (P<sub>lpv</sub>/P<sub>nss</sub> &ne; 0.5 or 1; see text)</td></tr><tr><td>5341773936978279296</td><td>220 &plusmn; 61</td><td>1252 &plusmn; 113</td><td>0.18</td><td>21</td><td>7.7</td><td>0.25</td><td>0.05</td><td>0.053</td><td>0.28</td><td>73</td><td></td></tr><tr><td>5597415372601747456</td><td>168 &plusmn; 54</td><td>656 &plusmn; 6</td><td>0.26</td><td>43</td><td>11.1</td><td>0.36</td><td>0.03</td><td>0.076</td><td>0.33</td><td>56</td><td></td></tr><tr><td>5414646307794529792</td><td>196 &plusmn; 42</td><td>753 &plusmn; 17</td><td>0.26</td><td>34</td><td>6.2</td><td>0.4</td><td>0.04</td><td>0.015</td><td></td><td></td><td></td></tr><tr><td>5875470387113872768</td><td>214 &plusmn; 28</td><td>746 &plusmn; 16</td><td>0.29</td><td>29</td><td>15.3</td><td>0.35</td><td>0.09</td><td>0.229</td><td></td><td></td><td></td></tr><tr><td>5347893273248921984</td><td>279 &plusmn; 75</td><td>913 &plusmn; 40</td><td>0.31</td><td>29</td><td>13.3</td><td>0.07</td><td>0.03</td><td>0.220</td><td></td><td></td><td></td></tr><tr><td>5404683839108805248</td><td>215 &plusmn; 28</td><td>662 &plusmn; 1</td><td>0.32</td><td>89</td><td>11.5</td><td>0.33</td><td>0.11</td><td>0.088</td><td></td><td></td><td></td></tr><tr><td>5796098502440628864</td><td>244 &plusmn; 28</td><td>701 &plusmn; 4</td><td>0.35</td><td>59</td><td>6.5</td><td>0.08</td><td>0.08</td><td>0.020</td><td></td><td></td><td></td></tr><tr><td>1642955252784454144</td><td>374 &plusmn; 93</td><td>503 &plusmn; 6</td><td>0.74</td><td>33</td><td>6.0</td><td>0.28</td><td>0.04</td><td>0.010</td><td></td><td></td><td></td></tr><tr><td>304717076269774336</td><td>310 &plusmn; 102</td><td>158 &plusmn; 1</td><td>1.96</td><td>22</td><td>12.0</td><td>0.01</td><td>0.10</td><td>0.028</td><td>0.39</td><td>26</td><td></td></tr><tr><td>6661657003818388480</td><td>197 &plusmn; 92</td><td>42 &plusmn; 0.1</td><td>4.66</td><td>32</td><td>26.3</td><td>0.11</td><td>0.04</td><td>0.078</td><td>0.25</td><td>7</td><td></td></tr><tr><td>187075684355571200</td><td>161 &plusmn; 64</td><td>26 &plusmn; 0.01</td><td>6.29</td><td>73</td><td>22.9</td><td>0.08</td><td>0.05</td><td>0.031</td><td></td><td></td><td></td></tr><tr><td>5473442554645523712</td><td>209 &plusmn; 57</td><td>32 &plusmn; 0.02</td><td>6.62</td><td>30</td><td>36.4</td><td>0.06</td><td>0.04</td><td>0.157</td><td></td><td></td><td></td></tr><tr><td colspan="12" style="text-align:center; font-weight:bold;">Short-period (P<sub>lpv</sub> &lt; 100 d) light and RV variations with P<sub>lpv</sub>/P<sub>nss</sub> = 1: starspot modulation or short-period pulsators?</td></tr><tr><td>5498026500770376576</td><td>46 &plusmn; 1</td><td>45.7 &plusmn; 0.12</td><td>1.003</td><td>10</td><td>4.9</td><td>0.41</td><td>0.14</td><td>0.0005</td><td></td><td></td><td></td></tr><tr><td>4498425604828703104</td><td>50 &plusmn; 4</td><td>49.57 &plusmn; 0.05</td><td>1.003</td><td>39</td><td>32.5</td><td>0.03</td><td>0.08</td><td>0.18</td><td>0.24</td><td>7</td><td></td></tr><tr><td>3047643956417931264</td><td>64 &plusmn; 1</td><td>63.4 &plusmn; 0.1</td><td>1.003</td><td>13<sup>(c)</sup></td><td>8.3</td><td>0.21</td><td>0.24</td><td>0.0036</td><td>1.44<sup>(c)</sup></td><td>52</td><td></td></tr><tr><td>5637220068643463424</td><td>57 &plusmn; 4</td><td>57.17 &plusmn; 0.03</td><td>1.004</td><td>66</td><td>33.6</td><td>0.04</td><td>0.06</td><td>0.2240</td><td>0.27</td><td>9</td><td></td></tr><tr><td>5883587875302126592</td><td>78 &plusmn; 4</td><td>78.1 &plusmn; 0.1</td><td>1.004</td><td>16</td><td>12.2</td><td>0.42</td><td>0.08</td><td>0.0128</td><td></td><td></td><td></td></tr><tr><td>5701792904776417152</td><td>43 &plusmn; 4</td><td>43.38 &plusmn; 0.01</td><td>1.005</td><td>85</td><td>25.2</td><td>0.02</td><td>0.06</td><td>0.0718</td><td></td><td></td><td></td></tr><tr><td>1869696952997313664</td><td>53 &plusmn; 3</td><td>52.56 &plusmn; 0.05</td><td>1.005</td><td>31</td><td>22.5</td><td>0.13</td><td>0.08</td><td>0.0610</td><td>0.26</td><td>8</td><td></td></tr><tr><td>52350000057883364864</td><td>43 &plusmn; 1</td><td>42.5 &plusmn; 0.03</td><td>1.005</td><td>30</td><td>35.6</td><td>0.10</td><td>0.06</td><td>0.1969</td><td>0.40</td><td>11</td><td></td></tr></tbody></table>

**Notes.** Radii are the FLAME DR3 estimates (see text for how the filling factors $R/R_R$ were estimated). The column labelled $\Delta G$ lists the field mad\_mag\_g\_fov (median absolute deviation) from table *vari_summary*. $^{(a)}$This is likely a young star, of 'Orion-variable' type (V1540 Cyg). $^{(b)}$This star has been added to the Mira category, despite its $P_{\text{lpv}}/P_{\text{nss}}$ ratio vastly different from 1, to illustrate some kind of aliasing problems (see text). $^{(c)}$Doubtful case: significance is only 13 and filling factor is 1.4.

stars from the *vari_long_period_variable* table belong to the sequence $P_{\text{lpv}}/P_{\text{nss}}$ around unity. They correspond to LPVs with a RV variation caused by the envelope pulsation. Although displayed in Fig. 27, the full source list is not given here as they are easily obtained in a way similar to that discussed above for ellipsoidal variables. Table 6 nevertheless lists a few randomly selected examples.

These LPVs are easily identified by their velocity semi-amplitudes, which are smaller than 10 km s⁻¹ (in that sense, they

differ markedly from the ellipsoidal variables which generally have much larger $K_1$ values) and periods in excess of 180 d, as expected for Mira pulsations (Alvarez et al. 2001; Hinkle et al. 2002). Therefore, given these relatively small values of $K_1$, the significance of the SB1-like solution (namely $K_1/\sigma_{K_1}$) may in several cases be smaller than 20, but the identity of the NSS and LPV periods is in itself an indication of the reliability of the RV model. We note that the filling factor has no meaning in this stellar category, because there is no true orbit
<figure><img src="image_28.png" /></figure>

**Fig. 26.** Orbital period from the *nss_two_body_orbit* table vs. photometric period from the *vari_long_period_variable* table. *Top, middle, and bottom panels:* correspond to different filtering based on the SB1 significance (respectively, larger than 5, 20, and 40). The two sequences observed in all panels correspond to *P*<sub>lpv</sub>/<i>P</i><sub>nss</sub> = 0.5 (ellipsoidal variables; *upper sequence*) and *P*<sub>lpv</sub>/<i>P</i><sub>nss</sub> = 1 (LPVs or rotational modulation in a synchronised system; *lower sequence*). *Top panel:* crosses denote NSS solutions for which the Roche-lobe filling factor is above unity, and therefore unphysical. The filtering with significance larger than 40 makes these latter disappear almost entirely.

associated. Mira variables are recognised as well by their large
amplitude in G (>0.1 mag). The pseudo-eccentricities found by
Hinkle et al. (2002) for Miras and semi-regular variables were
clustered around 0.35, with a few cases below 0.1 as well. Here,
the pseudo eccentricities range all the way from 0.09 to 0.48
(Table 6). Furthermore, it has been checked that the maximum
RV is reached at phase 0.8 while maximum light is reached
at phase 1.0, a phase lag that is expected for Mira pulsators.
Furthermore, as for these stars, $K_1$ is relatively small and $P$ is
long, the pseudo mass functions are consequently smaller than
$10^{-3} M_{\odot}$, with some values as small as $10^{-5} M_{\odot}$, in agreement
with the findings of Hinkle et al. (2002; their Table 2) for Mira
and semi-regular variables. LPVs with low values of $f(M)$ are
most clearly seen in Fig. 23a as the yellow tail extending down
to $f(M) \sim 10^{-5} M_{\odot}$ for periods between 300 d and 1000 d. On
that same figure, many more stars with large radii ($R > 100 R_{\odot}$)
are found at shorter periods, but those are spurious ‘SB1-like’
solutions because their periods do not even match the LPV one,
and when available, their filling factors are above unity, which is
non-physical. Furthermore, their mass functions are quite small
(down to $10^{-8} M_{\odot}$). Therefore, these targets cannot be genuine
binaries.

Genuine binaries

Genuine binaries among Miras are expected to have much longer
orbital periods than currently detectable by Gaia DR3 (as is the
case for instance for the carbon Mira V Hya quoted above).
Intriguingly, several genuine SB1s have nevertheless been found
among stars with $P_{\text{lpv}} > 150$ d, a property generally associ-
ated to LPVs. In the fourth part of Table 6 are listed 14 SB1s
selected among the 1189 SB1 solutions in common with the
vari_long_period_variable table. These SB1s have a sig-
nificance of greater than 20, the $1\sigma$ confidence range of $P_{\text{lpv}}/P_{\text{nss}}$
falling outside the ranges 0.45–0.55 and 0.9–1.1 (to avoid SB1-
like variations caused by pulsations), $P_{\text{nss}} > 20$ d and $P_{\text{lpv}} >
150$ d. Their RV curves were checked visually and showed no

<figure><img src="image_29.png" /></figure>

**Fig. 27.** Location in the infrared colour–magnitude diagram of the stars with $0.45 \le P_{\text{lpv}}/P_{\text{nss}} \le 0.55$ (ellipsoidal variables) from Table 6 (dots). Stars with $0.95 \le P_{\text{lpv}}/P_{\text{nss}} \le 1.05$ are represented by crosses; they appear in two different locations, among LPVs with low orbital significance on one hand, and among less luminous giants with much larger orbital significance on the other, perhaps suggesting starspot modulation or short-period pulsators. The dots ($P_{\text{lpv}}/P_{\text{nss}} \sim 0.5$) fall in between these two groups, as they are located just below the tip of the RGB.

peculiarity that would make the solution dubious. This visual
inspection nevertheless revealed that some kind of aliasing prob-
lems remain with the NSS SB1 periods. The star Gaia DR3
1989628623330891904 was originally considered as a possible
genuine binary among LPVs because $P_{\text{lpv}} = 419$ d as compared
to $P_{\text{nss}} = 25$ d. However, the visual inspection of the RV curve
revealed that the LPV period of 419 d is clearly present in the
RV curve, although it was not selected by the period-selection
algorithm, which gave no warning about a possible problem
with that solution (significance = 21, period confidence = 1.000,
ruwe = 1.09) except for the goodness-of-fit of 2.5. Therefore,
that star has been added to the ‘Large-amplitude LPVs’ section.

Rotational modulation on a spin-orbit synchronised star

The final category of interest in Table 6 contains targets with
short periods (i.e. $P \le 100$ d) on the $P_{\text{lpv}}/P_{\text{nss}} = 1$ sequence.
These are listed in the fourth part of Table 6 and identified in
the HRD of Fig. 27 as the crosses at the bottom of the giant
branch. Contrary to the situation prevailing for ellipsoidal vari-
ables and long-period variables discussed above, the phase lag
between velocity and light curves now appears to be anything
between 0 and $\pi$. For this reason, their light variation could be
due to starspot modulation on a spin-orbit synchronised primary
star (e.g. Mazeh 2008). A less likely possibility is that they could
be small-amplitude pulsating stars.

6.3. Identifying EL CVn systems in Gaia data

EL CVn systems are short-period eclipsing binaries (EBs) con-
sisting of an A/F-type main sequence (MS) primary and a low-
mass pre-helium white dwarf (pre-He-WD) secondary. These
systems are a result of mass transfer from the evolved pre-
He-WD progenitor to the currently observed primary star (e.g.
<figure><img src="image_30.png" /><figcaption>**Fig. 28.** Folded *Gaia* *G*, *G*<sub>BP</sub>, and *G*<sub>RP</sub> photometry and RV data of HD 23692, together with TESS binned data. **Top panel:** *Gaia* RV data, while the *second panel* presents the *Gaia* *G* data. **Third panel:** *Gaia* *G*<sub>BP</sub> and *G*<sub>RP</sub> data, with medians shifted to the *Gaia* *G* median for clarity, and the *bottom panel* presents the TESS data binned to 200 phase bins. All plots were folded using the *Gaia* EB-model period and deeper-eclipse epoch as the folding period and phase zero, respectively. We note that the primary eclipse is at phase 0.5, while the secondary eclipse is at phase zero. Observed TESS-eclipse phase drift is due to the more than 1300 day delay from the last *Gaia* point to the first TESS point. For clarity, the three *bottom panels* use the same y-axis scale.</figcaption></figure>

van Kerkwijk et al. 2010; Maxted et al. 2011; Rappaport et al. 2015). EL CVn systems are at a rare stage of binary evolution in which the young pre-He-WD is bloated, with a radius of up to ~0.5 R⊙, and hotter than the more luminous A/F-type primary. As a result, such systems, harbouring a low-mass WD precursor, are detectable even in ground-based photometric surveys. EL CVns with smaller and cooler He-WD secondaries can be detected in space photometry (Faigler et al. 2015). Consequently, 10, 18, and 36 such systems were discovered in the *Kepler* (van Kerkwijk et al. 2010; Carter et al. 2011; Breton et al. 2012; Rappaport et al. 2015; Faigler et al. 2015), WASP (Maxted et al. 2011, 2014), and PTF (van Roestel et al. 2018) photometric surveys, respectively.

The detection of these systems in photometric surveys is based on identifying an eclipsing-binary folded light curve with a 'boxy' deeper eclipse (steep ingress and egress and a flat bottom) and a shallower eclipse with a limb-darkening curved bottom. In an EL CVn, the deeper boxy eclipse is actually the secondary eclipse (total eclipse of the pre-He-WD secondary by the MS primary), while the shallower eclipse is the primary eclipse (pre-He-WD transit of the primary star). This is because the pre-He-WD secondary is hotter than the primary. Such photometric detections usually require confirmation through follow-up spectroscopic RV observations, which enable the light-curve primary and secondary eclipses to be identified from the RV-curve phase.

However, the *Gaia* data enable direct detection of EL CVn systems by combining the *Gaia* photometry and RV data. Figure 28 shows the folded *Gaia* *G*, *G*<sub>BP</sub>, and *G*<sub>RP</sub> photometry and RV data, for a known EL CVn-type system (HD 23692, Maxted et al. 2014), together with the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) binned data. Detrending of the TESS data was done using cosine detrending following Faigler et al.

<figure><img src="image_31.png" /><figcaption>**Fig. 29.** Histogram of phase difference between SB-model primary eclipse and EB-model deeper eclipse, for 1174 stars in our sample.</figcaption></figure>

(2015). The *Gaia* EB-model period and deeper-eclipse epoch were used as the folding period and phase zero, respectively. The RV plot enables us to identify the phase-zero eclipse as the secondary eclipse, and the 0.5-phase eclipse as the primary eclipse. The figure shows that for this system, indeed the secondary eclipse is box-shaped and deeper than the primary one, the main signatures of an EL CVn system. In addition, we see that the *G*<sub>BP</sub> secondary eclipse is much deeper than the *G*<sub>RP</sub> one, an additional indication for the high temperature of the secondary.

### 6.3.1. Sorting through the *Gaia* data

To build the initial sample, from which we can identify EL CVn systems, we selected from the *Gaia* DR3 data systems with (a) an eclipsing-binary solution from *Gaia* photometry, (b) a SB solution (SB1, SB1C, SB2 or SB2C) derived from the *Gaia* RV data, (c) an orbital-frequency difference between the EB and SB solutions of smaller than $\frac{1}{100}$ d$^{-1}$, and (d) an orbital period of shorter than 2 d. The maximum orbital-frequency difference was selected as significantly larger than the inverse of the data time span (~1000 d), a rough estimate for the orbital-frequency uncertainty lower limit. Limiting the orbital-frequency difference to $\frac{1}{500}$ d$^{-1}$ yielded the same sample. An orbital-period limit of 2 days was chosen because most discovered EL CVn systems are below it (see Fig. 5 of van Roestel et al. 2018). These criteria resulted in an initial sample of 1174 systems.

Next, we calculated the phase difference between the SB-model primary eclipse and the EB-model deeper eclipse for all stars in our sample. For a common binary, for example one consisting of two MS stars, we expect this phase difference to be zero. However, for an EL CVn, in which the secondary is hotter and therefore the secondary eclipse is deeper, we expect the phase difference to be ~0.5, assuming a small eccentricity. Figure 29 shows the phase-difference histogram of our initial sample, with a main peak at phase zero, and a much smaller peak at phase 0.5, as expected.

Based on this, we selected an initial list of EL CVn candidates with: (a) an eclipse phase difference in the 0.4–0.6 range, (b) an eccentricity smaller than 0.3, and (c) an EB-model eclipse-depth difference with a S/N of higher than 5. The eclipse-depth difference S/N was required because our method relies on reliably identifying a secondary eclipse that is significantly deeper than the primary one. These criteria yielded 16 systems. Finally, we visually inspected the *Gaia* photometry and RV data and
models of the 16 systems in our initial list, and identified five systems as the most promising EL CVn candidates.

### 6.3.2. Five EL CVn-type candidates

After identifying the five EL CVn candidates, we realised that all have a Gaia SB1 model, and one of them is actually a known EL CVn-type system (Gaia DR3 5087757377681887232 (G5087); TIC-ID 121078334; HD 23692; Maxted et al. 2014), which is shown in Fig. 28. This system serves as an initial validation for our discovery method and the rest of the candidates. Figure 30 shows the Gaia and TESS data (except for Gaia DR3 2048990809445098112 (G2048), for which we could not find TESS photometry) for the four new candidates presented as in Fig. 28. A selected set of Gaia parameters of the five candidates is listed in Table 7.

In principle, one can use the rich Gaia photometry, RV, and derived properties, together with the TESS data, to fit an astrophysical model and estimate the pre-He-WD mass, radius, effective temperature, and other properties. Such an analysis was performed by Maxted et al. (2014), Faigler et al. (2015), and van Roestel et al. (2018) for multiple EL CVn systems they identified. However, this analysis is beyond the scope of this 'teaser' paper.

## 6.4. Ultracool dwarf binaries

Multiplicity studies of ultracool dwarfs (UCDs, which comprise both very low-mass stars and brown dwarfs) at separations $≤1$ au have long since been hampered by the relative faintness of those objects and the associated observational limitations. The separation and mass (or magnitude) ratio distribution of known UCD binaries therefore carries a significant observational bias, which is also affecting the estimated UCD binary fraction of 10%–30% (e.g. Burgasser et al. 2007). Surveys of small samples indicate that the occurrence of compact UCD binaries is significant (Blake et al. 2010; Bardalez Gagliuffi et al. 2014; Sahlmann et al. 2014a) and that many of those systems have photocentre orbit amplitudes measurable in milliarcseconds. It has therefore been predicted that Gaia astrometry will eventually enable the characterisation of hundreds of UCD binary orbits (Sahlmann et al. 2014b) and significantly improve our knowledge of the occurrence and properties of compact UCD binaries.

Here we have a first look at the UCD orbits in Gaia DR3. Figure 31 shows the Gaia colour–magnitude diagram of all sources with nssSolution_type = OrbitalTargetedSearch*. Large grey circles indicate the known UCD sources from the Gaia ultra-cool dwarf (GUCD, Smart et al. 2019) sample, where we used the gaiaedr3.dr2_neighbourhood table to match a source_id from Gaia DR2 to Gaia DR3.

The only non-single star solutions for GUCD sources are found in the nss_two_body_orbit table with solution type OrbitalTargetedSearch*. No GUCD could be matched with an Orbital solution or an acceleration solution. This is mainly because a large fraction (~75%) of GUCDs are fainter than the $G < 19$ cut-off for processing with the nominal NSS pipelines (Sect. 2.2.1). As described in Holl et al. (2023b), the full GUCD sample was nevertheless included in the targeted search for orbital signals.

Thirteen sources with DR3 orbits are part of the GUCD catalogue, and only five of those are brighter than $G = 19$. Table 8 lists the GUCD sources with DR3 orbital solutions.

There are three binaries with previously published astrometric orbit solutions. These are J0805+4812 (Sahlmann et al. 2020), J0823–4912 (Sahlmann et al. 2013, 2015), and J1610–0040 (Dahn et al. 2008; Koren et al. 2016). Generally, the DR3 orbit parameters agree with these published solutions.

The J0320–0446 binary has a published RV orbit and both the Gaia period and eccentricity agree well. The Gaia solution indicates an almost edge-on configuration, in agreement with the expectations from the RV modelling by Blake et al. (2008). The Thiele-Innes coefficients for this low-eccentricity solution are highly correlated, which leads to correlated and skewed distributions when resampling the geometric parameters. This has to be accounted for when using the Gaia solution parameters for estimating the companion mass in particular.

Two sources in this list have only been identified as spectrum binaries, that is, typically L+T-dwarf systems in which the spectrum of the companion is discernible in the combined-light near-infrared spectrum. In principle, the Gaia orbital solutions will make it possible to constrain the masses of the binary components. The orbital parameters refer to the system photocentre, but the applicable constraints depend on the brightness- and mass-ratio of the system, which are not usually determined by Gaia. Therefore, external information and assumptions have to be incorporated. As an example, we explore the orbit of J2026–2943, which has previously been identified as a spectrum binary with components of spectral types L1+T6 (Bardalez Gagliuffi et al. 2014; Gelino & Burgasser 2010). If we assume a field-age mass of $0.080 \pm 0.005 M_\odot$ for the L1 primary and that the light contribution of the T6 companion is negligible in the $G$ band, then the Gaia orbit solution implies a companion mass of $0.041_{-0.009}^{+0.016} M_\odot$, where we account for all parameter covariances using Monte Carlo resampling. This mass estimate is compatible with expectations for a T6 brown dwarf and adds a valuable entry in the list of low-mass systems with dynamically determined masses (Dupuy et al. 2019; Sahlmann et al. 2020). Examples of combining astrometric orbit solutions with RVs, spectrum-binary indicators, and spatially resolved observations to investigate the physics of UCDs can be found in the literature (e.g. Garcia et al. 2017; Sahlmann et al. 2021, 2020; Brandt et al. 2020).

For the remaining seven sources, we find no previously identified multiplicity indicators in the literature. These are therefore potentially new UCD binary discoveries made in Gaia DR3. These could be confirmed by independent observations of their spectroscopic properties or with RV monitoring. Because of its long period and proximity, the J0031–3840 system has an estimated relative semi-major axis of ~60 mas and could possibly be spatially resolved with specialised instruments, which can give access to model-independent mass determinations.

As expected, the UCD binaries discussed above are compact systems with estimated relative separations $≤1.5$ au because a large fraction of their orbit is covered by the DR3 data. Their period–eccentricity distribution is mostly unaffected by the complications in terms of mass determination discussed above and can be used to investigate UCD formation mechanisms or dynamical histories (e.g. Dupuy & Liu 2011). Figure 32 shows these parameters in comparison with the Orbital solutions. The high eccentricity of the long-period solution for J0031–3840 may be affected by the incomplete orbit coverage with Gaia data, which tends to push eccentricity up as also shown by the Orbital solutions.

Comparison with Fig. 18 of Dupuy & Liu (2017, which includes a few sources in common) shows that these generally intermediate eccentricities are in agreement. Importantly, Gaia
<figure><img src="image_32.png" /><figcaption>**Fig. 30.** Gaia and TESS data of four new EL CVn candidates presented as in Fig. 28. We could not find TESS photometry for Gaia DR3 2048990809445098112, so its TESS panel was left empty.</figcaption></figure>
<table><caption>**Table 7.** Parameters of five EL CVn candidate systems.</caption><thead><tr><th>Gaia ID</th><th>5087757377681887232</th><th>1987680971620394624</th><th>480611242765860992</th><th>6637219674994191744</th><th>2048990809445098112</th></tr></thead><tbody><tr><td>TIC ID</td><td>121078334</td><td>197604137</td><td>400028476</td><td>120066508</td><td>378080617</td></tr><tr><td>Other ID</td><td>HD 23692</td><td>TYC 3615-2289-1</td><td>TYC 4106-576-1</td><td>TYC 8757-1969-1</td><td>TYC 3135-13-1</td></tr><tr><td>GSP-Phot T<sub>eff</sub> (K)</td><td>7360</td><td>7504</td><td>7470</td><td>NA</td><td>7148</td></tr><tr><td>GSP-Phot log g (dex)</td><td>3.98<sup>0.05</sup><sub>0.03</sub></td><td>4.01<sup>0.01</sup><sub>0.03</sub></td><td>4.08<sup>0.005</sup><sub>0.004</sub></td><td>NA</td><td>3.77<sup>0.03</sup><sub>0.01</sub></td></tr><tr><td>Parallax (mas)</td><td>3.447 ± 0.063</td><td>1.169 ± 0.012</td><td>2.647 ± 0.013</td><td>1.197 ± 0.020</td><td>1.251 ± 0.013</td></tr><tr><td>Radius FLAME (R<sub>☉</sub>)</td><td>1.975<sup>0.053</sup><sub>0.050</sub></td><td>2.132<sup>0.047</sup><sub>0.047</sub></td><td>1.803<sup>0.037</sup><sub>0.038</sub></td><td>NA</td><td>3.006<sup>0.067</sup><sub>0.067</sub></td></tr><tr><td>G/G<sub>BP</sub>/G<sub>RP</sub> (mag)</td><td>9.56/9.70/9.29</td><td>11.86/12.05/11.52</td><td>10.47/10.65/10.16</td><td>11.64/11.86/11.28</td><td>10.95/11.13/10.64</td></tr><tr><td>RV/G/G<sub>BP</sub>/G<sub>RP</sub> points</td><td>18/55/55/54</td><td>32/64/67/67</td><td>33/69/67/67</td><td>28/47/46/46</td><td>17/48/48/48</td></tr><tr><td>EB period (day)</td><td>0.92859504 ± 0.00001141</td><td>1.16189659 ± 0.00002522</td><td>0.64410724 ± 0.00000429</td><td>1.27337301 ± 0.00005718</td><td>1.36819733 ± 0.00005130</td></tr><tr><td>EB T<sub>0</sub> (BJD)</td><td>2457389.055 ± 0.004</td><td>2457389.680 ± 0.013</td><td>2457388.877 ± 0.003</td><td>2457389.784 ± 0.019</td><td>2457388.853 ± 0.010</td></tr><tr><td>SB1 K<sub>1</sub> (km s<sup>-1</sup>)</td><td>24.28 ± 0.94</td><td>30.42 ± 3.57</td><td>28.72 ± 1.47</td><td>32.28 ± 1.77</td><td>22.28 ± 1.67</td></tr></tbody></table>

<figure><img src="image_33.png" /><figcaption>**Fig. 31.** Colour–magnitude diagram of 533 sources with OrbitalTargetedSearch* solutions (black circles). The larger grey circles indicate sources that are listed in the GUCD sample (Smart et al. 2019), the grey squares indicate red sources discussed in the text, and the diamond indicates the WD discussed in Sect. 8.8.</figcaption></figure>

is filling in the period range of ~0.5–5 yr which until now has been sparsely populated because of the resolution limit of direct-imaging instruments. This will help to build statistically robust samples of UCD binaries that can be used for comparison with stellar binaries. Finally, we inspected the orbits of the three reddest objects; these are not in the GUCD catalogue, and are highlighted with squares in Fig. 31:

**J0219–3925.** This is 2MASS J02192210–3925225, which was characterised as a young late-M dwarf with a wide (4′′) substellar companion by Artigau et al. (2015). The Gaia astrometric orbit corresponds to an inner companion to the M-dwarf, which (if dark) could have a mass as low as 11.2 ± 0.9 $M_{Jup}$ for the primary mass of 113 ± 12 $M_{Jup}$ (Artigau et al. 2015). Another possible explanation is a more massive companion, whose light contribution dilutes the photocentre orbit. Auxiliary data or observations have to be considered to better characterise the inner companion.

**LHS1610.** This mid-M dwarf was identified as an RV binary by Winters et al. (2018) and the Gaia astrometry independently confirms the eccentric 10.6-day orbit. The Gaia solution indicates a close-to edge-on configuration and a companion-mass estimate of $0.052^{+0.004}_{-0.004} M_{⊙}$ when assuming a primary mass of $0.17 \pm 0.02 M_{⊙}$, i.e. it establishes the substellar nature of the companion.

**L 601–78 A.** This is the primary component of the wide binary L 601–78. It was identified as a lens candidate for

mass determination using astrometric microlensing by Gaia (Klüter et al. 2020).

## 7. Compact-object companions

In what follows, we point out a few methods for identifying binary candidates in our tables that might harbour compact-object companions. The discussion is meant to provide ideas for further studies that are needed to confirm the nature of these binaries. We first underline the method used for astrometric orbits, and then discuss white dwarf secondaries, and then larger masses, including those found using SB1 orbits.

### 7.1. Astrometric binaries with compact-object companions using the triage algorithm

To identify unresolved astrometric binaries that are likely to host a compact object as their faint binary companion, we use the triage classification of Shahaf et al. (2019). The algorithm divides the astrometric binaries into three classes: (a) class-I binaries, where the companion is most likely a single MS star (but can also be a close binary or a compact object), (b) class-II binaries, where the companion cannot be a single MS star; therefore, it is most likely a close MS binary (but can also be a compact object), and (c) class-III binaries, where the companion cannot be a single MS star or a close MS binary; therefore, these systems most likely host a compact object as secondary.

The distinction between the three classes depends on the value of the newly defined astrometric mass ratio function (AMRF), $\mathcal{A}$, given by

$$ \mathcal{A} \equiv \frac{a_0}{\omega} \left( \frac{M_1}{M_{\odot}} \right)^{-1/3} \left( \frac{P}{\text{yr}} \right)^{-2/3}, \qquad (9) $$

where $a_0$ is the derived angular semi-major axis of the photocentric orbit, $\omega$ is the parallax, $M_1$ is the mass of the primary star, and $P$ is the orbital period of the binary.

The AMRF can be written as a function of the mass ratio $q = M_2/M_1$ and the luminosity ratio of the two components of the astrometric binary $S = F_2/F_1$ as

$$ \mathcal{A} = \frac{q}{(1+q)^{2/3}} \left( 1 - \frac{S(1+q)}{q(1+S)} \right), \qquad (10) $$

(see details in Shahaf et al. 2019). The luminosity ratio modelling is based on the Pecaut & Mamajek (2013) MS colour and effective temperature tables, assuming no extinction. As emphasised by Shahaf et al. (2019), there are two limiting AMRF values: the maximal value for a single MS companion (class I
<table><caption>**Table 8.** Identifiers and basic properties of 13 UCD binaries in DR3.</caption><thead><tr><th>Gaia DR3</th><th>Name</th><th>nssSolution_type</th><th>Period (d)</th><th>a<sub>0</sub> (mas)</th><th>Notes</th></tr></thead><tbody><tr><td>4997505546262260096</td><td>J0031-3840</td><td>OrbitalTargetedSearch</td><td>1665.4 ± 281.5</td><td>23.96 ± 3.47</td><td>New binary candidate</td></tr><tr><td>2576389458819793920</td><td>J0106+0557</td><td>OrbitalTargetedSearch</td><td>726.2 ± 71.0</td><td>4.48 ± 0.60</td><td>New binary candidate</td></tr><tr><td>5182151481717042944</td><td>J0320-0446</td><td>OrbitalTargetedSearch</td><td>250.6 ± 1.7</td><td>7.75 ± 2.76</td><td>Known RV binary <sup>(d)</sup></td></tr><tr><td>3269943938874146688</td><td>J0344+0111</td><td>OrbitalTargetedSearch</td><td>652.9 ± 23.4</td><td>7.55 ± 0.42</td><td>Known spectrum binary <sup>(e)</sup></td></tr><tr><td>144711230753602048</td><td>J0435+2115</td><td>OrbitalTargetedSearch</td><td>607.4 ± 25.2</td><td>5.48 ± 0.34</td><td>New binary candidate</td></tr><tr><td>3361210791323909504</td><td>J0659+1717</td><td>OrbitalTargetedSearch</td><td>753.6 ± 132.8</td><td>7.90 ± 1.55</td><td>New binary candidate</td></tr><tr><td>933054951834436352</td><td>J0805+4812</td><td>OrbitalTargetedSearchValidated</td><td>735.9 ± 23.0</td><td>14.18 ± 2.06</td><td>Known astrometric binary <sup>(a)</sup></td></tr><tr><td>5514929155583865216</td><td>J0823-4912</td><td>OrbitalTargetedSearchValidated</td><td>250.0 ± 1.2</td><td>4.99 ± 0.21</td><td>Known astrometric binary <sup>(b)</sup></td></tr><tr><td>1610979010812148224</td><td>J1429+5730</td><td>OrbitalTargetedSearch</td><td>445.4 ± 8.5</td><td>4.64 ± 0.46</td><td>New binary candidate</td></tr><tr><td>4406489184157821952</td><td>J1610-0040</td><td>OrbitalTargetedSearch</td><td>612.5 ± 7.7</td><td>9.41 ± 0.25</td><td>Known astrometric binary <sup>(c)</sup></td></tr><tr><td>6797628972554531840</td><td>J2026-2943</td><td>OrbitalTargetedSearch</td><td>638.3 ± 14.5</td><td>5.69 ± 1.05</td><td>Known spectrum binary <sup>(f)</sup></td></tr><tr><td>1754495583527340416</td><td>J2036+1051</td><td>OrbitalTargetedSearch</td><td>696.7 ± 50.4</td><td>4.57 ± 0.53</td><td>New binary candidate</td></tr><tr><td>6616442994033876480</td><td>J2200-3038A</td><td>OrbitalTargetedSearch</td><td>203.5 ± 1.9</td><td>3.84 ± 0.68</td><td>New binary candidate <sup>(g)</sup></td></tr><tr><td>4963614887043956096</td><td>J0219-3925</td><td>OrbitalTargetedSearch</td><td>538.0 ± 3.0</td><td>1.41 ± 0.05</td><td>New binary candidate <sup>(h)</sup></td></tr><tr><td>43574131143039104</td><td>LHS1610</td><td>OrbitalTargetedSearch</td><td>10.6 ± 0.0</td><td>1.39 ± 0.04</td><td>Known RV binary <sup>(i)</sup></td></tr><tr><td>5600272625752039296</td><td>L 601-78 A</td><td>OrbitalTargetedSearch</td><td>14.3 ± 0.0</td><td>1.87 ± 0.07</td><td>New binary candidate</td></tr></tbody></table>

**Notes.** The 'Name' column corresponds to the SHORTNAME in the GUCD catalogue. The uncertainties of $a_0$ were computed using linear error propagation. The three additional sources at the bottom of the table are the reddest OrbitalTargetedSearch sources at the bottom of the main sequence, which are not in the GUCD catalogue.

**References.** <sup>(a)</sup>Sahlmann et al. (2020). <sup>(b)</sup>Sahlmann et al. (2013). <sup>(c)</sup>Dahn et al. (2008). <sup>(d)</sup>Blake et al. (2008). <sup>(e)</sup>Bardalez Gagliuffi et al. (2014).

<sup>(f)</sup>Bardalez Gagliuffi et al. (2014), Gelino & Burgasser (2010). <sup>(g)</sup>This would be a new inner binary as component A in a known 1"-wide binary (Burgasser & McElwain 2006; Smart et al. 2019). <sup>(h)</sup>This would be a new inner binary in a known 4"-wide binary (Artigau et al. 2015).

<sup>(i)</sup>Winters et al. (2018).

<figure><img src="image_34.png" /><figcaption>**Fig. 32.** Orbital eccentricity as a function of period for the UCD systems listed in Table 8 (black symbols). The parameters of Orbital solutions within 200 pc are shown in grey.</figcaption></figure>

sources), and the maximal value assuming a close binary of two identical MS stars as the secondary companion (class II sources).

Figure 33 presents the derived AMRF values for the Gaia unresolved astrometric binaries presented in this work, with primaries in the range of 0.2–2.0 $M_\odot$ and significance larger than 20, using the primary mass values reported in Table 3. Systems with AMRF values that exceed the maximal possible value for triple stars by more than $4\sigma$, where the uncertainty $\sigma$ was calculated by propagating the uncertainties of the quantities in Eq. (9). These are presented in Fig. 33 as bold black points and are likely to host a compact-object companion. As the light contribution of the companions of these systems is negligible, namely $S \approx 0$, we can derive the mass ratio and then the mass of the secondary of these systems. Their mass values are presented in the right hand panel of the figure.

We compare the obtained masses with the conservative lower limit estimate of the companion mass (Sect. 5.1) in the left panel

of Fig. 34. Additionally, because the photocentre coincides with the position of the primary star for faint companions, we expect the semi-major axes derived from the astrometry and the RV spectroscopy to be similar, as demonstrated in the right panel of Fig. 34 for the AstroSpectroSB1 cases. The CMD of these class III systems is shown Fig. 35.

Figure 36 presents a mass histogram of the secondaries of the astrometric binaries assumed to have a compact companion of up to $2.1 M_\odot$. It seems as though most of the companions are white dwarfs, with a clear narrow peak at ~0.6 $M_\odot$, as is the case for field white dwarfs. Obviously, the secondary mass population is heavily biased by the way it was derived, and so any astrophysical interpretation should be made carefully. In any case, the circularisation at large periods is striking (see Fig. 37).

The histogram of secondary masses in Fig. 36 has been limited to $2 M_\odot$. There are four sources with a larger mass (identified as AMRFClassIII in the table binary masses), but we find indications that they may be artefacts.

## 7.2. A closer look at the astrometric binaries with white-dwarf companions

White dwarfs are often present in binary systems. The co-eval context with their companion star makes such systems important benchmarks for understanding stellar evolution. WDs in wide systems can be detected relatively easily through searches for common proper motion objects (e.g. El-Badry & Rix 2018). However, in closer systems, the WD can be very difficult to detect because of the overwhelming brightness of the companion, particularly for early spectral types. In that case, the WD may be hidden until revealed by astrometric motion, spectroscopic variability, or a photometric excess. A classic example is the discovery of Sirius B (Bessel 1844), which is both an astrometric and spectroscopic binary (e.g. Barstow et al. 2005; Bond et al. 2017). Sirius represents a class of binary systems, the Sirius-type binaries, consisting of a primary star of spectral type earlier than late-K and a WD. Examples of such
<figure><img src="image_35.png" /><figcaption>**Fig. 33.** Triage of the *Gaia* astrometric binaries, with classes I to III from bottom to top delineated by dotted and dashed lines respectively. **Left:** AMRF vs. mass of the primary for the astrometric solutions of this paper. The systems with a probable compact-object companion (class III) are presented as bold black points (see text). For reference, the rest of the sample is plotted as fine black points. **Right:** masses of the compact companions derived from the AMRF as a function of their primary mass. The remaining systems do not appear in this panel. The yellow star is the neutron star candidate *Gaia* DR3 5136025521527939072 discussed in Sect. 7.3.</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>**Fig. 34.** Left: comparison between the minimum companion mass derived in Sect. 5.1, and the AMRF-derived masses for the compact-object candidates. The sources where the AMRF mass is smaller than the minimum mass are AstroSpectroSB1, which have a non-negligible flux ratio. Right: comparison between semi-major axes derived for the AstroSpectroSB1 systems using the astrometric parameters (horizontal axis) and the spectroscopic parameters (vertical axis). The yellow star is *Gaia* DR3 5136025521527939072.</figcaption></figure>

systems have often been identified by flux excesses at wavelengths shorter than those spanned by the primary, in the UV, Extreme UV (EUV), or X-ray (see e.g. Barstow et al. 1994). A fraction have subsequently been resolved by space-based observations (e.g. Barstow et al. 2001).

The number of known Sirius-type binaries lies in the tens of objects, with selection effects playing a strong role in identification of an individual system. For example, unless resolved, the flux of any cool WD will always be buried in the light of the primary companion. Whether or not a system can be resolved depends on the separation and distance of the components. Binary systems comprising two WDs (double degenerates) or a WD with an M dwarf companion are easier to find as they will sit closer to the main WD cooling tracks in the HRD. Even

so, the nature of any double degenerates might not be apparent if the stars have similar or featureless spectra. The SPY survey sought to identify double degenerates from radial velocity variations, finding 39 double degenerate systems and 46 WDs with cool companions from a sample of 643 stars (Napiwotzki et al. 2020).

The *Gaia* stellar catalogue is an enormous resource that will potentially increase the number of known binary systems with WD components by at least an order of magnitude. In *Gaia* DR2 and *Gaia* EDR3, the number of known WDs expanded by such a factor (Gentile Fusillo et al. 2019, 2021). While many WD+M systems can be identified by their location in the HRD, double degenerates will typically show significant overlap with the isolated WD cooling tracks and Sirius-like systems largely
<figure><img src="image_37.png" /><figcaption>**Fig. 35.** Class-III CMD. Black points show Orbital and AstroSpectro objects for reference. Red points are AMRF class-III. The yellow star is Gaia DR3 5136025521527939072.</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>**Fig. 37.** e-P diagram. Black points are Orbital and AstroSpectro objects for reference. Red points are AMRF class-III. The yellow star is Gaia DR3 5136025521527939072.</figcaption></figure>

<figure><img src="image_39.png" /><figcaption>**Fig. 36.** A histogram of the companion masses for compact object candidates up to a mass of 2.1 $M_{\odot}$.</figcaption></figure>

overlap with the main sequence. The release of eclipse, astrometry, and spectroscopy data related to the identification of NSSs in Gaia DR3 is an important step forward. In principle, these new resources can be used to search for the presence of WDs in a variety of binary systems.

## Selection of candidate binary systems with WD components

The wavelength coverage of the Gaia RVS is not optimised for the study of WDs, which typically have broad absorption lines in their photospheres, when present. Therefore, we would expect only the primary stars in Sirius-like binaries to be detected as radial velocity variables. These will therefore most likely be found in the sample of SB1 systems. If the secondary is a WD, it will not contribute significantly to the brightness of the system

in the Gaia bands. However, if hot enough, there may be a measurable excess at shorter wavelengths. In addition, the secondary mass will lie between ≈0.4 and 1.4 $M_{\odot}$, where the Chandrasekhar limit defines the upper bound.

Binaries with WD components might also be detected astrometrically or as eclipsing binaries. Therefore, we assembled an initial list of potential candidate binary systems with WD components from the NSSs selected for all these possibilities using the following nssSolution_type keywords: AstroSpectroSB1, SB1C, SB1, Orbital, OrbitalAlternative, Eclipsing*, and OrbitalTargetedSearch. We did not apply any quality selection criteria except to reject any objects with $G$ greater than 20. This selection yielded a total of 355 524 NSSs for further analysis. The AMRF sample, which is based on AstroSpectroSB1 and Orbital solutions alone, is a subset of these candidates for which we have good estimates of the component masses.

In the search for WD companions, we use the AMRF data to restrict the mass range of compact objects to lie below the 1.4 $M_{\odot}$ Chandrasekhar limit. Applying this criterion yields 676 objects, which are shown in green in Fig. 38 and compared to the locus of the GCNS (grey data points). The secondary mass alone cannot be used to definitively determine whether or not these are WD components, as F, G, K and the earliest M main sequence stars also occupy this mass range. However, several factors indicate that these objects are highly likely to be Sirius-type binaries. Any unresolved main sequence binaries should appear to be over-luminous. Evolution on the main sequence and the range of possible luminosity combinations may prevent a clear separation of binaries and isolated stars, but unresolved main sequence binaries should appear as SB2 systems in the NSS Gaia catalogue. Finally, as noted above, the mass distribution for the secondaries in these unresolved astrometric binaries has a strong peak at 0.55–0.6 $M_{\odot}$ corresponding to the known peak of the mass distribution of field WDs (Fig. 36). This is in contrast to the smooth mass distribution expected for MS stars.

While the vast majority of selected objects lie on the MS, as shown in Fig. 38, there are 39 objects that match WD colours and magnitudes, indicating a WD primary; these are shown in
<figure><img src="image_40.png" /></figure>

**Fig. 38.** HRD of the candidate NSSs with WD components with a secondary mass solution below the Chandrasekhar limit (<1.4 $M_\odot$, green data points). These are compared with the locus of stars in the GCNS (grey data points).

<figure><img src="image_41.png" /></figure>

**Fig. 39.** WD with orbital solutions (green points, corrected from extinction) overplotted on the *Gaia* DR3 low-extinction HRD. Most of the points lie above the hydrogen sequence. The red dots and WD 0141-675 (orange square) are discussed in Sect. 8.8.

Fig. 39. The majority of these objects lie above the main concentration of the isolated white dwarfs, and therefore these systems are highly likely to be double degenerates, where the brightness of two unresolved objects combines to yield an apparent excess in luminosity.

As discussed above, when we know the secondary mass and the binary is not revealed as an SB2 system, we can be very confident that the secondary is a WD and therefore that the binary is a Sirius-type system. However, it is likely that there are many more Sirius-type systems in the non-SB2 sample. An unresolved binary system can be revealed by a flux excess in a waveband where the contribution from the primary star is expected to be weak. A number of Sirius-type binary discoveries have been made by detecting the WD in the EUV and UV wavebands. The GALEX mission surveyed most of the sky in two broad far-UV (FUV) and near-UV (NUV) bands. Cross-correlating the GALEX database with the *Gaia* DR3 non-SB2 binaries will potentially reveal the Sirius-type systems with a hot WD component. This is illustrated by applying this to the astrometric binaries in the sample. Figures 40 and 41 show the *G* vs. *G*<sub>BP</sub>-*G*<sub>RP</sub> HRD for the cross-match of the GALEX GR6+7 AIS catalogue with this sample for NUV and FUV bands, respectively. The small grey data points are the GCNS stars in each figure while the coloured symbols are the NUV (Fig. 40) and FUV detections (Fig. 41) colour-coded according to the absolute NUV or FUV magnitude, as indicated in the side bar. These magnitude ranges can be compared to the typical values for white dwarfs in the optical colour-absolute magnitude diagram, as indicated in Fig. 39. The absolute NUV magnitude correlates well with the *G*<sub>BP</sub>-*G*<sub>RP</sub> colour, an indicator of the temperature of the primary star. However, a few systems show a strong NUV excess for the systems with cooler main sequence primaries, indicated by red to yellow colours compared to green to blue in that region of the diagram. Hence, the integrated NUV flux is not generally a good indicator of the presence of the white dwarf. In contrast, there is little if any correlation between the absolute FUV magnitude and *G*<sub>BP</sub>-*G*<sub>RP</sub> colour, indicating that the FUV is a better discriminator than the NUV, the measured magnitudes potentially providing an estimate of the WD temperature. However, this can only be applied to the relatively few stars that are sufficiently hot to have a measurable FUV flux. We note that the FUV magnitude is not a completely unique indicator of the presence of a WD, as MS stars with an active corona can also generate an enhancement in the total FUV flux through the strong C IV (154.8 nm & 155.0 nm) and He II (164 nm) emission lines.

We also cross-matched the full *Gaia* DR3 non-SB2 binaries with the GALEX GR6+7 AIS catalogue. The results are shown in Fig. 42, with 29 000 stars of the list of 355 000 objects having a GALEX FUV counterpart. The FUV detections in the WD region of the HRD provide an indication of the range of FUV absolute magnitudes – namely between about 8 and 20 – that correspond to WDs. Many of the FUV counterparts in Fig. 42 have similar magnitudes, but without further information it is not possible to categorically identify these as WDs and rule out alternative explanations for the FUV flux.

A more detailed modelling of the predicted primary and WD fluxes across the expected range of temperatures should be able to refine the discriminatory power of this approach to selecting Sirius-type systems, but this is beyond the scope of this *Gaia* DR3 companion paper.

### 7.3. A possible binary with a dormant neutron star with an AstroSpectroSB1 orbit

Only a few tens of dynamically confirmed Galactic stellar black holes (BHs) and neutron stars (NSs) are known to reside in binary systems. These are discovered either by their X-ray emission, fueled by mass transfer from their non-compact stellar companions (e.g. Fabian et al. 1989; Remillard & McClintock 2006;
<figure><img src="image_42.png" /><figcaption>**Fig. 40.** G vs. $G_{BP}-G_{RP}$ HRD showing the cross-match between the GALEX GR6+7 AIS catalogue with the GCNS (small symbols) and the candidate list of binaries with WD components with computed secondary star masses below the Chandrasekhar limit (<1.4 $M_\odot$). The symbols are colour coded with the absolute NUV magnitude.</figcaption></figure>

<figure><img src="image_43.png" /><figcaption>**Fig. 42.** G vs. $G_{BP}-G_{RP}$ HRD showing the cross-match between the GALEX GR6+7 AIS catalogue and the full list of non-SB2 binaries selected here (large symbols). The symbols are colour coded according to absolute FUV magnitude as indicated by the side-bar. The small grey data points are the full list of non-SB2 binaries.</figcaption></figure>

<figure><img src="image_44.png" /><figcaption>**Fig. 41.** G vs. $G_{BP}-G_{RP}$ HRD showing the cross-match between the GALEX GR6+7 AIS catalogue with the GCNS (small symbols) and the candidate list of binaries with WD components with computed secondary star masses below the Chandrasekhar limit (<1.4 $M_\odot$). The symbols are colour coded with the absolute FUV magnitude.</figcaption></figure>

Orosz et al. 2007; Ziolkowski 2014), or, in the case of active pulsars, by their radio pulsed emission.

Obviously, most BH in binaries have not yet been detected, because their optical counterparts are well within their Roche lobes, and so mass is not transferred and X-rays are not generated, making these systems dormant (see discussion on the frequency of such systems and the prospect of their detection with Gaia astrometry by Breivik et al. 2017; Mashian & Loeb 2017; Shao & Li 2019; Wiktorowicz et al. 2019). Similar arguments apply to dormant NSs – the pulsation phase lasts

for only 10 to 100 million years when the pulsar is young (Faucher-Giguère & Kaspi 2006; Bransgrove et al. 2018) – and to binaries with WD companions (see discussion above). Such dormant binaries can be found by the orbital motion of the primary, detected either by astrometry or RVs. In all three classes of dormant companions, the challenge is to identify the binaries, estimate the mass of the unseen companion, and rule out a faint MS companion.

One of the systems identified by the triage algorithm as having a compact companion, Gaia DR3 5136025521527939072, is in fact an AstroSpectroSB1 binary, with a primary mass of $1.2 M_\odot$ and a secondary mass of $1.5 M_\odot$, consistent with a binary having a dormant NS with a period of 536 days. Its location is marked in the pertinent figures of the triage analysis above.

The astrometric orbit and the phase-folded radial velocity of this source are shown in Fig. 43¹⁵. In order to validate the orbit, we requested observing time on the SOPHIE spectrograph mounted at the 1.93 m telescope of the Observatoire de Haute-Provence (France). The SOPHIE pipeline (Bouchy et al. 2009) together with a G2 mask was used and we obtained a RV = 40.603 ± 0.023 km s⁻¹ with a FWHM = 9.274 km s⁻¹ on BJD 2459541.389492. The consistency of this RV obtained about 4.5 years after the end of the Gaia data segment used for Gaia DR3 confirms the quality of the predicted orbit.

### 7.4. Compact objects in SB1 solutions

While the search for compact object companions above was carried out using the astrometric orbits, we complete the search using the SB1 solution. A search for SB1 sources with large mass functions has long since been proposed as a way to identify candidates with a BH or NS companion (Trimble & Thorne 1969;

<footnote n="15">¹⁵ The astrometric orbit figure was obtained on the basis of the pystrometry package (https://github.com/Johannes-Sahlmann/pystrometry, Sahlmann 2019). Other examples and a description are given in Holl et al. (2023b).</footnote>
<figure><img src="image_45.png" /><figcaption>**Fig. 43.** Top panel: phase-folded radial velocity data of Gaia DR3 5136025521527939072, together with the orbits using the astrometric (red dot-dashed line) and spectroscopic (blue solid line) orbital elements separately; the OHP/Sophie external measurement (green squared point) was not part of the fit. Bottom panel: along-scan residuals of the mean epoch astrometric measurements (black symbols) relative to the model positions (grey circles) and the astrometric orbit (red solid line) of the same source. The red cross marks the focus of the orbit and the grey square is the periastron location.</figcaption></figure>

Guseinov & Zel'dovich 1966). Among the SB1 sources, 94 have significance larger than 20 and $f(M) > 1.4 M_⊙$, and 20 among them $f(M) > 3 M_⊙$. The SB1 solution of Gaia DR3 2006840790676091776 shall be dismissed because of contamination by a nearby bright source. Inspection of RVS spectra of Gaia DR3 5259215388421037696 shows that the source is probably an SB2 and the radial velocities, computed with an incorrect template, are most probably incorrect, and so the SB1 solution of this star will be discarded. Gaia DR3 878555832642451968 has a RV measurement in the LAMOST (Luo et al. 2015) survey (−100.86 km s⁻¹ at BJD 2458068.5) which does not agree with the SB1 solution. A reanalysis of the RVS epoch RV shows that an alternative solution with a period of 8.438 days is also possible and in better agreement with LAMOST data. The SB1 solution in the Gaia archive should therefore be considered as dubious. In Fig. 44 we show the position of the sources with $f(M) > 1.4 M_⊙$ in the colour–magnitude diagram. The relevant data of the sources with $f(M) > 3 M_⊙$ are reported in Table 9.

From Fig. 44, we can see that the vast majority of the selected sources are not main sequence stars. It is therefore challenging to determine the real nature of these systems, because if the pri-

<figure><img src="image_46.png" /><figcaption>**Fig. 44.** HRD of SB1 solutions with $f(M) > 1.4 M_⊙$ and significance > 20. Squared symbols are for sources with $1.4 M_⊙ < f(M) \le 3 M_⊙$, star symbols for sources with $f(M) > 3 M_⊙$. The background grey scale shows the density distribution of all SB1 solutions.</figcaption></figure>

mary is a giant star, it can easily outshine a companion on the main sequence. In some cases, the secondary, although on the main sequence, can be more massive than the primary because of mass transfer, as in Algol-type systems (see El-Badry et al. 2022, for recent examples of BH candidates dismissed as main sequence companions of stripped stars). We recall that such systems are much more common objects than dormant BH. Another possible explanation for such large mass-function values is that the unseen companion is itself a binary composed of two main sequence stars. The understanding of the nature of the other systems would require a deeper analysis using external data and follow-up observations, but such an analysis is beyond the scope of this paper. However, we can comment on some of these objects. For Gaia DR3 5863544023161862144, the presence of eclipses allows us to classify it as an Algol system and to exclude the compact object companion hypothesis. The Gaia photometry of the source Gaia DR3 5857059996952633984 shows a light curve with eclipses of Algol type, albeit with a period of 1.17143 days, typical of Algol systems, in contrast to the period from the SB1 solution. By analysing the epoch radial velocities and the epoch photometry, we can exclude an aliasing in both the SB1 solution and the photometry. A possible solution is that this source is a triple system where the RV data are from the outer component, and the eclipses involve the two inner components.

A particularly interesting source is Gaia DR3 4429923 11418593664 (HIP 15429), a B5Ib star (Navarro et al. 2012) with $f(M) = 4.77 M_⊙$. In order to validate the orbit, this source was observed with the HERMES spectrograph mounted on the 1.2 m Mercator telescope<fnref n="16" /> (Raskin et al. 2011) at the Roque de los Muchachos Observatory on La Palma Island. An RV of −47.2 ± 3.5 km s⁻¹ at BJD 2459650.358 was obtained, which is compatible with the Gaia SB1 solution. The HERMES spectrum also confirms the spectral classification of Navarro et al. (2012). Using the 3D extinction map of Lallement et al. (2019), we estimate a dereddened absolute magnitude and colour, $M_{G,0} = -3.168$ and $G_{BP,0} - G_{RP,0} = 0.073$, respectively. Comparing these values with the PARSEC evolutionary tracks (Bressan et al. 2012) for solar metallicity, we can interpret this source as being

<footnote n="16">¹⁶ http://www.mercator.iac.es/</footnote>
<table><caption>**Table 9.** SB1 solutions with $f(M) > 3 M_\odot$.</caption><thead><tr><th>Gaia DR3</th><th>f(M)<br>(M<sub>☉</sub>)</th><th>Period<br>(days)</th><th>a<sub>1</sub> sin i<br>(R<sub>☉</sub>)</th><th>R<br>(R<sub>☉</sub>)</th><th>M<sub>G</sub></th><th>G<sub>BP</sub>-G<sub>RP</sub></th></tr></thead><tbody><tr><td>4661290764764683776<sup>(a)</sup></td><td>13.67</td><td>204.930 ± 0.862</td><td>349.49</td><td>60.52</td><td>-6.707</td><td>0.474</td></tr><tr><td>5863544023161862144<sup>(b)</sup></td><td>7.80</td><td>10.605 ± 0.001</td><td>40.25</td><td></td><td>-1.531</td><td>1.783</td></tr><tr><td>442992311418593664<sup>(c)</sup></td><td>4.77</td><td>216.531 ± 1.463</td><td>255.33</td><td>20.16</td><td>-1.592</td><td>0.862</td></tr><tr><td>206292746724589824<sup>(d)</sup></td><td>4.53</td><td>347.002 ± 0.364</td><td>343.50</td><td>42.25</td><td>-2.741</td><td>2.067</td></tr><tr><td>5857059996952633984<sup>(e)</sup></td><td>4.25</td><td>155.085 ± 0.228</td><td>196.63</td><td>7.42<sup>(h)</sup></td><td>-0.893</td><td>0.684</td></tr><tr><td>2174777963318889344</td><td>3.83</td><td>82.723 ± 0.158</td><td>124.88</td><td>34.82</td><td>-1.970</td><td>2.021</td></tr><tr><td>2031113506311851904<sup>(f)</sup></td><td>3.78</td><td>35.908 ± 0.030</td><td>71.29</td><td></td><td>-0.145</td><td>1.736</td></tr><tr><td>1996704839648530816</td><td>3.75</td><td>7.54574 ± 0.00077</td><td>25.13</td><td>7.29</td><td>-1.414</td><td>0.520</td></tr><tr><td>251157906379754496</td><td>3.62</td><td>296.676 ± 2.176</td><td>287.10</td><td></td><td>-0.928</td><td>1.714</td></tr><tr><td>3331748140308820352</td><td>3.56</td><td>225.268 ± 1.189</td><td>237.61</td><td></td><td>0.485</td><td>1.836</td></tr><tr><td>1828150428697001472</td><td>3.54</td><td>333.688 ± 0.205</td><td>308.23</td><td></td><td>-3.716</td><td>1.583</td></tr><tr><td>3112097229257687680<sup>(g)</sup></td><td>3.33</td><td>260.978 ± 0.608</td><td>256.40</td><td>23.98<sup>(h)</sup></td><td>-1.711</td><td>1.422</td></tr><tr><td>5963629779180627968</td><td>3.19</td><td>11.369 ± 0.002</td><td>31.30</td><td>11.86<sup>(h)</sup></td><td>0.922</td><td>2.078</td></tr><tr><td>512307478642441984<sup>(f)</sup></td><td>3.14</td><td>145.578 ± 0.074</td><td>170.44</td><td></td><td>-1.885</td><td>1.886</td></tr><tr><td>527155253604491392</td><td>3.13</td><td>149.155 ± 0.318</td><td>173.06</td><td>12.15<sup>(h)</sup></td><td>0.371</td><td>1.856</td></tr><tr><td>5869320651099982464<sup>(f)</sup></td><td>3.09</td><td>63.924 ± 0.011</td><td>97.95</td><td></td><td>-1.615</td><td>1.214</td></tr><tr><td>2929565719083290240</td><td>3.09</td><td>32.473 ± 0.014</td><td>62.31</td><td>7.84<sup>(h)</sup></td><td>0.484</td><td>1.237</td></tr></tbody></table>

**Notes.** The radii *R* are from GSP-Phot or FLAME when available. <sup>(a)</sup>LHA 120-S 80: B8Ie (Rousseau et al. 1978) star in the LMC with emission lines. A distance of 49.59 kpc from Pietrzyński et al. (2019) was used to compute absolute magnitude $M_G$. <sup>(b)</sup>V878 Cen: eclipsing binary star classified as a hot semi-detached system (Avvakumova et al. 2013) with the same period, confirmed by Gaia photometry. <sup>(c)</sup>HIP 15429: B5Ib star (Navarro et al. 2012); belongs to PMa sample of Kervella et al. (2022). <sup>(d)</sup>EM* GGA 311: Emission-line star (González & González 1956). <sup>(e)</sup>Classified as Algol type eclipsing binary from Gaia photometry with period of 1.17143 days. <sup>(f)</sup>Gaia light curve show ellipsoidal behaviour. <sup>(g)</sup>EM* RJHA 92: Emission-line Star (Robertson & Jordan 1989). <sup>(h)</sup>Radius from FLAME.

a $4.9 \pm 0.3 M_\odot$ star that has just left the main sequence. The resulting minimum mass for the companion would be $10.4 M_\odot$. Under the hypothesis that this is a triple system, the secondary would then be a binary where at least one component should have a mass equal to or larger than $5.2 M_\odot$. However, if all the stars in the system are coeval, this most massive star in the inner binary should be evolved too, and should therefore be brighter than the primary, refuting the triple-star hypothesis. Excluding HIP 15429 as an Algol system is more difficult because even a $12 M_\odot$ companion on the main sequence would be fainter than the B5Ib primary. However, we note that the absorption lines in the HERMES spectrum do not show any clear double profile, despite the fact that the spectrum was obtained at the phase with maximum radial-velocity difference between the two components. Moreover, there are only a few known Algol systems with such a long period, ≈216 days, and consisting of early-type stars (e.g. μ Sgr). Another possibility is that this source may have a dormant BH companion. More observations and modelling will be needed to decide between the different hypotheses. We finally note that the astrometric *ruwe* parameter of this star is 2.10, which suggests that upon the next data release it will be possible to obtain an astrometric orbit.

We now move our attention to SB1 sources which can be classified as belonging to the main sequence, for which an estimate of the mass of the primary is provided by IsocLum. Restricting the search for compact object companions to main sequence primaries allows us to reduce the number of false detections where the secondary is a normal main sequence star outshined by an evolved primary. We then selected from the table presented in Sect. 5.1 the SB1 sources for which $m2\_lower > m1\_upper$ and significance > 20. This results in 68 sources; among them 15 have $m2\_lower > 3 M_\odot$ and 25 have $1.4 M_\odot < m2\_lower \le 3 M_\odot$. Their position in the magnitude-colour diagram is shown in Fig. 45.

<figure><img src="image_47.png" /><figcaption>**Fig. 45.** Dereddened HRD of compact object companion candidates from SB1 solutions on the main sequence. Circle symbols are for sources with $m2\_lower \le 1.4 M_\odot$, square symbols are for sources with $1.4 M_\odot < m2\_lower \le 3 M_\odot$, and stars symbols are for sources with $m2\_lower > 3 M_\odot$. The background grey scale shows the density distribution of all SB1 solutions classified as belonging to the main sequence by IsocLum.</figcaption></figure>

It should be noted that the spectroscopic RVs of stars cooler than 3875 K were not processed by the NSS pipeline. This introduces a selection on the mass of the primary that means that almost no SB1s are present in the catalogue with a primary mass below 0.6 $M_\odot$. It is therefore not possible with this selection to obtain candidates with more massive companions belonging to the main population of white dwarfs.
<table><caption>**Table 10.** Source candidates with compact object companions with m2_lower > 3 M⊙ and m2_lower > m1_upper from SB1 solutions with significance > 20.</caption><thead><tr><th>Gaia DR3</th><th>Period<br>(days)</th><th>f(M)<br>(M<sub>☉</sub>)</th><th>M<sub>1</sub><br>(M<sub>☉</sub>)</th><th>m2_lower<br>(M<sub>☉</sub>)</th><th>R<br>(R<sub>☉</sub>)</th><th>a<sub>1</sub> sin i<br>(R<sub>☉</sub>)</th><th>G<sub>BP,0</sub>-G<sub>RP,0</sub></th></tr></thead><tbody><tr><td>2219809419798508544</td><td>10.8653 ± 0.0025</td><td>1.287</td><td>1.949</td><td>3.129</td><td>3.95<sup>+0.23</sup><sub>-0.11</sub></td><td>22.44</td><td>0.598</td></tr><tr><td>4514813786980451840</td><td>22.0204 ± 0.0124</td><td>1.559</td><td>2.477</td><td>3.746</td><td>4.86<sup>+0.38</sup><sub>-0.36</sub></td><td>38.30</td><td>0.368</td></tr><tr><td>5694373091078326784</td><td>12.8848 ± 0.0040</td><td>1.660</td><td>2.161</td><td>3.708</td><td>3.82<sup>+0.19</sup><sub>-0.16</sub></td><td>27.37</td><td>0.341</td></tr><tr><td>2966694650501747328</td><td>10.3980 ± 0.0011</td><td>1.158</td><td>2.082</td><td>3.096</td><td>3.64<sup>+0.05</sup><sub>-0.05</sub></td><td>21.04</td><td>0.385</td></tr><tr><td>948585824160038912</td><td>8.2019 ± 0.0015</td><td>1.472</td><td>2.016</td><td>3.283</td><td>3.67<sup>+0.09</sup><sub>-0.21</sub></td><td>19.45</td><td>0.427</td></tr><tr><td>2197954362764248192</td><td>17.5097 ± 0.0070</td><td>1.470</td><td>2.178</td><td>3.359</td><td>5.71<sup>+0.49</sup><sub>-1.37</sub></td><td>32.24</td><td>0.591</td></tr><tr><td>2933630927108779776</td><td>14.7175 ± 0.0007</td><td>1.225</td><td>2.178</td><td>3.221</td><td>4.39<sup>+0.19</sup><sub>-0.16</sub></td><td>27.02</td><td>0.443</td></tr><tr><td>448452383082046208</td><td>23.4939 ± 0.0131</td><td>1.474</td><td>2.318</td><td>3.584</td><td>4.61<sup>+0.36</sup><sub>-0.43</sub></td><td>39.25</td><td>0.514</td></tr><tr><td>5243109471519822720</td><td>14.9137 ± 0.0005</td><td>1.565</td><td>2.014</td><td>3.649</td><td>4.23<sup>+0.09</sup><sub>-0.08</sub></td><td>29.58</td><td>0.603</td></tr><tr><td>5536105058044762240</td><td>12.1766 ± 0.0039</td><td>1.180</td><td>2.178</td><td>3.000</td><td>4.50<sup>+0.15</sup><sub>-0.17</sub></td><td>23.52</td><td>0.481</td></tr><tr><td>6734611563148165632</td><td>14.3444 ± 0.0016</td><td>1.695</td><td>2.103</td><td>3.883</td><td>4.22<sup>+0.12</sup><sub>-0.13</sub></td><td>29.60</td><td>0.462</td></tr></tbody></table>

Notes. The radius *R* and dereddened *G*<sub>BP,0</sub>−*G*<sub>RP,0</sub> colour were obtained with IsocLum.

Particularly interesting are sources with m2_lower > 3 M⊙, which could have a dormant BH companion. We checked each of the candidates and found that, among sources with m2_lower > 3 M⊙, the sources Gaia DR3 548272473920331136 and Gaia DR3 6000420920026118656 are known eclipsing binaries (Otero 2008; Avvakumova et al. 2013) classified as Algol type, while Gaia DR3 185054898 8047789696 is an Algol-type eclipsing binary detected by Gaia.

We then checked the Gaia and TESS (Ricker et al. 2015) photometry for the other 11 sources, and all show a modulation of the flux that is in phase with the radial velocity, similar to that expected for an ellipsoidal star<fnref n="17" />, confirming the binary nature. However, this ellipsoidal behaviour suggests that these stars are rather evolved, but the small amplitude of the modulation (a few percents) tells us that the primaries do not fill their Roche lobe. Using the relation between the mass ratio and the effective radius of the Roche lobe provided by Eggleton (1983), we get that the mass required for the primary to fill the Roche lobe, given the radii estimated with the IsocLum code, would be always below 0.1 M☉, which is too low for an evolved star and for the observed effective temperature. A more detailed modelling of the light curve of these objects is out of the scope of this article.

The 17 known X-ray binaries with BH companions (Corral-Santana et al. 2016) have periods of 0.3–5 days. We expect the similar dormant binaries to have longer periods, and therefore the range we find here is consistent with the expected periods. Our sources are nevertheless only considered to be candidates, because other explanations are possible that do not invoke a compact companion. With the information that we have, we cannot rule out the possibility that these sources are Algol-type systems, but the bluest sources should be considered as more promising candidates of dormant BHs because they are nearer the main sequence than the redder sources, and therefore cannot easily outshine a MS companion. Finally, as mentioned above, we cannot exclude that the unseen companion is the inner

<figure><img src="image_48.png" /><figcaption>**Fig. 46.** Top panel: phase-folded radial velocity of Gaia DR3 2966694650501747328 (*P* = 10.398 d). Bottom panel: phase-folded TESS (black circles) and Gaia normalised flux (green, blue, and red circles: flux in *G*, *G*<sub>BP</sub>, and *G*<sub>RP</sub> bands respectively).</figcaption></figure>

binary composed of two MS stars. The periods of these 11 candidates range from 8.2 to 23.5 days, which is not short enough to exclude the triple system hypothesis.

The data for these 11 candidates are reported in Table 10. Figure 46 shows the phase-folded radial velocity of the source Gaia DR3 2966694650501747328, together with its phase-folded TESS and Gaia normalised flux.

## 8. Substellar companions

The two well-known categories of substellar companions, namely planets and brown dwarfs, have, for a few decades now, been the objective of long-term ground-based Doppler search

<footnote n="17">¹⁷ The sources Gaia DR3 2219809419798508544 and Gaia DR3 4514813786980451840 are also classified as eclipsing, but the light curve is clearly ellipsoidal. See Mowlavi et al. (2023) for more details about this type of misclassification.</footnote>