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A&A
Volume 670, February 2023
Article Number A102
Number of page(s) 38
Section Catalogs and data
DOI https://doi.org/10.1051/0004-6361/202245476
Published online 14 February 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Multiple stars have been observed since ancient times, but it has been accepted for millenia that the proximity of two stars was mainly due to chance (Fracastoro 1988). In the 17th century, Galileo was the first to propose the association between stars when trying to measure stellar parallaxes, based on the recommendations of Tycho Brahe (Hirshfeld 2001). The first visual binary, Mizar A and B (ζ Ursae Majoris), was discovered by Benedetto Castelli, who asked Galileo for his observations of it in 1616, although the discovering was falsely attributed to Giovanni Battista Riccioli in 1650 (Allen 1899; Burnham 1978). The first catalogue of binary stars was published in 1781 by Christian Mayer, who speculated about the possibility of them being physical systems, as predicted by Isaac Newton (Niemela 2001). Nevertheless, in the following century, William F. Herschel questioned that idea, considering that multiple systems could have a gravitational link only when their orbital motion were proven (Fracastoro 1988; Niemela 2001). Some years later, he published a work based on his observations (Herschel 1802), where he demonstrated that some real star systems were ruled by the universal gravitation laws (Niemela 2001). It was the first time that science confirmed that Newton’s laws are also valid outside the Solar System, which sparked a new revolution.

A double or binary system contains two stars that describe closed orbits around their common centre of gravity (Batten 1973), while multiple systems contain three or more stars with different hierarchical levels (Tokovinin 1997, 2008; Eggleton & Tokovinin 2008; Duchêne & Kraus 2013). The components of wide multiple systems have large separations between them and, therefore, relatively low gravitational energies. The classical maximum separation between components in wide systems rarely exceeds 0.1 pc, driven by the dynamic processes of the stars formation and evolution (Tolbert 1964; Kraicheva et al. 1985; Abt 1988; Weinberg & Wasserman 1988; Close et al. 1990; Latham et al. 1991; Wasserman & Weinberg 1991; Garnavich 1993; Allen et al. 1998; Caballero 2009) and strongly depends on their mass (i.e. spectral type), age, and kinematics (Duquennoy & Mayor 1991; Jensen et al. 1993; Patience et al. 2002; Zapatero Osorio & Martín 2004; Kraus & Hillenbrand 2009). There are newer studies that increase this maximum separation up to 1 pc (Jiang & Tremaine 2010; Caballero 2010) or even to 1–8 pc (Shaya & Olling 2011; Kirkpatrick et al. 2016; González-Payo et al. 2021). At these separations, the pairs are less likely bound for extended lifetimes (Retterer & King 1982; Weinberg et al. 1987; Dhital et al. 2010).

In this work, we perform a detailed characterisation of the widest pairs in the Washington Double Star (WDS) catalogue (Mason et al. 2001) by making use of the latest Gaia DR3 data (Gaia Collaboration 2023). The WDS, which is maintained by the United States Naval Observatory, is the world’s principal database of astrometric double and multiple star information. For each system, we ascertain their actual gravitational binding and search for additional companions. Since we are investigating pairs with angular separations, ρ, greater than 1000 arcsec, this work can be understood as a Gaia update of that by Caballero (2009), who also used ρ = 1000 arcsec as the minimum separation between the widest WDS pairs at that time, but had only HIPPARCOS (Perryman et al. 1997) parallaxes for a few bright stars and relatively insufficient proper motions for the faintest components. Furthermore, this work is the fourth item in the series initiated by Caballero (2009), which aims to shed light from an observational perspective on the formation and evolution of the most separated and fragile multiple stellar systems in the Milky Way. Although young systems play an important role in our analysis, here, we focus on field systems that are relatively evolved, old, and at the brink of disruption by the galactic gravitational potential.

This paper is structured as follows: In Sect. 2, we describe the stellar sample. Section 3 shows the analysis that we followed to filter, classify, and characterise WDS pairs, as well as to carry out our search for other possible members of the multiple systems. We present our results, along with a discussion in Sect. 4. Finally, we summarise our work in Sect. 5.

2 Sample

We built our sample from the latest version of the WDS1. For each of the 155 159 resolved pairs, WDS tabulates the WDS identifier (based on J2000 position), discoverer code and number, number of observations and of components (when there are more than two), date, position angle (θ, i.e. orientation on the celestial plane of the companion with respect to the primary), and ρ of the first and last observations, magnitudes, and proper motions of the two components, along with the equatorial coordinates of the primary of the pair and notes about the pair. In a few cases, WDS also tabulates the Durchmusterung number (Bonn, Córdoba, Cape – Schönfeld 1886; Argelander 1903) and the spectral type of the primary or companion (or both). There are numerous pairs that take part of multiple systems with, usually, the same primary star; in general, they share the same WDS identifier, but not always.

In Fig. 1, the cumulative number of WDS pair angular separations increases with a power law between ρ ~ 0.4 arcsec and ρ ~ 100 arcsec. This distribution follows Öpik’s law (Öpik 1924) for binaries with projected physical separations greater than 25 au (Allen et al. 1997). Outside the ρ ~ 0.4–100 arcsec range, the distribution flattens at both sides. This flattening is an observational bias at short angular separations, as micrometer, speckle, lucky imaging, adaptive optics, and even imaging from space are limited by the atmospheric seeing, telescope size, or optical quality (but there seems to be a slight overabundance of close pairs of ρ ~ 0.4–4.0 arcsec with respect to more separated ones).

The flattening of the ρ distribution at wide separations, especially at ρ ~ 200 arcsec, is mainly due to the actual formation and evolution of multiple stellar systems, although there may also be a contribution from another observational bias: until the advent of Gaia (Gaia Collaboration 2016, 2018, 2021), accurate proper motion and parallax measurements were available only for a tiny fraction of stars, while most wide WDS pairs come from pre-Gaia common proper motion surveys (e.g. Allen et al. 2000; Chanamé & Gould 2004; Lépine & Bongiorno 2007; Dhital et al. 2010; Raghavan et al. 2010; Tokovinin & Lépine 2012; and references therein2). In spite of numerous common proper motion surveys, the observational bias remains at ρ ≳ 200 arcsec because most of them looked for companions at angular separations of up to a few arcminutes only, mostly due to past computational limitations. However, this difficulty is starting to be alleviated thanks to new Gaia surveys (e.g. Kervella et al. 2022; Sarro et al. 2023). Due to the observational bias or the actual difficulty in forming wide binaries (Kouwenhoven et al. 2010; Reipurth & Mikkola 2012; Lee et al. 2017; Tokovinin 2017), the distribution of ultra-wide WDS pairs with ρ ≳ 1000 arcsec becomes extremely flat (Fig. 1).

At the time of our analysis, WDS contained 504 pairs separated by more than 1000 arcsec. For comparison, Caballero (2009) investigated about 105 000 WDS pairs, of which only 35 had ρ > 1000 arcsec. Together with the Gaia DR3 data, a sample about 15 times larger represents a qualitative and quantitative leap with respect to the first item of this paper series.

thumbnail Fig. 1

Cumulative number of WDS pairs as a function of ρ. Red data points with ρ > 1000 arcsec (to the right of the orange vertical dashed line) mark the 504 WDS pair candidates investigated by us. This figure can be compared with Fig. 1 in Caballero (2009).
thumbnail Fig. 2

Flowchart describing our analysis.

3 Analysis

Our analysis procedure is illustrated by the flowchart in Fig. 2, with the following elements: ovals represent the initial and final status of the process, diamonds are Boolean questions for which only possible answers are ‘Yes’ or ‘No’, rectangles are specific actions, trapezia are partial or final obtained results, and cylinders are databases (or catalogues) from where the data are collected or consulted. In Fig. 2, the incoming numbers in every block represent the number of processed WDS pairs in that block, and the outgoing numbers represent the number of pairs that match the condition or pass through to the next block of the flowchart.

3.1 Primary stars in Gaia DR3

For each primary star of the 504 WDS ultrawide pairs, we collected its main identifier in the Simbad astronomical database (Wenger et al. 2000). Of them, only six do not have a Simbad entry; they are shown in Table 1. Using TOPCAT (Taylor 2005) and the equatorial coordinates tabulated by WDS, we automatically cross-matched every primary with Gaia DR3. Next, we visually inspected all cross-matches with the help of the Aladin sky atlas (Bonnarel et al. 2000), and VizieR (Ochsenbein et al. 2000). When there were more than a single Gaia counterpart per primary within our ~5 arcsec cross-match radius, we chose the right star by comparing WDS and Gaia proper motions, magnitudes, and spectral types.

Of the 504 primaries, 44 are redundant (they belong to two or more pairs). Only 6 out of the 460 non-redundant primaries had no Gaia DR3 entry because of their extreme brightness (α Aur –Capella–, α Car –Canopus–, α PsA –Fomalhaut–, α Cen, γ Cen, and δ Vel), for which we took proper motions and parallaxes from HIPPARCOS. In addition, another 22 primaries are in Gaia DR3, but do not have a five-parameter astrometric solution. For 11 of them, namely, those of moderate brightness (G = 2.3–9.5 mag), we again took proper motions and parallaxes from HIPPARCOS, while for 9 of them, we took the data from Gaia DR2 (Gaia Collaboration 2018)3. The 2 remaining stars are LSPM J2323+6559 and 2MASS J00202956–1535280, for which there are only proper motions available from Lépine & Shara (2005) and Cutri et al. (2014), respectively. Since the 2 later primaries do not have published parallaxes, we discarded the corresponding pairs from the analysis. Accounting for these two discards, we retained 502 pairs for the next step of the analysis.

3.2 Search for WDS companions

The WDS catalogue provides the relative positions of the companion stars of the pairs with respect to the primaries through ρ and θ. To manually locate the companions to the primaries, we used Aladin. We loaded different catalogues and services, namely Gaia DR3, 2MASS (Skrutskie et al. 2006), Simbad, and WDS, and we used the dist tool. For the correct identification of the companion, we proceeded to carry out a visual confirmation of the primary cross-match and we chose the Gaia DR3 candidate companion within 10 arcsec around the expected location that matched the WDS values of proper motion, magnitude, and spectral type. If the companion had not been identified, especially in the widest systems (ρ > 10 000 arcsec), we enlarged the search radius in steps up to 120 arcsec. For these outliers, we used all the available information, namely, the WDS remarks and the original publications. There were only two cases where the companion star was not found by us with the ρ and θ provided by WDS, even after enlarging the search radius and scouring the literature4.

As for the primaries, we retrieved Simbad identifiers and Gaia DR3 for the corresponding companions. Only eight of the companions had not parallaxes (or even proper motions) available in any catalogue, and we also discarded them from the analysis5. We computed our own ρ and θ parameters for the 492 (502 − 2 − 8) remaining pairs using the standard equations of spherical trigonometry (e.g. Smolinski & Osborn 2006): ρ=arccos[ cos(Δαcos δ1)cos(Δδ) ],$ \rho = \arccos \left[ {\cos \left( {{\rm{\Delta }}\alpha \cos \,{\delta _1}} \right)\cos \left( {{\rm{\Delta }}\delta } \right)} \right], $(1) θ=π2−arctan[ sin(Δδ)cos(Δδ)sin(Δαcos δ1) ],$ \theta = {\pi \over 2} - \arctan \left[ {{{\sin \left( {{\rm{\Delta }}\delta } \right)} \over {\cos \left( {{\rm{\Delta }}\delta } \right)\sin \left( {{\rm{\Delta }}\alpha \cos \,{\delta _1}} \right)}}} \right], $(2)

where Δα = α2 − α1, Δδ = δ2 − δ1, and α1, δ1 and α2, δ2 are the equatorial coordinates of the primary and companion stars, respectively.

We compared the ρ and θ values we measured with those tabulated by WDS (in particular, with the latest measurements, i.e. sep2 and pa2). For the position angle, the standard deviation of the differences between our measurements and those from WDS is 0.84 deg. The distribution of the differences in θ is not Gaussian, with a narrow peak centred at 0 deg and wide, but shallow, wings at both sides. Of the 492 identified pairs with parallaxes, only 23 have absolute differences in θ greater than 1 deg (and up to 4.2 deg). Most of the kinds of differences ascribed to uncertainties propagated from inaccurate pre-Gaia coordinates, especially for the widest systems, such as WDS 23127+6317 (e.g. with Eq. (2) being highly non-linear). The distribution of the differences in ρ is similar to that of θ, with a narrow peak centred at 0 arcsec and a relatively large standard deviation of the differences of 21.0 arcsec. This large amount is originated by the difficulty in previous works to measure ρ or even to identify the companion of the widest systems, such as the ‘outliers’ described above and found at more than 10 arcsec from their expected locations6.

The distribution of our new values of ρ are plotted with red data points in Fig. 1. Of the 492 identified pairs with parallax, 298 have ρ = 1000–2000 arcsec, 117 have ρ = 2000–10 000 arcsec, and 77 have ρ > 10 000 arcsec. The latter ultra-wide pairs come mostly from the works by Probst (1983) and Shaya & Olling (2011). The widest pair has ρ = 66 094 arcsec (WDS 02157+6740, SHY 10; Shaya & Olling 2011). As described below, not all of them are physically bound.

Table 1

Primary stars without a Simbad entry.

3.3 Pair validation

To validate the 492 pairs, we used the criteria established by Montes et al. (2018) to distinguish between physical (bound) and optical (unbound) systems. For that purpose, we computed two astrometric parameters that quantify the similarity of the proper motions of two stars: μ ratio=(μαcosδ1−μαcosδ2)2+(μδ1−μδ2)2(μαcosδ1)2+(μδ1)2<0.15,$ \mu \,{\rm{ratio = }}\sqrt {{{{{\left( {{\mu _\alpha }\cos {\delta _1} - {\mu _\alpha }\cos {\delta _2}} \right)}^2} + {{\left( {{\mu _{\delta 1}} - {\mu _{\delta 2}}} \right)}^2}} \over {{{\left( {{\mu _\alpha }\cos {\delta _1}} \right)}^2} + {{\left( {{\mu _{\delta 1}}} \right)}^2}}}} &lt; 0.15, $(3)

and ΔPA=| PA1−PA2 |<15deg,$ {\rm{\Delta PA = }}\left| {{\rm{P}}{{\rm{A}}_1} - {\rm{P}}{{\rm{A}}_2}} \right| &lt; 15\deg , $(4)

where PAi are the angles of the proper motion vectors, with i = 1 for the primary star and i = 2 for the companion. We added an extra buffer in the µ ratio of up to 0.25 to account for projection effects on the celestial sphere of nearby ultrawide systems, as in the case of α Cen AB + Proxima (Innes 1915; Wertheimer & Laughlin 2006; Caballero 2009).

At the time of publication by Montes et al. (2018), Gaia parallaxes were not available except the for 2.5 million stars of the Tycho-Gaia Astrometric Solution (Michalik et al. 2015). With the advent of the third Gaia data release with precise parallaxes for ~700 times more stars, we added one additional condition to our validation. Cifuentes et al. (2021) imposed parallactic distances to agree within 10%, while González-Payo et al. (2021) did it within 15%, which is the value we chose to impose. In short, our third astrometric criterion was: | π1−1−π2−1π1−1 |<0.15,$ \left| {{{\pi _1^{ - 1} - \pi _2^{ - 1}} \over {\pi _1^{ - 1}}}} \right| &lt; 0.15, $(5)

with π1 and π2 as the parallaxes of both components of the pair (we did not apply any colour correction for computing distances – Bailer-Jones et al. 2018; Lindegren et al. 2021). In Fig. 3, we show the relations between µ ratio and ΔPA and between distances of the two components of the 153 pairs that satisfy the three imposed criteria simultaneously (and additionally, the multiple companions obtained in Sect. 3.4). Although we refer to them as pairs, in many cases they are actually part of hierarchical multiple (triple, quadruple, quintuple…) systems made of stars at very different angular separations to their primaries. This is described in detail below.

Except for 2 of them7, all the 153 pairs are located at heliocentric distances shorter than 150 pc, with a distribution peaking at 40–50 pc. The distribution of total proper motions is, however, flatter, with only one pair8 with a µ greater than 700 mas a−1 and none with a µ less than 25 mas a−1.

We did not keep in our final list of validated pairs an ultrawide system candidate at about 2400 pc towards the Magellanic Clouds, namely OGL 54 (Poleski et al. 2012). It is made of OGLE SMC-SC1 161–162 and Gaia DR3 4685747717242739328 (“SMC128.7.9551”), which are separated by about 12 pc. If truly linked, the pair would be much further and wider than any other system considered here. Last but not least, we revised the system ρ from 1017 arcsec to 977 arcsec, below our boundary at 1000 arcsec.

thumbnail Fig. 3

Astrometric criteria for pair validation. In both diagrams, we plot pairs between primaries and secondaries with blue circles, tertiaries with red triangles, quaternaries with green squares, and higher order companions with purple diamonds. Left: ΔPA1,i vs. µ1,i ratio diagram. Vertical and horizontal grey lines mark the µ ratios of 0.15 and 0.25 µ and ΔPA of 15 deg, respectively. Compare with Fig. 2 in Montes et al. (2018). Right: distance of companions vs. distance of primaries. Diagonal lines indicate the 1.15:1, 1:1, and 0.85:1 distance relationships. The α Cen AB + Proxima system, at d ~ 1.3 pc, is not shown.

3.4 Additional companions and stellar kinematic groups in Gaia DR3

We looked for additional proper motion and parallax companions within 1 pc around both the primary and the companion of the 153 validated pairs. We followed the methodology described in Sect. 3 of González-Payo et al. (2021); however, in our work, apart from TOPCAT and a customised code in astronomic data query language (Yasuda et al. 2004), we used Gaia DR3 and the criteria imposed by Eqs. (3)–(5). For a few cases of ultrawide WDS pairs with projected physical separations greater than 1 pc, we extended the search radius up to the maximum separation between known components.

In our Gaia search, we identified 349 additional common proper motion and parallax companions that satisfy the astrometric criteria of Eqs. (3)–(5). Of these, 111 additional companions are catalogued by WDS and 239 are not. The large multiplicity order of some system candidates, made of over a dozen pairs each (i.e. higher than dodecuple), together with the presence of debris discs in some of the components (e.g. α01 Lib, AU Mic – Kalas et al. 2004; Chen et al. 2005; Mizusawa et al. 2012; Gáspár et al. 2013; Mittal et al. 2015; Plavchan et al. 2020), has led us to investigate the membership of all our targets in young stellar kinematic groups (SKGs – Eggen 1965; Montes et al. 2001; Zuckerman & Song 2004), stellar associations (Ambartsumian 1949; Blaauw 1991; de Zeeuw et al. 1999), and even open clusters.

Of the 153 validated pairs in Sect. 3.3, there are 59 with at least one component (primary, companion, or both) that had previously been considered part of young SKGs, associations, and clusters such as the Tucana-Horologium and Coma Berenices moving groups, the ϵ Chamaeleontis association, or the Hyades open cluster (e.g. Perryman et al. 1998; Murphy et al. 2013; Kraus et al. 2014; Pecaut & Mamajek 2016; Riedel et al. 2017; Gagné et al. 2018a; Tang et al. 2019). Furthermore, of the 239 additional astrometric companions not catalogued by WDS, a total of 199 share proper motion and parallax companions with these young pairs. Table B.1 shows the name, equatorial coordinates, and G-band magnitude of 349 young stars and candidates, together with the corresponding group (SKG, association, or cluster) when available (309 cases), and references. The full names and acronyms of the 22 considered groups, with ages ranging from 4–8 Ma (of the Chamaeleon-Scorpius-Centaurus-Crux complex) to 600–800 Ma (of the Hyades and [TPY2019] Group-X), are provided in the table notes. Discoverer codes are given for all components tabulated by WDS (some stars that belong to different WDS systems can have different entries9), while the 199 additional companions have the string ‘…’ in the discoverer code column. The spatial distribution of the 309 young stars and candidates in SKGs, associations, and open clusters is shown in Fig. 4.

About 80% of the 199 additional companions had also been ascribed to young groups, but not all. We report 40 stars, marked with in the group column in Table B.1, that are new candidate members in young SKGs, associations, and clusters. Eight of them had actually been considered as previous members, but the most recent works have classified them as “improbable members” (e.g. HD 207377 AB in Tucana-Horologium; Zuckerman et al. 2001). In any case, some of the 40 stars, because of either their brightness (e.g. HD 71043, which is probably an A0V, G ≈ 5.9 mag, 200–300 Ma-old star in Carina) or faintness (e.g. 2MASS J12145318–5519494, which probably is a young brown dwarf in Lower Centaurus-Crux; Folkes et al. 2012), may be interesting to confirm in future works.

One more wide pair, composed by the bright stars γ Cas and HD 5408, resulted in a nonuple system after our initial astrometric analysis and bibliographic search. Since γ Cas is an extremely young classical Be star (Poeckert & Marlborough 1978; White et al. 1982; Henrichs et al. 1983; Stee et al. 1995), we also tabulated the resolved pair components in Table B.1, although it has never been ascribed to any group in particular (but see Mamajek 2017). The γ Cas system is discussed in further detail in Appendix A.

Despite the far-reaching title of this series of papers, in this particular work, we focus on relatively evolved and old systems in the galactic field. Common proper motion (and parallax) surveys of resolved companions to bona fide SKG members is indeed a widely used and successful technique for discovering new young stars and brown dwarfs (Alonso-Floriano et al. 2015, and references therein). However, a dedicated work on disentangling actual very wide binaries from unbound components in SKGs with similar galactocentric space velocities is planned.

After removing the 59 pairs with stars in young SKGs, associations, and clusters, we kept 94 wide pairs in the galactic field. To them, we added the 40 additional astrometric companions found in our Gaia DR3 search and not catalogued by WDS plus 39 already reported by WDS and separated by less than 1000 arcsec. As a result, there were 266 stars10 in 243 resolved Gaia sources and in 94 systems that passed to the next step of our analysis. All the systems and resolved Gaia sources are listed in Tables B.2 and B.3.

thumbnail Fig. 4

Spatial distribution of the 309 identified young stars in SKGs, associations, and open clusters.

3.5 New close binary candidates from Gaia data

We carried out a cross-matching with WDS and scoured the literature in search of additional companions not identified in our Gaia DR3 search. We did not find any additional WDS companion at ρ < 1000 arcsec that were resolvable by Gaia and that had not been recovered in our search. However, WDS also tabulates very close systems (ρ ≲ 1.3 arcsec) that were discovered and characterised with micrometers, speckle, lucky imaging, or adaptive optics, and which are unresolvable by Gaia thanks to the close separation or relatively large magnitude difference between components (e.g. HD 6101, HD 102590, HD 186957). In addition, there is a number of pair components that are spectroscopic binaries (e.g. HD 120510; Pourbaix et al. 2004) or triples (e.g. δ Vel, which is also an eclipsing binary with a close astrometric companion; Kervella et al. 2013), or very close binaries from proper motion anomalies (e.g. HD 125354; Kervella et al. 2019). We further consider all this information in Sect. 4.

Three pairs in multiple systems are in the 0.15–0.25 µ ratio buffer interval in the ΔPA vs. µ ratio diagram (Fig. 3), namely WDS 09487–2625, WDS 16278–0822, and WDS 23309–5807. The origin of their large µ ratio lies on wide amplitude orbital (i.e. proper motion) variations induced by additional components in the systems at 1.83 arcsec (HD 85043, I 205), ~1.0 arcsec (υ Oph, RST 3949), and 1.27 arcsec (HD 221252, I 145) to the primaries or companions. As a result, we also validated the three systems (one triple and two quadruples) in spite of not satisfying our original µ ratio criterion.

Next, we cross-matched our 243 Gaia sources in 94 systems with the HIPPARCOS-Gaia catalogues of accelerations of Kervella et al. (2019) and Brandt (2021). Of them, 54 have a measurable proper motion anomaly (Boolean variable set to unit in Gaia DR2, proper motion anomaly binary flag BinG2 – Kervella et al. 2019 –, or chi2 > 11.8 – Brandt 2021 –) that are probably induced by unseen companions. They are marked with a footnote in Tables B.2 and B.3.

In addition, we looked for new very close binary candidates among the 94 systems. First we used the Gaia re-normalised unit weight error (RUWE), which is a robust indicator of the goodness of a star’s astrometric solution (Arenou et al. 2018; Lindegren et al. 2018). Large RUWE values correspond to stars with angular separations small enough not to be resolved by Gaia, but large enough to perturb the astrometric solution. Gaia DR3 provides RUWE values for 234 Gaia entries. The nine sources without RUWE values are either very bright stars (δ Vel, α Cen A and B, υ Oph) or known close binaries with angular separations ρ ~ 0.2–0.9 arcsec (e.g. HD 6101). There are 14 stars with RUWE >10. They are also marked with a footnote in Tables B.2 and B.3. The five Gaia sources with the greatest RUWE, of about 20–40, are either already known close binaries below the Gaia resolution limit (e.g. G 210–44, ρ ~ 0.1 arcsec – HDS 2989 in the HIPPARCOS Double Stars catalogue) or strong, relatively faint, new binary candidates (e.g. 2MASS J02022892–3849021, UCAC3 109–11370, LSPM J0956+0441, and HD 59438 C). Of the other nine Gaia sources with moderate RUWE of about 10–20, some have also been tabulated as candidate binaries, such as HD 75514 and HD 139696, which were listed in the HIPPARCOS-Gaia catalogue of accelerations (Kervella et al. 2019), HD 210111, which is a λ Bootis-type spectroscopic binary (Paunzen et al. 2012), and HD 215243, which is subgiant spectroscopic binary (Gorynya & Tokovinin 2018). The rest of Gaia sources with RUWE > 10 would need an independent confirmation of binarity. Being less conservative, we could have extended our analysis down to RUWE = 5, which is about three times greater than the critical value of 1.41 of Arenou et al. (2018), Lindegren et al. (2018), or Cifuentes et al. (2020). There are only five Gaia sources (in double or multiple systems) with 5 ≤ RUWE ≤ 10. However, as some careful studies of nearby stars indicate, RUWE values slightly larger than 1.4 do not necessarily translate into close binarity (Ramsay et al. 2022; Ribas et al. 2023). Since the confirmation of actual close binarity requires a radial-velocity or high-resolution imaging follow-up, we imposed a very conservative RUWE limit.

Next, we used the standard deviation of the radial velocities, Vr, measured with the Gaia Radial Velocity Spectrometer, which receives the misleading label radial_velocity_error (Gaia Collaboration 2023; Katz et al. 2023). Of the 243 Gaia entries, 182 have Vr and its standard deviation, σVr. The median formal precision of the velocities for the brightest, most stable Gaia stars lies at about 0.12 km s−1 to 0.15 m s−1 and smoothly increases for fainter stars (Katz et al. 2023). However, we identified at least six Gaia sources that have significantly greater σVr than expected given their magnitudes. Being all stars of intermediate ages and spectral types in the main sequence (i.e. no pulsating giants or subgiants, nor very active T Tauri stars), we adscribed the large σVr to spectroscopic binarity. Actually, two of them had already been reported as spectroscopic binaries, namely HD 2000077 (Konacki et al. 2010; Montes et al. 2018 and references therein) and HD 215243 (Gorynya 6 Tokovinin 2018, which also has a large RUWE). A third one, namely HD 75514 (Kervella et al. 2019; Brandt 2021), has a significant proper motion anomaly. The other three new spectroscopic binary candidates have a large RUWE (8.1; BD+32 2868), moderate RUWE and (2.48, 2.86 km s−1), or a small RUWE but a huge σVr for a bright single star (G ≈ 7.7 mag, 17.76 km s−1; HD 201670).

At this stage, we may wonder why common parallax and proper motion criteria alone were used for system validation, instead of common radial velocities as well, at least for the 99 pairs with data for the two components. We note that a large difference in radial velocities may be a symptom of long-period spectroscopic binarity of one of the components (by “long period”, we mean longer than or of the same order of the 34 months of the Gaia DR3 radial-velocity coverage). Nevertheless, the above-mentioned properties of high RUWE, σVr, or, especially, proper motion anomaly do not always indicate unknown close companions, but can also be produced by the already detected close companions. Some examples of known pairs with astrometric accelerations and orbital periods of tens to hundreds years are HD 6101, HD 59438, and HD 85043.

In Table 2, we list 43 pairs of primaries and companions with radial velocity differences larger than three times the quadratic sum of the respective σVr. Among them, we can find known spectroscopic binaries, components with large RUWE values, proper motion anomalies, or a combination of them. Some of the pairs in Table 2 may be false positives, that is, two unrelated stars with very similar proper motions and parallaxes but very different radial velocities. However, with the data available to us, it is impossible to disentangle between them and true wide physical systems with one radial-velocity outlier component due to currently unknown long-period spectroscopic binarity.

thumbnail Fig. 5

H-R diagram of all investigated stars. Coloured open symbols stand for stars in double (blue circles), triple (red triangles), quadruple (green squares), and higher-order multiple systems (purple diamonds). Grey dots represent selected field stars from Gaia. The black solid line is the updated main sequence of Pecaut & Mamajek (2013). The stars outside the main sequence are discussed in the text.

3.6 Colour-magnitude diagram

Stellar masses are needed to compute gravitational binding energies, while luminosity classes are needed to estimate stellar masses. Estimated stellar ages are also needed to investigate the evolution of fragile multiple systems, while luminosity classes also shed light on stellar ages, especially outside the main sequence. The luminosity class of the stars in the 243 Gaia sources is illustrated by the Hertzprung-Russell (H-R) diagram of Fig. 5. We took parallaxes and G, GBP, and GRP magnitudes from Gaia DR3, except for four very brights stars (δ Vel, α Cen A and B, υ Oph), for which we estimated their magnitudes from their well-determined spectral types, published Johnson B, V, R photometry, and the main-sequence colour-spectral type relation of Pecaut & Mamajek (2013). We also plot this relation in the diagram, although the main sequence, together with the loci of white dwarfs and giants and subgiants beyond the turnoff point, is clearly marked by 57 345 field stars with good Gaia astrometry and photometry following the H-R example of Taylor (2021), but with the DR3 data set.

From their position in the H-R diagram, we identified eight giants and subgiants and five white dwarfs (listed in Table 3). We confirmed their classification with a comprehensive bibliographic study. Among the 13 stars, only one is part of a close pair unresolved by Gaia, namely δ Vel. Furthermore, all but one of the giants are so bright that were listed already by Bayer (1603) and Flamsteed (1725).

Four of the five white dwarfs have a spectral type determination, with only one presented as a white dwarf candidate by Gentile Fusillo et al. (2019). However, all of them are part of multiple systems (i.e. triple or higher). For example, WDS 01024+0504 is made of two spectroscopic binaries, namely the double, early K dwarf HD 6101 and the double, DA5.9 white dwarf EGGR 7 (Giclas et al. 1959; Maxted et al. 2000; Lajoie & Bergeron 2007; Caballero 2009; Gianninas et al. 2011; Toonen et al. 2017), while WDS 06536-3956 is made of the early M dwarf L 454–11 (Lépine & Gaidos 2011) and two white dwarfs, WT 201 (DA8.0) and WT 202 (DA7.0; Subasavage et al. 2008). The system may also be quadruple because L 454–11 has a RUWE = 18.0. The other two white dwarfs are in triple and quadruple systems.

Apart from the 13 giants, subgiants, and white dwarfs in Table 3, there are still some objects lying outside the main sequence in the colour-magnitude diagram of Fig. 5. In particular, there are 4 sources apparently below the main sequence. The origin of this discrepancy lies in the four cases on wrong photometry: 2MASS J02004917–3848535 in the double system WDS 02025–3849 is an ~M7–8 ultracool dwarf with GBP fainter than the Gaia limit (Smart et al. 2019); Gaia DR3 749786356557791744 in the triple system WDS 10289+3453 is another ultracool dwarf with GBP fainter than the Gaia limit, but with a spectral type at the M–L boundary; Gaia DR3 3923191426460144896 in the quadruple system WDS 11486+1417 is an ~M4–5 late-type dwarf at ρ ≈ 10.1 arcsec of the very bright (G ≈ 5.9 mag) A8+G2 binary HD 102590; and Gaia DR3 1367008242580377216 in the triple system WDS 17415+4924 is an ~M4–5 late-type dwarf with a relatively high value of GBP/GRP excess factor, E(BP/RP), which is an indicator of systematic errors in photometry (Riello et al. 2018). Remarkably, 2 of the 4 Gaia sources with the wrong photometry are the least massive stars in our sample (Sect. 3.7). The rest of the Gaia sources, which are especially redder than the subgiant turnoff point, are reasonably matched to the main sequence.

Table 2

Radial-velocity outlier candidates.

Table 3

Giants and white dwarfs in wide double and multiple systems.

3.7 Masses and gravitational binding energies

For stars in the main sequence, we determined stellar masses, M, from the G-band absolute magnitude, Gaia and 2MASS colours, spectral types, and the updated version of Table 4 in Pecaut & Mamajek (2013)11. The match between spectral types derived by us from colours and absolute magnitudes and compiled from the bibliography is excellent (although we estimated spectral types for some Gaia sources that had previously gone unreported in the literature). In the case of unresolved (spectroscopic binaries and close WDS astrometric binaries), very bright stars (e.g. α Cen A and B), giants, subgiants, and white dwarfs (Table 3), we compiled M values from the bibliography (e.g. Lajoie & Bergeron 2007; Soubiran et al. 2008; Feuillet et al. 2016; Eker et al. 2018; Stock et al. 2018; Gentile Fusillo et al. 2019). If unavailable, we determined M from colours and absolute magnitudes by assuming either two equal-mass stars in double-lined spectroscopic binaries or that the mass of the companion, M2 is much less than the mass of the primary, M1, in single-lined spectroscopic binaries (Latham et al. 2002). Because of this naïve approach, we established an uncertainty of 10% for our M values (Mann et al. 2019; Schweitzer et al. 1999), which may actually be larger in poorly investigated, single-lined spectroscopic binaries. In only two cases, namely, of white dwarfs without a public mass determination, we estimated their M as in Rebassa-Mansergas et al. (2021). For the giants, subgiants, and white dwarfs we also compiled ages from the literature, as summarised in the last column of Table 3; such ages can be extrapolated to their wide companions. While the masses of the white dwarfs vary between about 0.5 and 0.8 M⊙ and of the giants between 1.0 and 3.2 M⊙, the masses of the stars on or near the main sequence vary from about 0.08 to 2.8 M⊙. The latter extremes correspond to the new ultracool dwarf Gaia DR3 749786356557791744 at the M–L boundary, which is at 13.7 arcsec to the solar-like HD 90681 star and the B9.5 IV HD 188162, which is the most massive star of a septuple system candidate (Sect. 4).

Next, we computed the projected physical separation, s, between every two Gaia-resolved components in each pair from the angular separation, ρ, and the distance, d, to the primary. Given the wide separations considered, instead of using the s ≈ d ρ approximation, we used instead the exact definition from the trigonometry: s=dsinρ.$ s = d\sin \rho . $(6)

We considered the distance to the primary star (which usually has the smallest parallax uncertainty) as the distance to the whole system. The determined s vary from ~11 au in the case of nearby, close astrometric binaries (e.g. HD 6101), to ~2.3 × 106 au (about 11 pc) in the case of the very widest companions (see below). The uncertainty in s is underestimated for primaries whose parallaxes may be affected by close binarity.

Finally, we determined reduced binding energies of the wide systems as in Caballero (2009): | Ug* |=GM1M2s.$ \left| {U_g^*} \right| = G{{{M_1}{M_2}} \over s}. $(7)

They are “reduced” because we used the projected physical separation for computing | Ug* |$\left| {U_g^*} \right|$ instead of the actual separation or the semi-major axis, a, which is unknown. We did not apply a most probable conversion factor between a and s for easier computation and, especially, comparisons with previous works (Close et al. 2003; Burgasser et al. 2007; Radigan et al. 2009; Caballero 2010; Faherty et al. 2010). This conversion factor, resulting from a uniform distribution of tridimensional vectors projected on a bidimensional plane (Abt & Levy 1976; Fischer & Marcy 1992), would lead to about 26% larger actual separations and, therefore, 26% smaller (non-reduced) binding energies12 (Dhital et al. 2010; Oelkers et al. 2017).

The resulting M1, M2, ρ, θ, s, and | Ug* |$\left| {U_g^*} \right|$ are listed in Table B.3. We computed | Ug* |$\left| {U_g^*} \right|$ only for systems with double-like hierarchy, that is, actual doubles and multiple systems with ρ1,wide ≫ ρ1,i. Here, ‘wide’ indicates resolved companions at ρ1,wide > 1000 arcsec and ‘i’ other components. As a result, we did not compute | Ug* |$\left| {U_g^*} \right|$ of 14 multiple systems with ρwide ~ ρ1,i, which we called trapezoidal systems or trapezia.

4 Results and discussion

Among the 155 159 pairs contained in the WDS catalogue at the time of our analysis, 153 pairs with common-parallax, common-proper motion, ultrawide components at ρ > 1000 arcsec passed our astrometric criteria in Sect. 3.3, of which 59 (38.6+9.8%) are part of young SKGs, associations, or open clusters (Table B.1), and 95 (61.4±12.4%) are ultrawide pairs in 94 galactic systems – one triple is made of two pairs with ρ > 1000 arcsec and different WDS entries (see Sect. 3.4), which makes 95 WDS pairs. Because of the small sample size, we used the Wald interval (Agresti & Coull 1998) with a 95% of confidence to calculate the ratio uncertainties13. To the galactic systems, we added 39 companions from the literature and separated by ρ < 1000 arcsec. In our Gaia DR3 search, we also found 39 additional astro-metric companions not catalogued by WDS; that is, we found new companions in about a quarter of the investigated systems. In contrast, WDS tabulated a number of additional companion candidates with accurate Gaia DR3 data that did not pass our conservative astrometric criteria (Sect. 3.3). Most, but not all, of them are flagged by WDS with ‘U’ (’proper motion or other technique indicates that this pair is non-physical’).

The 94 galactic field systems and their components are listed in Tables B.2 (basic astrometry and photometry) and B.3 (stellar masses, angular and projected physical separations, position angles, and binding energies). We remark that we reclassified the stars in Tables B.2 and B.3 as primaries, secondaries, tertiaries, and so on, according to their G-band magnitudes. As a result, the WDS nomenclature “A”, “B”, “C” (etc.) does not always match our re-ordering.

Among the 94 galactic field systems, there are 48 double, 24 triple, 14 quadruple, 2 quintuple, 3 sextuples, and 2 septuples. The corresponding minimum multiplicity order rates are displayed in Table 4. The estimated multiplicity order rates and, therefore, the number of multiple systems increase significantly at the expense of the number of doubles if the new candidate companions with large RUWE, σVr, or proper motion anomaly are included (Sect. 3.5). When these close binary candidates are taken into account, most of the ultrawide systems (67.8%) become multiple: 23.7% are triple, 21.5% are quadruple, and 22.6% have a higher multiplicity order. These rates are far greater than what is found in less separated multiple systems in the field (Tokovinin 1997; Chanamé & Gould 2004; Duchêne & Kraus 2013). Such a higher-than-usual multiplicity order implies a larger total mass, which, in turn, implies a larger binding energy.

In the left panel of Fig. 6, we display the minimum reduced gravitational binding energy of the 80 systems for which we were able to compute their | Ug* |$\left| {U_g^*} \right|$ as a function of the total mass in the system, Mtotal = Σ Mi, i = 1:7 (i.e. all except for the 14 trapezia). This diagram would be complete only by adding systems with angular separations ρ < 1000 arcsec but with very low masses (e.g. Caballero 2007a,b; Artigau et al. 2007; Rica & Caballero 2012). It is complete, however, at the highest total masses and lowest binding energies. Actual total masses and binding energies, when close binary candidates are taken into account, are larger.

There are three systems with | Ug* |<1033$\left| {U_g^*} \right| &lt; {10^{33}}$ J, significantly lower that those of the other 77 systems. They are listed at the top of Table 5 with their WDS identifiers, discoverer codes (i.e. Wide-field Infrared Survey Explorer, WIS, Kirkpatrick et al. 2016), Simbad names, stellar masses, distances, projected physical separations, and gravitational binding energies. The three systems are doubles composed of M3–6 V primaries and M5–9 V secondaries. These spectral types were estimated by us from MG from the relations of Pecaut & Mamajek (2013) and Cifuentes et al. (2020), except for the secondary star in WDS 15488+4929, namely, LSPM J1550+4921, whose spectral type M7.0 V was determined by West et al. (2011) from low-resolution spectroscopy. With a mass of about 0.09 M⊙, the secondary in the system WDS 02025–3849, namely, 2MASS J02004917–3848535 (~M7–8 V), is the second-least massive star in our whole sample. The low masses of the system components and the wide separations, of about 68–85 × 103 au (six to eight times wider than α Cen + Proxima), explain the very low | Ug* |$\left| {U_g^*} \right|$. Actual binding energies may be larger, as the primary in WDS 02025–3849 has a RUWE = 40.7; assuming an equal-mass binary, the corrected binding energy would double. None of the three systems have radial-velocity determinations (from Gaia DR3 and West et al. 2011) for the two resolved components. Given their relatively large µ ratios and APA (but within our boundary conditions), a dedicated radial-velocity follow-up would be necessary to ascertain whether the three fragile binaries are actually triples.

Even if each of the three systems had an additional component and, therefore, higher total masses and binding energies than estimated above, there seems to be a lower boundary of | Ug* |$\left| {U_g^*} \right|$ for the most fragile systems at about 1033 J (first mentioned by Caballero 2010). This lower limit may be a consequence of the tidal disruption of wide systems by the galactic gravitational potential, via energy and momentum exchange in encounters with other stars or even the interstellar medium (Heggie 1975; Draine 1980; Bahcall & Soneira 1981; Dhital et al. 2010; Jiang & Tremaine 2010). Actually, during the lifetime of a stellar system, the continuous small and dissipative encounters with other stars are much more disruptive than occasional single catastrophic encounters (Retterer & King 1982; Weinberg et al. 1987). As a result of these interactions, the initial distribution of separations of stellar systems change (increase) over time until eventual disruption. Using the Fokker–Planck coefficients to describe the effects produced on the orbital binding energies due to those small encounters over time, Weinberg et al. (1987) estimated the average lifetime of a binary as: t*(a)≃18 Ga(n*0.05pc−3)−1(M*M⊙)−2(MtotM⊙)(Vrel20km s−1)(a0.1pc)−1ln−1Λ,$ \matrix{ {{t_*}\left( a \right) \simeq } \hfill &amp; {18\,{\rm{Ga}}{{\left( {{{{n_*}} \over {0.05{\rm{p}}{{\rm{c}}^{ - 3}}}}} \right)}^{ - 1}}{{\left( {{{{M_*}} \over {{M_ \odot }}}} \right)}^{ - 2}}\left( {{{{M_{{\rm{tot}}}}} \over {{M_ \odot }}}} \right)} \hfill \cr {} \hfill &amp; {\left( {{{{V_{{\rm{rel}}}}} \over {20{\rm{km}}\,{{\rm{s}}^{ - 1}}}}} \right){{\left( {{a \over {0.1{\rm{pc}}}}} \right)}^{ - 1}}{{\ln }^{ - 1}}{\rm{\Lambda }},} \hfill \cr } $(8)

where n* and M* are the number density and average mass of the perturber objects, Vrel is the relative velocity between the binary system and the perturber, Mtot and a are the total mass and semi-major axis of the binary system, and ln Λ is the Coulomb logarithm. The calculation was simplified by Dhital et al. (2010) by setting the values n*, = 0.1 M⊙ pc−3, M* = 0.7 M⊙, Vrel = 20 km s−1, and ln Λ = 1 (Close et al. 2007), and produced an equation that describes in a statistical way the maximum separation of a surviving stellar system at a given age: a≃1.212Mtotalt*,$ a \simeq 1.212{{{M_{{\rm{total}}}}} \over {{t_*}}}, $(9)

where the total mass is in M⊙, the average lifetime in Ga, and the semi-major axis in pc.

We plot the projected physical separation s as a function of the total mass M⊙ of the 94 ultrawide systems in the right panel of Fig. 6. Overplotted on them, we display the physical separations corresponding to 0.1, 1.0, and 10 Ga and the orbital periods for 0.1, 1.0, and 2 Ga. The three most fragile systems may have survived in their current configuration by about 1 Ga or slightly less in the case of WDS 15488+4929. However, there are other systems that are less fragile (i.e. have higher reduced binding energies, comparable to those of well-recognised systems) but that can be disrupted in a few hundred million years. As we may expect, they are among the most separated systems.

There are seven system candidates with s = 1.1−2.3 × 106 au (5.1–11.1 pc), listed at the bottom of Table 5. These refer to the kinds of systems that lend their name to the topic of this work (Reaching the boundary between stellar kinematic groups and very wide binaries). In the spherical volume of radius 10 pc centred on the Sun, according to the exhaustive compendium by Reylé et al. (2021), there are 339 systems containing stars, brown dwarfs, and exoplanets. As a result, regardless of their (unknown) age, the ultrawide binary and multiple systems may be at the last stages of disruption and follow the formation-evolution-dissolution sequence described by Close et al. (2003), who predicted an overabundance of very low-mass binaries far from the centre of the original ‘minicluster’. This is the case of the most separated components in the systems WDS 02315+0106 and WDS 15330–0111, which have low masses and large σVr for their G magnitudes. The seven system candidates, all of them identified by Shaya & Olling (2011), may be the remnants of previous SKGs that are being dissolved in the Milky Way and that are older than the ones identified in Sect. 3.4. Three system candidates, including the sextuple (perhaps septuple) WDS 02315+0106 system, are trapezia and, therefore, their reduced binding energies were not computed. The other four systems consist of three very wide binaries made of two bright Henry Draper stars (Cannon & Pickering 1918) and one double-like hierarchical quadruple (perhaps quintuple) system. The latter, namely WDS 15330-01110, is made of the K0 giant 11 Ser (Table 3), the G1 dwarf HD 142011, and two anonymous early M dwarfs, one of which has a large σVr for their G magnitude. These two (or three) M dwarfs are very close to each other (s ~ 92 au) and to the Sun-like star (s ~ 630–690 au), which allowed us to compute However, the K0 giant and the G1+M+M triple are separated by about 1.5 × 106 au (7.2 pc). Between them, dozens of unrelated stars with similar parallaxes must exist, but with very different proper motions that exert smooth ‘continuous small and dissipative’ gravitational thrusts.

Something similar may occur in the case of the 14 ultrawide trapezia, which tend to have a high multiplicity hierarchy: 1 of the 2 septuple systems, the 3 sextuples, 7 of the 15 quadruples, and 3 of the 25 triples are trapezia. In particular, the trapezoidal septuple system WDS 19507–5912 is sketched in Fig. 7. It consists of three late-B-to-early-A stars (one is a spectroscopic binary) and three intermediate-to-late M dwarfs (one is close to an A star). Given the early spectral types of the most massive stars, this system may approximately be the age of the Hyades (600–700 Ma; Perryman et al. 1998; Gossage et al. 2018; Martín et al. 2018) and, therefore, stand as an unidentified sparse young SKG14. All these results are in accordance with the suggestions by Basri & Reiners (2006) and Caballero (2007b), who proposed a major prevalence of wide triples over wide binaries. We also confirm that the individual components of systems at very wide separations are often multiple systems themselves, as stated by Cifuentes et al. (2021).

Five of the seven ultrawidest systems have orbital periods of the order of 1 Ga, even older than the Hyades. Such long orbital periods stand as a challenge to the ‘binary’ definition itself, namely: a system of two stars that are gravitationally bound to and in orbit around each other. As a result, the ultrawidest pairs may have not completed one revolution either because of their young age or because they were recently disrupted by passing stars and, therefore, should not be called ‘binaries’. This statement should also be extrapolated to the system candidates in young stellar kinematic groups (Sect. 3.4), including less separated but also less massive, pairs. Furthermore, Caballero (2009) already claimed that the AU Mic+AT Mic system in the β Pictoris moving group has only completed at most two orbital periods since its formation. All of this makes the boundary between stellar kinematic groups and very wide binaries blurrier and blurrier.

Finally, we used the accurate Gaia astrometry to measure the relative transverse velocity, ΔV, as a function of the projected physical separation of the 48 widest systems with s > 0.1 pc, and compared it with the maximum velocity allowed for a bound binary, as done by some other authors (e.g. El-Badry 2019; El-Badry et al. 2021). This comparison may interpret several observational studies that have reported that the difference in the proper motions or radial velocities of the components of nearby wide binaries appear larger than predicted by Kepler’s laws, indicating a potential breakdown of general relativity at low accelerations. However, our data, which are relatively scarce compared to extensive simulations (cf. El-Badry 2019), do not even show projection effects. Furthermore, inner subsystems, which are frequent, disturb our ΔV estimates. As a result, the actual bound nature of our most fragile system is hardly verifiable.

To sum up, wide pairs with very low-mass components and | Ug* |~1033$\left| {U_g^*} \right|\~{10^{33}}$ J (e.g. ultracool dwarf binaries with late-M and early-L spectral types and projected physical separations of a few thousand astronomical units – Caballero 2007a,b; Artigau et al. 2007) are perhaps more relevant for investigating the disruption of fragile systems by the galactic gravitational potential rather than ultrawide systems of gargantuan projected physical separations (much larger than those proposed by Tolbert 1964; Bahcall & Soneira 1981; or Retterer & King 1982) caught in the act of destruction and, that probably are the leftover of past SKGs.

Table 4

Multiplicity order rates of ultrawide galactic systems.

thumbnail Fig. 6

Reduced binding energy (left) and projected physical separation (right) as functions of ultrawide system total mass. In both panels, the three most fragile systems (top of Table 5) and the most separated systems (bottom of Table 5) are plotted in red triangles and green squares, respectively, while the rest of investigated ultrawide systems are plotted in blue circles. The error bars in s are smaller than the used symbols. In the left panel, the horizontal line marks the limit of | Ug* |$\left| {U_g^*} \right|$ at 1033 J. In the right panel, the grey solid diagonal lines mark the statistical maximum ages of 0.1, 1, and 10 Ga at which the systems are likely bound (computed with Eq. (9)), while the red dashed diagonal lines mark the corresponding orbital periods of 0.1, 1, and 2 Ga (computed with Kepler’s third law). In both cases we used the correction a ≈ 1.26 s (Fischer & Marcy 1992).
Table 5

The most fragile (| Ug* |<1033$\left| {U_g^*} \right| &lt; {10^{33}}$ J) and the most separated (s ≥ 5 pc) systems.

thumbnail Fig. 7

Spatial distribution of the septuple system WDS 19507–5912. The size of the spheres representing every star, labelled in blue, are proportional to their brightness. The projected physical separations from the primary star, HD 188162, in red, are in 103 au. The overall proper motion, in green, is in mas a−1.

5 Summary

Thanks to the Gaia DR3 (Gaia Collaboration 2023) and a number of parallax and proper motion searches in the previous decade (e.g. Caballero 2010; Shaya & Olling 2011; Tokovinin & Lépine 2012; Kirkpatrick et al. 2016), we present a leap forward with respect to the first item of this series of papers, on the Washington double stars with the widest angular separations (Caballero 2009). Accordingly, we increase by over an order of magnitude the sample size and the astrometric precision of systems with angular separations ρ > 1000 arcsec. Among other results of our analysis, we present: (i) 40 additional astrometric companions not catalogued yet by WDS, including several ultracool dwarfs at the M–L boundary and one hot white dwarf, not counting several dozens close binary candidates from large Gaia DR3 RUWE and σRV; (ii) a general confusion in the literature between actual, physically bound, ultrawide pairs and components in young SKGs, associations, and even clusters with identical galactocentric space velocities; (iii) three very fragile systems discovered by Kirkpatrick et al. (2016) that are made of intermediate and late M dwarfs with large projected physical separations of 0.33–0.41 pc and small reduced binding energies | Ug* |≲1033$\left| {U_g^*} \right| \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} {10^{33}}$ J, which is probably the smallest value found among gravitationally bound systems; (iv) the individual components of systems at very wide separations are often multiple systems themselves (Cifuentes et al. 2021), which implies an overabundance of high-order multiples (triples, quadruples, quintuples, and more) among the widest systems, and larger binding energies and total masses than systems with comparable separations but lower multiplicity order; and (v) an additional observational confirmation of classical theoretical predictions (e.g. Weinberg et al. 1987) of disruption of binary systems by the galactic gravitational potential, which destroys the ultrawidest systems with total masses below 10 M⊙ in less that 600–700 Ma (the age of the Hyades cluster). As incidental results, we report 40 new candidate stars in known young SKGs and at least one new young stellar association around the bright star γ Cas, although some of our highest-order multiple systems, such as the septuple around the B9.5 IV star HD 188162, may also be association remnants.

In conclusion, the total mass, binding energy, and probability that an ultrawide system is actually bound increase as the stellar multiplicity order increases. Many systems reported here have overwhelmingly large projected physical separations, but have instead total masses large enough for the binding energies being comparable to those of less separated, less massive systems that are widely accepted as physical. However, none of the ultrawide systems will survive for another few hundred million years. In a sense, the widest multiple systems of today, which are now being torn apart by the Galaxy, will be the single stars of tomorrow.

Acknowledgements

We thank the anonymous reviewer for their constructive suggestions and comments, Jesus Maíz Apellániz for discussion on the γ Cas system, Alberto Rebassa-Mansergas for estimating masses of two white dwarfs, Brian D. Mason for help with five unidentified wide WDS companions, and Andrei Tokovinin for providing us the ρ of a wide pair and very useful discussion on hierarchical multiplicity. We acknowledge financial support from the Agencia Estatal de Investigación 10.13039/501100011033 of the Ministerio de Ciencia e Innovación and the ERDF “A way of making Europe” through projects PID2019-109522GB-C51 and PID2020-112949GB-I00, and the Centre of Excellence “María de Maeztu” award to the Centro de Astrobiología (MDM-2017-0737), and from the European Commission Framework Programme Horizon 2020 Research and Innovation through the ESCAPE project under grant agreement no. 824064. This research made use of the Washington Double Star Catalog maintained at the US Naval Observatory, NASA’s Astrophysics Data System Bibliographic Services, the Simbad database, VizieR catalogue access tool, and Aladin sky atlas at the CDS, Strasbourg (France), and the TOPCAT tool.

Appendix A The γ Cas association

Figure A.1 shows the spatial distribution around γ Cas in two panels. The left panel shows the 145 stars in Table B.4 forming a circle area with a radius of 6 degrees. The right panel reduce the radius to about 2 degrees to have only 30 stars including γ Cas. The IC 63 nebula emission, also named the ‘Phantom nebula’, is easily observed in the right panel.

The stars γ Cas and HD 5408, separated by 1274.5 arcsec, constitute the wide pair MAM 20 AD (Mamajek 2017). They actually form a quintuple system, as they are reported to be close double (B0.5 IV + F6 V)15 and triple (B7 V + B9 V + A1V) stars, respectively (Morgan et al. 1943; Osterbrock 1957; Christy & Walker 1969; Fekel 1979; Nemravová et al. 2012; Hutter et al. 2021).

With such an early spectral type and an age of only about 8 Ma (Zorec et al. 2005), γ Cas is the ionising source of the nearby (ρ ~ 1200 arcsec) reflection nebulae IC 63 (The Ghost of Cassiopeia) and IC 59 (Hubble 1922; Sharpless 1959; Jansen et al. 1994), as well as of an irregular, ~3 deg-diameter, H II region (Karr et al. 2005). With a mass of about 19 M⊙ and a surrounding disc, it is also the prototype of the γ Cas type of stars (Poeckert & Marlborough 1978; Stee et al. 1995; Nazé et al. 2022).

Our astrometric search for common proper motion and parallax with the criteria in Sect. 3.3 resulted in four additional stars not tabulated by WDS. Of them, only one, namely UCAC4 752–011208 (M4 Ve), had been catalogued in the literature (Nesci et al. 2018). Together with the five components of the γ Cas+HD 5408 system, they made an agglomerate of nine stars of 8 Ma at about 188 pc. Since 19 M⊙-mass stars do not form in isolation (Kroupa 2001; Chabrier 2003; Peña Ramirez et al. 2012), we extended our astrometric search and found additional stars that satisfy our criteria. In particular, we enlarged our search radius centred on γ Cas in consecutive steps and, besides γ Cas and HD 5408, we found 10, 30, 51, 85, 115, and 143 Gaia DR3 stars with a 2MASS counterpart, and that satisfy our astrometric criteria, up to 1, 2, 3, 4, 5, and 6 deg, respectively (Fig. A.1). Some of these stars are in turn spectroscopic binaries, so their total number is larger. Most selected stars follow the 10 Ma theoretical isochrones of PARSEC16 (Bressan et al. 2012, version 1.2S with the default values) at 188 pc in Gaia-2MASS colour-magnitude diagrams. Besides, the mass function computed from masses derived from the J-band absolute magnitude and PAR-SEC models do not deviate too much from Salpeter’s. However, we did not find a clustering of stars towards the most massive stars, as it is usually observed in open clusters of similar age (e.g. Caballero 2008). The hypothetical stars of an open cluster or, more likely, a stellar association around γ Cas (Mamajek 2017) overlaps with the extended and also young population of the Cas-Tau OB1 association (Blaauw 1991; de Zeeuw et al. 1999). As a result, additional work is necessary to disentangle the stars that were born together with γ Cas and HD 5408.

thumbnail Fig. A.1

Spatial distribution of candidate young stars (open yellow circles) at less than 6 deg (left) and 2 deg (right) to γ Cas. In the right panel we also highlight HD 5408 (the most massive star after γ Cas) and the IC 63 emission nebula. The images were created with the Aladin sky atlas and blue, red, and infrared Digitised Sky Survey data.

Appendix B Additional tables

Table B.1

Stars in young stellar kinematic groups.

Table B.2

Basic data of the 94 galactic field systems.

Table B.3

Masses, ρ, θ, separations and gravitational binding energy of the systems identified in the sample of work.

Table B.4

Candidate stars to be part of the γ Cas association, in order of the distance to the central star γ Cas.

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2

There are also relevant unpublished contributions to the WDS, such as that of the Observatori Astronòmic del Garraf (Caballero et al. 2013). See further details at http://www.astro.gsu.edu/wds/wdstext.html#intro

3

The nine primary stars with Gaia DR2 data are: LP 295–49, G 202–45, 36 And A, 4 Sex, HD 111456, HD 125354, HD 340345, BD-12 6174, and HD 213987.

4

The two WDS pairs with unidentified companion stars are WDS 03074–5655 (TSN 110) and WDS 03353–4020 (TSN 111). In a preliminary analysis, there was a third unidentified system, namely WDS 05463+5627 (LDS 3673), but it suffered from a typographical error in WDS that was corrected afterwards (Carro 2021; B. D. Mason, priv. comm.). We revise its relative astrometry to ρ = 57.1 arcsec, θ = 262.5 deg, and epoch = J2016.0.

5

The eight companions without parallax are: LSPM J1536+2856, SCR J1900–3939, UCAC3 208–200112, 2MASS J13543510–0607333, 2MASS J14313545–0313117, Gaia DR3 276070675205077632, Gaia DR3 4655216993788228480, and Gaia DR3 601133385210548736.

6

For example, Tokovinin & Lépine (2012) and we ourselves measured ρ = 1684.2 arcsec and 1684.49 arcsec, respectively, for the outlier system HD 45875 + Gaia DR3 1115649542191409664 (TOK 503, WDS 06387+7542 AD), but WDS instead tabulates 1898.64 arcsec collected in 2015.

7

The two systems at d > 150 pc are γ Cas + HD 5408 (188 pc) and G 143-33 + G 143–27 (324pc).

8

The high proper motion pair with µ > 700 mas a−1 is α Cen AB + Proxima (3710 mas a−1).

9

For example, HD 1466 is SHY 113 G, SHY 114 G, and CVN 33 G.

10

HD 79392 is catalogued by WDS as the primary of two different systems (WDS 09150+3837/TOK 525 and WDS 09150+3837/DAM1575).

12

Fischer & Marcy (1992) determined the statistical correction ā ≈ 1.26 s¯$\bar s$ between projected separation (s) and true separation (a) from Monte Carlo simulations over a full suite of binary parameters.

13

Wald 95% confidence interval is (λ−1.96λ/n,λ+1.96λ/n$\lambda - 1.96\sqrt {\lambda /n} ,\lambda + 1.96\sqrt {\lambda /n} $), where λ is the number of successes in n trials.

14

If confirmed in the future, we propose naming the SKG following the discovery name of the brightest, earliest star: HD 188162.

15

BU 499 AC is an optical pair, with “ADS 782 C” at 53 arcsec to γ Cas being a background star.

All Tables

Table 1

Primary stars without a Simbad entry.

In the text
Table 2

Radial-velocity outlier candidates.

In the text
Table 3

Giants and white dwarfs in wide double and multiple systems.

In the text
Table 4

Multiplicity order rates of ultrawide galactic systems.

In the text
Table 5

The most fragile (| Ug* |<1033$\left| {U_g^*} \right| &lt; {10^{33}}$ J) and the most separated (s ≥ 5 pc) systems.

In the text
Table B.1

Stars in young stellar kinematic groups.

In the text
Table B.2

Basic data of the 94 galactic field systems.

In the text
Table B.3

Masses, ρ, θ, separations and gravitational binding energy of the systems identified in the sample of work.

In the text
Table B.4

Candidate stars to be part of the γ Cas association, in order of the distance to the central star γ Cas.

In the text

All Figures

thumbnail Fig. 1

Cumulative number of WDS pairs as a function of ρ. Red data points with ρ > 1000 arcsec (to the right of the orange vertical dashed line) mark the 504 WDS pair candidates investigated by us. This figure can be compared with Fig. 1 in Caballero (2009).
In the text
thumbnail Fig. 2

Flowchart describing our analysis.
In the text
thumbnail Fig. 3

Astrometric criteria for pair validation. In both diagrams, we plot pairs between primaries and secondaries with blue circles, tertiaries with red triangles, quaternaries with green squares, and higher order companions with purple diamonds. Left: ΔPA1,i vs. µ1,i ratio diagram. Vertical and horizontal grey lines mark the µ ratios of 0.15 and 0.25 µ and ΔPA of 15 deg, respectively. Compare with Fig. 2 in Montes et al. (2018). Right: distance of companions vs. distance of primaries. Diagonal lines indicate the 1.15:1, 1:1, and 0.85:1 distance relationships. The α Cen AB + Proxima system, at d ~ 1.3 pc, is not shown.
In the text
thumbnail Fig. 4

Spatial distribution of the 309 identified young stars in SKGs, associations, and open clusters.
In the text
thumbnail Fig. 5

H-R diagram of all investigated stars. Coloured open symbols stand for stars in double (blue circles), triple (red triangles), quadruple (green squares), and higher-order multiple systems (purple diamonds). Grey dots represent selected field stars from Gaia. The black solid line is the updated main sequence of Pecaut & Mamajek (2013). The stars outside the main sequence are discussed in the text.
In the text
thumbnail Fig. 6

Reduced binding energy (left) and projected physical separation (right) as functions of ultrawide system total mass. In both panels, the three most fragile systems (top of Table 5) and the most separated systems (bottom of Table 5) are plotted in red triangles and green squares, respectively, while the rest of investigated ultrawide systems are plotted in blue circles. The error bars in s are smaller than the used symbols. In the left panel, the horizontal line marks the limit of | Ug* |$\left| {U_g^*} \right|$ at 1033 J. In the right panel, the grey solid diagonal lines mark the statistical maximum ages of 0.1, 1, and 10 Ga at which the systems are likely bound (computed with Eq. (9)), while the red dashed diagonal lines mark the corresponding orbital periods of 0.1, 1, and 2 Ga (computed with Kepler’s third law). In both cases we used the correction a ≈ 1.26 s (Fischer & Marcy 1992).
In the text
thumbnail Fig. 7

Spatial distribution of the septuple system WDS 19507–5912. The size of the spheres representing every star, labelled in blue, are proportional to their brightness. The projected physical separations from the primary star, HD 188162, in red, are in 103 au. The overall proper motion, in green, is in mas a−1.
In the text
thumbnail Fig. A.1

Spatial distribution of candidate young stars (open yellow circles) at less than 6 deg (left) and 2 deg (right) to γ Cas. In the right panel we also highlight HD 5408 (the most massive star after γ Cas) and the IC 63 emission nebula. The images were created with the Aladin sky atlas and blue, red, and infrared Digitised Sky Survey data.
In the text

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