Multiplicity and Clustering in Taurus Star-Forming Region I

A&A 599, A14 (2017) Astronomy DOI: 10.1051/0004-6361/201629398 & c ESO 2017 Astrophysics

Multiplicity and clustering in Taurus star-forming region I. Unexpected ultra-wide pairs of high-order multiplicity in Taurus

Isabelle Joncour1, 2, Gaspard Duchêne1, 3, and Estelle Moraux1

1 Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France e-mail: [email protected]; [email protected] 2 Department of Astronomy, University of Maryland, College Park, MD 20742, USA 3 Astronomy Department, University of California, Berkeley, CA 94720-3411, USA Received 26 July 2016 / Accepted 24 November 2016

ABSTRACT

Aims. This work analyses the spatial distribution of stars in Taurus with a specific focus on multiple stars and wide pairs in order to derive new constraints on star formation and early dynamical evolution scenarios. Methods. We collected the multiplicity data of stars in Taurus to build an up-to-date stellar/multiplicity catalog. We first present a general study of nearest-neighbor statistics on spatial random distribution, comparing its analytical distribution and moments to those obtained from Monte Carlo samplings. We introduce the one-point correlation Ψ function to complement the pair correlation function and define the spatial regimes departing from randomness in Taurus. We then perform a set of statistical studies to characterize the binary regime that prevails in Taurus. Results. The Ψ function in Taurus has a scale-free trend with a similar exponent as the correlation function at small scale. It extends almost 3 decades up to ∼60 kAU showing a potential extended wide binary regime. This was hidden in the correlation function due to the clustering pattern blending. Distinguishing two stellar populations, single stars versus multiple systems (separation ≤1 kAU), within Class II/III stars observed at high angular resolution, we highlight a major spatial neighborhood difference between the two populations using nearest-neighbor statistics. The multiple systems are three times more likely to have a distant companion within 10 kAU when compared to single stars. We show that this is due to the presence of most probable physical ultra-wide pairs (UWPs, defined as such from their mutual nearest neighbor property), that are themselves generally composed of multiple systems containing up to five stars altogether. More generally, our work highlights; 1) a new large population of candidate UWPs in Taurus within the range 1–60 kAU in Taurus and 2) the major local structural role they play up to 60 kAU. There are three different types of UWPs; either composed of two tight and comparatively massive stars (MM), by one single and one multiple (SM), or by two distant low-mass singles (SS) stars. These UWPs are biased towards high multiplicity and higher-stellar-mass components at shorter separations. The multiplicity fraction per ultra-wide pair with separation less than 10 kAU may be as high as 83.5 ± 19.6%. Conclusions. We suggest that these young pre-main sequence UWPs may be pristine imprints of their spatial configuration at birth resulting from a cascade fragmentation scenario of the natal molecular core. They could be the older counterparts, at least for those separated by less than 10 kAU, to the ≤0.5 Myr prestellar cores/Class 0 multiple objects observed at radio/millimeter wavelengths. Key words. open clusters and associations: individual: Taurus – stars: variables: T Tauri, Herbig Ae/Be – binaries: general – binaries: visual – methods: data analysis – stars: statistics

1. Introduction (Dobbs et al. 2014), fragment, cool, and collapse to form dy- namic clusters of young multiple objets whose sizes are approxi- The formation of stars results fundamentally from the runaway mately a solar radius. Since newly born stellar objects are closely unbalance between overwhelming inwards self-gravity and out- linked to their gaseous progenitors (Hartmann 2002), their spa- wards pressure-gradient forces (thermal, turbulence, magnetic, tial distribution and their multiplicity properties offer important radiation, etc.) inside a perturbed gas cloud. Star formation has tests on star formation models. been known to be a complex process since at least the first model proposed almost three decades ago of a single isolated low-mass Giant molecular clouds appear to be anything but uniform. star formed out of one dense gas core (Shu et al. 1987). It also They are highly substructured into a hierarchy of gas clumps involves radiative processes (heating and cooling), generation and into highly intertwined filamentary networks, as strikingly and decay of turbulence and magnetic fields, chemical evolu- revealed by the recent Herschel Gould Belt Survey (André et al. tion of molecules, as well as dust and feedback mechanisms of 2014). In turn these filaments shelter single or chains of molec- newly formed stars in their natal environment. A realistic pic- ular cores (Tafalla & Hacar 2015). Whether such heterogeneous ture must be even more complicated since the stars are rarely patterns remain as the relics of the star formation processes in born in isolation (Lada & Lada 2003) and, moreover, they are young stellar populations or are totally and quickly erased by generally not single but part of multiple systems (Mathieu 1994; subsequent dynamical evolution is an important question. Duchêne & Kraus 2013). Overall, the whole story of star for- To seek such imprints of star formation, the giant Taurus mole- mation spans over ten orders of magnitude length-scale range. cular cloud is an ideal nursery. Its proximity (137 pc, Torres Giant gas clouds, having typical sizes from 10 pc to 100 pc et al. 2007), the youth (1–10 Myr) of its stellar population

Article published by EDP Sciences A14, page 1 of 33 A&A 599, A14 (2017)

(Bertout et al. 2007; Andrews et al. 2013), and its low stellar ultra-wide pairs (UWP) as mutual nearest neighbors in the range density bring a complete census of approximately 350 young of 1–100 kAU and we show the crucial role they play in spatial low-mass stars down to 0.02 M (Luhman et al. 2010; clustering features (Sect. 4). We make a synthesis of results and Rebull et al. 2010). As there is a small spatial dispersion of open a discussion (Sect. 5) before a summary to conclude the (proto-)stars within the gaseous filament (Hartmann 2002; paper (Sect. 6). Covey et al. 2006), these stars are most probably born where they are now observed. The current paradigm of star formation attributes a seem- 2. Data ingly fundamental role to dense molecular cores thought to be 2.1. Input catalog the very cradles of stars (Ward-Thompson et al. 2007). The long- standing scenario proposed so far to form one low-mass star Although a recent catalog of Taurus members has been re- from one collapsing single core (Shu et al. 1987) predicts that leased including newly detected mid-infrared Wide-field In- the dense cores set the final mass of young stars. This is sup- frared Survey Explorer (WISE) sources (Esplin et al. 2014), we ported by the correspondence of the shapes of the core mass adopted the catalog containing 352 Taurus members that offers function (CMF) and the initial mass function (IMF) of stars, a full census of members down to 0.02 M (Luhman et al. 2010; although the peak of the IMF is shifted by a factor 2–3 to- Rebull et al. 2010), which we supplemented with stellar multi- wards lower mass. This shift may be due to a partial 30–40% plicity data. The newly identified WISE members are mainly due efficiency gas to star conversion (Alves et al. 2007; Lada et al. to a wider coverage of the Taurus region compared to Spitzer’s, 2008; Marsh et al. 2016; Könyves et al. 2015), although this es- similar to the new candidates recently identified in Taurus us- timate is higher than the star-formation efficiency (1–10%) esti- ing the Sloan Digital Sky Survey (Luhman et al. 2017). These mated for the whole cloud. Alternatively, such a shift between new members belong primarily to the dispersed stellar popula- the core mass function and the initial mass function may also tion and have typically not been observed at high angular res- result from the multiplicity of stars born within one individual olution (HAR), hence multiplicity information is not complete core that has undergone multiple fragmentation (Goodwin et al. for these sources. Therefore, setting this population aside should 2008). This may lead to a core-to-stars efficiency as high as not significantly affect our conclusions surrounding local pairing 100% (Holman et al. 2013; see for a reviewO ffner et al. 2014). statistical properties. Moreover, the Luhman et al.(2010) catalog The multiplicity appears to be a key feature in star- provides a full and coherent analysis of SEDs as obtained from forming regions. The companion frequency of young stars in the Spitzer Infrared Array Camera and Multiband Imaging Pho- Taurus is generally twice that of field stars (Duchêne & Kraus tometer, leading to a system of four Classes of SED (Class 0, 2013), and the formation of coeval and wide binaries up to I, II, and III objects) that we will use in our statistical stud- 5 kAU is a common outcome of the star formation process ies. This classification is widely used to assess the evolution- (Kraus & Hillenbrand 2009a). Furthermore, since multiplicity ary state of the material surrounding the star (Lada & Wilking appears to decrease with age (see for a review Duchêne & Kraus 1984; Lada 1987; Andre et al. 1993; Greene et al. 1994). Further 2013) due to dynamical evolution, observing multiplicity at this studies have revealed that pure SED analyses can be misleading young age means that the multiple system-core picture of star (Carney et al. 2016) for individual objects. However, although formation is the rule rather than the exception. In this picture, the uncertainties remain on the individual classification, there is a maximal size of multiple systems cannot exceed the size of their clear statistical sequence of ages as a function of SED classifica- progenitor cores, typically approximately 20 kAU, that is, 0.1 pc tion when the population is taken as an ensemble. (Ward-Thompson et al. 2007). If the dense cores are de facto the Taurus is known to be the archetype of low-mass star for- smallest bricks to build a young stellar population, we then ex- mation in loose groups (Jones & Herbig 1979; Gomez et al. pect that spacing between stars as well as binary semi-major axes 1993; Kirk & Myers 2011). The star mass estimates were taken be related to parental molecular core size and spacing, provided from the latter work exploiting the same catalog of stars from that dynamical evolution has not erased early imprints. Further- Luhman et al.(2010). We note that the stellar masses have been more, if the formation of multiple systems and single stars share estimated from their spectral type while assuming a constant age a common scenario, we do not a priori expect any difference in of 1–2 Myr for all stars of the complex and using an ad hoc spatial distribution between the two. isochrone at 1–2 Myr composed of a sequence of several the- Several spatial studies have been performed in Taurus. Some oretical evolutionary tracks depending on the mass range (see were based on the stellar two-point correlation function and Kirk & Myers 2011, for details). Since a recent careful analy- the related mean surface density of companions to examine sis based on optical spectroscopic study of young stars in star- the scale-free behavior of clustering modes (Gomez et al. 1993; forming regions, including Taurus, has shown that spectral types Larson 1995; Simon 1997; Gladwin et al. 1999; Hartmann 2002; measured over the past decade are mostly consistent with the Kraus & Hillenbrand 2008). Other studies based on first-nearest- new evaluation (Herczeg & Hillenbrand 2014), the main source neighbor separation (1-NNS) statistics analysis aimed either at of uncertainties surrounding mass estimation comes from the hy- comparing the spatial distribution of stars in Taurus to a random pothesis of a unique age for all the members (1–2 Myr). distribution (Gomez et al. 1993) or at studying their distribution The mass was estimated for each star using the effective tem- as a function of their mass and spectral energy distribution (SED) perature converted from its spectral type and an ad-hoc isochrone (Luhman 2006; Luhman et al. 2010). at 1–2 Myr composed of a sequence of several theoretical evolu- In this work, after a description of the stellar data catalog tionary tracks depending on the mass range (see Kirk & Myers we have built to perform our studies (Sect. 2), we apply these 2011, for details). For a given spectral type, assuming a younger two statistical tools (1-NNS distribution and two-point correla- age for a star than reality will tend to underestimate its mass. tion function) to analyse the spatial distribution of stars in Taurus But, even if the absolute value of the mass is subject to great un- with a focus on multiples with respect to single stars, while in- certainties (30 to 50%), yet we do not expect a systematic differ- troducing the one-point correlation function Ψ (Sect. 3). We then ential bias in mass estimation. Besides, there is no indication of a assess the statistical properties of 1-NNS couples while defining mixture of components in the age distribution that would suggest

A14, page 2 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus the presence of distinct episodic generation of stars, nor any ev- Table 1. Sub-samples of stars in Taurus. idence of a systemic dynamical evolution that would divide the stars into distinct age-based populations. New generation of stars Sub-sample Spatial region Class HAR N and dynamical evolution appear to be continuous processes that S 1 whole All No 338 globally lead to a smooth dispersion of age. For instance, multi- S 2 Win All No 252 ple systems and single stars have a same mean age and display S 3 whole II, III Yes 179 the same age dispersion (White & Ghez 2001). Thus, assuming a single age for all the stars will bias the absolute value of each Notes. Sub-samples of our star catalog depending on their spatial loca- derived mass, but the relative diﬀerence between them, which is tion (whole region of Taurus or within Win, see Fig.1), their Class, or used in our analysis, should be much less aﬀected. whether or not they all have been observed at HAR. N: total numbers of stars within the sub-sample.

2.2. Multiplicity

To construct a census of stellar systems in Taurus, we began 2.3. Samples by compiling a list of all known multiple members of the region from almost three decades of increasingly higher-angular- The sources in Taurus, as was first pointed out by Gomez et al. resolution observations (see references in Table C.1). We also (1993), are not randomly distributed on the sky (see Fig.1). assigned a flag to each star when it has been observed at HAR. Some sets of stars appear grouped at a global scale in two struc- In order to separately study the populations of single stars tures located North (in L1507 molecular cloud) and South-West and multiple systems and to distinguish clustering from multi- (in L1543 molecular cloud) with respect to the three main fila- plicity, we grouped together all stars that are separated by less ments, while some of them are tightly subgrouped at small scales than 700 (0.92 kAU ∼ 1 kAU) to form a single entity. Throughout within the main central filaments. Yet, other stars appear more this paper we refer to them simply as “multiple systems”. This spatially dispersed between the main structures. One of the goals threshold is, to a certain extent, arbitrary. However, two reasons of this work is to more precisely quantify their spatial distribu- motivate this choice. First of all, it is the lower threshold that de- tion based on nearest-neighbor analysis, now that the census of fines wide binaries (separation >1 kAU) and secondly (the main star population in Taurus has more than doubled since the semi- reason), this threshold is close to the 600 beam of the Spitzer- nal work of Gomez et al.(1993). MIPS data. Thus, we ensure that the census of neighbor stars be- From our catalog we extracted three distinct samples (de- yond 1 kAU is completely independent of the Class of the Taurus fined in Table1) that we use to test di fferent hypotheses through- members. out this work, notably for multiplicity testing. We assigned the total number of stars within a 1 kAU radius n∗ (for a single star n∗ = 1, for a binary n∗ = 2, . . . ) to each entry of the catalog, and we note that this parameter is only reliable for Class II and III type stars that have been observed at 3. Local spatial analysis HAR, using techniques such as speckle interferometry imaging and adaptive optics with spatial resolution between 0.0500 to 200. In this section, we perform the spatial analysis of stars in the These techniques probe the immediate neighborhood of a star, entire Taurus region and we assess the difference in the spatial at least beyond ∼10 AU at the distance of Taurus (i.e., 5−20 AU distribution between multiple systems and single stars based on depending on the technique). Very close binaries (i.e., .10 AU) their respective first nearest neighbor separation (1-NNS) statis- most probably originate from a distinct scenario from other bi- tics. Nearest-neighbor statistics have been used for decades in naries, as they are probably not formed by fragmentation in situ Taurus to; (1) demonstrate departures from random uniform dis- (Bate et al. 2003). We thus consider spectroscopic binaries and tributions (Gomez et al. 1993); (2) show that the spatial distribu- the closest visual binaries (below ∼20 AU) as single stars to en- tion of brown dwarfs and stars are undistinguishable (Luhman sure the consistency and completeness of our visual binary anal- 2004); and (3) study the spatial distribution of stars as a function ysis, since no exhaustive spectroscopic binaries survey has been of their Class (Luhman et al. 2010). We start with some prelim- performed till now. inary work on 1-NNS statistics to advocate the use of the theo- The resulting catalog (see Table C.1) contains 338 sources. retical 1-NNS distribution derived for a random distribution in Of these, 250 have been observed at HAR and amongst the latter an infinite medium as a reliable proxy for a random distribution 94 are multiple systems, resulting in a mean multiplicity fraction enclosed in a finite and irregularly shaped window provided that (MF) of 40%, which could truly be as high as 54%, if all the re- the window is large and well-populated. We then define the one- maining stars that have not been observed at HAR are multiple point correlation function Ψ, which complements the two-point systems. A similar multiplicity fraction is obtained when consid- correlation function, to study the binary regime. This function al- ering only Class II/III stars (i.e., MF = 40% ± 10%). The mean lows us to quantify the departure of a population from a random companion frequency for Class II/III stars observed at HAR is uniform one and to identify distinct spatial regimes (clustering, 48%. We note that a chi-squared test shows that the proportion inhibition, and dispersion). of Class I, II, and III in the star sample observed at HAR is statis- Most of our work was performed using the free R soft- tically the same when considering either single stars or multiple ware environment for statistical computing and graphics (R Core stars. The disk fraction (the number of Class II stars over the Team 2015) using a set of packages such as Spatstat, Hmisc, number of Class II and III stars) is also statistically the same fields, FITSio, calibrate, xtable, astrolab, deming, mixtools, in the two populations. Using Class as a proxy for the age, we and magicaxis (Baddeley & Turner 2005; Harrell et al. 2015; obtain, as already stated by White & Ghez(2001) that uses the- Nychka et al. 2015; Harris 2013; Graffelman 2013; Dahl 2014; oretical stellar evolution models, that the two populations share Chakraborty et al. 2014; Therneau 2014; Benaglia et al. 2009; the same age and the same range of age dispersion. Robotham 2015).

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Fig. 1. Spatial distribution of stars within the Taurus region superimposed on near-infrared extinction (unit mag, gray scale) from Juvela & Montillaud(2016). Dashed polygon: restricted spatial window Win in Taurus complex; blue ﬁlled dots: random sampling. Color-coding for Taurus stars: red plus marks: clustered stars [1-NNS ≤ 0.1◦]; black plus marks: “inhibited” regime stars [0.1◦ < 1-NNS ≤ 0.55◦]; green plus marks: isolated stars [1-NNS beyond 0.55◦] (see Sect.3).

3.1. 1-NNS study in Taurus 3.1.1. Mean stellar surface density in Taurus

To derive an estimate of the mean surface density ρw of the spa- This subsection aims at analyzing the spatial distribution in Tau- tial process in Taurus, we focus on its central part as the least rus based on a 1-NNS analysis. The 1-NNS of a star is, by defini- heterogeneous area and define the spatial polygonal window tion, the distance to its nearest neighbor star. Throughout this pa- Win that encloses the central three main filaments (see Fig.1), per, we deal with the projected 1-NNS, computed for each star as to get: the minimum value of projected angular distance between each −2 −2 pair of stars onto the celestial sphere (see AppendixA). ρw = Nw/Aw ∼ 5 deg ∼ 1 pc , (1) 2 2 After estimating the mean surface density of stars, we first where Aw = 48.5 deg (i.e. 289.57 pc ) is the projected area of compare the Taurus 1-NNS distribution in the three main fil- the window Win that encloses Nw = 252 stars. This window de- aments to that associated to the entire region. We then com- fines our star sample S 2 (see Table1). pare the theoretical random 1-NNS distribution obtained for an In the following paragraph, we estimate the uncertainty of infinite random spatial process to the 1-NNS distribution de- the mean projected stellar surface density of Taurus. A conserva- rived from Monte Carlo samplings in a finite irregularly shaped tive estimate of the uncertainty on the surface density may be ob- window, and finally we compare Taurus 1-NNS distribution to tained when choosing for the window, the convex hull of the stars the 1-NNS random distribution. enclosed within the polygonal window Win. The convex hull of

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Table 2. Moments of the 1-NNS distribution in Taurus.

2 2 Spatial window Stars sample r [pc] r0.5 [pc] σ [pc ] σ [pc] γ whole region Taurus S 1 0.38 ± 0.04 0.17 ± 0.06 0.55 ± 0.05 0.74 ± 0.03 5.91 ± 0.32 Win Taurus S 2 0.28 ± 0.02 0.16 ± 0.03 0.14 ± 0.01 0.37 ± 0.02 3.18 ± 0.19 Inﬁnite Rand. Theo 0.54 0.50 0.08 0.28 0.63

Win Rand. MC 0.55 ± 0.02 0.51 ± 0.02 0.09 ± 0.01 0.30 ± 0.01 0.84 ± 0.05

Notes. The moments of the 1-NNS distribution are given for: all stars in the whole Taurus region (sample S 1, see Table1), stars within the Win win- 2 dow (sample S 2, see Table1 and Fig.1), the random theoretical 1-NNS distribution “Rand. Theo” in an inﬁnite medium wR(r) = 2πρr exp(−πρr ) (Eq. (B.1)), and the 1-NNS distribution obtained from the 10 000 random Monte Carlo samplings “Rand. MC” within the Win window. The two random distributions are computed using the same intensity process ρ = 5 deg−2 (see Eq. (1)). The uncertainties are evaluated from Eq. (5), with N = 252.

◦

1 region of Taurus below this angular scale. Above the 0.1 scale, the two cumulative distributions diverge due to the presence of highly dispersed stars between the three main ﬁlaments and other main stellar concentrations in Taurus. As a result of these, the

0.8 1-NNS distribution of the whole region has a more populated large-scale tail. Nonetheless, up to the third quantile, the 1-NNS quartiles are similar. As a matter of fact, due to its highly asym-

0.6 metrical shape, the Taurus 1-NNS distribution is better evaluated using quantiles rather than the mean and standard deviation that are more conveniently suited for symmetrical functions. 0.4

Cumulative function Cumulative 3.1.3. 1-NNS distribution: theoretical random vs. Monte Carlo samplings 0.2

In this subsection, we compare the theoretical 1-NNS distribution for a spatially random process in an infinite media to the 0 1-NNS distribution obtained from Monte Carlo samplings in a −3 −2 −1 0 10 10 10 10 finite, irregularly-shaped window to establish that the former can 1-NNS [°] be used as a reliable proxy for the latter. The random theoretical 1-NNS distribution w (log r) derived Fig. 2. R Empirical cumulative distribution of the 1-NNS distribution for for an infinite media (see AppendixB for the full development) the whole region (black) and for the central part within Win region ◦ is given by: (blue). The blue vertical line represents the clustering length, rc = 0.1 .

2 2 wR(log r) = 2 ln(10) π ρ r exp(−πρr ), (3) a set of points in the Euclidean space is deﬁned as the smallest convex set of points that contains the whole set of points.The 2 where ρ is the mean intensity of the random process (the av- area of the convex hull, A ∼ 33 deg , being less than the polygo- erage surface density of stars) and r is the 1-NNS. We want to nal window, the surface density estimate mechanically increases −2 compare this theoretical distribution to the 1-NNS histogram ob- by a factor of 1.6 (Nw/A ∼ 8 deg ). Conversely, taking the con- tained from 10 000 random Monte Carlo samplings within the vex hull area of the whole Taurus region (∼202 deg2) contain- −2 ﬁnite and irregularly-shaped window Win (see Fig.3). Their re- ing 338 objects lowers the mean surface density to ∼2 deg . spective moments are similar (see Table2), with theoretical mo- Combined, these extreme cases yield a probable range for the ments computed from the following expressions: projected stellar density of Taurus of √ ρ ∼ 5 ± 3 stars/deg−2. (2) r¯ ' 1/(2 ρ), (4a)

σ2 = (4 − π)(4πρ)−1, (4b) √ 3.1.2. 1-NNS distribution across Taurus γ = 2 π(π − 3)/(4 − π)3/2, (4c) p The 1-NNS median value evaluated within the full region of Tau- r0.5 = ln 2/(πρ), (4d) rus (see Table2) does not di ffer from the 1-NNS median value evaluated within the three main filaments, and their 1-NNS cu- 2 2 mulative distributions do not differ either for length scale below where r, r0.5, σ , σ , and γ are the mean, median, variance, stan- ◦ rc ∼ 0.1 (see Fig.2). This indicates that the spatial properties dard deviation, and skewness factor (see AppendixB for their of the spatial distribution of stars are similar across the whole derivation). The moments from random Monte Carlo samplings

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2 sample of N ∼ Nw = 252 1-NNS obtained from standard rejec- tion sampling technique using analytical random 1-NNS distribution (Eq. (3)) to b) the 1-NNS associated to random Monte Carlo samplings of 252 stars enclosed within Win. The two- sample Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) 1.5 statistical tests indicate that the two 1-NNS distributions cannot be statistically distinguished with a mean p-value and standard deviation respectively of 0.36 ± 0.28 for the KS test and 0.34 ± 0.27 for the AD test. 1

PDF We have therefore shown that the random theoretical 1-NNS probability density function (Eq. (3)) may be used as a reliable proxy to describe a 1-NNS random distribution even in the case of a random population enclosed in a finite and irregularly 0.5 shaped window, such as Win. We mention, as an asset, that using random theoretical 1-NNS distribution proxy avoids large Monte Carlo sampling computations required to populate highly improbable bins of very small spacings associated with tightly 0 clustered regions. 0.01 0.1 1 1-NNS [°] 3.1.4. Spatial distribution in Taurus Fig. 3. Probability distribution function (PDF) of the 1-NNS distributions observed in Taurus (solid blue histogram: within the limited win- The comparison between the Taurus and random 1-NNS distri- dow Win, that is, the three main filaments; dashed blue histogram: the butions clearly reveals an excess of short spacings in Taurus (see entire Taurus region) and predicted for a random distribution (black Fig.3), for which the 1-NNS distribution has smaller central val- histogram: for a Monte Carlo sampling within the window Win; red ues (median and mean) and a wider dispersion (see Table2). The curve: unlimited theoretical random 1-NNS distribution, see Eq. (3)). 2-sample KS and AD tests, give a p-value less than ≤2.2 × 10−16 Both random populations are drawn using the same mean surface den- −40 2 and ≤10 , respectively, that the two samples are mutually con- sity ρw = 5 deg . Increasing the mean density by a factor of two leads to a shift towards the left whose amplitude is represented by the green sistent. Thus, we can firmly reject the hypothesis that the spatial arrow. The Monte Carlo sampling in a finite window and the unlim- distribution of stars within Taurus is random. ited theoretical random 1-NNS do not significantly differ. The 1-NNS This result is not surprising, since the same conclusion was distributions computed either in the whole Taurus or within Win do not already reached by Gomez et al.(1993) based on a sample of significantly differ either. However, the Taurus and random 1-NNS dis- 139 stars. But the expansion of the stellar census by nearly −16 tributions are statistically highly inconsistent, with a p-value of ∼10 200 new stars in Taurus strengthens this conclusion. The me- for the KS test. The spatial distribution in Taurus is clearly far from dian value of the 1-NNS distribution we derived is r ∼ 0.067◦ being random. 0.5 (∼0.16 pc, i.e. 33 kAU); almost half the value obtained by these authors. This is what we expect when the spatial distribution of were obtained from: additional stars follows a similar spatial pattern from the original population, since√ from Eq. (4d), the median value is reduced by 1 XN a factor of ∼ 338/139 ∼ 1.5. r = r ± [N − 1]−1/2 σ , N − 1 i i Tau This also underlines the modest usefulness of the absolute 1 value of the median nearest-neighbor distance to determine clustering property when the stellar census is incomplete. In the fol- 1 XN √ σ2 = (r − r)2 ± 2 [N − 1]−1/2 σ2, lowing section, we introduce an alternative criterion based on the (N − 1) i 1 one-point correlation function to quantitatively assess local departures from pure randomness and to determine characteristic v tu clustering scales. 1 XN σ = (r − r)2 ± [2 (N − 1)]−1/2 σ, N − 1 i 1 3.2. One and two-point correlation statistics N XN In order to identify a criterion that quantifies the departure of a γ = (r − r)3 ± (N − 1)−1/2 γ, ((N − 1)(N − 2)) i spatial distribution of stars from randomness, we introduce the 1 one-point correlation function based on the 1-NNS distribution. p This function is a new tool to assess and quantify the binary and ± − r0.5 = Λ0.5 σ π/(2(N 1)) (5) spatial clustering regimes of stars and aims at complementing where Λ is the ordered sequence of the 1-NNS from the small- the two-point correlation statistics. est to the highest value, the standard errors of the moments and the standard error of the median are taken respectively from 3.2.1. The two-point and pair correlation functions Ahn & Fessler(2003) and Kendall & Stuart(1977). We thus conclude that finite size and edge window effects The two-point correlation function (TPCF) ξV (r) is defined for do not significantly alter the distribution of 1-NNS from that ob- a 3D spatial process as a measure of the probability to get any tained in an infinite medium at the level of our observational excess of stellar pairs with a separation distance vector r above 2 uncertainties. To prove this statement quantitatively, we use a random expectation: dP = ρV (1 + ξV (r))dV1dV2, where ρV is the bootstrapping technique, comparing 10 000 realizations of a) a mean volumic density of the uniform random process and dP is

A14, page 6 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus the inﬁnitesimal joint probability to ﬁnd a pair of stars respec- Clustering Dispersion tively centered in the volume elements dV1 and dV2 and sepa- 1000 rated by r (Peebles 1980). Similarly, for an isotropic and sta- tionary spatial process, the standard projected angular two-point (blue)

correlation function ξ(r) is then deﬁned as the probability to ﬁnd Inhibition Ψ

a pair of stars each separated by a projected angular distance r 100 2 above random expectation: dP = ρ (1 + ξ(r))dΩ1dΩ2, where ρ is the density of stars per steradian and dP is the inﬁnitesimal joint probability to ﬁnd a pair of stars each within a unit solid angle dΩ1, dΩ2 and separated by a projected angular distance r. 10 Besides the two-point correlation function, the second order statistics may also be evaluated from related entities: – the main surface density of companions (MSDC) above ran- 1 dom expectation: Σ(r) = ρξ(r); – the pair correlation function g(r) as a measure of the probability to have any pair of stars separated by r: g(r) = 1 + ξ(r). One-point correlation function function correlation One-point

When the spatial distribution is random, all these functions are 0.1 ξ r , g r , r −3 −2 −1 0 1 constant ( ( ) = 0 ( ) = 1 Σ( ) = 0). Although different es- 10 10 10 10 10 timators may be used to compute the pair correlation function r [°] (Landy & Szalay 1993; Kerscher et al. 2000), we use the simple and natural one defined as: Fig. 4. One-point correlation function Ψ (Eq. (7), blue symbols) and estimated pair correlation function g (gray symbols) using the sample of NPairs(r) stars within W . The pair correlation function has been estimated using gˆ(r) = Tau , (6) in NPairs(r) the estimator given in Eq. (6) while performing 10 000 random Monte R Carlo samplings within Win. The 1σ vertical errorbars of Ψ and g are estimated from Poisson statistics. The solid horizontal blue line repre- NPairs r NPairs r where Tau ( ) and R ( ) are the histogram of separations be- sents both the constant Ψ = 1 andg ˆ = 1 functions, that is, the one-point tween stars within Taurus and in a randomly distributed cata- and pair correlation function expected for a spatial random distribution. logue, respectively. Vertical black solid lines delimit three spatial regimes, clustering, inhi- Since the pair correlation function estimate is mainly sensi- bition, and dispersion, derived from the crossing of the Taurus Ψ func- tive to the shape and extension of the window, no straightfor- tion with the Ψ = 1 horizontal line associated to random spatial distribu- Pairs tion. The vertical dashed purple line indicates the 700 spacing threshold ward theoretical expression can be derived for NR (r) on general grounds, even in the random spatial distribution case. We used to group stars into a unique multiple system. The dotted-dashed − then compute the pair correlation function using Eq. (6) while green line is the Ψ ∝ r 1.5 function resulting from a linear regression fit taking into account vertical errorbars over ten 1-NNS logarithm bins performing 100 000 random Monte Carlo samplings within Win (see Fig.4). (∆log r = 0.2). The Ψ function may reveal an extended binary regime from 1.6 kAU to 100 kAU in Taurus, which has remained unidentified The slope and the shape of the resulting Taurus pair cor- beyond approximately 5 kAU in previous works that used the pair corre- relation fonction are comparable to those obtained in pre- lation function alone, since the latter reveals a power law break around vious works studying the two-point correlation function or that separation. the main surface density of companions (Gomez et al. 1993; Larson 1995; Simon 1997; Gladwin et al. 1999; Hartmann 2002; Kraus & Hillenbrand 2008). Together with our own, these studies show that the second order statistics exhibit at least two distinct power-laws: a steep binary/multiple regime at small especially when the spatial distribution of stars deviates from scale and a smoother clustering regime beyond a breaking point. isotropy. Indeed the standard form of the two-point correla- Larson(1995) suggested that; (1) the observed break at 0.04 pc tion function is obtained with the hypothesis of a homogeneous (8.25 kAU) can be the signature of the transition from a binary and isotropic distribution. However, the Taurus complex is not to a clustering regime; (2) it could correspond to the Jeans length isotropic, as evidenced by its elongated gaseous structures in for the gas in cool dense molecular cores; (3) the scale-free bi- which stars are preferentially located. The break in the two- nary regime may reflect the scale-free fragmentation of collaps- point correlation function between the binary and the clustering ing clumps; and (4) the self-similar clustering regime may reflect regimes may thus be partly due to the filamentary geometrical the hierarchical, fractal, and spatial distribution of the gas from anisotropy, rather than being only a signature of a hierarchi- which the stars formed. cal/fractal gas structure as proposed by Larson(1995). Later on, Kraus & Hillenbrand(2008) found an extended transition zone between the binary regime and the global clus- Indeed, the observed break in the two-point correlation func- tering of stars in groups rather than a sharp break between the tion could also be linked to the observed width of filaments, two regimes. This transition zone was found to begin at 0.02 pc which was found to be relatively universal at approximately (4.25 kAU) and end at 0.2 pc (42.5 kAU). They proposed that 0.1 pc (André et al. 2014) even though Ysard et al.(2013) found part of this transition zone, which is almost flat from 0.11 pc that filament width may vary by up to a factor of approximately (23.52 kAU) to 0.2 pc (42.5 kAU), is due to the random motion four. This spread of filament widths may also contribute to the of stars that may smooth out primordial stellar association and transition elbow zone that is present between the binary and clus- lead to a quasi-constant surface density of pairs. tering regimes. Thus, the elbow in the correlation function that However, some caution has to be taken when interpreting extends up to 0.25 pc may be related to geometrical spatial stellar the two-point correlation function beyond the binary regime, structures (see Joncour et al., in prep.).

A14, page 7 of 33 A&A 599, A14 (2017)

3.2.2. The one-point correlation function 0.2 Similarly to the pair correlation function, we deﬁne the one-point correlation function, Ψ, as the probability of having a closest star located at r from any chosen star at random, which in turn de-

ﬁnes an equivalent local stellar density function σ: dP = σ(r)dV, 0.15 with σ(r) = ρΨ(r). The Ψ function, which describes the spatial location of stars, gives ﬁrst order variation trends of the spatial process relative to a random distribution. Instead, the pair corre-

lation function is associated to second-order characteristics de- 0.1 scribing the spatial co-location of stars. One estimator of the Ψ function may be defined from the ratio of the 1-NNS Taurus dis- 1-NNS fraction 1-NNS tribution wTau(log r) to the 1-NNS random distribution wR(log r) obtained either by Monte Carlo simulations or from theoretical 0.05 random probability density function (Eq. (3)): w (log r) Ψ(log r) = Tau · (7) w (log r) R 0 We note that this function is usually called the nearest neighbor 103 104 105 106 ratio when it is evaluated as the average over the whole range of r (1-NNS) [AU] 1-NNS values. Here we evaluate it bin per bin of spacing. For a random spatial distribution, the one-point correlation function Fig. 5. First nearest neighbor separation fraction distribution of mul- reduces to unity (Ψ(r) = 1). tiple systems (solid blue histogram) versus single stars (dashed black The one-point correlation Ψ function can be fitted from histogram) for Class II and III objects observed at high angular resolu- 1.6 kAU to ∼100 kAU, by a power law using Pearson’s chi- tion (HAR) in Taurus region. Each bin represents the number density of stars per unit logarithmic interval in projected separation, that is, the squared linear regression taking into account vertical errorbars number density fraction of 1-NNS per (∆log r = 0.2) interval. There (see Fig.4): is a marked excess of 1-NNS in the range 1−10 kAU for the multiple w systems with respect to single stars. Ψ = Tau ∝ r−α, (8) wR +0.2 with α = 1.50.3 at the 95% confidence level. This allows us to 3.2.4. Ultra-wide binary regime in Taurus? derive a fractal dimension Df associated to the binary regime in 2 The comparison between the pair correlation and the Ψ functions Taurus. Since√ the random distribution in 2D increases as wR ∝ r for r 1/ πρ (see AppendixB), the 1-NNS distribution within yields new insight into an extended binary regime. Both of them have the same scale-free trend at least in the four logarithm bins Taurus wTau follows a shallow, rising power-law function with the following exponent: of separation (see Fig.4), from 1 .5 to 5 kAU. While the correlation function reaches an elbow from that point on, breaking from Df ∼ 2 − α = 0.5. (9) the binary regime to reach the clustering regime, the Ψ func- We note, that this scale-free behavior of the Ψ function with an tion extends the same power-law trend up to ∼100 kAU. Thus, exponent lower than the projected 2D euclidian space dimension although it remains hidden in the correlation function because is equivalent to a uniform distribution in a 2D projected fractal of mixing between binarity and clustering, the binary regime in space with the fractal dimension Df = 0.5 (Sakhr & Nieminen Taurus appears to extend to much larger scales than previously 2006). realized.

3.2.3. Departure from randomness 3.3. Local neighborhood of multiples versus single stars The one point correlation function Ψ may be used to assess de- In this subsection, we study the spatial distribution of multiple parture from a spatially random distribution. From its definition, systems and single stars based on the comparison of their 1-NNS regimes where Ψ is below unity indicate a deficit of stars (inhi- statistics. bition) with respect to random, whereas where it is above unity The S 1 sample in the whole Taurus contains 96 stars flagged reveals an excess of stars, either a clustering trend at small spac- as visual multiple systems (in the range of 10 AU to 1 kAU) and ings (aggregation) or a dispersion trend at large spacings. The Ψ 242 a priori single stars. To limit biases, we define the S 3 sample function evaluated for Taurus thus reveals three spatial regimes composed exclusively of Class II and III stars that have been (see Fig.4). The stellar clustering regime covers the range of observed at HAR. From that sub-sample, we separately con- spacings below ∼0.1◦, where Ψ(r) > 1. This defines the upper struct the 1-NNS histograms of the 89 multiple systems and the clustering length threshold rc: 140 single stars (see Fig.5) that appear very di fferent one from each other. Both the KS and AD statistical tests indicate that we ◦ ∼ ∼ rc = 0.1 0.24 pc 50 kAU. (10) can reject the theory that they come from the same parent popu- The clustering regime is followed by an “inhibition zone” where lation with a confidence level of 99.8%. The 1-NNS fraction of Ψ(r) < 1 associated with a typical length scale between ∼0.1◦ multiple systems having a projected separation less than 10 kAU (0.2 pc) and ∼0.3◦ (0.7 pc). Finally, Taurus faces an excess of is noticeably higher than for the single stars in the same range highly dispersed stars for typical length scale above ∼0.3◦. The (see Fig.5). “clustered stars” are tightly packed together in specific locations The excess fraction of 1-NNS at close spacings is remark- while the “inhibited stars” are more widely spread between the ably high: nearly 40% of the 1-NNS of all multiple systems are zones of clustered stars (see Fig.1). located within the first five bins, that is, between 1 and 10 kAU.

A14, page 8 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus

This is more than 2.5 times the fraction found in the same range of separations for the single stars (15%). It is also twice as 0.3 high as the frequency of visual companions per decade of projected separation found in the 10−2000 AU separation range (see Duchêne & Kraus 2013, Fig.5). Moreover, 63% of the compan- 0.25 ions of multiple systems in the ﬁve ﬁrst bins are themselves multiple systems (25% of the total multiple systems), against 43% 0.2 for the singles (6% of total single stars sample). The local neighborhood of multiple stars is thus more populated than that of simple stars: a multiple system has almost 0.15 three times more chance of having a companion within 10 kAU, 1-NNS fraction 1-NNS

and that companion in turn has a higher chance of being a close 0.1 multiple system itself than a single star.

3.4. Beyond local neighborhood 0.05

To test whether this striking difference between the neighbor- 0 hood of multiple systems and single stars extends beyond the 103 104 105 106 first neighbor, we analyse the second nearest neighbor distribu- 1-NNS [AU] tions, again using the bias-free S 3 sample. Although there is still a slight excess of companions for multiple systems within the Fig. 6. Distribution of ultra-wide pair fraction as a function of separation first bin up to 10 kAU, this difference does not appear statistically in the three main Taurus filaments (i.e., for stars enclosed within Win, significant: the KS and AD tests both give a p-value of 0.15. solid blue histogram) versus pair fraction of random mutual pairs (ob- We further compare their respective k-NNS distributions, up to tained from 10 000 Monte Carlo samplings, thick black histogram) and k p 1-NNS fraction of non-mutual pairs (dashed blue histogram). The solid = 8. They too cannot be statistically distinguished ( -value of blue line represent a log-normal fit to the distribution of non-mutual 1 for both KS and AD tests). This confirms the statistical identity pairs in Taurus. The distribution of mutual pairs of Taurus does not re- between the neighborhood of the two populations, multiples and sult from a random process (p-value of 10−16), and is statistically dif- singles, beyond their first neighbor. ferent from non-mutual pairs distribution in Taurus (p-value of 10−14). Since the 2-NNS distribution is not statistically different for Conversely, the 1-NNS distribution of non-mutual pairs in Taurus is rea- single stars and multiple systems, we can use its median value sonably well fitted (p-value of 0.2) by a long-normal function, with a (0.13◦, 0.3 pc or ∼60 kAU) as a typical length scale at which mean value µ = 4.74 ± 0.04 and a standard deviation σ = 0.46 ± 0.03. these two populations cannot be statistically distinguished. This value is close to the upper clustering threshold r = 0.24 pc de- c the other, while the second one has a different nearest neighbor) rived in the second section. whereas 55% of the whole pairings are mutual pairs. Interestingly, we also note that the distribution of the second The 1-NNS distribution for mutual pairs is markedly differ- nearest neighbor of multiple systems cannot be statistically dis- ent from that of non-mutual pairs; the KS test returns a p-value tinguished from the first nearest neighbor of single stars either of 10−14 when assuming, as a null hypothesis, that these two pop- (p-value of 0.1224 for the KS test). This suggests that, although ulations are drawn from a same parent population (see Fig.6). the neighborhood of multiple systems has been found to be more The distribution for non-mutual pairs is reasonably well fitted populated within 10 kAU, this trend fades away beyond 60 kAU. by a log-normal function (p-value = 0.2, showing that two dis- ≥ Based on the k-nearest neighbor analysis (k 2), we therefore tributions are statistically the same) with a mean µ = 4.74 ± 0.04 define a scale of 60 kAU beyond which the stellar environment (i.e. 55 kAU) and a standard deviation σ = 0.46 ± 0.03 (∼20 is statistically identical for single stars and multiple systems. to 160 kAU range). This suggests that, unlike the mutual pairs, the distribution of 1-NNS for non-mutual pairs in Taurus may be seen as a statistical realization of a multiplicative process, 4. From multiples to ultra-wide pairs which is converted to an additive process in the log domain, for which the central limit theorem may be applied. Although In this section, we further analyze the reasons for such a diver- it is beyond the scope of this paper to establish the physical ori- gence between neighborhoods of multiple systems and single gin of this multiplicative process, we can speculate that relative stars. random motion and gravitational encounters between physically unrelated stars may contribute to randomization of the spatial 4.1. Mutual nearest neighbors as ultra-wide pairs location of individual stars. This is not the case for gravitational binaries or common proper motion pairs, however, as they are From the list of all nearest neighbor pairings (see Table C.2), kept together at the same mutual nearest distance over time. we selected the subset of all mutual nearest neighbors, that is, The mutual pairs in Taurus are very unlikely due to random pairs in which the nearest neighbors are reciprocal. This property mutual pairing (see Fig.6). A KS test comparing the distribution serves to probe the most “connected” pairs. It has been used, for of 1-NNS separation of mutual pairs with the Win window to instance, as part of the process to identify physical binary can- that of the mutual first nearest pairs from an ensemble of random didates in simulations (Parker et al. 2009; Kouwenhoven et al. Monte Carlo Poisson samplings within the same window returns 2010). a p-value lower than 10−16. We find that over the 338 first nearest neighbor pairings of Moreover, it is worth noting that the mutual pairs we iden- stars in Taurus, 45% of pairings are non-mutual pairs (within tified in the separation range 1–5 kAU, are already known to this type of couples, only one star is the nearest neighbor of be true physical binaries, that is, gravitationally bound binaries

A14, page 9 of 33 A&A 599, A14 (2017)

Table 3. Class fraction in Taurus. 1

Class I Class II Class III N All Taurus stars 0.11 0.52 0.37 338 Stars in UWPs (δ ≤ 10 kAU) 0.18 0.61 0.22 74 Stars in UWPs (all separations) 0.13 0.56 0.31 186

Notes. N is the total number of stars in each subsample.

Class pairing within UWP (sep < 10 000 AU) Random Class pairing 0.1 (II,II) (II,II)

(I,I)

F: Wide pair F:fraction pair Wide (III,III) (I,I)

(I,II) (I,II)

(III,III) (I,III)

0.01 (I,III) (II,III) (II,III) 103 104 105 106 δP[AU] Fig. 8. Distributions of SED Class pairings expected from a random pairing process based on the global proportions of Class I, II, and III Fig. 7. Ultra-wide pair fraction F within the whole Taurus region (sam- stars in Taurus (left) and observed among Taurus UWPs (right). The ple S 1) as a function of separation, plotted using ∆δP = 0.25 dex bins. β SED Class pairing within UWPs deviates significantly from random The solid blue line is a power law fit to the data (F = α δP, with pairing, suggesting coevality within these systems. log α = −1.21 and β = 0.14) between 3 and ∼60 kAU (vertical black dashed line). The gray area represents the 95% confidence band. In terms of the power law parameters, the corresponding parameter 95% 4.3. Class pairing in UWPs confidence intervals are log α = [−1.78, −0.65], β = [0, 0.28]. We first focus on the 37 mutual pairs with separation less than 10 kAU (from sample S 1), a regime where the distinction be- (Kraus & Hillenbrand 2009b). This further validates our selec- tween multiple systems and single stars strongly suggests that a tion of mutual nearest neighbors to identify physically related physical process is at play. Within this sub-population, Class I pairs in that range. We thus expect that a large majority of these and Class II are over-represented (and, accordingly, Class III mutual pairs to be at least common proper-motion pairs, and under-represented) relative to the overall Taurus population (see plausibly even gravitationally bound. From now on, we refer to Table3). A chi-squared test confirms that this di fference is sta- these systems as ultra-wide pairs (UWPs). tistically significant (p-value of 0.01). In other words, the stellar population within UWPs separated by less than 10 kAU is The present-day distribution of separations for these UWPs less evolved, i.e., younger, than the rest of the population in the should reflect its counterpart at birth, provided that dynamical Taurus molecular cloud. encounters are rare enough to keep it unchanged (see discus- In the following, we show that the class pairing found in sion Sect.5). These mutual pairs covering separations from 1 to these UWPs deviates from random pairing. The probability P ∼60 kAU are the only type of pairs (versus non-mutual pairs) i j of getting an unordered pair (i, j) without replacement is given found in the short-separation end of the 1-NNS distribution. Ap- by: proximately 60% (resp. 90%) of 1-NNS have separations below 20 kAU (resp. 60 kAU) with a relatively long-uniform distribu- · · · · 0 − tion. Thus, the continuous power-law trend at small and inter- Pi j = γ Pi P j = γ (Ni/N) N j/(N 1) , (11) mediate scales observed in the Ψ function is mainly due to the existence of these mutual pairs, which define the binary regime. where N is the the total number of stars in the sample under They generate a scale-free clustering pattern and constitute a ma- consideration, {i, j} = I, II, III is the SED Class of stars, Pi is the fraction of Class i type star, Ni is the number of stars of Class i, jor structural spatial imprint in Taurus. 0 0 and γ = 1 and N j = Ni − 1 for i = j whereas γ = 2 and N j = N j for (i , j). 4.2. An Öpik law for the UWPs separation We compute the random Class pairing probability for each type of pairings from Eq. (11) and the number of stars of each In this subsection we discuss the distribution of UWP separation Class Ni derived from the first line in Table3. These probabilities based on the data that we derived (see Table C.2). are quite different from those observed among UWPs in Taurus The UWPs fraction F in Taurus follows a slightly increasing (see Table4 and Fig.8). The main di fference can be summarized 0.14 power law, F ∝ δP (see Fig.7), at least up to an upper cut- as follows: there are more pairs of the same Class, that is, (I, I), off of ∼60 kAU (i.e., 0.27 pc). The robustness of this simple (II, II) and (III, III) pairs, than expected from random pairing. fit is confirmed by performing a power law fit to the empirical Correspondingly, there are fewer pairs from mixed Classes, (I, II) cumulative function that explains 97.73% of observed variations. and (II, III) pairs, and there are no (I, III) pairs at all despite the Beyond this cut-off, there is a sharp decrease in the two last bins expectation that there should be ∼10% of such pairs based on of separations. The first two bins overlap the study conducted by random pairing. These differences are found to be statistically Kraus & Hillenbrand(2009b), who found that the separation of significant at the 99.74% level based on a chi-squared test. binaries below 4.2 kAU is log-uniform in this range (F(log δ) = Applied to the larger sample of UWPs covering the whole 1 const. or, equivalently FO(δ) ∝ δ ), i.e., following Opik’s law. range of separation (sample P3), we obtain the same result as A14, page 10 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus

Table 4. Class pairings fraction in UWPs compared to random Class pairing. 1

WP type p(I, I) p(II, II) p(III, III) p(II, III) p(I, III) p(I, II) δ < P 10 kAU UWPs .11 .46 .14 .16 .00 .14 0.8 Rand .02 .36 .06 .30 .08 .18

Notes. p(I, I) is either the fraction of Class I stars paired with another

Class I star within UWPs (separation δP less than 10 kAU) or the prob- 0.6 ability to obtain this pairing from a random distribution (Rand). above with an even higher significance level (p = 10−4). These 0.4 results indicate that the UWPs are most likely coeval. F Multiplicity fraction F Multiplicity 0.2 4.4. High multiplicity fraction within UWPs Considering that the stars are part of UWPs, there are almost equal numbers of single stars (50) and multiple systems (44). 0 The resulting multiplicity fraction of 47% is ∼15% higher than 103 104 105 106 that of the sample of Class II and III stars observed at HAR that δ [AU] are not in UWPs, a result that is statistically significant (p-value of 0.007 for a chi-squared test). In other words, multiple sys- Fig. 9. Multiplicity fraction of Class II and III stars observed at HAR tems are more often within UWPs than not. More interestingly, and members of UWPs as a function of their separation. For a given the multiplicity fraction within UWPs depends on the separation value of δ, the black (resp. blue) symbol represents the multiplicity ∼ fraction computed over all separations smaller (resp. greater) than δ. range: it declines from a maximum of 70% at short separations Errorbars are standard errors computed from the standard formula: (at approximately 5 kAU) to the average multiplicity fraction of √ √ SEi = Fi ∗ (1 − Fi)/ni· (N − ni)/(N − 1) where ni is the sample size, 47% at large separation of approximately 6 × 10 kAU, above and N is the total population size of Class II and III stars observed at which the multiplicity fraction remains constant (see Fig.9). HAR within UWPs independently of their separation. The dashed black Thus, with a confidence level higher than 95%, the multiplicity line represents the mean multiplicity fraction for stars within UWPs fraction within UWPs is higher when their separation is shorter. whereas the gray line marks the corresponding mean multiplicity fraction for stars that are not in UWPs. The red dotted lines define the interval within which the multiplicity fraction within UWPs is significantly 4.5. Multiplicity pairing within UWPs (p-value of 0.05 or less based on a chi-squared test) higher than the mean value. In this subsection, we look at the multiplicity nature (single or multiple) of individual components composing the UWPs. There are 47 UWPs in sample S 3 with 12 of them being composed of two multiple systems (MM pairs), 15 of them of two single stars systems having their 1-NNS less than 10 kAU, 20 of them are (SS pairs) and the remaining 20 pairs of one multiple system within multiple/multiple UWP (65%), 7 members (25%) are and one single star (SM pairs). The probabilities associated to within single/multiple UWPs and 3 (10%) are non-mutual pairs. random multiplicity pairings are computed from Eq. (11) and Therefore, the spatial neighborhood difference between multiple give 0.28, 0.22, and 0.50 to get a SS, SM or MM pair, respec- systems versus single stars comes down to a higher fraction of tively. Using a Pearson’s χ2 test, we cannot rule out a random “tighter” MM UWPs with respect to the SS UWPs. multiplicity pairing (p-value 0.59) of the observed UWPs over the whole range of separation. But, the observed probability is not uniform along with the separation. For instance, considering 4.6. UWP multiplicity only UWPs whose separation is less than 10 kAU, more than double the expected MM pairs are observed (48% of the UWPs In this subsection, we study the properties of UWPs, as a func- are of MM pair type, 19% of SS and 33% of SM). The same tion of their multiplicity n∗, defined as the sum of the total num- χ2 test indicates that a random multiplicity pairing can be re- ber of stars within each pair (2 ≤ n∗ ≤ 5). jected with a high significance level (p-value 0.018). Thus the For this analysis, we continue focusing on sample S 3 (half higher multiplicity fraction for tighter UWPs, as shown in the the population of UWPs), which has the most reliable multi- previous subsection, stems primarily from the fact that multiple plicity data, since each of the components has been observed systems tend to be paired with other multiple systems in that at HAR. Within it, we investigate the distribution of the UWPs range of separation (≤10 kAU). as a function of their degree of multiplicity. The number of A comparison of the pair fraction distribution between MM, UWPs seems to be rather uniform up to a multiplicity of four SM, and SS UWPs as a function of their separation reveals (see Table5), and exhibits a sharp decrease for a multiplic- indeed that nearly 90% of MM pairs are concentrated below ity of five. We note that this behavior differs from the geomet- 10 kAU, the SM pairs are distributed essentially log-uniformly ric progression for pre-main sequence closer binaries in Taurus −n∗ −n∗ over the whole range, and SS pairs are preferentially sepa- Nn∗ ∝ b = 2.6 (Duchêne & Kraus 2013). rated far apart (median separation at 35 kAU, see Fig. 10). As Following Correia et al.(2006), we define the multiplicity a consequence, MM systems are the main contributor to the fraction per ultra-wide binary (MFuw) as the number of higher observed “bump” in the 1-NNS distribution of multiple sys- multiplicity systems over the total number of UWP systems tems outlined in the previous section. Of the 30 multiple stellar of the sample with projected component separations typically

A14, page 11 of 33 A&A 599, A14 (2017) 0.6 4.6 0.5 4.4 0.4 4.2 [AU] P δ 4.0 0.3 Log 3.8 0.2 Ultra-wide pair fraction pair Ultra-wide 3.6 0.1 3.4 0

103 104 105 106 2 3 4 5 δP[AU] UWPs multiplicity n*

Fig. 10. SS (dashed blue), SM (dashed red) and MM (solid blue) pair Fig. 11. Mean√ separation δP of UWPs (sample S 3) and standard er- fraction as a function of their separation. MM pairs are tighter (most rorbars (±σ/ n∗) as a function of their multiplicity n∗ = 2, 3, ... The −n∗ are found below 10 kAU) whereas SS pairs are far apart (with a peak separation is consistent with a geometric progression δP ∝ a with at approximately 50 kAU); on the other hand, SM pairs are relatively a ∼ 1.8 (shown as the blue line). uniformly distributed.

Table 5. Number and type of high order multiplicity in UWPs. The values we obtained are far above the values of multiplicity fraction (26.8 ± 8.1%) and companion frequency (0.68 ± 0.13) per wide binary found in young T Tauri wide binaries in the n 2 3 4 5 ∗ range 14–17 AU up to 1.7–2.3 kAU (Correia et al. 2006), high- N P 16 14 13 4 lighting the ubiquity of high-order ultra-wide binaries in Taurus UWP Type (S, S) (S, B) 8 (B, B) 4 (B, T) found in our sample. 5 (S, T) Based on the previous subsection, and since tighter pairs N 13 11 10 4 P60 are mostly composed by MM pairs, we expect them to have a UWP Type (S, S) (S, B) 6 (B, B) 4 (B, T) higher multiplicity. Indeed, the mean projected separation δP of 4 (S, T) UWPs is negatively correlated with the degree of multiplicity N 4 6 7 4 P10 (see Fig. 11). We obtain the best geometric progression ﬁt as: UWP Type (S, S) (S, B) 6 (B, B) 4 (B, T)

1 (S, T) −n∗ −n∗ δP(n∗) ∝ a ∼ 1.8 , (14)

Notes. Number NP (resp. NP60 and NP10 ) of UWPs in the whole range of separation (resp. for separation less than 60 kAU and 10 kAU) as where δP(N∗) is the mean separation of UWPs per bin of degree a function of their multiplicity n∗ and their hierarchical type (S, B, T: of multiplicity n∗. Thus, UWPs composed of two single stars single, binary, triple). are wider on average than UWPs composed of a single star and a binary, which in turn are wider on average than UWPs composed of two multiple systems. In summary, tighter UWPs are biased higher than 1 kAU. Over the whole range of separation we towards higher-order multiplicity. obtain: T + Q + ... MF = = 65.6 ± 11.85%. (12) 4.7. Ultra-wide pairs and mass function uw B + T + Q + ... The mass function of single stars and primaries of multiple sys- We similarly define the companion frequency per ultra-wide bi- tems within UWPs depends on their type (see right Fig. 12). A nary (CF ) as: uw KS test indicates that the mass distribution for SM pairs can- 2 × T + 3 × Q + ... not be distinguished from that of either the SS or the MM pairs. CF = = 1.77 ± 0.19. (13) uw B + T + Q + ... However, a similar KS test shows that the difference in mass distribution between SS and MM pairs is significant with a con- We use the Poisson error to estimate the error made on MFuw fidence level of 97.8%. (resp. CFuw), that is, we use the square root of the number of Specifically, compared to SS pairs, MM pairs exhibit: higher order multiple systems (resp. the total number of companions in higher order systems 2 × T + 3 × Q + ...) divided – a deficit of mass below 0.1 M , with a frequency of only 5% by the total number of systems (B, T, . . . ). We also estimate (against 20%); the multiplicity fraction and companion frequency per ultra- – a deficit of stars with mass in the 0.1–0.6 M range, with a wide binary for UWPs separated by less than 60 kAU (resp. frequency of 25% for the MM pairs (against 50%); 10 kAU): MF60 = 65.79 ± 13.16% and CF60 = 1.79 ± 0.22 – an excess of stars with mass between 0.6 and 0.8 M , with a (resp. MF10 = 80.95 ± 19.63% and CF10 = 2.33 ± 0.33). frequency of 45% (against 25%);

A14, page 12 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus 1 1

Secondary at 0.8 M MM 1 1 SM

SM MM SS SS

Secondary at brown-dwarf/star limit 0.1 SS

SM 0.1 0.1

Secondary at brown-dwarf/planet limit Ultra-wide pair mass ratio Separation of ultra-wide [pc] of ultra-wide Separation Mass of (primary) stars Mass of [Msun] (primary) Sum of primary mass Sum of [Msun] primary 0.01 0.1 MM 0.01

0.1 1 10 0.01 0.01

Ultra-wide pair primary mass [M¡ ] Fig. 12. Boxplot for the distribution of the (primary) star mass within UWP (left), the sum of the masses of the two (primary) stars within Fig. 13. Primary mass versus mass ratio within MM (ﬁlled dark blue each UWP (center), and the separation (right) of UWPs. The SS, SM circle), SS (ﬁlled light red circle), and SM (open light blue circle) and MM types of systems are shown separately to illustrate that MM UWPs. Intermediate (resp. smallest) size of marks: UWPs separated pairs are tighter and more massive than SS pairs. by less than 35 kAU (resp. less than 10 kA), the largest size devoted to wider UWPs beyond 35 kAU. Dashed lines: brown dwarfs (BD)/planet (0.012 M ) and BD/star (0.075 M ) limits. Dotted line: 0.8 M star – a predominance of stars more massive than 0.8 M (20% of limit. The superpositions are due to the discretized nature of mass de- the most massive stars in Taurus are in MM pairs but only termination models from the spectral type and evolutionary tracks. 5% are in SS pairs).

Thus, 70% of stars within SS pairs have a mass of less than and 0.4–0.8 M for MM and SS pairs, respectively). The difference in mass range between SS and MM pairs would be even 0.6 M and ∼65% of stars within MM pairs are more massive more pronounced if the mass of inner companions within MM than 0.6 M . As a result of these trends (see Fig. 12), the median pri- pairs were also included in the sum; unfortunately, the current mary mass of MM pairs is twice as high as the median pri- multiplicity data are insufficient to evaluate this in a consistent manner across the entire sample. In summary, the median of the mary mass in SS pairs (0.7 M compared to 0.3 M ). Further- more, they have a much smaller dispersion as indicated by the stellar mass in MM pairs is twice as high as that within SS pairs, and they are also ten times less divergent; the masses of stars interquartile range for MM pairs (0.5–0.8 M versus 0.1–0.7 M for SS pairs, see left panel in Fig. 12). The median primary within SS pairs spread a larger range unlike the primary masses mass of MM pairs is intriguingly close to the unusual peak at in MM pairs. The SM pairs have intermediate properties between these two classes. 0.8 M in Taurus reported by Briceño et al.(2002). This peak was tentatively explained by a fragmentation/ejection hydrody- namical model (Goodwin et al. 2004) of molecular cores that 4.8. Mass ratio in UWPs have unusual properties (extended envelope, a narrow range of core mass function with a peak near 5 M , and a low level The study of the mass ratio of the secondary mass over the pri- of turbulence). The results of simulations show that 50% of mary mass in the UWPs as a function of the primary mass shows the low-mass objects that form within the cores are ejected several interesting features (see Fig. 13). First the secondary from their cradles to produce an extended population of low- mass covers the whole range of mass, from equal mass down mass stars and brown-dwarfs, whereas the remaining stars in to brown dwarf type mass (0.075 M ) suggesting the same con- multiple systems accrete the gas reach a mass of up to 0.8– tinuous formation scenario from star to brown dwarf. Secondly, 1 M . This type of dynamical ejection model was also ad- there is a clumping trend of MM UWPs towards the upper part of vocated by Reipurth & Clarke(2001), Boss(2001), Bate et al. the diagram. Further, we note that there are no UWPs composed (2003), Kroupa & Bouvier(2003a), Kroupa et al.(2003). How- of two brown dwarfs. ever, Briceño et al.(2002) and Luhman(2006) argued that the Some other features appear to be spurious. The apparent con- absence of a widely dispersed brown-dwarf population is strong centration of secondary brown dwarfs pairing with 0.6–0.8 M enough evidence to reject this type of model. Therefore up to stars showing up in Fig. 13 is in fact due to the preeminence now, there is no clear consensus to explain the peak at 0.8 M in of these 0.6–0.8 M stars in the mass function. By performing the mass function of Taurus. 10 000 Monte Carlo mass pairing samplings amongst the mass Summing the two (primary) masses within each UWP am- sample of UWP stars, we obtain indeed a p-value of 0.15 com- plifies the contrast between the lower mass threshold needed to patible with the hypothesis that this pattern is due to chance pair- produce MM pairs with respect to SS pairs (see the middle panel ing. The next intriguing pattern that appears at first glance is the in Fig. 12). The median sum of primary masses within MM pairs empty top right “wedge”, where no secondary stars heavier than (1.5 M ) is twice as high as that within SS pairs (0.7 M ), but 0.8 M lie in for primary stars heavier than 0.8 M . By per- the width of the interquartile ranges are comparable (1.2–1.7 M forming a similar Monte Carlo sampling, we obtain a p-value of

A14, page 13 of 33 A&A 599, A14 (2017)

rewritten as follows:

2.0 1/2 ∆v < (2G(M1 + M2)/r) " # " #! −1/2 M1 M2 r 1.6 < 0.3 + km s−1. (15) 0.5 M 0.5 M 10 kAU

1.2 This relative velocity between the stars is low compared to the observed already low velocity dispersion in the Taurus stellar 0.8 complex; 2–4 km s−1 in the whole region (Frink et al. 1997; Rivera et al. 2015) and as low as 1–2 km s−1 in stellar subgroups

0.4 (Jones & Herbig 1979). However, as we will see in the following

Mean stellar mass [Msun] stellar Mean subsection, the low stellar density of Taurus and the low stellar

0.0 velocity dispersion prevent efficient exchanges of energy during random encounters between wide pairs and other stars, such that 3 1 2 3 4 5 6 the characteristic disruption time τd of a few ∼10 Myr is much Degree of multiplicity longer than the age of the Taurus pre-main sequence population, that is, 1–10 Myr old (Kenyon & Hartmann 1995; Bertout et al. Fig. 14. Correlation between multiplicity and primary (large size mark) 2007; Andrews et al. 2013). Therefore, we consider in the fol- & secondary (small size mark) mass of stars in MM (filled dark blue lowing that UWPs are physically linked. This hypothesis will be triangle), SS (filled light red triangle), and SM (light blue open triangle) UWPs. further tested by results of the Gaia survey that will provide 3D spatial data and 2D/3D velocity measurements (proper motions of stars and radial velocity for part of them). 0.005, which seems to indicate that we can apparently reject the hypothesis that this occurs by chance. This result, however, is 5.2. A short review on wide binaries: models not based on a large sample size (median expectation: four pairs and observations within that wedge), and the stellar mass determination from the- From the theoretical side, different models and numerical sim- oretical evolutionary tracks, as well as the spectral type classi- ulations have been performed to produce multiple systems (see fication, artificially stretches the width of this empty wedge. At Reipurth et al. 2014, for a complete review on recent numerical this stage, we cannot therefore ensure that it is a reliable pattern. simulation improvements). One notable result from simulations The increase of the multiplicity goes along with the primary of star formation from collapsing gas is that they do not gen- mass of the UWPs (see Fig. 14). This trend was also noted for erate wide pairs at birth beyond 1 kAU because of the strong closer binaries (Kraus & Hillenbrand 2007). The mass of the dynamical interactions that occur in simulations of the collapse secondary star does not correlate with the multiplicity to the of turbulent cores (Bate 2012). same extent. Nonetheless, wide pairs are present among field stars, al- beit in relatively small numbers: approximately 10% of all solar-type field stars have a companion with separations larger 5. Discussion than 1 kAU (Raghavan et al. 2010; Lépine & Bongiorno 2007; In this section, we discuss the possible nature of the UWPs iden- Longhitano & Binggeli 2010) and maximum separations as high tified in Taurus. as 20 kAU (Chanamé & Gould 2004; Shaya & Olling 2011; Dhital et al. 2015). The low-but-not-negligible fraction of visual wide pairs in 5.1. UWPs as physical pairs the field could not solely be the result of random gravitational capture: the binary creation rate in the field is estimated to be of The findings surrounding UWPs obtained in the previous section −21 −3 −1 amount to an array of circumstantial evidence suggesting that the order 4×10 pc Gyr (Kouwenhoven et al. 2010) show- these pairs are probably physical pairs: ing that random creation of bound pairs in the field, as well as in the star-forming regions, is an extremely rare event. – non-random 1-NNS distribution of mutual pairs (versus log- An alternate mechanism must be at play to produce such normal 1-NNS distribution for non-mutual pairs); pairs either at birth or as the result of subsequent dynamical evo- – approximate log-uniform separation distribution (Öpik’s law lution. But wide pairs with separations beyond 0.1 pc appear to distribution) for mutual pairs, extending up to ∼60 kAU (i.e., be particularly unlikely pristine products of star formation pro- 0.27 pc) at least, observed for binaries at closer separations cess because their separations exceed the typical size of a col- (Kraus & Hillenbrand 2009b); lapsing cloud core, precluding a scenario based exclusively on – non-random Class pairings within mutual pairs suggesting core fragmentation. coevality; Consequently, two scenarios based on dynamical evolu- – UWPs in the range of separation <5 kAU are already known tion have been proposed to explain their origin. One pos- to be true physical binaries (Kraus & Hillenbrand 2009b). sibility is that an initially compact triple system could dy- namically unfold, with the tighter pair shrinking while the To be gravitationally bound, the internal energy of UWPs must third component being ejected onto an extremely long orbit 2 be negative, that is, 1/2µ∆v − GM1 M2/r < 0, with µ being the (Reipurth & Mikkola 2012). Alternatively, the gradual dissolu- reduced mass (µ = M1 M2/(M1 + M2), M1 and M2 being the tion of a star cluster could leave behind wide binaries that are mass of the stars), G the gravitational constant, r and ∆v the sep- barely bound if two stars happen to be very close in the 6D aration and the relative velocity between the two stars, respec- phase space (Kouwenhoven et al. 2010; Moeckel & Bate 2010; tively. Thus, the condition to meet for a pair to be bound can be Moeckel & Clarke 2011). For most star clusters, the dissolution

A14, page 14 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus time, when this “pairing” could occur, is of the order of a that is, a few crossing times, or approximately a few 10 kyr few Gyr (Lamers & Gieles 2006). (Reipurth 2000), far less than the Taurus age (few Myr). The model of Kouwenhoven et al.(2010) also predicts that Disruption and dissolution of wide binary stars in the Galaxy these wide pairs are high-order multiples as a reflection of the by gravitational encounters with other stars, molecular clouds, high multiplicity of individual stars at birth. This matches nicely and tidal forces due to gravitational potential of the Galaxy is a with our findings on UWPs in Taurus, however their mechanism long-standing study (Chandrasekhar 1944; Heggie 1975, 1977; also induces random pairing with respect to mass and Class be- Retterer & King 1982; Bahcall et al. 1985; Jiang & Tremaine cause the binding pairs are generated by chance depending on 2010). It was estimated that in the solar neighborhood, the half- the proximity of the objects once the gas of the cluster is re- life of a binary composed of two solar-type stars separated by moved. This is not what is observed within UWPs in Taurus, 31 kAU is 10 Gyr (Jiang & Tremaine 2010). since we have shown in the previous section that the Class- We expect that in a low-stellar-density region such as Taurus pairing is not random and that the distributions of mass is not (i.e., 1–10 pc−2), dynamical interactions between stellar systems the same in SS and MM pairs. are rare and soft. We thus expect minor dynamical destruction of Another inadequacy of both the “pairing during cluster dis- the wide pairs in Taurus, such that most probably wide binaries solution” theory and the “unfolding of triple systems” theory is in Taurus reveal their pristine configuration. The following argu- that they occur on timescales that are orders of magnitude longer ments on characteristic times associated with the destruction of than the age of the Taurus population (0.1–0.5 Myr for Class I binaries due to dynamical encounters will give some support to stars and a few Myr for Class II and III stars). these expectations. The large fraction of UWPs in Taurus is reminiscent of Binney & Tremaine(2008) have estimated the e ffects of dy- the surprisingly large number of UWPs (10–50 kAU) recently namical encounters of binaries with random stars, allowing us identified in slightly older moving groups (10–100 Myr) such to derive two destruction timescales for wide binaries. First, as in the β Pic moving group (Alonso-Floriano et al. 2015). A we consider catastrophic single encounters, characterized by a preference has also been identified for high-order multiplicity timescale among these UWPs, as well as in AB Doradus, TW Hydrae p −1 1/2 1/2 3/2 −1 and Tucanae-Horologium moving groups (Torres et al. 2006; τD = 3/14 π Mtot (G ρc Mc a ) ; Elliott et al. 2016). Elliott & Bayo(2016) suggest that the bi- !1/2 −3 4 !3/2 Mtot 0.05 pc 1 M 10 AU nary population from close (0.1 AU) to very wide systems τD ∼ 7.2 Gyr · (16) (100 kAU) in β Pic Moving Group can be accounted for by 2 M ρc Mc a the internal dynamical interaction of triple systems as proposed by Reipurth & Mikkola(2012). But, as an alternative, these very Secondly, we evaluate the destruction timescale in the diffusive wide pairs may be the survival part of the wide pairs population regime: formed at an earlier time. τ ∼ 0.085 (σ M b2 )(GM2ρ a3)−1; Some of these wide pairs may even survive longer since d rel tot min c c !2 −3 4 solar-type stars within high-order multiplicity UWPs with pe- k σ M 1 M 0.05 pc 10 AU τ ∼ . diff rel tot · d 3 5 Gyr −1 riods that peak around 100 yr (separations about 36.5 kAU) have 0.085 4 km s 2 M Mc ρc a also been observed in the field (Tokovinin 2014) as well as for (17) late-spectral-type M1–M5 dwarf UWPs (Law et al. 2010). In the latter case, a very high value was found for the multiple frac- In both cases, a is the semimajor axis, Mtot is the total mass of +9 tion per ultra-wide pair, that is, 77−22% for systems with separa- the pair, ρc is the stellar volumic density, Mc is the mass of the tions >4 kAU, very close to what we obtain for the high-order- random encounter star, σrel is the stellar dispersion velocity, and 2 multiple fraction derived in Taurus UWPs with separation less kdiff = 0.085(bmin/a) is a diffusive parameter with bmin ∼ a than 10 kAU. being the impact parameter cut off. On the other hand very wide pairs composed of extremely While the semi-major axis a cannot be estimated directly young (∼0.1 Myr) Class 0 objects are relatively common for these long period binaries, it is statistically correlated with (Looney et al. 2000; Tobin et al. 2010, 2016; van Kempen et al. the projected separation δ, as δ ≈ a (Leinert et al. 1993; 2012; Chen et al. 2013; Lee et al. 2015; Pineda et al. 2015). We Tokovinin & Lépine 2012). The closeness of the two values thus conclude that the UWPs in Taurus must have been produced depends on the chosen eccentricity distribution type, either by a mechanism that acts extremely early on and, indeed, that flat ( f (e) = const.), as observed in solar-type stars from the these systems may well be the pristine outcome of star forma- Hipparcos catalog by Raghavan et al.(2010) for wide bina- tion itself, as is suggested moreover by the coevality trend. ries, or thermalized ( f (e) = 2e), as first theoretically pro- We contend that the population of UWPs that we identified posed by Jeans(1919), generalized to broader types of distri- in Taurus supports the idea that very wide binary systems are al- bution by Ambartsumian(1937) and observed in field stars by most universally produced in star-forming regions, even though Duquennoy & Mayor(1991). the physical mechanism leading to their formation remains under We evaluate the volume density through ρc = ρw/∆ ∼ −3 debate. 1/25 ∼ 0.04 pc , with ρw being the mean projected surface density (Eq. (1)) and ∆ ∼ 20 pc the depth of Taurus (Torres et al. 5.3. A pristine origin for these UWPs 2007). Both destruction times are much larger than the age of the To argue for pristine UWPs, one must ensure that they can sur- young Taurus star-forming region. Therefore, in such an envi- vive dynamical interactions. The destruction of multiple stars oc- ronment, it is extremely unlikely that wide binaries, even with curs either due to the intrinsic instability of the non-hierarchical separation as large as 100 kAU, can be destroyed by dynam- multiple stellar system itself or due to the decay of a few Nbody ical encounters. Numerical simulations have indeed confirmed systems driven by hard or soft encounters with other stars of that that loose associations such as Taurus provide an environment region. For the former mechanism, the timescale is very short, that is inefficient at binary disruption even at large separation

A14, page 15 of 33 A&A 599, A14 (2017)

We then question whether those kinds of cores would be instable or stable against any perturbation. As the Jeans instability length d/nC" is given by:

!1/2 π λ = c , (20) s Gρ

−1 where cs = 0.2 km s is the sound speed at T = 10 K, we derive the following Jeans length estimates for the three types of pairs: δ λ = 1.2 SS pc, (21a) SS 0.17 δ=d/2 δ λ = 0.7 SM pc, (21b) SM 0.12

d" δMM Fig. 15. Schematics for a prolate core with a length d in the main di- λ = 0.2 pc, (21c) MM 0.017 rection and a width of d/nc giving birth to two multiple systems whose primaries are separated by δ. where δSS, δSM, δMM are the median separations of the three types of UWPs. (Kroupa & Bouvier 2003b; Marks & Kroupa 2012). Even if they The Jeans length is therefore slightly larger than the charac- use an initial distribution of binary separation up to 10 kAU, we teristic length of the SS fictitious clumps (Eq. (21a)), while it is expect that a same result would be obtained with an extended smaller for the MM and SM ones (Eqs. (21b) and (21c)). In other binary separation up to 100 kAU. words, the latter two appear to be instable against gravitational We may thus feel confident that the very wide pairs popula- (Jeans) instability, while the former appears to be marginally tions in Taurus may trace the initial spatial distribution at birth stable. without being destroyed by dynamical encounters up to now. Therefore, it is plausible that SM and MM pairs formed within the same core, while the SS pairs may have formed through an alternative scenario. We may still consider a pris- 5.4. Core properties for pristine UWPs tine origin for them. The two stars may be born in two distinct In the context of a pristine configuration for the wide pairs, we but proximate cores. Or alternatively, the two stars may be born look for the initial conditions that could lead to the formation of within the same low-density core that becomes supercritical due such pairs in a core fragmentation model (see Fig. 15). to the external potential of the Galaxy (Ballesteros-Paredes et al. We thus make the hypotheses that; (1) these UWPs are pris- 2009b,a) or due to the tidal potential of the parent molecular tine remnants of the star-formation process; and (2) they form cloud (Horton et al. 2001), both scenarios triggering enhanced within a single core with a core-to-star efficiency factor αC ∼ fragmentation. 40% (Könyves et al. 2015). The total mass of parental clump can be evaluated as M (1 + α )/α , where M is the sum of (pri- tot B C tot 5.5. Towards a fragmentation cascade scenario mary) masses and αB Mtot is the mass of inner companion stars (αB = 0 for SS pairs). We also introduce a geometrical shape We note a negative correlation between the multiplicity within factor nc to quantify the propension of clumps to be elongated the UWPs and their separation (see Fig. 11): the multiplic- and prolate rather than roundish or oblate (nc ∼ 2–4, Myers et al. ity decreases with wider separation. The fragmentation of 1991; Ryden 1996; Lomax et al. 2013). From those assumptions, dense molecular cores into UWPs with at least one high-mass we get the mean particle density ρ of an initial core as: (&0.5 M ) component seems to have an impact on the probability that either one component, and most probably both, will fur- −1 2 3 ther fragment. The extent of this fragmentation cascade would ρ = Mtot/(µ mH) 4/3 π nCδ (1 + αB)/αC, (18) depend on the separation of the first two fragments. It suggest where µ = 2.33 is the mean molecular weight and mH is the a competitive scenario between collapse and an efficient frag- atomic hydrogen mass. mentation process of the gas core/clump to create multiple sys- We proceed to compute the median density estimate of tems rather than one single object. The densest and most massive initial cores that would be required to produce each type of molecular cores in Taurus would produce high multiplicity hier- pair ρSS, ρSM, ρMM: archical MM UWPs. Based on the work of Kraus et al.(2011), this fragmentation cascade scenario may be inhibited at lower h i h i3 2 4 −3 Mtot 0.17 pc [nC /4] spatial scales, since they found that there is no relation between ρSS ∼ 10 cm , (19a) 0.72 M δ [αC /0.5] a 1–5 kAU-wide binary and innermost high-order multiplicity distribution. h i h i3 2 The probable primordial nature of UWPs suggests a sce- 5 −3 Mtot 0.12 pc [nC/4] (1+[αB/0.2]) ρSM ∼ 10 cm , (19b) 1.24 M δ [αC/0.5] nario in which the turbulent fragmentation of a molecular filament forms over-densities (Pineda et al. 2015) that undergo a fragmentation cascade, producing wide pairs that are themselves h i h i3 2 7 −3 Mtot 0.017 pc [nC/4] (1+[αB/0.2] ρMM ∼ 3 × 10 cm · (19c) closer multiple systems. These systems may be stable enough to 1.47 M δ [αC/0.5] A14, page 16 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus survive 1–30 Myr in a low-density environment. This link be- fraction of UWPs follows an almost flat Öpik function (r0.14), tween multiple systems and wide pairs has also been outlined by extending what has been found for the young binaries at lower millimeter observations that show that fragmentation of clumps range. This coevality clue and Öpik law behavior coupled with can proceed through separate envelopes or inside a common en- the fact that their 1-NNS distribution differs from random mu- velope (Looney et al. 2000). tual pairs suggests that these may be true physical pairs; indeed, UWPs with separation less than 5 kAU have been found to be wide binaries (Kraus & Hillenbrand 2009b). 5.6. Distributed and clustered modes of formation clues Amongst the UWP population in Taurus, we distinguish in Taurus three different types of UWPs, depending on whether they are Taurus is considered as the archetypical star-forming region composed either of two multiple systems (MM pairs), a sin- that gives rise to isolated prestellar cores, with a typical den- gle star and a multiple system (SM pairs), or two single stars sity of 105 cm−3 and a size of 0.1 pc. The consensus model for (SS pairs). Their properties differ in terms of (primary) mass and star formation therefore predicts that this cloud will produce a separation range. The MM pairs are composed of more mas- distributed star population, in contrast with the clustered star- sive stars (median mass: 0.65 M ) and tighter (median value formation mode that is associated with denser regions such as 3.5 kAU, 75% of them having separation below 9 kAU). The 7 −3 ρ Ophiuchus, with typical core densities of 10 cm and sizes median mass of stars within SS pairs is 0.25 M and their me- of 0.02–0.03 pc (Ward-Thompson et al. 2007). In this context, it dian separation is 35 kAU (75% of them have a separation above is worth noting the significant (more than two orders of magni- 12 kAU). SM pairs have intermediate properties (median mass of tude) difference between the typical densities derived for the hy- primaries of 0.5 M and a uniform separation distribution cover- pothesized cores that give birth to the SM pairs and MM pairs. ing the whole range 1−60 kAU). Multiplicity in these UWPs is These results suggest that, despite its overall low core densities, a decreasing function of stellar primary mass. We also show that the Taurus molecular cloud may harbor the two modes of star the multiplicity within UWPs increases as the separation of (pri- formation, isolated and clustered. mary) stars decreases, showing an increased high-order-multiple fraction for the tightest UWP targets in Taurus. Class These differences suggest a different scenario for the forma- 6. Conclusion tion of UWPs in Taurus. The “massive” MM pairs most probably In the Taurus star-forming complex, we have identified an ex- reflect the imprints of the star-formation process within the same tended binary regime up to ∼60 kAU using the one point cor- molecular core. Based on estimates of their hypothesized natal relation function, Ψ, which further allowed us to distinguish core properties, Taurus may generate both isolated and clustered three spatial regimes. The clustering regime has an upper clus- star formation. The “low-mass” SS pairs could point to a differ- tering threshold of 0.1◦ (0.24 pc, i.e., 50 kAU, at the distance ent formation scenario or may result from a dynamical process, of Taurus). The Ψ function appears to be scale-free (ψ = r−1.53) such as low-mass star ejection from multiple systems. over three decades and extends the usual binary regime, as de- Obtaining parallaxes and proper motions for all Taurus mem- fined by the two-point correlation function, to a very wide pair bers would help tremendously in identifying which of the UWPs regime. We note that the value of the upper clustering length co- are physical binaries, common proper motion pairs and those incides with the local maximum of Taurus NH2+ molecular cores which may form from a dynamical process. This will ultimately correlation function reported by Hacar et al.(2013). As the lat- be achieved thanks to the Gaia survey that will determine the ter indicates a typical separation between the cores, we expect astrometric quantities (angular position, proper motion, and par- to see a clustering imprint of stars starting at this value, as is allax) of stars with an accuracy of 20 µ and at a brightness of observed. This length is more than twice the universal typical 15 mag, and determine the radial velocity of stars brighter than width (0.1 pc) of filamentary structures highlighted by Herschel 16 mag. in Taurus and more generally in Gould Belt star-forming re- Unfortunately, the first Gaia release (Gaia Collaboration gions (André et al. 2014). The clustering regime is followed by 2016) does not provide enough data on the whole sample of stars a regime of stellar inhibition between 0.1◦ and 0.5◦ (0.24 pc up in Taurus (only ∼5%). We expect that future releases of Gaia, to 1.2 pc), and ends beyond this with a third regime associated perhaps as early as the second release, will allow us to firmly to highly isolated stars. establish the physical status of the UWPs, in turn providing a We have highlighted a major structural pattern in the spa- means to discriminate between different scenarios for their for- tial distribution of stars in Taurus based on their multiplicity sta- mation, and more generally will provide invaluable information tus. Distinguishing single stars from multiple systems, defined on the structure and dynamics of Taurus as a young association as having at least one physical companion within 1 kAU, we (Moraux 2016). highlight a major and unexpected difference in their spatial dis- In summary, we identified a new category of ultra-wide pairs tribution based on 1-NNS study: the stellar neighborhood in the (UWPs) in Taurus outlining a high order of multiplicity for range of 1−10 kAU of multiple stars is more “crowded” than the tighter ones (separation less than 10 kAU). We suggest that part single star neighborhood: 40% of multiple systems have a com- of these UWPs may be pristine imprints of their spatial configu- panion within that range compared to 15% for single stars. The ration at birth and put forward a cascade fragmentation scenario probability that a multiple system has a wide companion is three- for their formation. Furthermore, UWPs may constitute a poten- fold that of a single star. We have shown that this excess within tial link between the wide pairs recently identified in very young 10 kAU is due to the very wide pairs candidates that are more- Class 0 type objects (∼<0.5 Myr) and the somewhat older but still over generally composed themselves of two multiple systems. young moving groups (∼20–30 Myr). We have identified a potential very wide pairs population in Taurus. Our work shows that 55% of our stellar catalog in Taurus Acknowledgements. The authors would like to thank Lee Mundy for helpful dis- − cussions and Marc Pound for reading the first draft of this article. We also want to are UWPs in the range of 1 60 kAU. These UWPs are composed sincerely thank the anonymous referee who helped us to improve both the scien- preferentially of stars of the same Class, departing from random tific and language aspects of this paper. This work was funded by the French na- Class pairing, and, thus, pointing towards coeval pairs. The pair tional research agency through ANR 2010 JCJC 0501-1 DESC (PI E. Moraux).

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Appendix A: Spherical geometry B.2. Moments of first nearest neighbor distribution As a reminder, this section gives the formulae to obtain the angu- B.2.1. Mean lar distance ∆σ between two stars on the celestial sphere, given by the spherical law of cosines: The theoretical meanr ¯t of the first nearest neighbor distance in an infinite medium is computed from the PDF as: ∆σ = arccos sin α1 sin α2 + cos α1 cos α2 cos ∆δ , (A.1) Z +∞ where φi, λi (i = 1, 2) are, respectively, the declination and right r¯t = E(r) = r w(r)dr 0 ascension of the star i, and ∆δ = |δ2 − δ1| their absolute differ- √ "erf( πρr) #+∞ ence in declination. Since this above equation is ill-conditioned = √ − r exp(−πρr2) , (B.6) σ for small ∆ , it is better to use the following Vincenty formula 2 ρ 0 (Vincenty 1975) applied to a sphere where =E(r) is the expected value of r, and erf(x) is the error ∆σ = function. Taking the value at 0 and infinity, we end up with a q   2 2  simple analytical result of first nearest neighbor distance theo-  (cos α2 sin ∆δ) +(cos α1sin α2−sin φ1cos α2 cos ∆δ)    retical meanr ¯t in a random process of intensity ρ in an infinite arctan   ·  sin α1 sin α2 +cos α1 cos α2 cos ∆δ  medium, i.e.,r ¯t is strictly equal to half of the inverse square root of the density: (A.2) 1 r¯t ' √ · (B.7) Appendix B: Analytics for k-Nearest Neighborhood 2 ρ statistics B.1. Theoretical probability density function (PDF) B.2.2. Variance and cumulative distribution of 1-nearest neighbor 2 From the PDF w(r), we now compute the theoretical variance σt separation (1-NNS) for spatial random distribution (σt being the standard deviation) of the first nearest neighbor In this section, we derive the theoretical distribution of 1-NNS distance for a random Poisson process, for a random point process in an infinite medium, following Z +∞ the work done in 3D by Chandrasekhar(1943). The probabil- 2 2 σt = (r − r¯) w(r) dr ity w(r)dr that the first neighbor of a star is located at a distance 0 ∞ !2 between r and r + dr in 2D, is given by the product of the proba- Z + 1 bility that there is no stars in a disk of radius r multiplied by the = 2 π ρ r r − √ exp(−πρr2) dr. (B.8) probability of having stars in a shell area between r and r + dr: 0 2 ρ Z r ! The integration gives: w(r)dr = 1 − w(r)dr × 2πr dr ρ, (B.1) 0 " −1 √ σ2 = exp(−πρr2) 2π exp(πρ r2) erf( πρ r) where ρ is the mean intensity of the process in an infinite t 4πρ medium, that is, the average number of stars per unit of surface. √ #+∞ Equation (B.1) may be written as: + π(1 − 2 a r)2 + 4 . (B.9) ! 0 d w(r) w(r) = −2πrρ · (B.2) dr 2πrρ 2πrρ We then compute series expansions of the integral at x = 0:

Once integrated, from the equation above, we get the probabil- 2 2 4 + π πr 2 √ 3 ity density function (PDF) of the first neighbor distance for a lim σt = − + − π ρr random Poissonnian process: r→0 4πρ 4 3 1 4 5 2 − (π − 4)πρr + O(r ), (B.10) w(r) = 2πρr exp(−πρr ). (B.3) 8 R +∞ w r r The PDF integral is unity (i.e., we have 0 ( )d = and then at x = +∞: h i+∞ − exp(−πρr2) = 1). 0 2 2 2 √ Furthermore, from the 1-NNS PDF (Eq. (B.3)), we get the lim σ = −1/(2ρ) exp(−πr ) 2ρr − 2 ρ → ∞ t related cumulative distribution function W(r) as: r + √ −1 Z r + (1/2 + 2/π) − ( ρ πr) W(r) = 2πρr exp(−πρr2)dr ! 2/3 2 −1 −4 0 + (2ρ π r3) + O(r ) + 1 , (B.11) = 1 − exp(−πρr2), (B.4) to finally get: that allows us to define the characteristic value rq associated to 2 the quantile q from: q = W(rq) = 1 − exp(−πρrq), to get: 2 −1 −1 σt = −(2ρ) + (4 + π)(4πρ) p −1 rq = ln(1/(1 − q))/(πρ). (B.5) = (4 − π)(4πρ) . (B.12)

A14, page 20 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus

B.2.3. Skewness In a Poisson point process in a d-dimensional space with intensity ρ, the distance r between a point and its kth neighbor is dis- The skewness of a distribution quantifies its asymmetry, and is tributed according to the generalized Gamma distribution: defined from the third moment of the distribution. When it is positive, the peak of the distribution is shifted to the left, that is, k P ≈ d [ρVd(r)] · − there is a tail towards the right. When it is negative, it is the other k(r) r Γ(k) exp ( ρVd(r)) . (B.19) way round. The skewness may be defined from the moments of the distribution: where Vd(r) is the volume ball or radius r in d-space. 3 2 3 3 γt = E(r ) − 3r ¯tE(r ) + 2r ¯t /(σt) d Vd(r) = cdr 3/2 3 3 , (B.20) = 3/(4πρ ) − 3r ¯t/(πρ) + 2r ¯t /(σt) √ and c is the unit volume ball in d-space given by: = 2 π(π − 3)/(4 − π)3/2 d d/2 ≈ 0.63. (B.13) cd = π /Γ(d/2 + 1), (B.21) We note that the skewness of the first nearest neighbor distribu- and Γ is the Gamma function. So, in a planar (2D) distribution, tion of a random spatial distribution is constant, that is, indepen- we get: dent of the density/intensity of the random process. k 2(πρ) 2k−1 2 Pk(r) = · r · exp −ρπr . (B.22) B.3. Log PDF Γ(k) Based on transformation rules, we then derive the theoretical The cumulative distribution is then: PDF for the Log(1-NNS) in a random process. Let y = Log(r), Z r where r is the 1-NNS variable, and thus we have: Wk(r) = Pk(r)dr. (B.23) 0 w(r)dr = w(y)dy, (B.14) So for the second nearest neighbor cumulative distribution we get: where w(r) is the PDF of the 1-NNS variable (Eq. (B.3)) and w(y) is the PDF of the logarithm variable. We get the following Z r 2 2 moments for the random k1-NNS theoretical distributions: W2(r) = P2(r)dr = 1 − (πρr + 1) exp(−πr ), (B.24) 0 ∂r dr w(y) = w(r) = w(r) · (B.15) and for the third nearest neighbor cumulative distribution, we

∂y dy have:

From this relation, we get the PDF of the ﬁrst neighbor distance Z r h 2 2 2 i logarithm for a random process as: W3(r)= P3(r)dr =1/2 exp(−πr ) −πρr (πρr +2) − 2 +2 . 0 w(y) = 2 ln(10) π ρ r2 exp −πρr2 , (B.16) (B.25) √ where it reaches its maximun value (mode) at rmod = πρ . From Taylor expansion for x 1, we get: Appendix C: Catalogs w(y) ∼ 2 ln(10) π ρ r2 + O(x4), (B.17) This section gathers the catalogs described respectively in Sects.2 and 4.1 of the paper. as we expect in 2D for a random distribution, the ﬁrst nearest neighbor 1-NNS distribution√ function increases as a squared power law for r 1/ πρ. From Eq. (B.16) above, we derive its logarithmic expression: log w(y) = log(2 ln(10) π ρ ) + 2 r − (πρ/ ln 10 )r2. (B.18)

A14, page 21 of 33 A&A 599, A14 (2017) N) to mention wether the / 15, CIDA13. Columns 1–3: star reference + N N YYY L93 N L93 P99, C08 N YN N C08 YN K12, T14 YYY L93, K11 Y L93, G93, K11 L93, G93, K11 W16 YN Y L93, K11 L93, K11 N YYN K06 N K12, T14 N YY K07 K12, T14 ] HAR HAR Ref. 1.,0.491 Y L93, G93 00 − 1.,0.049,0.244 Y L93, G93, D03, D15 1., Sep [ − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ∗ n ] Class

M stellar system. / 354), HBC356, V410TauAnon20, LH0422 + 2000 SpT M [ J 2000 Dec_ J 62.033 28.12 M3.7563.550 0.303 III 28.20 M6.25 2 0.052 0.086 II 1 Y K11, K12 63.85063.91363.992 29.1864.050 28.32 M764.079 M3.75 27.77 27.94 M5.5 0.303 0.057 27.87 M4.75 II III M6.25 0.137 0.201 II 0.086 1 II 1 III 1 1 1 C 60.955 26.18 M3.5 0.335 III 4 0.15,1.58,3.15 Y L93, D99 + 2610 61.179 26.32 K3 1.796 I 1 2803A2803B2910 63.472 63.4782800G 63.489 28.19 63.551 28.19 M4c M2c 29.31 M0 28.14 0.271 0.575 M2c I I 0.701 0.575 II 1 I 1 1 1 2902 63.928 29.17 M1.25 0.618 II 1 B 63.554 28.20 K3 1.796 II 3 + + + + + + B + + B 63.700 27.88 M1 0.633 III 2 B 63.705 28.21 M3.5 0.335 II 2 0.166 Y L93, G93 + + IRAS 04111 − − − − − − − ) within 1000 AU (spectroscopic binaries not counted as membership), Separation of companions stars with the primary, Flag (Y ∗ n 26105202620382 HBC358A XEST06-006 60.958 26.34 M5.25 0.157 III 1 26105312158186 HBC3592158215 HBC3602618563 HBC3612151106 IRAS 04016 2807280 HBC36228162472811233 Anon1 60.9622811328 IRAS 61.164 04108 2918193 IRAS 61.166 04108 2811535 IRAS 04108 26.18 61.379 21.972812124 M2 21.972812492 M3.5 V773TauA 2827580 M3 FMTau 21.852810578 63.363 FNTau 0.575 0.3352806096 M2 CWTau III2805597 III CIDA1 0.3982805147 MHO2 28.27 III2646264 MHO3 0.575 1 1 M02803055 FPTau III2648110 XEST20-066 1 63.5572752346 CXTau 63.561 0.701 LkCa3A 1 63.571 III 63.573 28.21 63.610 28.47 M0 63.697 63.627 28.18 2 M5 63.697 28.10 K3 0.0149 28.10 M5.5 63.699 0.701 28.05 28.09 M2.5 0.178 II M5.25 26.77 K7 1.796 0.137 II M4 Y II 26.80 0.486 II 0.157 1 M2.5 II III 0.801 1 L93, K11 0.271 1 II 1 0.486 II 3 1 II 0.050,4.00 2 1 0.031 1 Y C08, W16 Y W16 2819108 LkCa1 63.309 28.32 M4 0.271 III 1 28123052805598 FOTauA XEST20-071 63.718 28.10 M3.25 0.366 III 1 28084622800096 CIDA22910434 KPNO12818586 29095972746175 IRAS 04125 2756385 2752155 63.771 63.811 28.15 28.00 M5.5 M8.5 0.137 0.022 III III 2 1 0.053 Y W16 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − #1 2MASS2 J04034930 J04034997 Name RA_ 34 J04035084 5 J04043936 6 J04043984 7 J04044307 8 J04053087 J04080782 9 J04131414 1011 J04132722 12 J04135328 13 J04135471 14 J04135737 15 J04141188 1617 J04141291 18 J04141358 19 J04141458 20 J04141700 21 J04141760 22 J04142639 23 J04143054 24 J04144730 25 J04144739 26 J04144786 J04144797 2728 J04144928 J04145234 2930 J04150515 31 J04151471 32 J04152409 33 J04153916 34 J04154278 35 J04155799 36 J04161210 J04161885 star has been observed at High Angular Resolution and reference papers associated to each star / B96: Burrows et al. ( 1996 ); C04: Chakraborty & Ge ( 2004 ); C08: Connelley et al. ( 2008 ); C09: Connelley et al. ( 2009 ); C06: Correia et al. ( 2006 ); D15: Daemgen et al. ( 2015 ); Taurus stars catalog. This catalog was built from Luhman et( 2010 ) al. and Kirk & Myers ( 2011 ). All the multiple systems with a separation less than 1 kAU is set to be one entry (see 2 ). Sect. The following Table C.1. Notes. sources are listed in Luhman et al. ( 2010 ) but not included here: HBC351, HBC352, HBC353, HBC355( number (this work), 2MASSColumns Point 9–15: Source total Catalog number and of common stars Name. ( Column 4–5: ecliptic right ascension and Declination (Epoch J2000). Columns 6–8: spectral type, (Primary) mass, Class. stellar system D99: Duchêne ( 1999 ); D03: ( 1997 ); I05: Duchêne etItoh al. ( 2003 ); et( 2011 ); al. ( 2005 ); D07: K12: I08: KrausDuchêneIrelandS98: & et &( 2012 ); Hillenbrand al. ( 2007 );Sartoretti Kraus ( 2008 ); et L93: D16: K98: al. ( 1998 );W16:LeinertKohler S95: Duchêne White et &Simon et al. ( 1993 ); Leinert ( 1998 ); et et al. L97: K07: al. ( 1995 ); (in al. prep.). Konopacky S99: Leinert et etSimon (in al. ( 2007 );( 1997 ); al. et K00: al. ( 1999 ); prep.); M08: ( 2000 ); S05: Koresko Monnier F14: K06: Smith et et al. ( 2008 );DiKraus al. ( 2005 ); Folco et P99: et T10: al. ( 2006 ); al. ( 2014 );PadgettTodorov K11: et et G93: al. ( 1999 ); al. ( 2010 );Kraus et T14: R93: Ghez al. etTodorovReipurth et( 1993 ); al. & al. ( 2014 );( 1993 ); Zinnecker G97: W01: WhiteGhez & et Ghez ( 2001 ); al. References.

A14, page 22 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus YYN W16 Y K07 YY C08 N C08 Y K07, K12 Y W16 K12 YYN K12 Y L93, K11 Y K12 Y L93, G93,Y K11 K12 N K11, W16 YYN K06, W16 N S98 N N N N YY K06 N N L93, K11 YY K06 Y W16 YN L93, G93, K11 L93, G93,N K11 N N YYY T14 N D16 N K12 N ] HAR HAR Ref. 00 1.,0.0284 Y L93, G93, K11 Sep [ − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ∗ n ] Class

M 2000 SpT M [ J 2000 Dec_ J 64.114 20.89 M5 0.178 III 1 65.067 28.36 M6.5 0.076 II 1 64.12764.163 30.62 28.98 M4.5 M5.5 0.225 0.137 III II 1 1 65.08965.10665.109 28.23 27.01 M1 M5.2565.283 28.0765.289 M3.5 0.157 0.633 II II 27.0465.394 0.335 27.84 M5.25 II M5.25 1 1 65.443 0.157 27.03 0.157 II M5.5 1 II 26.99 1 0.137 M5.75 1 II 0.116 II 1 1 C 64.630 28.45 K7 0.801 III 3 0.123,0.287 Y L93, G93, G97 + 2805 64.742 28.21 M5.2527082706 0.157 I2702 64.923 64.927 1 64.994 27.272812 27.23 M0c M3c 27.17 65.108 0.701 M0c 0.398 I2654B I 28.322654A 0.701 M3c I 1 65.293 65.298 1 1927 0.398 2 27.03 II 0.18 27.02 65.430 K7 M3 1 19.57 0.801 Y 0.398 M0 I I C08 0.701 1 1 II 1 2823 64.633 28.52 M2.5 0.486 I 1 B + + + + + + + + + + B 64.630 28.27 M3.5 0.335 II 2 0.56 Y L93, G93 1 64.715 28.34 M0 0.701 II 2 0.25 Y P99, W16 B 64.803 28.49 M3 0.398 II 2 0.79 Y L93 B 64.632 28.28 M3 0.398 II 2 0.33 Y L93 B 64.922 27.83 M0 0.701 III 2 1.05 Y L93 / + + + + − − − − IRAS 04166 − − − − − − − 2053091 2906269 BPTau2716070 IRAS 04166 2821325 64.816 29.11 K7 0.801 II 1 28073583037053 LkCa42858491 28204682833005 CYTau2813318 LkCa52829362 KPNO102826036 V410X-ray12519574 V410X-ray32828419 64.117 V409Tau1658470 V410Anon132826191 HBC372 64.3912743208 V410Anon25 28.132827162 64.457 64.412 64.456 KPNO11 K7 64.533 V410TauA 28.35 64.571 64.545 28.49 28.55 28.23 M1.52830302 0.801 28.43 64.621 M4 M22824245 M5 V410X-ray2 64.589 III M62819155 28.48 V410X-ray4 0.604 25.332827250 64.626 V892Tau M5.75 II M1.52818498 0.271 28.44 0.575 LR1 0.178 1 16.982820073 0.096 V410X-ray7 II M1 III II 0.1162814332 K5 Hubble4 III 0.604 27.72 1 2820264 II 64.644 KPNO2 II1723165 M5.5 64.668 2 CoKuTau 1 1 0.6332812234 2 HBC376 1.121 0.0482819420 1 III 64.669 IRAS 04158 28.51 0.049 0.137 III2802487 1 64.677 V410X-ray6 28.41 M02822332 III KPNO12 M4 1 64.6722829330 Y V410X-ray5a 64.696 28.32 1 Y FQTauA 28.31 64.713 1 B92826142 0.701 L93, M0.75 S98,2827218 0.271 K11 V819Tau 64.715 28.46 II K06, K12, 28.342749484 64.755 W16 FRTau III K4.5 0.650 28.24 K7 LkCa7A 3.250 64.758 64.755 II M7.5 1 II 17.392712552 1 28.33 1.3782709570 K7 [GKH94]41 0.801 M5.5 II 28.38 0.044 IRAS 2 04169 28.05 32813491 III 64.859 M5.5 III 0.0322700355 M9 0.060,4.10 0.137 0.801 1 2819237 64.898 2 II III Y2804089 0.137 1 IRAS 04173 28.442717317 64.944 Y 0.013 III K71746415 XEST16-045 28.46 L97, II 1 S05, 1 M08 2702204 J2-157 M5.25 W16 2750368 1 27.222701372 0.801 1 2701094 M7.5 0.157 IRAS 04181 II2701388 IRAS II 04181 65.1632814224 0.0441934133 XEST21-026 1 2659296 I IRAS 1 04187 65.220 27.29 M4.5 1 17.78 65.417 0.225 M5.5 III 28.24 0.137 1 M5.75 III 0.116 1 III 1 28162902816585 DDTauA 2831153 CZTauA IRAS 04154 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − # 2MASS Name RA_ 69 J04191583 73 J04194148 77 J04201611 6162 J04185115 63 J04185147 64 J04185170 65 J04185813 66 J04190110 67 J04190126 68 J04190197 J04191281 7071 J04192625 72 J04193545 J04194127 74 7576 J04194657 J04195844 7879 J04202144 80 J04202555 81 J04202583 82 J04202606 83 J04203918 84 J04205273 85 J04210795 86 J04210934 87 J04211038 88 J04211146 89 J04213459 90 J04214013 91 J04214323 J04214631 37 J04162725 3839 J04162810 40 J04163048 41 J04163911 42 J04173372 J04173893 4445 J04174965 J04180796 4748 J04181710 49 J04182147 50 J04182909 51 J04183030 J04183110 5556 J04183444 57 J04184023 J04184061 59 J04184250 43 J04174955 46 J04181078 58 J04184133 60 J04184703 5253 J04183112 54 J04183158 J04183203 continued. Table C.1.

A14, page 23 of 33 A&A 599, A14 (2017) YYN K12, T14 L93, G93, K11 Y L93, G93,Y S95, K11 P99, C08 N YYN K12, T14 N K07 YN N K12 YYY L93, K11 N T14 N K12 YY L93, K11 Y K06 T14 YY W16 Y P99 YY L93, G93,Y S95, C08, C09, K12, K11 T14 K06 N T14 YN K12, T14 N N N Y K06 ] HAR HAR Ref. 2.23 Y S95, W01, K14 / 00 1 Y L93, G93, K11 Sep [ − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ∗ n ] Class

M 2000 SpT M [ J 2000 Dec_ J 65.477 26.88 M8.5 0.022 III 1 65.55565.56865.570 19.58 M8 25.8265.775 26.92 M7.75 M1.565.826 0.031 0.038 III 28.02 III 0.604 M666.087 26.69 II66.110 1 M3.5 1 0.051 0.096 26.51 1 II 0.335 26.83 M6.5 II M5.7566.627 0.076 1 Y 0.116 II 1 II T14 24.73 M8.75 1 1 0.01866.781 II66.939 1 22.25 M6.7567.178 23.9667.253 M8.25 0.067 III 27.23 0.026 27.92 M5.25 III M8.25 1 0.15767.384 0.026 1 II II 2 24.52 1 0.627 M3c 0.398 I Y 1 K07, K12 1522 65.487 15.50 M5c 0.178 0 1 C 67.374 26.28 M5.5 0.137 III 3 0.160 1523A 65.502 15.51 M3c 0.398 I 2 5.97 Y C08 26382759 65.699 65.782 26.762603 M1 28.10 M5c 66.186 0.633 II 0.178 II 26.17 1 2436 M0.5 1 0.667 66.735 II 24.73 1 2612 M2c 0.575 66.9892642 I2654 26.32 67.271 2 M4.52433 0.3 67.340 0.225 26.82 I K5.5 67.375 27.02 M5.25 1.013 Y 3 24.67 II 0.157 0.160,4.55 M1 II D07, C08 1 Y 0.633 2 I 1.29 P99, C08 1 Y K07 + + + + + + + + + + + B 66.727 26.11 M2.5 0.486 II 2 0.743 Y L93, S95 B B 67.423 26.55 M1 0.633 II 2 2.34 Y L93, S95, I05, K11, K14 B 67.349 24.55 K5 1.121 I 2 1.29 Y D07 + BB 66.723 26.12 K5 66.762 1.121 25.71 II M2 2 0.575 0.69 II 2 0.088 Y L93, G93, S95, D15 Y L93, G93, S95 B 65.509 26.96 M0 0.701 II 2 0.264 Y L93, S95, C08, C09 B 67.427 26.55 M0 0.701 III 2 0.12 Y L93, G93, S95, K11 + + + + + S 65.498 19.54 K0 2.430 II 3 0.053,0.71 Y L93, G93, K00 + + cA + / IRAM 04191 − − − − − − − − − − − − − − 2755060 DETau2826355 RYTau 65.482 65.489 27.92 M1 28.44 K1 0.633 II 2.265 II 1 1 2652315 28180661932063 HD 283572 TTauN 65.495 28.30 G5 2.616 III 1 1530212 IRAS 04191 2657304 FSTauA 2657324 Haro6-5B2825389 LkCa21 65.503 65.513 26.96 K5 28.43 M3 1.121 I 0.398 III 1 2 0.0444 Y L93, K11 1934392 26570602549118 XEST11-0782654570 26462582645530 XEST11-0872801194 IRAS 04196 2805573 65.5652641156 IRAS 04200 2503026 FUTauA 65.6002630511 26.952649503 M126101412701447 26.77 IRAS 04216 2711565 J1-4423 M4.75 0.6332617504 IPTau I J1-4872A 65.897 0.2012443558 2606543 III FVTauA 1 25.05 1 M7.25 66.18826053042542223 66.324 DGTauB 66.238 0.051 DFTauA II2215037 27.032612052 M5 26.30 27.202357243 KPNO4 2 K72619183 M0 5.7 IRAS 04248 0.1782714039 66.7612755033 III 0.801 0.7012649073 III II2633406 IRAS 04260 26.09 1 J1-507 66.867 K2c N 4 1 0.051,0.174,3.3224395502430597 Y 26.20 2.134 IRAS 04264 2435556 M9.5 I2632582 XEST13-010 D99, C06, W16 DHTauA 67.336 0.013 1 III 26.56 67.400 1 M4 24.60 0.271 M3 III 0.398 2 III 0.0794 1 Y K11, W16 2456141 FTTau2624137 KPNO3 65.91326065102443353 FVTau 2606284 IRAS 04239 24.94 KPNO13 M1c2606163 66.622 DGTau 0.633 II 26.40 66.739 M6 1 26.11 0.096 66.7702701259 M5 II2433002 IRAS 04263 GVTauA 26.10 1 0.178 K6 II2632493 0.906 1 DITauA II 1 2616532 FWTauA 2630468 KPNO5 67.440 26.51 M7.5 0.044 III 1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − # 2MASS Name RA_ 9394 J04215563 95 J04215740 92 J04215450 9697 J04215884 J04215943 98 J04220043 99 J04220069 100 J04220217 101 J04220313 102 J04221332 103104 J04221568 105 J04221644 106 J04221675 107 J04222404 108 J04224786 109 J04230607 110 J04230776 111 J04231822 J04233539 113114 J04242090 115 J04242646 116 J04244457 117 J04244506 118 J04245708 J04251767 120121 J04263055 J04265352 125126 J04270266 J04270280 128129 J04270739 130 J04272799 131 J04274538 J04275730 133134 J04284263 135 J04290068 136 J04290498 J04292071 140141 J04293008 142 J04293209 143 J04293606 J04294155 112 J04233919 119 J04262939 122123 J04265440 124 J04265629 J04265732 127 J04270469 132 -137138 J04292165 J04292373 L1521F-IRS144 J04294247 67.162 26.86 M7c 0.057 I 1 139 J04292971 145 J04294568 continued. Table C.1.

A14, page 24 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus YN Y L93, G93, S95, K11 Y K07, K12 K06 Y K12, T14 N Y W16 Y K06 Y K11, W16 Y W16 Y K12, T14 Y K98, K06, W16 Y K12, T14 Y D07, C08 Y W16 Y B96 N N Y L93, S95, K11 N Y K12, T14 Y K11 Y L93, G93, C08, K11 Y K06, W16 Y W16 Y W16 Y K12, T14 N Y W16 Y L93, S95, K11 Y L93, G93, S95, K11 Y D07, C08 Y S98, K11 N N Y K06 N ] HAR HAR Ref. 00 1 Y L93, S99, K11 1.,0.34,3.78 Y L93, G93, S95, K11, D15 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − Sep [ − − − − ∗ n ] Class

M 2000 SpT M [ J 2000 Dec_ J 67.47667.498 17.9067.599 24.55 M4 M5 23.99 0.271 M8.25 0.178 III II 0.026 1 III 1 1 67.829 23.58 M7.75 0.038 III 1 67.861 27.06 M7.5 0.044 III 1 68.014 25.47 M6.25 0.086 III 1 68.074 24.37 M5.75 0.116 III 1 68.097 24.05 M7.75 0.038 III 1 68.101 22.85 M4.5 0.225 II 1 68.209 24.37 M7.5 0.044 III 1 68.289 22.78 M6 0.096 II 1 B 67.710 23.00 G8 2.562 I 1 + 2251 68.134 22.96 K7 0.801 I 1 2253A B 67.849 24.18 M4.75 0.201 III 2 0.3 Y K12, T14 B 68.066 18.03 K7 0.801 III 1 B 68.079 24.37 M0.5 0.667 III 2 0.22 Y L93, G93, S95, K07, K12 B 68.278 24.17 K5 1.121 II 3 0.023,0.41 Y L93, G93, S95, D15 + + Ab 68.126 17.53 K7 0.801 II 3 0.288,0.0317 Y L93, G93, S99, F14 Bb 68.126 17.53 M5.5 0.137 II 2 1.4 Y L93 + + + + C 67.517 18.23 K5 1.121 II 4 0.138,2.7,5.9 Y L93, D99, K11 B 67.961 24.41 M0.5 0.667 II 2 2.4 Y L93, S95, K11 B 68.276 24.16 M2 0.575 II 2 0.314 Y L93, G93, D15 B 67.917 18.23 M2 0.575 II 2 0.311 Y L93, G93 B 67.623 24.45 M1 0.633 II 2 0.9 Y L93, G93, S95 + + 17 68.213 17.50 M8.25 0.026 III 1 + + + + + + IRS5 67.892 18.13 K0c 2.430 I 1 / − − − − − − − − − − − 2606448 IQTau 67.465 26.11 M0.5 0.667 II 1 1754041 2433078 18134932608207 UXTauA 2359129 KPNO6 67.530 26.14 M8.5 0.022 II 1 2601244 DKTauA 67.684 26.02 K7 0.801 II 2 2.53 Y L93, G93, S95, K11 2426450 FXTauA 2300088 IRAS 04278 2442222 ZZTau 67.714 24.71 M3 0.398 II 2 0.029 Y L93, S95 2441475 ZZTauIRS 67.715 24.70 M5 0.178 II 1 2556394 KPNO7 67.738 25.94 M8.25 0.026 II 1 2710179 JH56 67.810 27.17 M0.5 0.667 II 1 1820072 MHO9 67.816 18.34 M4.25 0.248 III 1 2335047 1800215 MHO4 67.850 18.01 M7 0.057 III 1 2410529 V927TauA 2703188 1808049 L1551 1813432 LkHa358 67.901 18.23 K8 0.790 I 1 1812244 HH30 67.906 18.21 M0 0.701 I 1 1813576 HLTau 67.910 18.23 K7 0.801 I 1 18135711808315 XZTauA L1551NE 67.935 18.14 K0c 2.430 I 1 24241801821380 HKTauA V710TauA 67.991 18.36 M0.5 0.667 II 2 3.24 Y L93 2543299 J1-665 67.993 25.72 M5.5 0.137 III 1 1821305 LkHa267 67.999 18.36 M1.5 0.604 II 1 2528078 1757227 L1551-51 68.039 17.96 K7 0.801 III 1 1820147 V827Tau 68.061 18.34 K7 0.801 III 2 0.0929 Y L93, K11 2428597 Haro6-13 68.064 24.48 M0 0.701 II 1 1801387 V826TauA 1812464 MHO5 68.067 18.21 M6 0.096 II 1 2422149 1827426 MHO6 68.092 18.46 M4.75 0.201 II 1 2422271 V928TauA 2403013 2251083 1827521 MHO7 68.109 18.46 M5.25 0.157 III 1 2419572 FYTau 68.127 24.33 K5 1.121 II 1 1731406 GGTauAa 1731303 GGTauBa 2420029 FZTau 68.132 24.33 M0 0.701 II 1 2257266 IRAS 04295 2552311 UZTauA 68.179 25.88 M1 0.633 II 3 1802563 L1551-55 68.182 18.05 K7 0.801 III 1 2253027 JH112 68.205 22.88 K6 0.906 II 4 0.66,1.52,6.4 Y W16 2422115 1730092 LH0429 2616066 KPNO14 68.283 26.27 M6 0.096 III 1 2421000 MHO82409549 V807TauA 68.258 24.35 M6 0.096 III 2 0.037 Y K06, K12, W16 2409339 GHTauA 2246487 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + # 2MASS Name RA_ 146 J04295156 147148 J04295422 149 J04295950 150 J04300399 151 J04300724 J04302365 153 J04304425 152 J04302961 154 J04305028 155 J04305137 156 J04305171 157 J04305718 158 J04311444 159 J04311578 160 J04311907 162 J04312405 161 J04312382 163 J04312669 164 J04313407 165 J04313613 166 J04313747 167 J04313843 168169 J04314007 J04314444 170171 J04315056 J04315779 172 J04315844 173 J04315968 174 J04320329 175 J04320926 176 J04321456 177 J04321540 178 J04321583 179 J04321606 180 J04321786 182 J04322210 181 J04321885 183 J04322329 184 J04322415 185 J04322627 188 J04323058 187 J04323034 186 J04323028 189 J04323176 190 J04323205 191 J04324303 192 J04324373 193 J04324911 194 J04325026 195 J04325119 199 J04330781 196 J04330197 198 J04330664 197 J04330622 200 J04330945 continued. Table C.1.

A14, page 25 of 33 A&A 599, A14 (2017) N YYN Y P99, C08 W16 L93, G93, S95, K11 N YN YN L93,Y S95, K11 Y K12,N T14 L93, K11 K12 Y S95, K11 Y K06 Y K12 YN YY L93, S95, K11 Y T14 N S95,N K11 Y L93,N S95, K11 YYN K06 YN T14 S95 K06 N YN YY L93,Y G93, S95, K11 N Y T14 Y K06 N L93, K11 K06 T14 ] HAR HAR Ref. 00 1 Y L93, G93, S95, K11 Sep [ − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ∗ n ] Class

M 2000 SpT M [ J 2000 Dec_ J 68.413 22.46 M1.75 0.590 II 1 68.42468.42968.436 17.84 25.45 M468.469 26.25 M8.75 M4.75 0.018 0.271 26.22 0.201 III II M8.5 II 1 0.022 1 1 II 1 68.689 23.13 M5.25 0.157 III 1 68.785 23.19 M6 0.096 III68.939 1 27.62 M9.25 0.013 III 1 69.04369.090 21.99 M8.569.404 23.85 0.022 M5.25 23.52 II L0 0.157 II 1 0.009 1 III 1 B 68.897 24.14 M0c 0.701 I 1 + B 68.921 24.19 M1 0.633 II 2 2.04 Y L93, S95, K11 2608 68.310 26.24 M0 0.701 II 1 22472240 68.319 68.329 22.89 22.78 M0c M0.5 0.701 0.667 I II 1 1 2402C 68.897 24.14 M8c 0.031 II 1 2402A B 68.987 22.91 M3 0.398 II 2 0.66 Y L93, S95 + + + + + + B 68.852 17.86 M2 0.575 III 2 0.7 Y L93 + + B 68.414 17.86 K5 1.121 II 2 3.2 Y L93, S99, K11, D15 B 68.837 22.91 K7 0.801 III 2 0.0363 Y L93, S95, K11 B 68.403 26.16 M0 0.701 II 2 0.221 Y L93, G93, S95, D15 + + + G3 68.973 22.90 K7 0.801 III 2 0.022 Y L93, G93, S95, K11 G2 68.976 22.90 G0 2.659 III 1 / / − − − − − − − − − − − 2433433 V830Tau 68.292 24.56 K7 0.801 III 2 6.95 Y L93, S98, K11 2614235 IRAS 04301 22532042246342 IRAS 04302 2245293 IRAS 04303 2421170 XEST17-0362421058 GITau GKTau 68.359 68.392 22.76 68.394 M4 24.35 24.35 0.271 K7 K7 III 0.801 1 0.801 II II 1 2 2.5 Y L93, G93, R93, S95, K11 26094922227207 ISTauA 2520382 DLTau 68.413 25.34 K7 0.801 II 1 17515231750402 HNTauA 2526470 2615005 18100992250301 DMTau2612548 CITau22562692613275 XEST17-059 ITTauA 68.453 68.469 68.467 18.17 68.478 22.94 M1 22.84 M5.75 K7 26.22 0.116 0.633 K2 III II 0.801 II 1 2.134 1 II 1 2 2.48 Y S95, K11 1838390 J2-2041 68.481 18.64 M3.5 0.335 III 2 0.418 Y W16 2251445 JH108 68.546 22.86 M1 0.633 III 1 2250309 CFHT1 68.564 22.84 M7 0.057 III 1 1830066 HBC407 68.575 18.50 G8 2.562 III 2 0.13 Y S98 2308027 2428531 AATau 68.731 24.48 K7 0.801 II 1 22583582311398 XEST08-00322321462254242 HOTau1751429 FFTauA 2414589 HBC412A DNTau2408194 68.7372411087 IRAS 04325 2234115 CoKuTau3A 2252226 KPNO82737130 XEST08-033 22.982250216 68.834 M1.52252401 HQTau2249119 KPNO152255039 68.864 KPNO9 0.604 22.542254231 XEST08-047 III M0.5 HPTau 68.925 24.25 68.924 1 0.667 M0 II 22.87 68.947 22.57 68.963 M4.75 68.967 0.701 M5.75 68.964 1 II 0.201 22.84 0.116 22.88 68.970 III 22.92 K2 III M2.75 22.82 1 M4.5 M8.5 1 0.442 22.91 1 2.134 0.225 III K3 0.022 II III III 1 1.796 1 1 1 II 2 0.017 Y L93, G93, S95, K11 2250585 XEST08-049 68.970 22.85 M4.25 0.248 III 1 2254089 HPTau 2254134 HPTau 22543602238353 Haro6-28A 2159364 XEST09-04222595602542589 CFHT22351165 LkCa1422581192331080 CFHT32546229 68.996 ITG1 22.64 69.043 M0 69.080 69.162 23.00 0.701 25.72 M7.5 III M0 69.486 22.97 0.044 M7.75 1 III 0.701 25.77 0.038 III M5c III 1 1 0.178 1 II 1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + # 2MASS Name RA_ 201 J04331003 202 J04331435 203204 J04331650 205 J04331907 206 J04332621 207 J04333405 J04333456 208209 J04333678 J04333905 210 J04333906 211212 J04333935 213 J04334171 214 J04334291 215 J04334465 216 J04334871 217 J04335200 218 J04335245 219 J04335252 J04335470 220 J04335546 221 J04341099 222 J04341527 223 J04341803 224 J04344544 225 J04345542 226227 J04345693 228 J04350850 229 J04352020 230 J04352089 231 J04352450 232 J04352737 233 -234 J04353539 235 J04354093 236 J04354183 237 J04354203 238 J04354526 239 J04354733 240 J04355109 241 J04355143 IRAS242 04325 J04355209 J04355277 243 J04355286 244 J04355349 245 J04355415 246247 J04355684 248 J04355892 249 J04361030 250 J04361038 251 J04361909 252 J04362151 253 J04363893 254 J04373705 J04375670 continued. Table C.1.

A14, page 26 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus YYY K12 Y K12, T14 N K12 Y T14 Y K12, T14 D07 N YN Y D07, C08 N Y K06 Y C08 N D07, C08 YN S95 N YN C08 Y D07 Y T14 YY W16 N L93, K11 YYN K07, K12, T14 K98, D15 Y L93, G93, S99, K11 YN N K07, K12 YY K06, W16 L93, G93, S95, K11 ] HAR HAR Ref. 4.00 Y L93, S95, K11 / 00 1.,3.07 N 1 Y L93, S99, K11 Sep [ − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ∗ n ] Class

M 2000 SpT M [ J 2000 Dec_ J 69.56269.568 26.19 23.44 M7.25 M4.75 0.051 0.201 II III 1 1 69.744 23.61 M4.25 0.248 II 1 69.74569.75769.76769.772 23.4069.777 23.60 M6.5 25.74 M6 23.63 M7.25 0.076 23.57 M4c III M7.5 0.051 0.096 II II 0.271 0.044 1 I III 1 1 70.003 1 1 70.00770.166 23.97 25.94 M6 M5.5 25.32 M5.25 0.096 0.137 II III 0.157 II 1 270.437 0.57570.440 270.451 0.049 23.03 Y 23.03 M8.5 25.58 M4.5 Y K07 M7.75 0.022 K07, 0.225 K12 II 0.038 III II 2 2 0.108 1 0.224 Y Y T10, T14 T10, K11, T14 69.890 23.99 M5 0.178 II 1 68.387 18.01 M1 0.633 II 1 BB 70.523 70.531 25.38 25.38 M0 M1 0.701 0.633 III III 2 2 0.3 0.215 Y Y L93 L93, G93 + + 2547 69.8082535 25.89 K2c 69.8972557 2.134 69.974 25.702559 I K2c 26.05 70.033 1 K5c 2.134 I 26.09 1.1212540 M2c 0 1 70.3032550 0.575 1 II 70.412 25.78 M2c 1 25.94 0.575 M0 I 0.701 1 II25061550 1 71.113 71.464 25.20 M7.25 15.93 M2.5 0.051 II 0.486 II 1 1 C 68.387 18.02 B9 3.250 II 2 2459 71.677 24.98 M4 0.271 III 2 0.051 Y W16 B 70.532 25.39 K7 0.801 II 2 0.33 Y L93 + + + + + + + + + + + B 69.647B 26.18 M1 69.823 0.633 III 22.80 3 M0 0.036 0.701 II 2 0.66 Y L93, S95 B 69.837 25.75 M2.5 0.486 II 2 0.041 Y S95 4 70.320 28.67 M1.5 0.604 II 2 0.054 Y I08 B 70.270 24.85 K7 0.801 III 2 0.27 Y L93, S95 G2A G1A / / / + + + + − − − − − − − − IRAS 04368 − − − − − − − − 2558572 ITG2 69.503 25.98 M7.25 0.051 III 1 2611399 2326402 2609137 GMTau 69.589 26.15 M6.5 0.076 II 1 2336351 26104942610386 DOTau HVTauA 2323595 2336029 2544264 2337450 2334179 2553208 69.6192247533 IRAS 04361 2221034 VYTauA LkCa15 26.182541447 M02601527 IRAS 04365 2601407 ITG15 CFHT4 0.7012545020 II2358211 69.824 IC2087IR2556292 2605253 1 2519061 IRAS 04370 22.352551191 69.937 K5 69.948 JH2232451062 69.982 IWTauA 26.032555116 1.121 26.032546354 M5 ITG34 II 25.75 M72840000 IRAS 04381 2543530 G5c CoKuTau 2556267 ITG40 70.206 0.178 22301513 0.057 IRAS 04385 II2301580 0.078 2.616 II2534304 I2522562 25.86 70.295 1 Y LkHa332 M2 1 1 70.353 L93, K11, 25.922515374 K12 0.575 M5.5 DPTau2940060 II 25.73 CIDA14 0.1371801004 M3.52512164 2 II HD 28867A 1555496 IRAS 2.1 04414 0.3351555367 HD 301712459034 II IRAS 1 70.657 04429 1700001 RX J04467 70.8341702381 DQTau Y Haro6-37A 1 25.26 K11, M0.5 W16 29.67 71.464 M5 0.667 71.746 15.93 II 71.721 0.178 G5 II 2 17.04 17.00 0.1067 K7 2.616 M0 2 III 0.053 Y 0.801 0.701 1 II II L93, Y K11 W16 3 1 0.33,2.7 Y L93, D99 2545021 GNTauA 2557561 Haro6-322556074 ITG33A 70.268 70.284 25.972523032 M52523118 LkHa332 25.942520343 V955TauA M3 CIDA7 0.1782520187 III GOTau1800436 0.398 II 1 70.588 1 70.763 25.341658428 M4.75 DRTau 25.34 M0 0.201 II 0.701 1 II 71.776 1 16.98 K5 1.121 II 1 2359212 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + − # 2MASS Name RA_ 255 J04380083 256257 J04381486 258 J04381630 J04382134 261 J04385859 259260 J04382858 J04383528 262263 J04385871 264 J04390163 265 J04390396 266 J04390525 267 J04390637 268 J04391389 269 J04391741 J04391779 272273 J04393519 274 J04394488 275 J04394748 276277 J04395574 278 J04400067 279 J04400174 280 J04400800 281 J04403979 J04404950 283 J04410470 285286 J04411078 287 J04411267 288 J04411681 289 J04412464 290 J04413882 291 J04414489 292 J04414565 293 J04414825 J04420548 297 J04423769 299 J04432023 301302 J04333297 303 J04442713 304 J04455129 305 J04455134 306 J04464260 307 J04465305 J04465897 270 J04392090 282 J04410424 284 J04410826 294295 J04420732 296 J04420777 J04422101 298 J04430309 300 J04333278 308 J04470620 271 J04393364 continued. Table C.1.

A14, page 27 of 33 A&A 599, A14 (2017) YN N K12 YN L93, G93, C04,Y K11 N Y K12, T14 Y L93, S93, K11 K11, W16 YY K12 Y K11, W16 K11, W16 YYY L93, K11 Y K12, T14 Y L93, K11 Y K12 K07 N L97, K11 Y L93, K11 Y T14 Y D07 ] HAR HAR Ref. 00 1.,0.0323 Y L93, K11, S13 Sep [ − − − − − − − − − − − − − − − − − − − − − − − ∗ n ] Class

M 2000 SpT M [ J 2000 Dec_ J 72.175 17.06 M7 0.057 III 1 73.985 30.83 M5 0.178 III76.694 1 21.07 M5.25 0.157 III 1 74.454 30.26 M9.25 0.013 III 1 73.94873.95773.970 30.47 M4.75 30.33 30.11 M6 0.201 M5.25 III 0.157 0.096 2 III II 6.368 1 2 Y 0.056 K11, K12 Y K12 73.84773.91973.939 30.46 M6.25 30.65 30.33 M5.25 0.086 M4.75 III 0.157 0.201 III 1 II 1 1 3042 73.028 30.79 M4 0.271 I 1 2437 76.800 24.62 K6 0.906 III 1 + + B 76.956 30.40 K3 1.796 II 3 0.120,1.39 Y L93, G93, K11 B 72.947 30.79 M0 0.701 II 2 0.88 Y L93, G93 + + − − − − − − − − − − 30362093049374 XEST26-06230340153026348 SUAur3021037 XEST26-071 HBC427 73.98429503702523197 MWC4802509544 V836Tau 74.0052531312 CIDA8 30.612446102 73.997 CIDA9 M42432199 CIDA10 74.0082104296 CIDA11 30.442437163 74.693 M3.5 30.57 0.2713024050 RX 75.777 J05072 G2 II 30.35 RWAurA 0.335 76.172 K5 29.84 76.345 II 76.570 A2 25.39 1 2.632 76.597 K7 II 1.121 25.17 1 25.53 III M3.5 24.77 3.076 K8 24.54 1 M4 II 0.801 0.335 2 M3.5 II II 0.790 1 0.271 0.335 II 1 III II 1 2 2 2 2.28 0.083 0.0972 Y Y Y W16 K11, K11, W16 W16 3015195 2500156 CIDA12 76.979 25.00 M4 0.271 II 1 3028077 30301603019400 XEST26-0523006523 73.951 30.50 M4.5 0.225 III 1 2925112 DSTau 71.952 29.42 K5 1.121 II 1 1703374 30471343047175 UYAurA IRAS 04489 30215953027366 GMAur30175533039057 LkCa193019389 3033043 ABAur 73.796 73.904 30.37 K7 73.941 30.30 K0 0.801 30.55 II B9 2.430 III 1 3.250 1 II 1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + # 2MASS Name RA_ 309 J04474859 310 J04484189 311312 J04514737 J04520668 323324 J04555605 325 J04555636 326 J04555938 327 J04560118 J04560201 329330 J04584626 331 J05030659 332 J05044139 J05052286 336337 J05071206 J05074953 333334 J05061674 335 J05062332 J05064662 328 J04574903 338 J05075496 313314 J04551098 315 J04552333 316 J04553695 317 J04554046 318 J04554535 319 J04554582 320 J04554757 321 J04554820 322 J04554969 J04555288 continued. Table C.1.

A14, page 28 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus b C C C WP [Conf.] a − − − HAR P ∗ n [AU] 1 0181 1441 407 21 454 2 1 462 31 ** 723 41 725 41 ** 814 41 ** 836 42 ** 120 22 ** 379 3 C 2 C ** 396 4 [Y] 2 C 423 3 [Y] *2 C ** 562 2 [Y] 2 C ** 784 4 [Y] 2 C 888 3 [Y] 2 ** 963 33 C ** 048 5 [Y] 3 C C ** 252 2 [Y] 3 ** 277 53 C 623 3 [Y] *3 914 4 * [Y] 4 ** 218 44 C 393 3 [Y] C *4 ** 907 44 ** 998 25 C C 028 3 [Y] *5 C ** 186 5 C [Y] 5 C ** 293 2 [Y] 5 ** 870 2 [Y] 6 ** 087 4 C [Y] 6 223 3 * 6 353 3 C *7 ** 367 3 C 7 485 3 C * 7 ** 572 2 C 7 ** 740 27 ** 886 28 C ** 412 2 8 ** 633 38 ** 763 28 807 4 C ** 3 ** 4 C ** C * * C C C C C P δ stellar system A (“S” means one spectroscopic binary, “SS” means Class (Star B) / 2 III 12 II II B ∗ n first nearest neighbors. Column 1: couple reference (this work). Columns 2– 1 2 II − − − B 1BB 2 2B I C 2 II 2 II BB 2 2 III B II BB 3B 2 III 3 II B 2 2 II II II III B II 3B 2 II II C 3 III / G2Ab 1 2 III II G3 2 III G2 1 III + + + + + + + + + + + + + + + / / / + B 1550 1 II cA cA + + 2803B 1 I 2654B 1 I 2654A 1 I 1523A 2 I / / G1A + + + + / stellar system A (“S” means one spectroscopic binary, “SS” means two spectroscopic mutual / 2402A + 5 HBC361 13 III HBC359 1 III 1216 S IRAS 04108 538759 V773TauA IRAS 04181 16 S CZTauA V410X-ray7 V773TauA 2865562 IRAS 04181 98 II 51 V410X-ray2 IRAS 04191 1 V410TauA CoKuTau II 233245187295 IRAS 04325 122291 304207144 GGTauAa HPTau 301 V955TauA 189 S FVTau IRAS244 04429 181100 HD 28867A DITauA 198 GKTau168 2 V928TauA HPTau 294 FZTau173 FSTauA 1 V807TauA 156 II LkHa332 XZTauA 167274 II 242 LkHa267245219 1 ZZTauIRS122263 1127 HLTau CFHT4321 II 1 HPTau 185 1 HPTau FVTau II ITTauA 2 2 DGTau I II 1 II MHO7 II 1 II III Star #B Name (Star B) Class (Star A) : the total number of stars, above the unity if the star is not single (spectroscopic binaries are counted as one component), the class B ∗ 21 II 1 II III 1 II 111 II 1 II II II A n ∗ n − − − − − − − − B 2 II BB 2 2B 2 III II II B 2B 2 II III B 2 II C 4 III Bb 2 II G3 2 III + + + + + + + + / + B 2823 11522 1 I 0 + + + 2402C 1 II 2654B 1 I 2803A 1 I G1A G2A + + + / / the total number of stars, above the unity if the star is not single (spectroscopic binaries are counted as one component), the class of the (primary A ∗ n 4 HBC360 1 III 1 HBC358A 991114 IRAS 04108 Haro6-5B5286 157 IRAS 04181 17 DDTauA I V892Tau 384 FMTau54 160 IRAS 04154 94 II S49 IRAM 04191 II Hubble4 V410Anon25 2 1 III III 232244186294 IRAS 04325 121290 303206 LkHa332 GGTauBa HPTau 143300 188 FVTauA 242180 HD 30171 DHTauA 1 GITau197167 1 FYTau293 HPTau171 1 III 2 GHTauA 155 LkHa332 II 165 HLTau II 273 V710TauA II 1241 2246217 124 ZZTau261 LkHa358125 I 2 XEST08-047 ITG15 1 Haro6-28A II 1317 1182 KPNO13 II DGTauB 1 I III II 1 MHO6 II 1 I II Star #A Name (Star A) 2 4 5 6 7 8 9 3 1 10 11 13 14 15 16 17 18 19 20 21 22 23 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 42 24 12 38 # Couple Catalog of the first nearest neighbor couples of stars. Amongst the first-nearest-neighbor couples of stars (A, B), the ultra wide Pairs (UWPs) are defined as Table C.2. Notes. 5 (Star A): the star reference (this work, see Table C.1 ), presence of a spectroscopic binary associated to the star star). Columns 6–9 (Star B): the star reference (this work, see Table C.1 ), presence of a spectroscopic binary associated to the star binaries), the common Name of the star A, two spectroscopic binaries), the common Name of the star B, of the (primary star). Columnsstar 10–11: A the and separation B ofindicates has the a been two ultra observed stellar wide at components pairspectroscopic high A candidate techniques angular and since as resolution B the reported (**), and couple inmarked their are if the by mutual total only work a nearest number one of single neighbours. ofKraus component horizontal The stars & has line presence as( 2009b ) Hillenbrand in been of a who the observed an (hierarchical) focused table. at [Y], couple. on HAR this binaries Column couple (*) with 12: has or separation flag been if less to confirmed than none indicate as 4200 of whether gravitationally AU. the them bound The each have binaries delimitation been using of observed astrometric separation and at range HAR in (no their study mark). is Column 13: “C”

A14, page 29 of 33 A&A 599, A14 (2017) b C C C WP [Conf.] a − − − − − HAR P ∗ n [AU] 9 1519 5819 939 2 2 5 ** C 11 15511 35011 882 312 270 212 571 212 717 2 *13 ** 218 213 231 4 *13 ** 272 214 ** 677 315 ** 900 316 C ** 343 216 ** 543 216 C 999 4 * 17 ** 315 217 320 2 C * 17 ** 699 2 C 18 004 2 C *18 176 2 * 18 ** 180 3 C 18 717 2 * 18 854 318 928 2 *18 C 991 3 *19 ** 124 419 440 2 * 20 418 2 * 21 018 2 * 21 C 028 2 *21 C ** 131 221 518 2 *22 288 2 *22 ** 935 223 247 2 *23 C 835 2 - 23 949 3 * 24 C 016 2 *24 C 557 2 * 25 019 2 *25 C 112 3 * 25 217 3 * 25 350 4 * 25 C 454 4 *26 069 2 * 27 C ** 846 227 ** 860 2 28 414 328 545 3 *31 C 518 232 ** 071 2 C 32 449 3 * ** 2 ** 3 C * C * ** C C C P δ Class (Star B) 1 II 11 II 1 II II 11 II 1 II I 22 II III 1 II 1 II B ∗ n 1 2 II − − − − − − − − − − − B 3 III B 2 III B 2 II C 3 III / G3 2 III + + + + / B 2240 12608 1 II II 27062805 1 1 I I 2812 1 II + + + + + + 2402C 1 II + 752214 [GKH94]41 1 MHO325 221 I II CXTau MHO2 162 351 II 71 V410TauA II CoKuTau 741964 IRAS 04166 FRTau IRAS 04158 165 CWTau 1 II 5880 V410X-ray62847 1 II IRAS 04173 91 XEST20-071 V410Anon13 II LR1 1 1 1 III II II 285212 165243238260 ITG34222101 1 XEST08-049244 LkHa358 1263 1 HVTauA HQTau205 II 284 CFHT1 1263 LkCa21 HPTau 274 III 1239 I 2320 XEST17-036105 144 II 1204 ITG33A III III 1 XEST26-052 CFHT4202 KPNO15 IRAS 04303 259 1 1 1 III DITauA 325 IRAS 04301 317 169 II III II III DOTau217 141 1258 SUAur L1551NE320 1196 1232307 II 321 XEST26-052 IRAS 04325 GMTau II 1 I 1 MHO8319 Haro6-37A306 2 3173 III S288 II 270 III II DQTau LkHa267 GNTauA 1 ITG40 1 1 II II II Star #B Name (Star B) Class (Star A) 11 I 2 III 1 III II 111 II II 1 III 1 II 1 II II A ∗ n − − − − − − − − − − B 2 II B 2B 2 I II + + + 2240 12557 1 II 0 2540 1 I 2706 1 I 2708 1 I IRS5 1 I / + + + + + 2800G 1 I + 7421 IRAS 04166 1995 MHO2 S23 3 CWTau20 1 RYTau II 1 FPTau II CIDA1 165 158 II 70 II II V410X-ray673 115 LR161 V819Tau IRAS 04166 1 IRAS 04111 1 II 67 KPNO2 II II 156 V410X-ray5a77 24 14588 III V410X-ray4 XEST20-066 1 III V410X-ray3 1 2 III III III 284211166238240 ITG33A259221 HNTauA 1239 HH30 HQTau265 1 KPNO9204 1 II DOTau282 1266 JH108275 1 KPNO15 IRAS 04303 236 1319 1 I II 103 IRAS 04368 145 III 200 Haro6-32 II XEST08-033 III 1 III 199 XEST11-078 1258 1323 KPNO5315 III 164 1 III KPNO14 GMTau XEST26-062214 I 1138 1 1256 L1551 III LkCa19318 1194 III 234306 GVTauA II II 327 S S III CoKuTau3A ABAur326 1 DQTau HBC427308176 1286 2264 XEST26-071 II IRAS 1 04381 II III DRTau V827Tau 1 2 II III II Star #A Name (Star A) 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 89 91 92 93 94 95 96 63 88 90 43 46 44 45 # Couple continued. Table C.2.

A14, page 30 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus b C C WP [Conf.] a − − − − HAR P ∗ n [AU] 32 46932 77333 260 233 303 2 33 371 333 ** 561 334 032 334 758 3 * 34 ** 814 334 823 3 * 34 836 2 C *35 413 3 * 36 ** 423 436 639 2 *37 ** 298 238 ** 164 438 C 176 338 645 2 C * 38 ** 905 239 C ** 026 3 C 39 ** 336 2 C 39 ** 613 241 ** 386 343 ** 010 443 406 3 *43 ** 701 4 C 44 ** 092 344 ** 299 244 ** 896 3 C 45 051 3 * 46 C ** 718 2 46 ** 782 247 540 2 * 47 708 349 ** 200 249 520 2 *49 ** 607 349 952 5 * 50 ** 555 250 ** 864 2 C 51 ** 265 251 C 711 5 C * 51 901 3 * 52 147 3 * 52 223 3 C * 52 ** 257 2 C 52 540 2 * 53 ** 048 353 ** 092 253 ** 928 553 ** 990 2 54 967 2 *55 ** 358 256 296 3 C 56 ** 740 3 2 * ** 2 C ** * ** C P δ Class (Star B) 1 III 1 III 1 II 2 III 111 III 1 III 1 II III III B ∗ n S 3 II − − − − − − − − − B 2B 2 III I BB 1 2BB III 2 2 II II II B 2 II BB 2 1 III III Bb 2 II + + + + + + + + + + + 2557 129023042 0 1 1 II I 2759 1 II 2638 1281225352436 1 1 II 2 II I I 2642 1 II + + + + + + + + + G1A / 28751044 XEST20-07133 1 [GKH94]41 IRAS 04125 1 V410X-ray1 Anon19770 1 2 III I 36 TTauN III II V819Tau 12999 II 96 CIDA2 Haro6-5B80 2 1 IRAS 04173 HD 283572 III 1 I III 24 XEST20-066 1 III 150275294 IRAS 04368 138 LkHa332 KPNO6312 1102 142 GVTauA 323 IRAS 04489 II 178221 XEST13-010 S270 XEST26-062 1109 1 V826TauA 217 143234 IRAS 04200 GNTauA JH108 III 186 II 1319 CoKuTau3A DHTauA 236107 GGTauBa 235157 III IRAS 04196 XEST08-033272123 1193235 KPNO8 IRAS 04365 216 IRAS 04239 142 KPNO7 1 S193 III 274 1285246 JH112213 KPNO8 XEST13-010 III 314 CITau 4296 1 1 II 277 1 JH112 Haro6-28A 193 CFHT4135 ITG34 4227 1285 II III 1 III 180 IRAS 04260 II 181 CIDA7178 1 II JH112 II S II 4 V928TauA ITG34 V826TauA 1 II II II Star #B Name (Star B) Class (Star A) 11 III III 11 II II 11 III III 11 II 11 II 2 II II III 11 II III A ∗ n S 3 II − − − − − − − − − − − − − B 2 II B 2 II B 2 II B 2B II 2 III B 2 II 17 1 III + + + + + + + + 2702 2 I 1927 1 II 2559 1 II 2433 12535 1 I I 2251 1 I 2247 12550 1 I II + + + + + + + + 9 LkCa1 1 III 297642 IRAS 04169 31 CIDA297 29068 LkCa5 IRAS 04187 TTauN 2 III 35 FQTauA III 2792 FOTauA 8978 XEST21-026 1 III 30 KPNO1 1 III 146279296 IRAS 04370 142 IQTau311 1 CIDA7140 XEST13-010316 1 1 IRAS 04264 UYAurA 175 II 216272 S II III 108 208 IRAS 04365 136 L1551-51231 CITau 1195 1 ISTauA 314 229106 J1-507228 III DNTau LH0429 2153 II 1 FFTauA 276 XEST11-087120 190 1247 III HOTau218 II DKTauA148 IRAS 04295 1184 IC2087IR 2278 III 281 XEST09-042 1249 XEST17-059210 1313 II 1297 II 271 203 I 132 JH223 III 224 CFHT2 III 289 IRAS 04302 DLTau 2170 GMAur 1177 DPTau 1 IRAS 1 04385 L1521F-IRS192 2 1 II HKTauA III II Haro6-13 II II L1551-55 1 I 1 II III Star #A Name (Star A) 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 147 148 149 150 151 126 146 # Couple continued. Table C.2.

A14, page 31 of 33 A&A 599, A14 (2017) b WP [Conf.] a − − HAR P ∗ n [AU] 57 08857 65058 221 262 261 362 832 362 ** 994 363 355 3 *65 694 2 * 67 ** 348 267 ** 562 267 ** 886 268 929 2 * 71 C ** 078 278 ** 616 2 80 ** 665 380 ** 679 3 C 80 734 281 ** 682 281 ** 920 381 ** 988 2 C 83 201 2 * 84 ** 385 484 645 3 * 84 763 288 ** 546 489 284 2 * 90 553 2 *92 ** 995 593 845 2 * 94 578 2 *94 593 2 *96 679 2 * 97 C 217 4 C * 98 944 2 *99 ** 191 2 C ** 3 C ** 3 ** ** C * P 100 935101 912103 966 2105 891 3105 901 3106 340 2 * 108 ** 012 2113 364 3 * 116 288 3 * 116 916 4 * 123 803 2 * 127 248 4 C * 128 ** 758 4129 422 2 * ** 4 ** 2 ** ** C ** δ Class (Star B) 1 III 11 II II 1 II 1 III 1 II 11 III 1 III III 1 III B ∗ n − − − − − − − − − − B 2 III B 2 II C 2 II B 2 II B 2 II + + + + + 2638 12805 1 II I 27022437 2 144232642 1 I 1 III III 2654 II 2 II IRS5 1 I / + + + + − + + 3 HBC359 1 III 2 XEST06-006 15 III HBC361 1 III 36 4384 64 KPNO103078 1 IRAS 04158 KPNO1 II 193 III 35 76 DETau IRAS 04169 129 II 17 CIDA2 2 FMTau III 1 II 249112229297176163 127 CFHT2 FFTauA 165 FTTau 1164 DPTau 1 V827Tau107270 2 2148 IRAS DGTau 04196 LkHa358 III L1551 II 1 1 GNTauA III II 129301257 S223 II I 257 HD117 28867A 118288 KPNO4316 1 HBC407258146 2 J1-4872A IPTau315197 4 ITG40 III 1 1336 GMTau III 194 IQTau255 1 GHTauA III 116 LkCa19 II RX 1 J05072 135 1 II 191 S II 334 IRAS 04260 170 II J1 ITG2 III 137172 1 UZTauA IRAS 04263 3 HKTauA CIDA11 2 III J1-665 II 1 II III Star #B Name (Star B) Class (Star A) 11 II 1 II 1 II 1 II 11 III 11 III II 1 III 1 II III III 11 II II 21 II III A ∗ n − − − − − − − − − − − − − − − B 2B 2 II III C 3 III B 2 III + + + + B 2547 12612 I 32603 1 I II 2610 12654 2 I II + + + + + + 2 XEST06-006 1 III 6 IRAS 04016 7 HBC362 1 III 34 4179 6626 CYTau81 SS 1 LkCa3A KPNO12 1 II 85 II 3882 LkCa4 XEST16-04532 1 118 III III FNTau 1 II 252111226298179158129 XEST08-003 CFHT3159 FUTauA 1 1162 2 GOTau110 MHO5267 1152 JH56 1 KPNO4 III III 1 IRAS 04361 MHO9 II 1 MHO4 1 II 131 FXTauA II 215 1253 II 220 III IRAS 04248 262 III 116115 III 292 324 DMTau IRAS 04216 255 J2-2041 1139 J1-4423 2322 183 1 FWTauA II 334201 III ITG2254114 III 1137172 CIDA11333 V830Tau IRAS 04263 161 III 2 2 ITG1133 174 1 J1-665 V927TauA II CIDA10 III 1 2 II III III Star #A Name (Star A) 153 154 155 156 157 158 159 160 161 162 163 165 166 167 168 169 170 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 152 164 171 # Couple continued. Table C.2.

A14, page 32 of 33 I. Joncour et al.: Unexpected ultra-wide pairs of high-order multiplicity in Taurus b WP [Conf.] a − − − − HAR P ∗ n [AU] P 131 827132 054139 651 2142 579 3145 196 2146 ** 597 3151 ** 345 5152 590 2 * 154 420 3 * 165 ** 802 5167 075 2 * 168 ** 337 4171 ** 241 5173 274 2 186 ** 829 2194 340 2 * 196 526 2196 707 3 * 197 ** 874 2199 912 2 * 205 ** 652 3209 ** 691 3212 426 3214 ** 489 2225 ** 390 2229 015 2 * 232 ** 165 4239 ** 911 2280 ** 537 2 C 290 ** 923 4294 ** 777 3304 098 2 * 312 ** 079 2330 ** 781 2 C 345 ** 964 2 C 506 ** 030 2526 ** 157 3553 ** 244 3553 251 2 * 574 ** 507 4575 ** 274 2717 882 2 * 909 ** 525 3 ** 2 2 * C * ** δ 1 026 0571 746 426 4 3 * ** Class (Star B) 1 II 11 III 1 II 1 II 121 III 1 III II 2 II 1 III II III B ∗ n − − − − − − − − − − − B 2B 2BC III B 2 4 1 III III II I B 1 I + + + + + + 2902 1 II 2437 12506 III 12603 1 II II 29101927 1 1 II II + + + + + + G2A / 2402A 2253A + + 9 LkCa1 1 III 663372 IRAS 04125 KPNO12 LkCa7A 131 II 6340 HBC37663 1 III HBC3761390 1 IRAS 04108 IRAS 04187 III 231118110 161159205293 DNTau149233 1 J1-4872A V927TauA 298254 IRAS LkHa332 04325 4 XEST17-036125308 MHO9 II 184 1 UXTauA 332 1327 III 212 S336331 GOTau III DGTauB III ITG1269 1151 DRTau 1 1328 RX J05072 280 HBC427 CIDA9 1302228 2 2 II 151 CIDA8 I II LkCa15 II IRAS115 04414 1133 III II 2309104 299 IRAS158 04216 HOTau II 154 1 II IRAS 04278 329334 DSTau CIDA14 II 1 2 JH56 1 MWC480 II CIDA11 1 II 2 II II II Star #B Name (Star B) Class (Star A) 2 III 111 II 121 II 1 III II II III 1 II 1 III III 11 III 111 II III 1 III 1 II 11 III 1 III III III III A ∗ n 4 2 II − − − − − − − − − − − − − − − − − − − − B 2C III 4 II BB 2 1B 2 II B I 2B III 2 II III B 3 II / + + + + + + + + 2910 1 II 2506 1 II 2459 2 III + + + 2253A + 8 7240 50 LkCa7A KPNO1113 1 IRAS 04108 III 4869 HBC37283 146 III BPTau J2-157 139 37 1 V409Tau 1 II III II 225119113 151 149209 AATau280 147 1251 KPNO3302 UXTauA 250 1126310 II 154 IRAS 04414 331328 IRAS 04278 230 II 338 DFTauA 330 LkCa14268 1160 329 HBC412A CIDA8283305 1248 CIDA12 V836Tau III VYTauA 130 1 1 RX104 J04467 MWC480 IWTauA 134 II 299 1287 II II 237 128 II 337 CIDA14335 CoKuTau 2 RWAurA II Star #A Name (Star A) 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 201 245 continued. # Couple Table C.2.

A14, page 33 of 33