Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
P.A.B. Galli, L. Loinard, H. Bouy, L.M. Sarro, G.N. Ortiz-León, S.A. Dzib, J. Olivares, M. Heyer, J. Hernandez, C. Román-Zúñiga, M. Kounkel, K. Covey
AAstronomy & Astrophysics manuscript no. arXiv_version c (cid:13)
ESO 2019September 4, 2019
Structure and kinematics of the Taurus star-forming region fromGaia-DR2 and VLBI astrometry
P. A. B. Galli , L. Loinard , , H. Bouy , L. M. Sarro , G. N. Ortiz-León , S. A. Dzib , J. Olivares , M. Heyer ,J. Hernandez , C. Román-Zúñiga , M. Kounkel , and K. Covey Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Allée Geo ff roy Saint-Hilaire, 33615 Pessac, France Instituto de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, Apartado Postal 3-72, Morelia 58089,México Instituto de Astronomía, Universidad Nacional Autónoma de México, Apartado Postal 70-264, 04510 Ciudad de México, México Depto. de Inteligencia Artificial , UNED, Juan del Rosal, 16, 28040 Madrid, Spain Max Planck Institut für Radioastronomie, Auf dem Hügel 69, D-53121, Bonn, Germany Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA Instituto de Astronomía, Universidad Nacional Autónoma de México, Unidad Académica en Ensenada, Ensenada 22860, México Department of Physics and Astronomy, Western Washington University, 516 High St, Bellingham, WA 98225, USA.Received ; accepted
ABSTRACT
Aims.
We take advantage of the second data release of the Gaia space mission and the state-of-the-art astrometry delivered from verylong baseline interferometry observations to revisit the structure and kinematics of the nearby Taurus star-forming region.
Methods.
We apply a hierarchical clustering algorithm for partitioning the stars in our sample into groups (i.e., clusters) that areassociated with the various molecular clouds of the complex, and derive the distance and spatial velocity of individual stars and theircorresponding molecular clouds.
Results.
We show that the molecular clouds are located at di ff erent distances and confirm the existence of important depth e ff ects inthis region reported in previous studies. For example, we find that the L 1495 molecular cloud is located at d = . + . − . pc, whilethe filamentary structure connected to it (in the plane of the sky) is at d = . + . − . pc. We report B 215 and L 1558 as the closest( d = . + . − . pc) and most remote ( d = . + . − . pc) substructures of the complex, respectively. The median inter-cloud distance is25 pc and the relative motion of the subgroups is on the order of a few km / s. We find no clear evidence for expansion (or contraction)of the Taurus complex, but signs of the potential e ff ects of a global rotation. Finally, we compare the radial velocity of the starswith the velocity of the underlying CO molecular gas and report a mean di ff erence of 0 . ± .
12 km / s (with r.m.s. of 0.63 km / s)confirming that the stars and the gas are tightly coupled. Key words. open clusters and associations: individual: Taurus - Stars: formation - Stars: distances - Methods: statistical
1. Introduction
The Taurus-Auriga star-forming region (or simply Taurus) is oneof the most intensively studied regions of low-mass star forma-tion and an ideal laboratory for observing young stellar objects(YSOs) from the most embedded sources at the early stagesof evolution (i.e., protostars) to disk-free stars that are activelyforming planets (see, e.g., Kenyon et al. 2008). Previous stud-ies suggest that Taurus hosts a few hundred YSOs spread over alarge area on the sky of about 15 ×
15 deg (Esplin et al. 2014;Esplin & Luhman 2017). The sky-projected spatial distributionshows that the stars are not randomly distributed but clustered insmall groups and overdense structures in and around the di ff er-ent star-forming clouds and filaments of the region (Gomez et al.1993; Joncour et al. 2017, 2018). The morphology and kine-matics of these gaseous clouds and filaments have been clearlycharacterized in recent years based on CO surveys and extinc-tion maps (see, e.g., Ungerechts & Thaddeus 1987; Cambrésy1999; Dame et al. 2001; Dobashi et al. 2005; Goldsmith et al.2008), and increasing progress is being made to constrain thethree-dimensional structure and stellar kinematics of the indi-vidual clouds. However, until recently many studies have been hampered by the lack of accurate data for a significant number ofstars, in particular stellar distances and spatial velocities, whichcould provide us with valuable information about the star forma-tion history in this region.Distances to individual stars are, in general, derived fromtrigonometric parallaxes; until recently there were very few par-allaxes for Taurus stars. Bertout et al. (1999) used the trigono-metric parallaxes of 17 stars from the Hipparcos catalog (ESA1997) and estimated the distances to three groups in this sam-ple, 125 + − , 140 + − , and 168 + − pc, which are roughly associatedwith the central, northern, and southern clouds of the complex,respectively. The situation did not improve significantly with thefirst data release of the Gaia space mission (Gaia-DR1, GaiaCollaboration et al. 2016). The
Tycho-Gaia Astrometric Solution (TGAS, Lindegren et al. 2016) catalog provided trigonometricparallaxes for only 19 stars in Taurus that are obviously moreprecise than the
Hipparcos results for the same stars, but stillrepresent a small fraction of the sample of known members. Thissample is restricted to the brightest stars (i.e., G <
12 mag) andthe parallaxes were nevertheless a ff ected by systematic errors onthe order of 0.3 mas (see Lindegren et al. 2016). Article number, page 1 of 28 a r X i v : . [ a s t r o - ph . S R ] S e p & A proofs: manuscript no. arXiv_version
A major e ff ort to determine the distance to individual stars inthe Taurus region was successfully undertaken using very longbaseline interferometry (VLBI, Lestrade et al. 1999; Loinardet al. 2007; Torres et al. 2007, 2009, 2012). In recent yearsthe Gould’s Belt Distances Survey (GOBELINS, Loinard et al.2011) has targeted a number of YSOs in nearby star-formingregions to deliver state-of-the-art trigonometric parallaxes andproper motions (see Ortiz-León et al. 2017a,b; Kounkel et al.2017; Ortiz-León et al. 2018). In one paper in this series, Galliet al. (2018) measured the trigonometric parallaxes of 18 starsin Taurus with precision ranging from 0.3% to 5%. The result-ing distances suggest that the various molecular clouds of thecomplex are located at di ff erent distances and reveal the exis-tence of significant depth e ff ects in this region. For example, theLynds 1531 and 1536 molecular clouds (hereafter L 1531 andL 1536) were reported to be the closest ( d = . ± . d = . ± . / s among the various clouds in Taurus. This is sig-nificantly lower than the value of 6 km / s used by Bertout & Gen-ova (2006) to derive kinematic distances based on the convergentpoint method. Such a discrepancy could arise, for example fromthe internal motions within the complex, indicating that morestudy is clearly warranted in this regard.The small number of sources with complete data in the sam-ple (proper motion, parallax, and radial velocity) compared tothe number of known members prevented Galli et al. (2018) frominvestigating in more detail the three-dimensional structure andkinematics of the various subgroups. In this context, the recentlypublished second data release of the Gaia space mission (Gaia-DR2, Gaia Collaboration et al. 2018b) o ff ers a unique opportu-nity to revisit the previous analysis with a much more signif-icant number of stars and the same level of astrometric preci-sion obtained from VLBI observations. For example, Gaia-DR2increases the number of Taurus stars with available astrometryby a factor of more than 20 compared to its predecessor Gaia-DR1 including the faintest members at G (cid:39)
20 mag and hav-ing smaller systematic errors on the trigonometric parallaxes ofabout 0.1 mas on global scales (Luri et al. 2018).In a recent paper Luhman (2018) used Gaia-DR2 data torefine the census of Taurus stars, to identify new candidateswith similar properties of known members, and to determine theshape of the initial mass function (IMF). The revised sample ofmembers shows that the older population of stars ( >
10 Myr)which was proposed to be associated with this region in otherstudies (see, e.g., Kraus et al. 2017; Zhang et al. 2018) has nophysical relationship with the Taurus molecular clouds, and theTaurus IMF resembles other star-forming regions (e.g., IC 348and the Orion Nebula Cluster). We incorporated this updatedcensus of stars in our analysis and we present here our discussionof the structure and kinematics of the region.This paper is organized as follows. In Section 2 we describethe sample of stars used in this study for our analysis and in Sec-tion 3 we compare the VLBI and Gaia-DR2 astrometry for thestars in common between the two projects in the Taurus region.In Section 4 we present our methodology based on hierarchicalclustering for partitioning the stars in our sample into di ff erentgroups with similar properties, for rejecting outliers in the sam-ple, and for defining the subsamples of stars that are associatedwith the various molecular clouds of the Taurus complex. In Sec-tion 5 we present our results for the distance and spatial velocityof individual stars and subgroups derived from Bayesian infer-ence using the most precise astrometric and spectroscopic data available to date and the existence of internal motions, expan-sion, and rotation e ff ects in the complex, and we compare thestellar velocities with the kinematics of the underlying gaseousclouds. Finally, we summarize our results and conclusions inSection 6.
2. Sample
To construct our initial sample of Taurus stars, we begin by com-piling known YSOs and new candidates associated with this re-gion that have been previously identified in the literature. Severalstudies in the literature have proposed di ff erent lists of Taurusstars (see, e.g., Joncour et al. 2017; Kraus et al. 2017; Zhang et al.2018; Luhman 2018), but the recent study performed by Luhman(2018) shows that the samples of stars proposed by Kraus et al.(2017) and Zhang et al. (2018) are older ( >
10 Myr) and showkinematic properties that are inconsistent with membership inTaurus. We therefore restricted our sample of stars to the listsgiven by Joncour et al. (2017) and Luhman (2018). We com-bined the sample of 338 stars from Joncour et al. (2017) with thelists of known members (438 stars) and new candidates (62 stars)given by Luhman (2018). The resulting sample consists of 519stars after removing the sources in common between the two sur-veys. Multiple systems are counted as one single source in oursample unless they were resolved in these studies or by the Gaiasatellite (as described below).We proceeded as follows to access the astrometric measure-ments in Gaia-DR2 for our targets and avoid erroneous cross-identifications. Gaia-DR2 provides cross-matched tables with anumber of external catalogs. First, we use the unique sourceidentifier from the 2MASS catalog (Cutri et al. 2003) given inthe original tables used to construct our sample and cross-matchour list of source identifiers with the
TMASS_BEST_NEIGHBOUR table provided by the Gaia archive . This procedure returns theunique Gaia-DR2 source identifier that corresponds to our tar-get, the number of sources in the 2MASS catalog that matchthe Gaia source, and the number of Gaia sources that have thesame source as best-neighbor. We find a direct one-to-one re-lationship for most sources in our sample, which confirms thatthey have been correctly identified. We note that three sources(2MASS J04210934 + + + GAIA_SOURCE ) and retrieve the astrometric measurementsthat will be used in the forthcoming analysis. We repeated thisprocedure for the 492 stars with known 2MASS identifiers in oursample and searched the remaining sources in Gaia-DR2 usingtheir stellar positions and a search radius of 1 (cid:48)(cid:48) . Doing so, wefound proper motions and trigonometric parallaxes for 411 starsfrom our initial sample.Radial velocities in Gaia-DR2 are available for only 34 starsin our sample, so we searched the CDS / SIMBAD databases(Wenger et al. 2000) to access more radial velocity measure-ments. Our search in the literature, which was as exhaustive aspossible, was based on Wilson (1953), Hartmann et al. (1986),Hartmann et al. (1987), Herbig & Bell (1988), Reipurth et al.(1990), Duflot et al. (1995), Mathieu et al. (1997), Wichmannet al. (2000), White & Basri (2003), Muzerolle et al. (2003),Gontcharov (2006), Torres et al. (2006), Kharchenko et al. see http: // gea.esac.esa.int / archive / Article number, page 2 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry (2007), Scelsi et al. (2008), Nguyen et al. (2012), and Kraus et al.(2017). In addition, we also used the more recent measurementscollected with the Apache Point Observatory Galactic EvolutionExperiment (APOGEE) spectrograph (Kounkel et al. 2019). Inthe case of multiple radial velocity measurements in the liter-ature we took the most precise result as our final estimate. Bycombining these external sources with Gaia-DR2 we found ra-dial velocities for a total of 248 stars.Table 1 lists the 519 stars in our initial sample with the datacollected from the literature and the membership status of eachstar as derived from our forthcoming analysis (see Sect. 4).
Article number, page 3 of 28 & A p r oo f s : m a nu s c r i p t no . a r X i v_v e r s i on Table 1.
Identifiers, positions (epoch = = probable outlier, 1 = confirmed member) of each starin the corresponding cluster (see Sect. 4.3). The last three columns indicate whether the star is included in one of the original tables from the literature used to construct our initial sample of stars (1 = included, 0 = not included). They refer to the samples of Joncour et al. (2017) and Tables 1 (members) and 6 (candidate members) of Luhman (2018), respectively. (This table will be available inits entirety in machine-readable form.) α δ µ α cos δ µ δ (cid:36) Source V r Ref. Cluster Member Table(h:m:s) ( ◦ (cid:48) (cid:48)(cid:48) ) (mas / yr) (mas / yr) (mas) (km / s) (literature)2MASS J04034930 + + B + C 04 03 49.32 26 10 52.0 0 0 1 0 02MASS J04034997 + . ± . − . ± .
221 6 . ± .
208 GaiaDR2 0 0 1 1 02MASS J04035084 + . ± . − . ± .
123 7 . ± .
129 GaiaDR2 14 . ± . + . ± . − . ± .
226 8 . ± .
237 GaiaDR2 0 0 1 0 02MASS J04043984 + . ± . − . ± .
221 8 . ± .
252 GaiaDR2 16 . ± . + + + . ± . − . ± .
126 7 . ± .
128 GaiaDR2 14 . ± . + . ± . − . ± .
135 7 . ± .
149 GaiaDR2 0 0 0 0 12MASS J04064263 + . ± . − . ± .
162 6 . ± .
168 GaiaDR2 0 0 0 0 12MASS J04064443 + . ± . − . ± .
159 6 . ± .
159 GaiaDR2 0 0 0 1 02MASS J04065134 + . ± . − . ± .
133 6 . ± .
138 GaiaDR2 16 . ± .
20 15 0 0 0 1 02MASS J04065364 + . ± . − . ± .
157 6 . ± .
157 GaiaDR2 0 0 0 0 12MASS J04080782 + − . ± . − . ± .
157 4 . ± .
146 GaiaDR2 0 0 1 0 02MASS J04105425 + + + . ± . − . ± .
151 6 . ± .
131 GaiaDR2 0 0 0 1 02MASS J04131414 + . ± . − . ± .
137 7 . ± .
115 GaiaDR2 9 . ± .
12 15 7 1 1 1 02MASS J04132722 + . ± . − . ± .
145 7 . ± .
121 GaiaDR2 21 . ± .
28 17 7 1 1 1 02MASS J04135328 + + . ± . − . ± .
889 6 . ± .
013 GaiaDR2 15 . ± .
27 17 0 0 1 1 02MASS J04135471 + + Notes.
References for radial velocities: (1) Wilson (1953), (2) Hartmann et al. (1986), (3) Hartmann et al. (1987), (4) Herbig & Bell (1988), (5) Reipurth et al. (1990), (6) Duflot et al. (1995),(7) Mathieu et al. (1997), (8) Wichmann et al. (2000), (9) White & Basri (2003), (10) Muzerolle et al. (2003), (11) Gontcharov (2006), (12) Torres et al. (2006), (13) Kharchenko et al. (2007),(14) Scelsi et al. (2008), (15) Nguyen et al. (2012), (16) Kraus et al. (2017), (17) Kounkel et al. (2019) and (18) Gaia Collaboration et al. (2018b). A r ti c l e nu m b e r , p a g e f . A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
3. Gaia-DR2 and VLBI astrometry in Taurus
In a recent study, Galli et al. (2018) derived trigonometric par-allaxes and proper motions of 18 YSOs in the Taurus regionbased on multi-epoch VLBI radio observations as part of theGOBELINS project (see Sect. 1). In the following we excludeV1110 Tau from the discussion because it is more likely to bea foreground field star (see discussion in Sect. 4.10 of Galliet al. 2018) and we count the V1096 Tau A-B binary sys-tem as one source. We note that 12 YSOs from their sampleare also included in Gaia-DR2. Figures 1 and 2 illustrate thecomparison of trigonometric parallaxes and proper motions forthe stars in common. The mean di ff erence (Gaia-DR2 minusVLBI) and r.m.s. of the trigonometric parallaxes between the twoprojects are 0 . ± .
152 mas and 0 .
526 mas, respectively. Thesame comparison in proper motions yields a mean di ff erence of0 . ± .
682 mas / yr and − . ± .
194 mas / yr, and the r.m.s. of2 .
410 mas / yr and 4 .
154 mas / yr, respectively, in right ascensionand declination.Although these numbers provide valuable information forevaluating the consistency (or discrepancy) between VLBI andGaia-DR2 results, two points are worth mentioning here re-garding this comparison. First, the trigonometric parallaxes andproper motions derived from VLBI astrometry for two stars incommon with Gaia-DR2 (V999 Tau and HD 282630) have beendetermined based on a small number of observational epochs.These results are therefore less precise and accurate comparedto the other stars in the VLBI sample (see Sect. 4.3 of Galli et al.2018). Second, the astrometric solutions delivered by Gaia-DR2assume a model with uniform space motion of the stars so thatnon-linear motions caused by binarity (and multiplicity) of thesource have not been taken into account. Galli et al. (2018) per-formed a dedicated analysis of the binaries in the VLBI sampleand solved for the full orbital motion of these systems with asu ffi cient number of detections. This explains the discrepancyobserved between the two projects for such systems (see alsoFigures 1 and 2).For the reasons discussed above we decided to prioritize thetrigonometric parallaxes and proper motions based on VLBI as-trometry for both single stars and binaries. In the specific casesof V999 Tau, HD 282630, and the V1096 Tau A-B binary systemwe prefer to use Gaia-DR2 data because of the small number ofobservations and the large errors produced in the VLBI solutionfor these specific sources (see also Sects. 4.1 and 4.3 of Galliet al. 2018). Thus, if we exclude V999 Tau, HD 282630, andV1096 Tau A-B from the comparison, the mean di ff erence andr.m.s. of the trigonometric parallaxes between the two projectsbecomes 0 . ± .
115 mas and 0.365 mas, respectively. Theformer is consistent with the systematic errors of about 0.1 masthat exist in the trigonometric parallaxes of the Gaia-DR2 cata-log (see Lindegren et al. 2018). One possibility to explain thisdiscrepancy for the sample of stars under analysis is indeed thedi ff erent source modeling used in each project. For example, ifwe remove binaries and multiple systems from this comparisonthe mean di ff erence between VLBI and Gaia-DR2 results dropsto − . ± .
010 mas (with r.m.s. of 0.086 mas).By combining the recently published Gaia-DR2 catalog withthe state-of-the-art VLBI astrometry delivered by the GOB-ELINS project in the Taurus region, we have a sample of 415stars with measured trigonometric parallaxes and proper mo-tions. We use the VLBI results obtained by Galli et al. (2018)for 13 stars and Gaia-DR2 data for the remaining 402 stars inthis list. The astrometry reference used for each star in this studyis indicated in Table 1. v (mas) − Gaia DR2 v ( m a s ) − V L B I l ll llll l ll ll l ll llll l ll ll lll ll lll ll V1096TauV773TauAHD283518 V1023TauHDE283572TTauV1201TauHD283641 V807TauHPTauG2 V999TauHD282630
Fig. 1.
Comparison of the trigonometric parallaxes obtained from theGOBELINS project (Galli et al. 2018) and Gaia-DR2. Blue circles andred triangles indicate the stars that have been modeled as single and bi-nary (multiple) sources for the VLBI astrometry, respectively. The greendashed line indicates perfect correlation between the measurements.
One important point to mention about Gaia-DR2, which isthe main source of data used in our study, is the presence ofsystematic errors in the catalog. They depend on the position,magnitude, and color of each source, but they are believed to belimited on global scales to 0.1 mas in parallaxes and 0.1 mas / yrin proper motion (see, e.g., Luri et al. 2018). We added thesenumbers in quadrature to the random errors given in the Gaia-DR2 catalog for each star. This procedure is likely to overes-timate the parallaxes and proper motion uncertainties for somestars in our sample, but the parameters that result from these ob-servables (e.g., distance and spatial velocity) will take this e ff ectinto account when propagating the errors. We also corrected theGaia-DR2 parallaxes by the zero-point shift of − .
030 mas thatis present in the published data, as reported by the Gaia collab-oration (see, e.g., Lindegren et al. 2018), although the final im-pact of this correction in our distances is not significant due tothe close proximity of the Taurus star-forming region.
4. Analysis
One of the main objectives of the current study is to comparethe properties of the various star-forming clouds in Taurus. Inthe following we describe our methodology for partitioning thestars in our sample into di ff erent groups that roughly define theclouds in the complex. We use the term “cluster” throughout thissection to refer to the grouping of stars with similar propertiesthat result from our clustering analysis, and we warn the readerthat the terminology used here is not related to the astronomicalcontext (i.e., star clusters). Article number, page 5 of 28 & A proofs: manuscript no. arXiv_version m a cos d (mas/yr) − Gaia DR2 ma c o s d ( m a s / y r) − V L B I l lll l ll ll lll l lll l ll ll lll l l lll l l lll V1096TauV773TauAHD283518V1023Tau HDE283572TTauV1201TauHD283641V807Tau HPTauG2V999TauHD282630 −35 −30 −25 −20 −15 −10 −5 − − − − − − − m d (mas/yr) − Gaia DR2 md ( m a s / y r) − V L B I ll lll l lll lll ll lll l lll lll ll lllll lll V1096TauV773TauA HD283518V1023TauHDE283572 TTauV1201TauHD283641V807Tau HPTauG2V999TauHD282630
Fig. 2.
Comparison of the proper motions in right ascension (left panel) and declination (right panel) obtained from the GOBELINS project (Galliet al. 2018) and Gaia-DR2. Blue circles and red triangles indicate the stars that have been modeled as single and binary (multiple) sources for theVLBI astrometry, respectively. The green dashed line indicates perfect correlation between the two measurements.
Our sample of YSOs in Taurus compiled from the literaturecontains 415 stars with measured trigonometric parallaxes andproper motions. However, some of these sources are spread wellbeyond the molecular clouds of the complex. Thus, we restrictour sample to the general region of the main star-forming cloudsin Taurus which roughly spans the following range of Galacticcoordinates: 166 ◦ ≤ l ≤ ◦ , − ◦ ≤ b ≤ − ◦ for the centraland northern clouds, and 176 ◦ ≤ l ≤ ◦ , − ◦ ≤ b ≤ − ◦ for the southernmost clouds of the complex. This reduces oursample to 388 stars.As explained in the previous section, we are using the astro-metric solution from Gaia-DR2 for most sources in this study.The Gaia-DR2 catalog is unprecedented for the quality andquantity of astrometric measurements, but it still contains somespurious solutions that need to be filtered for an optimal usageof the data (see, e.g., Arenou et al. 2018). We proceeded as fol-lows to obtain an astrometrically clean sample of stars. First, weselect only the sources with visibility_periods_used > RUWE > . This procedure flags 94 sources inour sample, and rejecting them yields the astrometrically cleansample of 284 stars that we use in the forthcoming analysis.
Mode association clustering is a non-parametric statistical ap-proach used for clustering analysis that finds the modes of akernel-based estimate of the density of points in the input space see technical note GAIA-C3-TN-LU-LL-124-01 for more details and groups the data points associated with the same modes intoone cluster with arbitrary shape (see Li et al. 2007, for more de-tails). Clustering by mode identification requires only the band-width σ of the kernel to be defined. When the bandwidth in-creases, the density of points becomes smoother and more pointsare assigned to the same cluster. Thus, a hierarchy of clusters canbe constructed in a bottom-up manner by gradually increasingthe bandwidth of the kernel functions and treating the modesacquired from the preceding (smaller) bandwidths as new in-put to be clustered. Hierarchical Mode Association Clustering(HMAC) has the advantage of elucidating the relationship (andhierarchy) among the various clusters in the sample when com-pared to other commonly used clustering algorithms, for exam-ple k -means (MacQueen 1967) and DBSCAN (Ester et al. 1996).It is used in this study to investigate the structure of the Taurusmolecular cloud complex and to reveal important clues to thestar formation process in this region.In the forthcoming analysis we use the Modalclust pack-age (Cheng & Ray 2014) which implements the HMAC algo-rithm in R programming language. We run HMAC from the phmac routine using a number of smoothing levels (i.e., band-widths) defined as described below, and use the hard.hmac func-tion to access the cluster membership of each star at a givenclustering level. We construct our dataset for the clustering anal-ysis with HMAC using only the five astrometric parameters( α, δ, µ α cos δ, µ δ , (cid:36) ). Many stars in our sample are still lackingradial velocity measurements, thus they will be included onlyin a subsequent discussion (see Sect. 5) to refine our results. Inthe first step of our analysis we rescaled the five astrometric pa-rameters so that the resulting distributions have zero mean andunit variance. We obtain the same results using rescaled and non-rescaled parameters, and we therefore decided to work with thenon-rescaled astrometry as given in the original sources.The hierarchical clustering is performed in a bottom-up man-ner using a sequence of bandwidths σ < σ < ... < σ L (in all Article number, page 6 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry dimensions) that need to increase by a su ffi cient amount to drivethe merging of the existing clusters at level l with l = , , ..., L ,where L is the highest level and merges the full sample into asingle cluster. We construct the sequence of bandwidths σ l asdescribed below. The smallest bandwidth σ that is associatedwith the lowest level is defined based on the uncertainties of theastrometric parameters used in our analysis. The median errorsin the stellar positions (right ascension and declination), propermotions (right ascension and declination), and parallax for thesample of 284 stars are, respectively, 0.093 mas, 0.054 mas,0.224 mas / yr, 0.162 mas / yr, and 0.142 mas. We take the max-imum value among the median uncertainties listed before as thebandwidth for the lowest level (i.e., σ = l > l (after removing theoutliers, see Sect. 4.3), and take the smallest variance observedamong all clusters in this level as the bandwidth for the follow-ing level. If the new bandwidth does not produce cluster mergersin the next level, we use the second smallest variance and repeatthe procedure until at least one merger is produced. This pro-cedure is repeated for all clustering levels until all clusters (andoutliers) are clustered into the only existing mode at level L .Figure 3 shows the resulting hierarchical tree (or dendro-gram) obtained with HMAC for the sample of 284 stars. It re-veals the existence of 21 clusters at the lowest clustering levelwhich we discuss in more detail in Sect. 4.4 (see cluster mem-bership for each star in Table 1). We also note the existence of 48clusters with one single data point, which we consider to be ex-treme outliers because they exhibit di ff erent (unique) propertiescompared to the other clusters in this level. Table 2 summarizesthe results obtained in each clustering level. In Figure 4 we showthat the various clusters obtained from HMAC are indeed as-sociated with di ff erent molecular clouds of the Taurus complex.Although the existence of a few additional outliers that could notbe identified by the current methodology is still apparent, HMAChas proven to be a useful tool to separate the stars that belong tothe several molecular clouds which often exhibit arbitrary shapesand unclear boundaries. The robustness of our clustering resultsobtained with HMAC is tested in Appendix A based on syntheticdata and confirms the results presented in this section. HMAC has shown to be able to detect the most extreme outliersin our sample which have been grouped into clusters of one sin-gle data point. However, we still note the existence of a moredispersed population of stars in some clusters that clearly ex-tends beyond the limits of the molecular clouds (see, e.g., clus-ter 7 in Fig. 4). In this section we revise the membership statusof these sources and reject potential outliers in the individualclusters. In this context, we use the minimum covariance deter-minant (MCD, Rousseeuw & Driessen 1999) method that is arobust estimator of multivariate location and scatter e ffi cient inoutlier detection.Our dataset used for the clustering analysis is stored in an n × p data matrix X = ( x , x , ..., x n ) t with x i = ( x i , x i , ..., x ip ) t for the i -th observation, where n is the number of stars in thesample and p is the number of dimensions (variables) used inour analysis ( p = h observations (out of n ) that returns the covariance matrix withthe lowest determinant. The tolerance ellipse is defined based onthe set of p -dimensional points whose MCD-based robust dis- tances RD ( x ) = (cid:113) ( x − µ ) t Σ − ( x − µ ) (1)equals (cid:113) χ p ,α . We denote µ as the MCD estimate of location, Σ as the MCD covariance matrix, and χ p ,α as the α -quantile of the χ p distribution. Here we use the value of α = .
975 to constructthe tolerance ellipse and identify outliers following the proce-dure described by Hubert & Debruyne (2010).We compute the robust distance of the stars in the clustersderived from the HMAC analysis and remove the outliers basedon the cuto ff threshold (cid:113) χ p , . . This procedure is applied to allclusters in our sample with h > p and repeated at each level ofthe hierarchical tree. The final membership status of each star isgiven in the last column of Table 1. In the following we discuss the individual clusters obtained withHMAC at the lowest level of the hierarchical tree. We presentthe clusters in order of ascending longitude and start with thenorthernmost clusters, as shown in Fig. 4. Figure 5 shows theproper motions and parallaxes of the stars in the various clusters,and Table 3 summarizes the cluster properties.
Cluster 1 is projected towards the northernmost molecularclouds of the complex, L 1517 and L 1519 (see Fig. 6). Itis interesting to note the existence of a more dispersed popu-lation of stars around these clouds with similar properties ofthe “on-cloud” population. We confirm that the mean parallaxof the more dispersed stars ( (cid:36) = . ± .
088 mas) is ingood agreement with the mean parallax of the on-cloud stars( (cid:36) = . ± .
046 mas), and both values are consistent with themean parallax of all stars in the cluster ( (cid:36) = . ± .
045 mas,see Table 3). The proper motions of the two populations are alsoconsistent within 1 mas / yr in both components. Clusters 2 and 3 overlap in the same sky region and they arenot projected towards any cloud of the complex, as shown inFig. 6. Their parallaxes di ff er significantly (see Fig. 5 and Ta-ble 3) which explains the clustering in separate groups. Cluster 4 is a grouping of seven sources located in the northernpart of the Taurus complex. Three of them (V836 Tau, CIDA 8,and CIDA 9B) are projected towards the molecular cloud L 1544(see Fig. 6), and their mean parallax ( (cid:36) = . ± .
095 mas) isconsistent with the mean parallax ( (cid:36) = . ± .
139 mas) of themore dispersed cluster members (RX J0507.2 + + Cluster 5 contains only two stars (2MASS J05010116 + + ff er-ent proper motions (see also Fig. 5), which justifies the clusteringin separate groups. Cluster 5 is therefore not associated with anymolecular cloud of the complex. Cluster 6 consists of only three stars (2MASSJ04154131 + + Article number, page 7 of 28 & A proofs: manuscript no. arXiv_version + ff er significantly fromthe sources in L 1495 (i.e., cluster 7, see below) despite theclose proximity in the plane of the sky (see Figs. 5 and 7). Thissuggests that L 1495 NW and L 1495 are di ff erent structures ofthe Taurus region. Cluster 7 is the most populated cluster in our analysis (39sources) and it is associated with the most prominent molecu-lar cloud of the complex, namely L 1495. The vast majority ofstars in this cluster are located in the direction of the dense coreB 10 of the cloud and many of the more dispersed sources inthe vicinity of L 1495 have been flagged as outliers by the MCDestimator, as illustrated in Figure 7.
Cluster 8 is associated with the filamentary structure connected(in the plane of the sky) to the central part of the L 1495 molec-ular cloud. Schmalzl et al. (2010) divided the filament into fiveclumps (B 211, B 213, B 216, B 217, and B 218) with rangesof 169 ◦ < l < ◦ and − . ◦ < b < − . ◦ (see Fig. 5of their paper). Most of our sources in this cluster are locatedbetween B 213 and B 216 (see Fig. 7), and we detect hintsof a gradient in parallaxes along the filament from l = . ◦ ( (cid:36) = . ± .
210 mas) to l = . ◦ ( (cid:36) = . ± .
162 mas).Figure 5 and Table 3 show that the parallaxes and proper mo-tions of the sources in the filament and central part of L 1495(i.e., cluster 7) are significantly di ff erent, which confirms them asindependent structures. This is also confirmed by the late merg-ing of the two clusters in the hierarchical clustering, as shown inFigure 3. Interestingly, the stars in the filament exhibit parallaxesand proper motions that are more consistent with the sources inthe L 1495 NW cloudlet despite the angular separation of a fewdegrees on the sky. Cluster 9 includes two sources (FU Tau A and FF Tau) whichare projected towards the B 215 star-forming clump (see Fig. 7).Their parallaxes are still consistent with the sources in L 1495(cluster 7), but the proper motions are shifted by about 4 mas / yrin declination (see also Table 3). Clusters 10 has the two stars with the largest proper motions(in right ascension) in the sample (2MASS J04312669 + + ◦ in the plane of the sky (see Fig. 8) and they are not associ-ated with any star-forming clump. The closest clusters in termsof similarity are clusters 6 and 8. Figure 3 shows that the treeclusters merge at level 11 of the hierarchical tree to form onesingle group. Clusters 11 and 12 are spread over 2 degrees in Galactic lon-gitude and each of them contains two stars (see Fig. 8). Thetwo clusters exhibit similar proper motions and parallaxes to thesources in cluster 7 (see Fig. 5). This is confirmed by the earlymerging of these two clusters with cluster 7 at level 2 of the hi-erarchical tree to form one single group (see Fig. 3).
Cluster 13 includes only two sources (DL Tau and IT Tau A).Their positions, proper motions, and parallaxes di ff er from theother clusters in the central region of the complex which jus- tifies the clustering into a di ff erent group. IT Tau is projectedtowards the molecular cloud L 1521 and DL Tau is located in adi ff erent cloudlet separated by about 1 ◦ in the plane of the sky(see Fig. 8), making it unclear whether this cluster is associatedwith any cloud of the complex. The small number of sources andtheir somewhat di ff erent sky positions led us to the decision toexclude it from our forthcoming discussion about the propertiesof the molecular clouds. Clusters 14 and 15 are collectively discussed because they areboth located in the Heiles Cloud 2 and overlap in the plane ofthe sky (see Fig. 8). The sources in these two clusters are spreadover the star-forming clumps L 1527, L 1532, L 1534, and B 220.Their parallax and proper motion values are somewhat di ff erent(see Table 3) and define a di ff erent locus in Fig. 5. This indi-cates the existence of substructures in this cloud that we discussin our forthcoming analysis using the three-dimensional spatialdistribution of the stars (see Sect. 5). Cluster 16 contains 11 stars spread over the molecular cloudsL 1535, L 1529, L 1531, and L 1524 (see Fig. 8). We note that thesources projected towards the various clouds associated with thiscluster exhibit similar properties. For example, the sources pro-jected towards the L 1535, L 1529, L 1531, and L 1524 molec-ular clouds have a mean parallax of (cid:36) = . ± .
105 mas, (cid:36) = . ± .
052 mas, and (cid:36) = . ± .
182 mas, respectively,and they are consistent among themselves. The proper motionsof the various sources are consistent within 1-2 mas / yr. Thus, wediscuss their properties collectively under the same group. Cluster 17 is a grouping of eight sources located north of L 1536(cluster 18, see below) that is not projected towards any cloudin the complex (see Fig. 8). Despite the close proximity (in theplane of the sky) to the L 1536 molecular cloud, we note that thetwo clusters define a di ff erent locus in the proper motion vectordiagram (see Fig. 5). Cluster 18 is one of the most populated clusters in our sampleand it contains 17 stars spread in and around the L 1536 molec-ular cloud. The most dispersed sources in this cluster have beenflagged as outliers by the MCD estimator, as illustrated in Fig-ure 8.
Cluster 19 hosts four sources (T Tau, IRAS 04187 + + + Cluster 20 is the second most populated cluster in our analysis.It includes 25 sources that are spread in and around the L 1551molecular cloud (see Fig. 9). The late merging of clusters 19 and20 in the hierarchical tree (level 13, see Fig. 3) and the di ff erentproper motions (see Fig. 5) suggest that L 1551 and the T Taucloud are indeed independent structures of the southern regionof the Taurus complex. Article number, page 8 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
Cluster 21 includes five sources projected towards the L 1558molecular cloud (see Fig. 9). As shown in Fig. 5 the sources inthis cluster exhibit the smallest parallaxes making it the mostdistant cluster in our sample (see also discussion in Sect. 5).
Article number, page 9 of 28 & A proofs: manuscript no. arXiv_version c l u s t e r i ng l e v e l C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r C l u s t e r Fig. 3.
Hierarchical tree (or dendrogram) obtained with HMAC for the sample of 284 stars. The di ff erent colors indicate the various clusters atthe lowest clustering level of the tree. Outliers that result directly from the HMAC analysis are shown in black. Table 2.
Results obtained with HMAC for each clustering level.
Level 1 2 3 4 5 6 7 8 9 10 11 12 13 14 σ l Notes.
We provide the bandwidth, number of clusters, and outliers for each clustering level of the hierarchical tree in Figure 3.Article number, page 10 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
183 182 181 180 179 178 177 176 175 174 173 172 171 170 169 168 167 166−22−20−18−16−14−12−10−8−6 llllllllll ll lll ll lllll llllllll ll lllll ll ll ll l lll lll l lll llll l ll lll l ll llll llll l llll ll ll ll lllll l llll ll ll lll lllll llll l l lll lllll l ll ll llllll lllll l llll lll lll llll lll llll ll lll ll llllll lll ll lllll lll ll llll ll lllll lllllllllll llll lll lllllll lll llll lllll lllllllllllll ll lllll llllllll lllll ll ll lll ll lll llll lllll llllll llll ll ll ll lllllll l l lll lllll ll ll lll llll llll lllllll l llll ll lll l lllllll llll llll llll ll lllllllllllllll llll lll lllllllllll Av (mag) L1495L1506L1517L1520L1521L1524L1527L1531L1534L1535L1536L1537L1538L1539L1540L1542L1543L1544L1551L1558 B10B210B213B215 B216B218 lllllllllllllllllllll l ( (cid:176) ) b ( (cid:176) ) Fig. 4.
Location of the 284 stars in our sample overlaid on the extinction map from Dobashi et al. (2005) in Galactic coordinates. The di ff erentcolors represent the sources that belong to the 21 clusters identified at the lowest level of the hierarchical tree obtained with HMAC. Outliers thatresult directly from the HMAC analysis are shown as black asteriks. The position of the most prominent clouds (Barnard 1927; Lynds 1962) areindicated in the diagram with black triangles. ll l ll llll l ll ll l llll llll ll ll lllllll ll ll lll ll lll lll l llll l lll l l lllll ll l ll ll l l l llll ll ll lllll llll lll llllll lll llll l lllllll ll lllll ll llllllll lllll lll l lll lll ll ll lll lllll lllll ll lll llll − − − − m a cos d (mas/yr) md ( m a s / y r) ll l ll lll l l ll ll l llll llll ll ll lllllll ll ll lll ll lll lll l llll l lll l l ll lll ll l ll ll l l l llll ll ll ll lll llll lll llllll lll ll ll l lllll ll ll lllll ll lllll lll lllll lll l lll lll ll ll lll lllll lllll ll lll llll ll l ll lll l l ll ll l llll llll ll ll lllllll ll ll lll ll lll lll l llll l lll l l ll lll ll l ll ll l l l llll ll ll ll lll llll lll llllll lll ll ll l lllll ll ll lllll ll lllll lll lllll lll l lll lll ll ll lll lllll lllll ll lll llll llll ll llllllll lll llllll l lll lll ll lll ll l ll llll l ll ll ll llll ll ll lllllll llll lll l lll lll lll ll ll ll ll ll l llll ll lllll ll lllll llll ll lllll l ll lll l l lll ll lllll l lll lll ll ll lll lllll lllll ll ll l llll ll l ll llll l ll ll l llll llll ll ll lllllll ll ll lll ll lll lll l llll l lll l l lllll ll l ll ll l l l llll ll ll lllll llll lll llllll lll llll l lllllll ll lllll ll llllllll lllll lll l lll lll ll ll lll lllll lllll ll lll llll m a cos d (mas/yr) v ( m a s ) ll l ll lll l l ll ll l llll llll ll ll lllllll ll ll lll ll lll lll l llll l lll l l ll lll ll l ll ll l l l llll ll ll ll lll llll lll llllll lll ll ll l lllll ll ll lllll ll lllll lll lllll lll l lll lll ll ll lll lllll lllll ll lll llll ll l ll lll l l ll ll l llll llll ll ll lllllll ll ll lll ll lll lll l llll l lll l l ll lll ll l ll ll l l l llll ll ll ll lll llll lll llllll lll ll ll l lllll ll ll lllll ll lllll lll lllll lll l lll lll ll ll lll lllll lllll ll lll llllllll ll lllll lll lll llll ll l lll lll ll lll ll l ll lll l l ll ll ll llll ll ll lllllll llll lll l l ll lll lll ll ll ll ll ll l l lll ll lll ll ll ll lll llll ll lllll l ll lll l l lll ll ll lll l lll lll ll ll lll lllll lllll ll ll l llll l lll l ll llll ll l l l llllllllll ll ll lll ll l ll llll l l lll ll llllll ll ll llll ll lll l lll lll lllll l l l lll ll ll llll ll llll ll lll lllll lllll ll ll lll lllllllllllll lll lll l lllll lllll ll ll l lll lll lllll l lllll −25 −20 −15 −10 m d (mas/yr) v ( m a s ) l lll l ll llll ll l l l lllll lllll ll ll lll ll l ll llll l l lll ll llllll ll ll llll ll lll l lll lll lllll l l l lll ll ll l lll ll l lll ll l ll lllll lllll ll ll lll l lllllll lllll lll lll l lllll ll lll ll ll l lll lll lllll l llllll lll l ll llll ll l l l lllll lllll ll ll lll ll l ll llll l l lll ll llllll ll ll llll ll lll l lll lll lllll l l l lll ll ll l lll ll l lll ll l ll lllll lllll ll ll lll l lllllll lllll lll lll l lllll ll lll ll ll l lll lll lllll l llllllll l lllllll lll ll l lllll ll lll lll ll l ll l lll l ll llll ll l llll lllll ll ll lll ll llll lll l lll lllll ll ll ll ll l l l lll ll l l llll lll lll lllll ll lll l l l l llllll lll l l lll ll l lll ll ll lll ll ll l lll lll lllll l lllll Fig. 5.
Clustering of the stars in the space of proper motions and parallaxes for the 21 clusters obtained with HMAC (after removing the outliers).Article number, page 11 of 28 & A proofs: manuscript no. arXiv_version
180 179 178 177 176 175 174 173 172 171 170−12−11−10−9−8−7−6 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l Av (mag)(mag)
30 mas/yr l ( (cid:176) ) b ( (cid:176) ) Fig. 6.
Location of the sources in clusters 1, 2, 3, 4, and 5 overlaid on the extinction map of Dobashi et al. (2005) in Galactic coordinates. The sizeof the symbols has been rescaled between the minimum and maximum parallaxes observed in each cluster to better distinguish between the closest(big symbols) and most remote (small symbols) members within each cluster. Filled and open symbols indicate, respectively, cluster members andoutliers that have been removed in our analysis (see Sect. 4.3). The vectors indicate the stellar proper motions converted to the Galactic referencesystem (not corrected for solar motion). The position of the most prominent clouds (Barnard 1927; Lynds 1962) is indicated in the diagram withblack triangles.
173 172 171 170 169 168 167 166−19−18−17−16−15−14−13 l l l l l l l l l l l l l l l l l lll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l lll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l l Av (mag)(mag)
30 mas/yr l ( (cid:176) ) b ( (cid:176) ) Fig. 7.
Same as Figure 6, but for clusters 6, 7, 8, and 9.Article number, page 12 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
178 177 176 175 174 173 172 171 170−18−17−16−15−14−13−12 l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l l lll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l ll l l Av (mag)(mag)
30 mas/yr l ( (cid:176) ) b ( (cid:176) ) Fig. 8.
Same as Figure 6, but for clusters 10, 11, 12, 13, 14, 15, 16, 17, and 18.
183 182 181 180 179 178 177 176−22−21−20−19−18−17−16 l llll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l llll l l l l l l l l l l l l l l l l l l l l l l l l l l l l l (mag) Av (mag)
30 mas/yr l ( (cid:176) ) b ( (cid:176) ) Fig. 9.
Same as Figure 6, but for clusters 19, 20, and 21. Article number, page 13 of 28 & A p r oo f s : m a nu s c r i p t no . a r X i v_v e r s i on Table 3.
Properties of the clusters obtained with HMAC.
Cluster N N α δ l b µ α cos δ µ δ (cid:36) Molecular Clouds(h:m:s) ( ◦ (cid:48) (cid:48)(cid:48) ) (deg) (deg) (mas / yr) (mas / yr) (mas)Mean ± SEM Median SD Mean ± SEM Median SD Mean ± SEM Median SD1 21 14 04:57:04.1 30:05:31 173.0 -8.0 4 . ± .
095 4.247 0.356 − . ± .
125 -24.644 0.470 6 . ± .
045 6.325 0.167 L 1517, L 15192 3 3 04:49:17.7 29:05:52 172.8 -10.0 7 . ± .
262 7.185 0.453 − . ± .
117 -25.800 0.203 5 . ± .
045 5.998 0.0783 9 7 04:48:29.6 29:25:15 172.4 -9.9 5 . ± .
200 5.336 0.529 − . ± .
126 -24.732 0.334 6 . ± .
089 6.316 0.2364 6 6 05:06:04.2 25:01:35 178.3 -9.5 2 . ± .
263 2.709 0.645 − . ± .
237 -17.273 0.580 5 . ± .
076 5.842 0.185 L 15445 2 2 05:01:50.5 25:00:37 177.8 -10.3 4 . ± .
112 4.923 0.522 − . ± .
085 -26.374 0.214 6 . ± .
087 6.304 0.1046 3 3 04:15:42.3 29:11:41 167.7 -15.4 12 . ± .
097 12.183 0.168 − . ± .
436 -17.754 0.755 6 . ± .
042 6.397 0.073 L 1495 NW7 54 39 04:17:16.9 28:08:55 168.7 -15.9 8 . ± .
157 8.614 0.981 − . ± .
179 -25.347 1.116 7 . ± .
037 7.692 0.233 L 14958 13 9 04:23:36.1 26:44:03 170.8 -15.8 11 . ± .
180 11.196 0.541 − . ± .
184 -17.730 0.552 6 . ± .
072 6.235 0.215 B 213, B 2169 2 2 04:23:37.3 24:59:38 172.2 -17.0 6 . ± .
209 6.907 0.023 − . ± .
129 -21.362 0.672 7 . ± .
106 7.741 0.226 B 21510 2 2 04:31:57.7 27:24:45 171.6 -14.0 13 . ± .
602 13.973 0.030 − . ± .
469 -20.344 0.906 6 . ± .
452 6.903 0.23111 2 2 04:31:36.8 27:10:48 171.7 -14.2 8 . ± .
123 8.803 0.736 − . ± .
105 -27.480 0.191 7 . ± .
089 7.780 0.18912 2 2 04:36:26.7 27:03:04 172.5 -13.5 8 . ± .
133 8.743 0.218 − . ± .
100 -27.082 0.186 7 . ± .
086 7.820 0.06913 2 2 04:33:46.9 25:47:03 173.1 -14.7 9 . ± .
119 9.397 0.135 − . ± .
093 -17.878 0.825 6 . ± .
084 6.255 0.10314 9 7 04:40:22.3 25:50:19 174.1 -13.6 6 . ± .
194 6.628 0.514 − . ± .
310 -21.340 0.820 7 . ± .
081 7.122 0.215 Heiles Cloud 2: L 1527, L 1532, L 1534, B 22015 5 5 04:41:38.0 25:38:26 174.4 -13.5 4 . ± .
237 4.727 0.529 − . ± .
155 -19.630 0.347 7 . ± .
084 7.366 0.188 Heiles Cloud 2: L 1527, L 1532, L 1534, B 22016 23 11 04:33:12.4 24:19:57 174.2 -15.8 6 . ± .
236 6.651 0.783 − . ± .
194 -21.444 0.642 7 . ± .
046 7.710 0.152 L 1535, L 1529, L 1531, L 152417 11 8 04:38:42.0 23:38:14 175.6 -15.3 8 . ± .
131 8.548 0.370 − . ± .
182 -21.570 0.516 7 . ± .
057 7.943 0.16118 24 17 04:34:50.4 22:49:58 175.6 -16.5 10 . ± .
280 10.082 1.156 − . ± .
238 -16.770 0.979 6 . ± .
042 6.212 0.171 L 153619 4 4 04:22:00.2 19:33:57 176.2 -20.9 6 . ± .
253 6.586 0.506 − . ± .
355 -12.082 0.711 6 . ± .
136 6.845 0.272 T Tau cloud20 34 24 04:32:59.4 17:57:15 179.3 -19.9 12 . ± .
168 12.118 0.822 − . ± .
236 -18.943 1.157 6 . ± .
032 6.908 0.158 L 155121 5 5 04:47:09.1 17:05:31 182.2 -17.8 4 . ± .
114 4.757 0.255 − . ± .
269 -13.254 0.602 5 . ± .
081 5.058 0.180 L 1558
Notes.
We list the initial number of members N , final number of members N (after removing outliers, see Sect. 4.3), position (equatorial and Galactic coordinates), proper motion, trigonometricparallax, and the molecular clouds associated with each cluster. We also provide the mean, standard error of the mean (SEM), median and standard deviation (SD) values of the proper motion, andtrigonometric parallax distributions of each cluster. The standard deviation given in the table represents the di ff erence between the individual measurements when the cluster has only two stars. A r ti c l e nu m b e r , p a g e f . A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry In a recent study Luhman (2018) divided a sample of Taurusstars into four populations with similar properties of proper mo-tions, parallaxes, and photometry. Two points are worth men-tioning here before comparing our results with that study. First,the two studies had distinct objectives which explains the dif-ferent strategy employed to explore the Gaia-DR2 data in theTaurus region. Luhman (2018) performed an extensive analysisto improve the census of Taurus stars by refining the sample ofknown members and identifying new candidates. In this context,the sources were not filtered (as done in the present study) tominimize as much as possible the rejection of potential membersof the Taurus region. On the other hand, we decided to apply theRUWE selection criterion in the present study, which is a moreconservative approach to filter the stars in the sample. This pro-cedure is likely to remove some bona fide members of the Tau-rus region, but at the same time it minimizes the number of starswith discrepant measurements in the sample due to a poor fit ofthe Gaia-DR2 astrometric solution or to non-membership. Thiswas made necessary to derive more accurate distances and spa-tial velocities for the subgroups, as we discuss in more detail inSection 5. Second, the methodology used by Luhman (2018) toidentify the four populations of stars is based on a manual selec-tion of the sources with similar properties rather than a cluster-ing algorithm. For these reasons, the number of sources and thesubgroups themselves identified in the two studies di ff er fromeach other, and the comparison between the two solutions is notstraightforward. We proceeded as follows to compare the resultsgiven by the two studies.To begin with, we cross-matched our sample of cluster mem-bers with the list of stars from Luhman (2018). Figure 10 showsthe distribution of Taurus stars in the four populations classifiedby Luhman (2018) among the various clusters obtained in ourclustering analysis with HMAC. We note that the HMAC clus-ters obtained in our analysis group only stars from one of thefour populations discussed by Luhman (2018) (i.e., we do notsee a mix of populations in the various clusters). The clustersderived from the HMAC analysis that contain only a subset ofthe sample of stars given by Luhman (2018), due to the di ff er-ent selection criteria used to filter the Gaia-DR2 sources in eachstudy, as explained before.Another interesting point to mention is that the four popula-tions of Luhman (2018) are closely related to the HMAC clus-tering results that we obtained at level 12 of the hierarchical tree(see Fig. 3), as explained below. At this level we have six groupsof clusters that include all 21 clusters discussed in Sect. 4.4 (seealso Table 2). We label them as follows (from the left to right inFig. 3): Group A (includes clusters 6, 8, 10, 13, and 18), Group B(includes cluster 20), Group C (includes clusters 1, 2, 3, 4, and5), Group D (includes cluster 19), Group E (includes cluster 21),and Group F (includes clusters 7, 9, 11, 12, 14, 15, 16, and 17).We note from Fig. 10 that groups A, B and groups D, F corre-spond to the blue and red populations, respectively. The posi-tion of the stars was not used by Luhman (2018) to define thevarious populations, which explains why the red and blue pop-ulations are separated into several groups in the HMAC analy-sis. Group C represents the cyan population (i.e., the northernclouds) and Group E is associated with the green population.We note that 51 stars from the sample of 62 new candidatemembers given in Table 6 of Luhman (2018) have been retainedfor the clustering analysis after applying the selection criteriadescribed in Sect. 4.1. Twenty-six of them were selected in ouranalysis and assigned to clusters 1, 2, 3, 5, 7, 10, 11, 12, 17, HMAC cluster N u m b e r o f s t a r s Population(Luhman 2018) blueredgreencyan
Fig. 10.
Comparison of the HMAC clustering results obtained in thisstudy with the four populations of Taurus stars (blue, red, green, andcyan) identified by Luhman (2018) from the sample of known Taurusmembers (Table 1 of that paper). The bar chart indicates the number ofstars of each population that are in common with the HMAC clusters.
20, and 21. In particular, we note that cluster 2 is formed exclu-sively by new candidate members, which explains in Figure 10the absence of known Taurus members of the four populationsidentified by Luhman (2018). In addition, we find 16 stars in thesample of Joncour et al. (2017) that are not included in the listof known members given by Luhman (2018). Only five of themsatisfy our selection criteria described in Section 4.1, and all ofthem have been identified as outliers in the HMAC clusteringanalysis. Table 1 lists the membership status of each star in oursample given by Joncour et al. (2017) and Luhman (2018) com-pared to the results obtained in this study.Thus, we conclude that our methodology based on theHMAC analysis is able to recover the four populations of Tau-rus stars that were previously identified by Luhman (2018), andthat the two studies return consistent results with respect to theclustering of the stars in several substructures across the Tauruscomplex.
5. Discussion
In this section we convert the observables used in our clus-tering analysis (positions, proper motions, and parallaxes) intodistances, three-dimensional positions, and spatial velocities todiscuss the properties of the stars projected against the variousmolecular clouds in this region. The forthcoming discussion willbe restricted to the 13 clusters listed in Table 3 that are associ-ated with a molecular cloud of the complex, and hereafter weuse the molecular cloud identifiers when refering to the individ-ual clusters rather than the cluster numbering from the HMACterminology.First, we convert the trigonometric parallaxes and proper mo-tions of individual stars into distances and two-dimensional tan-
Article number, page 15 of 28 & A proofs: manuscript no. arXiv_version −10 0 10 20 . . . . . . Radial Velocity (km/s) D en s i t y before removing outliersafter removing outliers Fig. 11.
Kernel density estimate (for a kernel bandwidth of 1 km / s)of the distribution of radial velocity measurements collected from theliterature for 102 stars in the sample of cluster members obtained in ourclustering analysis with HMAC. The tick marks in the horizontal axisindicate the individual measurements of each star. gential velocities using Bayesian inference and following the on-line tutorials available in the Gaia archive (see Luri et al. 2018).This procedure uses an exponentially decreasing space densityprior for the distance with length scale L = .
35 kpc (Bailer-Jones 2015; Astraatmadja & Bailer-Jones 2016) and a beta func-tion for the prior over speed. This methodology takes the fullcovariance matrix of the observables into account to estimateour uncertainties on the final distances and tangential velocitiesof the stars. Then we use the resulting distances to compute thethree-dimensional position
XYZ of the stars in a reference sys-tem that has its origin at the Sun, where X points to the Galacticcenter, Y points in the direction of Galactic rotation, and Z pointsto the Galactic north pole to form a right-handed system.Second, we combine the resulting two-dimensional tangen-tial velocities with the radial velocities collected from the litera-ture (see Sect. 2) to derive the UVW spatial velocity of the starsin the same reference system as described above and followingthe transformation outlined by Johnson & Soderblom (1987). Wenote that 102 stars among those that were confirmed as clustermembers in our previous analysis have published radial velocitymeasurements in the literature. Figure 11 shows the distributionof radial velocities in our sample. We flag the radial velocitiesfor ten stars as outliers based on the interquartile range (IQR)criterium. These measurements lie over 1 . ∗ IQR below the firstquartile (Q1) or above the third quartile (Q3) of the distribution,and in many cases they are likely to be a ff ected by binarity. Thus,we discard the radial velocities of LkCa 1, Anon 1, XEST 20-066, LkCa 3 (V1098 Tau), Hubble 4 (V1023 Tau), MHO 5,HD 28867, DQ Tau, 2MASS J04482128 + UVW spatial velocities (but we still retainthem as cluster members in the forthcoming discussion based onour previous results from Sect. 4).Table 4 lists the individual distances, three-dimensionalpositions and spatial velocities for the 174 stars that wereconfirmed as cluster members (i.e., Member = see also GAIA-C8-TN-LU-MPIA-CBJ-081 for more details We also provide in this table the spatial velocities uvw cor-rected for the velocity of the Sun relative to the local stan-dard of rest (LSR) using the solar motion of ( U , V , W ) (cid:12) = (11 . + . − . , . + . − . , . + . − . ) km / s from Schönrich et al.(2010). The formal uncertainties on the distances and spatial ve-locities provided in this paper are computed from the 16% and84% quantiles of the corresponding distributions, which roughlyprovide us with a 1 σ standard deviation. Although recent stud-ies based on Bayesian inference (e.g., Bailer-Jones 2015) rec-ommend using a 90% confidence interval (e.g., 5% and 95%quantiles) we decided to proceed as explained above to bettercompare our results with previous studies that only present the1 σ uncertainty on their results.We provide in Tables 5 and 6 the distance estimate and themean spatial velocity of the stars projected towards the molecu-lar clouds represented in our sample. The Bayesian distance foreach cloud is computed from the individual parallaxes and theiruncertainties based on the online tutorials for inference of clusterdistance available in the Gaia archive (see also Luri et al. 2018)and using the same prior over the distance as before. We also listthe distances obtained by the more common approach of sim-ply inverting the mean parallax of each molecular cloud. In thelatter case it is important to take into account the possible sys-tematic errors in the Gaia-DR2 parallaxes that largely dominateour sample. Although we have already included the systematicerrors of 0.1 mas in the uncertainties of Gaia-DR2 parallaxes (asdescribed in Sect. 3), this e ff ect is still present in the mean paral-laxes listed in Table 3 in the sense that averaging the individualparallaxes of cloud members will not reduce the final uncertain-ties below the 0.1 mas level. We note that the uncertainties onthe mean parallaxes given in Table 3 are much smaller than thethe systematic error of 0.1 mas for most clusters (i.e., molecu-lar clouds) in our sample. In these cases we used 0.1 mas as theuncertainty for the mean parallax to estimate the (asymmetric)uncertainties in the distances derived from the inversion method.Figure 12 shows the posterior probability density functionobtained for each sample of stars associated with a molecularcloud together with the distance estimates given in Table 5. In-terestingly, we note that the posterior probability distribution ofthe various clouds exhibit somewhat di ff erent shapes. For exam-ple, L 1495, the most populated cloud in the sample, has a verynarrow distribution (e.g., compared with L 1495 NW), which in-deed gives the most precise distance estimate in our analysis.Here we report the Bayesian estimates given in Table 5 as ourfinal results for the distance, because this methodology allowsfor a proper handling of the uncertainties in our data. Article number, page 16 of 28 . A . B . G a lli e t a l . : S t r u c t u r ea ndk i n e m a ti c s o f t h e T a u r u ss t a r-f o r m i ng r e g i on fr o m G a i a - D R a nd V L B I a s t r o m e t r y Table 4.
Distance and spatial velocity for the 174 confirmed cluster members. d /(cid:36) d X Y Z U V W u v w V LSRr (pc) (pc) (pc) (pc) (pc) (km / s) (km / s) (km / s) (km / s) (km / s) (km / s) (km / s)2MASS J04131414 + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . + + B 130 . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . ± . + + B 123 . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . + . + . − . . + . − . − . + . − . . + . − . − . + . − . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . + . + . − . . + . − . − . + . − . . + . − . − . + . − . + + . + . − . . + . − . − . + . − . . + . − . − . + . − . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . ± . + . + . − . . + . − . − . + . − . . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . − . + . − . . ± . Notes.
We provide for each star the 2MASS and Gaia-DR2 identifiers, distance obtained by inverting the parallax, distance derived from the Bayesian approach (see Sect. 5),
XYZ positions,
UVW components of the Galactic spatial velocity, uvw components of the peculiar velocity (with respect to the LSR), and radial velocity corrected for the solar motion. (This table will be available in itsentirety in machine readable form.) A r ti c l e nu m b e r , p a g e f & A proofs: manuscript no. arXiv_version
Our results show that the complex of clouds formed byL 1535, L 1529, L 1531, L 1524 and the B 215 clump are theclosest structures to the Sun in the Taurus region ( d = . + . − . and d = . + . − . , respectively). This is consistent with the dis-tance of d = . + . − . pc obtained previously by Galli et al.(2018) for L 1531 based on the VLBI trigonometric parallax ofV807 Tau. The GOBELINS survey in Taurus targeted the cen-tral and southern clouds of the complex, so Galli et al. (2018)presented L 1536 as the farthest cloud in the region based onthe VLBI parallax of HP Tau G2 ( d = . + . − . pc). This dis-tance estimate is in very good agreement with the result of d = . + . − . pc that we derive in this study for L 1536, but our cur-rent analysis in this paper suggests that L 1558 ( d = . + . − . pc)should hereafter be considered as the most remote molecularcloud in Taurus. In general, we see a good agreement betweenthe results reported in the two studies. The only exception isL 1519 for which Galli et al. (2018) used the Gaia-DR1 par-allaxes of three stars and the VLBI parallax of HD 282630 (seediscussion of this source in Sect. 3) to estimate the distance to thecloud. The reported distance of d = . + . − . pc is not consistentwith the new result that we derive in this paper using the moreaccurate and precise Gaia-DR2 parallaxes. The molecular cloudL 1513 listed in Table 10 of that study is not discussed here,because the only source projected towards this cloud (namelyUY Aur) was flagged as a potential outlier in our clustering anal-ysis presented in Sect. 4. In the following we investigate the internal and relative motionsof the stars projected towards the various molecular clouds in thecomplex. Figure 13 shows the spatial velocity of the stars pro-jected onto the XZ, YZ, and ZX planes after correcting for thesolar motion. The stellar motions appear less organized whenwe remove the velocity of the Sun relative to the LSR, but abulk motion for the various clouds in the complex is still ap-parent, as illustrated in Figure 13. It is interesting to note thatthe peculiar velocities of the stars projected onto the XY, YZ,and ZX planes reveal the existence of two groups of molecu-lar clouds with velocity vectors pointing towards di ff erent direc-tions. One of these groups is formed by L 1495, L 1535, L 1529,L 1531, L 1524, B 215, and Heiles Cloud 2 where the velocityvectors point towards the bottom left corner of the ZX plane, forexample. Not surprisingly, these clouds (i.e., clusters) are clus-tered under the same group in the HMAC hierarchical tree atlevel 12 (see Fig. 3). This suggests a potentially di ff erent forma-tion episode for the various clouds in the complex. Interestingly,this e ff ect is also apparent in the three-dimensional space of ve-locities (see Fig. 14). The Taurus subgroups listed above exhibitW velocities that are lower by about 2-3 km / s compared to thestars in L 1551, L 1536, B 213, and B 216, among others, whosevelocity vectors point towards a di ff erent direction.We present in Table 7 the relative motion of the variousclouds in the complex. The T Tau cloud is not included in thisdiscussion to avoid a biased result based on only one source withmeasured radial velocity. The relative motion among the variousclouds range from about 1 to 5 km / s. The highest value that weobserve (5 . ± . / s) occurs between L 1551 and the B 215clump. The relative motion between the northernmost cloud (i.e.,L 1517 and L 1519) and the southernmost cloud (i.e., L 1551)is only 3 . ± . / s. We measure a significant relative bulkmotion of 4 . ± . / s between the core of L 1495 and its fil-ament (i.e., B 213 and B 216) confirming that they are indeed independent structures. It is also interesting to note that they ex-hibit diverging motions in the Z direction (see also Fig. 13). Inaddition, we also measure a significant non-zero relative motionof ∆ v = − . ± . / s in the v component of the peculiar ve-locity of the stars in the two subgroups of the Heiles Cloud 2(i.e., clusters 14 and 15), which justifies our decision to discussthem separately throughout this paper. The high values that wefind here for the relative motions between some clouds of thecomplex (see also Luhman 2018) are consistent with the veloc-ity di ff erence among Taurus subgroups reported in the past byJones & Herbig (1979) and the velocity dispersion of 6 km / sused by Bertout & Genova (2006) in the convergent point searchmethod under the assumption that all stars (independent of themolecular cloud to which they belong) are comoving.Let us now assess the quantitative importance of random andorganized motions within the complex. We investigate the poten-tial expansion and rotation e ff ects in the Taurus region followingthe procedure described by Rivera et al. (2015). First, we com-pute the unit position vector ˆr ∗ = r ∗ / | r ∗ | for each star that rep-resents the distance of a given star with respect to the center ofthe corresponding molecular cloud to which it belongs. Second,we compute the velocity δ v ∗ of each star relative to its molecu-lar cloud. The dot product between the two quantities ( ˆr ∗ · δ v ∗ )is large and positive (negative) if the group is undergoing ex-pansion (contraction). Analogously, the cross product ( ˆr ∗ × δ v ∗ )stands as a proxy for the angular momentum of the group andit is large (small) in the case of significant (negligible) rotatione ff ects. We compute the dot and cross product for all stars inour sample with respect to the molecular clouds to which theybelong and take the mean of the resulting values as a proxy forthe expansion (contraction) and rotation velocities of each group.We run these calculations for all molecular clouds with a mini-mum of three representative stars with known spatial velocities(i.e., with measured radial velocities). The results of our analy-sis are presented in Table 8. We note that the resulting quantitiesare consistent with zero (within 5 σ of the corresponding uncer-tainties) suggesting that the expansion and rotation e ff ects in theindividual molecular clouds are negligible.We repeat the same experiment as described above but usingthe full sample of cluster members with measured radial veloc-ities (92 stars, see Sect. 5.1) to detect large-scale expansion androtation e ff ects in the Taurus complex. The resulting expansion(contraction) velocity of 0 . ± . / s for the entire complexis consistent with zero. This implies that the internal motionsin the radial direction of the complex are dominated by randommotions rather than an organized expansion or contraction pat-tern. On the other hand, the non-zero rotational velocity that wederive here ( | ˆr ∗ × δ v ∗ | = . ± . / s, see Table 8) suggests theexistence of possible rotation e ff ects in the Taurus complex as awhole. The rotation rate that we derive is nevertheless lower thanthe result of v rot (cid:39) / s obtained previously by Rivera et al.(2015) using a sample of only seven stars with VLBI astrome-try. However, it is important to mention that this number is stillsmaller than the observed three-dimensional velocity dispersionof the stars in our sample ( σ = (cid:112) σ u + σ v + σ w = . / s, seeTable 5). This value suggests that the rotation contributes signif-icantly to the velocity dispersion, but there is also an importantcontribution from random motions within the complex.The relative distances between the Taurus subgroups rangefrom about 4 to 50 pc with a median inter-cloud distance of25 pc (see Table 7). The crossing time between the various sub-groups in this region is on the order of several Myr. For example,if we assume a common origin and birthplace for L 1495 andL 1544, a timescale of about 20 Myr is necessary to explain their Article number, page 18 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
150 155 160 165 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1517, L1519 165 170 175 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1544 150 155 160 165 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1495 NW125 130 135 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1495 155 160 165 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) B213, B216 120 125 130 135 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) B215135 140 145 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) Heiles Cloud 2(Cluster . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) Heiles Cloud 2(Cluster . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1535, L1529,L1531, L1524155 160 165 170 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1536 140 145 150 155 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) TTau Cloud 140 145 150 155 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1551190 195 200 205 . . . . . . Distance (pc) P o s t e r i o r ( no r m a li z ed ) L1558
Fig. 12.
Posterior probability density function of the distance to the various molecular clouds of the Taurus complex. The solid and dashed linesindicate, respectively, the distances obtained from the Bayesian approach (see Sect. 5) and by inverting the mean parallax.Article number, page 19 of 28 & A proofs: manuscript no. arXiv_version
Table 5.
Distance of the Taurus molecular clouds.
Molecular Cloud Cluster N Distance X , Y , Z (pc) (pc)Inversion Bayesian Mean ± SEM Median SDL 1517, L 1519 1 14 159 . + . − . . + . − . ( − . , . , − . ± (1 . , . , .
3) ( − . , . , − .
1) (4 . , . , . . + . − . . + . − . ( − . , . , − . ± (2 . , . , .
5) ( − . , . , − .
7) (5 . , . , . . + . − . . + . − . ( − . , . , − . ± (0 . , . , .
2) ( − . , . , − .
7) (1 . , . , . . + . − . . + . − . ( − . , . , − . ± (0 . , . , .
3) ( − . , . , − .
9) (3 . , . , . . + . − . . + . − . ( − . , . , − . ± (1 . , . , .
7) ( − . , . , − .
1) (5 . , . , . . + . − . . + . − . ( − . , . , − . ± (1 . , . , .
5) ( − . , . , − .
8) (2 . , . , . . + . − . . + . − . ( − . , . , − . ± (1 . , . , .
5) ( − . , . , − .
9) (4 . , . , . . + . − . . + . − . ( − . , . , − . ± (1 . , . , .
3) ( − . , . , − .
9) (3 . , . , . . + . − . . + . − . ( − . , . , − . ± (0 . , . , .
3) ( − . , . , − .
2) (2 . , . , . . + . − . . + . − . ( − . , . , − . ± (1 . , . , .
5) ( − . , . , − .
5) (6 . , . , . . + . − . . + . − . ( − . , . , − . ± (2 . , . , .
0) ( − . , . , − .
1) (5 . , . , . . + . − . . + . − . ( − . , . , − . ± (0 . , . , .
2) ( − . , . , − .
3) (3 . , . , . . + . − . . + . − . ( − . , − . , − . ± (3 . , . , .
8) ( − . , − . , − .
6) (7 . , . , . Notes.
We provide for each cloud its identifier, corresponding cluster in the HMAC analysis (see Sect. 4), number of stars with measured parallax,distance obtained from the inverse of the mean parallax of the cloud (see Table 3), distance obtained from the Bayesian approach (see Sect. 5),mean, standard error of the mean (SEM), median, and standard deviation of the three-dimensional cartesian XYZ coordinates of the cloud center.
Table 6.
Spatial velocity of the Taurus molecular clouds.
Molecular Cloud Cluster
N U V W V space (km / s) (km / s) (km / s) (km / s)Mean ± SEM Median SD Mean ± SEM Median SD Mean ± SEM Median SD Mean ± SEM Median SDL 1517, L 1519 1 2 − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . .
3L 1551 20 12 − . ± . − . − . ± . − . − . ± . − . . ± . . − . ± . − . − . ± . − . − . ± . − . . ± . . Notes.
We provide for each cloud its identifier, corresponding cluster in the HMAC analysis (see Sect. 4), number of stars with measured radialvelocity, mean, standard error of the mean (SEM), median, and standard deviation of the Galactic
UVW velocity components (not corrected for thesolar motion). The standard deviation value given in the table represents the di ff erence between the individual measurements when the molecularcloud has only two representative stars. present-day positions given their relative distance of 50 . ± . . ± . / s. This number greatly exceedsthe median age of Taurus stars ( ∼ Article number, page 20 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry lllll lll lllll lll ll lll lll lllll l l l llll llll lll ll ll ll lll l ll llllll l lll l lll ll l ll lll lllllll −180 −160 −140 −120 −100
X (pc) Y ( p c )
10 km/sL1517L1519L1544 L1495B213,B216 B215Heiles Cloud(cluster 14) Heiles Cloud(cluster 15) L1535,L1529L1531,L1524L1536 TTau L1551 lllllllllllllll ll ll l ll llll ll lllll llllllllll ll llll llll lllll ll llll llll llll llllllll llll − − − − − Y (pc) Z ( p c ) lllll lll ll lll ll l lllll lll llll l l ll llll llll lll ll llll llll ll lll lll l lll llll ll l ll lll lll l lll −60 −50 −40 −30 −20 − − − − Z (pc) X ( p c ) Fig. 13.
Peculiar velocity of the stars in the various clouds of the Taurus complex projected onto the XY, YZ, and ZX planes.Article number, page 21 of 28 & A proofs: manuscript no. arXiv_version l l lll l ll lll l ll ll ll l ll ll l ll ll l l ll ll ll l ll l ll l l lll l l lll ll lll l l llll l lll lll ll ll ll l ll l llll −20 −18 −16 −14 −12 − − − − − − U (km/s) V ( k m / s ) ll L1495 ll B213B216 ll TTau ll B215 ll L1535,L1529,L1531,L1524 ll L1551 ll L1536 ll Heiles Cloud(cluster 14) ll Heiles Cloud(cluster 15) ll L1517L1519 ll L1544 l ll l llll l ll ll ll l lll ll lll ll l ll ll lllll lll llll ll llll llll ll lll lll l l ll lll l l l lll l ll llll ll −16 −14 −12 −10 −8 −6 − − − − − − − V (km/s) W ( k m / s ) ll L1495 ll B213B216 ll TTau ll B215 ll L1535,L1529,L1531,L1524 ll L1551 ll L1536 ll Heiles Cloud(cluster 14) ll Heiles Cloud(cluster 15) ll L1517L1519 ll L1544 l llll lll ll ll ll ll ll l l ll lll ll l l ll ll ll ll ll l ll ll ll l lll l lll ll l llll l lllll ll l ll l lll l lll l l l −12 −11 −10 −9 −8 −7 −6 − − − − − W (km/s) U ( k m / s ) ll L1495 ll B213B216 ll TTau ll B215 ll L1535,L1529,L1531,L1524 ll L1551 ll L1536 ll Heiles Cloud(cluster 14) ll Heiles Cloud(cluster 15) ll L1517L1519 ll L1544
Fig. 14.
Mean spatial velocity of the stars projected towards the various molecular clouds of the Taurus complex.Article number, page 22 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
Table 7.
Relative space motion among the various clouds of the Taurus complex.
Molecular Cloud 1 Molecular Cloud 2 ∆ u ∆ v ∆ w ∆ V bulk ∆ d (km / s) (km / s) (km / s) (km / s) (pc)L 1517, L 1519 L 1544 3 . ± . − . ± . − . ± . . ± . . ± .
7L 1517, L 1519 L 1495 1 . ± . − . ± . . ± . . ± . . ± .
2L 1517, L 1519 B 213, B 216 3 . ± . − . ± . − . ± . . ± . . ± .
8L 1517, L 1519 B 215 2 . ± . − . ± . − . ± . . ± . . ± .
0L 1517, L 1519 Heiles Cloud 2 (cluster 14) 1 . ± . − . ± . − . ± . . ± . . ± .
7L 1517, L 1519 Heiles Cloud 2 (cluster 15) 0 . ± . − . ± . − . ± . . ± . . ± .
7L 1517, L 1519 L 1535, L 1529, L 1531, L 1524 1 . ± . − . ± . − . ± . . ± . . ± .
3L 1517, L 1519 L 1536 1 . ± . − . ± . − . ± . . ± . . ± .
6L 1517, L 1519 L 1551 1 . ± . . ± . − . ± . . ± . . ± .
8L 1544 L 1495 − . ± . − . ± . . ± . . ± . . ± .
1L 1544 B 213, B 216 0 . ± . . ± . − . ± . . ± . . ± .
7L 1544 B 215 − . ± . − . ± . . ± . . ± . . ± .
8L 1544 Heiles Cloud 2 (cluster 14) − . ± . − . ± . . ± . . ± . . ± .
6L 1544 Heiles Cloud 2 (cluster 15) − . ± . − . ± . . ± . . ± . . ± .
6L 1544 L 1535, L 1529, L 1531, L 1524 − . ± . − . ± . . ± . . ± . . ± .
3L 1544 L 1536 − . ± . . ± . − . ± . . ± . . ± .
8L 1544 L 1551 − . ± . . ± . − . ± . . ± . . ± .
9L 1495 B 213, B 216 1 . ± . . ± . − . ± . . ± . . ± .
7L 1495 B 215 0 . ± . − . ± . − . ± . . ± . . ± .
5L 1495 Heiles Cloud 2 (cluster 14) − . ± . . ± . − . ± . . ± . . ± .
4L 1495 Heiles Cloud 2 (cluster 15) − . ± . − . ± . − . ± . . ± . . ± .
1L 1495 L 1535, L 1529, L 1531, L 1524 − . ± . − . ± . − . ± . . ± . . ± .
3L 1495 L 1536 0 . ± . . ± . − . ± . . ± . . ± .
5L 1495 L 1551 − . ± . . ± . − . ± . . ± . . ± .
5B 213, B 216 B 215 − . ± . − . ± . . ± . . ± . . ± .
4B 213, B 216 Heiles Cloud 2 (cluster 14) − . ± . − . ± . . ± . . ± . . ± .
8B 213, B 216 Heiles Cloud 2 (cluster 15) − . ± . − . ± . . ± . . ± . . ± .
8B 213, B 216 L 1535, L 1529, L 1531, L 1524 − . ± . − . ± . . ± . . ± . . ± .
7B 213, B 216 L 1536 − . ± . . ± . − . ± . . ± . . ± .
8B 213, B 216 L 1551 − . ± . . ± . . ± . . ± . . ± .
2B 215 Heiles Cloud 2 (cluster 14) − . ± . . ± . − . ± . . ± . . ± .
4B 215 Heiles Cloud 2 (cluster 15) − . ± . . ± . − . ± . . ± . . ± .
1B 215 L 1535, L 1529, L 1531, L 1524 − . ± . . ± . − . ± . . ± . . ± .
6B 215 L 1536 − . ± . . ± . − . ± . . ± . . ± .
3B 215 L 1551 − . ± . . ± . − . ± . . ± . . ± . − . ± . − . ± . . ± . . ± . . ± . . ± . − . ± . . ± . . ± . . ± . . ± . . ± . − . ± . . ± . . ± . − . ± . . ± . − . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . − . ± . . ± . . ± . . ± . . ± . − . ± . . ± . . ± .
5L 1535, L 1529, L 1531, L 1524 L 1536 0 . ± . . ± . − . ± . . ± . . ± .
6L 1535, L 1529, L 1531, L 1524 L 1551 − . ± . . ± . − . ± . . ± . . ± .
6L 1536 L 1551 − . ± . . ± . . ± . . ± . . ± . Notes.
We provide the relative motion for each component of the spatial velocity (in the sense molecular cloud 1 minus molecular cloud 2), theresulting bulk motion between the clouds, and their relative distance computed from the
XYZ coordinates of the cloud centers (see Table 5).
Table 8.
Results for the expansion and rotation velocity of each molecular cloud and the entire complex.
Molecular Cloud Cluster ˆr ∗ · δ v ∗ ˆr ∗ × δ v ∗ (km / s) (km / s)L 1495 7 − . ± . + . , − . , + . ± (0 . , . , . − . ± . − . , − . , + . ± (0 . , . , . + . ± . − . , + . , + . ± (0 . , . , . − . ± . − . , − . , + . ± (0 . , . , . + . ± . − . , − . , + . ± (0 . , . , . + . ± . − . , + . , + . ± (0 . , . , . + . ± . − . , + . , + . ± (0 . , . , . − . ± . − . , + . , + . ± (0 . , . , . Article number, page 23 of 28 & A proofs: manuscript no. arXiv_version
In this section we compare the radial velocities of the stars in oursample with the kinematics of the underlying gaseous clouds.We used the large-scale survey of the Taurus molecular cloudsin CO and CO performed by Goldsmith et al. (2008) usingthe Five College Radio Astronomy Observatory (FCRAO) tele-scope. The northernmost and southernmost clouds are not in-cluded in the surveyed region, so the analysis is restricted to themolecular clouds in the central region of the Taurus complex thatfall into the FCRAO maps.We proceeded as follows to compare the stellar velocitieswith the kinematics of the molecular gas. First, we convert the(heliocentric) radial velocities of the stars collected from the lit-erature to the LSR. For consistency with our FCRAO data, wededuce the velocity of the Sun with respect to the LSR computedfrom the solar apex of ( α (cid:12) , δ (cid:12) ) = (271 ◦ , ◦ ) and V (cid:12) =
20 km / s(see Jackson et al. 2006) rather than the solar motion used inSect. 5.1. The corrected radial velocities of individual stars arelisted in Table 4. Second, we extract the CO and CO spectrafrom the FCRAO maps at the position of each star in our samplein a velocity interval from -2 to 14 km / s which conservatively in-cludes the range of observed velocities (with respect to the LSR)in Taurus (see, e.g., Fig. 12 of Goldsmith et al. 2008). Then, wecompute the centroid velocity and estimate its uncertainty fromthe r.m.s. of the spectrum as described by Dickman & Kleiner(1985).Two points are worth mentioning here before comparing thestellar radial velocities with the CO velocity. First, the fraction ofbinaries and multiple systems in Taurus is high (see, e.g., Lein-ert et al. 1993; Duchêne 1999) and a complete census of thesesystems with their properties (e.g., orbital period, angular sepa-ration, and mass ratio) is still lacking in the literature. We rejectall known binaries and multiple systems for the current analy-sis (many of them have been flagged by Joncour et al. 2017) toavoid comparing the velocity of the gas with a radial velocitymeasurement that is variable in time. Second, a visual inspec-tion of the extracted spectra for the CO molecule reveals thatthe emission often exhibits complex structures and self-absorbedspectral profiles (see also Urquhart et al. 2007) making it di ffi -cult to compute a velocity centroid in such cases. Although the CO molecule is more abundant than its isotopolog CO, thelatter is more optically thin giving access to the full column den-sity that produces the emission (see, e.g., Cormier et al. 2018)and these absorption features are less common in our spectra.We therefore decided to work with the CO emission to deter-mine the velocity of the molecular gas along the line of sight.Another interesting feature that we observe in some of our spec-tra is the existence of multiple (overlapping) components for thevelocity of the gas as reported previously by Hacar et al. (2013).It is possible in principle to compare the stellar radial velocitieswith the closest component of the gas velocity, but we decidedto discard these spectra from our analysis to avoid a biased cor-relation between the two velocities.Table 9 lists the individual measurements for the veloc-ity of the stars and the CO molecular gas used in ourcomparison. This analysis is restricted to 28 stars in oursample that satisfy the conditions described above. We notethat three stars (CW Tau, 2MASS J04213459 + + ff erby more than 1 km / s with respect to the CO molecular gasvelocity. One possibility to explain the di ff erent velocities forthese sources is the existence of undetected binaries becausetheir proper motions and parallaxes are consistent with mem- bership in the corresponding clouds (as discussed in Sect. 4).In particular, we found three heliocentric radial velocity mea-surements in the literature for CW Tau: 14 . ± . / s (Hart-mann et al. 1986; Herbig & Bell 1988), 13 . ± .
10 km / s(Nguyen et al. 2012), and 16 . ± .
42 km / s (Kounkel et al.2019). As explained in Sect. 2, we used the most precisemeasurement throughout our analysis. The di ff erence betweenthe radial velocity of CW Tau and the CO molecular gaswould still be at the 1 km / s level if, for example, we used themost recent measurement of V r = . ± .
42 km / s in ourcomparison. In the case of 2MASS J04213459 + + CO molecular gasalong the line of sight is clearly evident. Here, we report a meandi ff erence between the two velocities of 0 . ± .
12 km / s (in thesense stars minus gas) and r.m.s. of 0.63 km / s. Previous studiesin this region performed by Herbig (1977) and Hartmann et al.(1986) reported a mean di ff erence of 0 . ± . / s (with r.m.s.of 3.9 km / s) and 0 . ± . / s (with r.m.s. of 1.7 km / s), respec-tively. Our results obtained in this paper reveal that the stars andthe gas are even more tightly coupled than previously thought.One reason to explain this result comes from the more preciseand accurate radial velocity measurements available to date thathave been incorporated in our analysis. In addition, it should alsobe noted that the sample of Taurus stars used in each study is notthe same.Our results in this section are consistent with the stars be-ing at the same velocity of the neighboring molecular gas. Thisfinding confirms that the stars in our sample are indeed associ-ated with the various substructures of the complex, and supportsour results for the existence of multiple populations, significantdepth e ff ects, and internal motions in the Taurus region. ll l l ll lll ll ll l lllll l l ll ll l ll ll l l ll lll ll ll l lllll l l ll ll l ll V starLSR (km/s) V ga s L S R ( k m / s ) Molecular Cloud l l l l l l l l l l l l l l B213/B216B215Heiles Cloud 2 (cluster 14)Heiles Cloud 2 (cluster 15)L1495L1535,L1529,L1531,L1524L1536
Fig. 15.
Comparison of the radial velocity of the stars (with respectto the LSR) with the centroid velocity of the CO emission extractedfrom the FCRAO maps at the position of each star. The black dashedline indicates a perfect correlation between the two measurements, andthe colors respresent the various molecular clouds to which the starsbelong.Article number, page 24 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
6. Conclusions
We used in this study the best astrometry available to dateby combining Gaia-DR2 data with the VLBI results deliveredby the GOBELINS project to investigate the three-dimensionalstructure and kinematics of the Taurus star-forming region. Bothprojects return consistent results for the targets in common andcomplement each other in this region of the sky.We applied a hierarchical clustering algorithm for partition-ing the stars in our sample into groups with similar propertiesbased on the stellar positions, proper motions, and parallaxes.Our methodology allowed us to identify the various substruc-tures of the Taurus region and discuss their relationship (i.e., hi-erarchy). We found 21 clusters in our sample at the lowest levelof the hierarchical tree and a number of outliers that exhibit dis-crepant properties. Thirteen of these clusters are associated withone molecular cloud of the Taurus complex and have been usedto derive the distance and spatial velocity of the correspondingclouds providing the most complete and precise scenario of thesix-dimensional structure of this region.We confirmed the existence of significant depth e ff ects alongthe line of sight. The median inter-cloud distance among the var-ious subgroups of the Taurus region is about 25 pc. We reportB 215 and L 1558 as the closest ( d = . + . − . pc) and mostremote ( d = . + . − . pc) substructures of the complex, respec-tively. In addition, we show that the core of the most prominentmolecular cloud of the complex L 1495 and the filament con-nected to it in the plane of the sky are located at significantlydi ff erent distances ( d = . + . − . pc and d = . + . − . pc, re-spectively) and diverge from each other in the velocity space.In a subsequent analysis, we computed the spatial veloci-ties of the stars and the relative bulk motion among the variousclouds. The highest values that we derive for the relative motionamong the various substructures occur between the B 215 clumpin the central region of the complex with the northernmost andsouthernmost clouds (L 1517, L 1519 and L 1551, respectively)and they reach about 5 km / s. The one-dimensional velocity dis-persion that we obtain from the full sample of Taurus stars withknown spatial velocities is on the order of 2 km / s. In addition,we have also investigated the existence of expansion, contrac-tion, and rotation e ff ects. We concluded that these e ff ects are toosmall (if present at all) in the individual molecular clouds rep-resented in our sample of stars. We do not detect any significantexpansion pattern for the Taurus complex as a whole, but we findevidence of potential rotation e ff ects that will require further in-vestigation with di ff erent methodologies.Finally, we compared the radial velocity of the stars in oursample with the velocity of the underlying gaseous clouds de-rived from the emission of the CO molecular gas, and showedthat they are consistent among themselves. We find a mean dif-ference of 0 . ± .
12 km / s (with r.m.s. of 0.63 km / s), whichsuggests that the stars are indeed following the velocity patternof the gas in this region. Acknowledgements.
We thank Alvaro Hacar, Estelle Moraux, and Isabelle Jon-cour for helpful discussions that improved the manuscript. This research hasreceived funding from the European Research Council (ERC) under the Eu-ropean Union’s Horizon 2020 research and innovation program (grant agree-ment No 682903, P.I. H. Bouy), and from the French State in the frame-work of the “Investments for the future” Program, IdEx Bordeaux, referenceANR-10-IDEX-03-02. L.L. acknowledges the financial support from PAPIIT-UNAM project IN112417, and CONACyT. G.N.O.-L. acknowledges supportfrom the von Humboldt Stiftung. This research has made use of the SIMBADdatabase, operated at CDS, Strasbourg, France. This work has made use ofdata from the European Space Agency (ESA) mission
Gaia ( ), processed by the Gaia
Data Processing and Anal-ysis Consortium (DPAC, ). Funding for the DPAC has been provided by national institutions,in particular the institutions participating in the
Gaia
Multilateral Agreement.
References
Arenou, F., Luri, X., Babusiaux, C., et al. 2018, A&A, 616, A17Astraatmadja, T. L. & Bailer-Jones, C. A. L. 2016, ApJ, 832, 137Bailer-Jones, C. A. L. 2015, PASP, 127, 994Barnard, E. E. 1927, Catalogue of 349 dark objects in the skyBertout, C. & Genova, F. 2006, A&A, 460, 499Bertout, C., Robichon, N., & Arenou, F. 1999, A&A, 352, 574Bertout, C., Siess, L., & Cabrit, S. 2007, A&A, 473, L21Cambrésy, L. 1999, A&A, 345, 965Cheng, Y. & Ray, S. 2014, Open Journal of Statistics, 4, 826Cormier, D., Bigiel, F., Jiménez-Donaire, M. J., et al. 2018, MNRAS, 475, 3909Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, 2MASS All Sky Catalogof point sources.Dame, T. M., Hartmann, D., & Thaddeus, P. 2001, ApJ, 547, 792Dickman, R. L. & Kleiner, S. C. 1985, ApJ, 295, 479Dobashi, K., Uehara, H., Kandori, R., et al. 2005, PASJ, 57, S1Duchêne, G. 1999, A&A, 341, 547Duflot, M., Figon, P., & Meyssonnier, N. 1995, A&AS, 114, 269ESA, ed. 1997, ESA Special Publication, Vol. 1200, The HIPPARCOS and TY-CHO catalogues. Astrometric and photometric star catalogues derived fromthe ESA HIPPARCOS Space Astrometry MissionEsplin, T. L. & Luhman, K. L. 2017, AJ, 154, 134Esplin, T. L., Luhman, K. L., & Mamajek, E. E. 2014, ApJ, 784, 126Ester, M., Kriegel, H.-P., Sander, J., & Xu, X. 1996, in (AAAI Press), 226–231Gaia Collaboration, Babusiaux, C., van Leeuwen, F., et al. 2018a, A&A, 616,A10Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018b, A&A, 616, A1Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2016, A&A, 595, A2Galli, P. A. B., Loinard, L., Ortiz-Léon, G. N., et al. 2018, ApJ, 859, 33Goldsmith, P. F., Heyer, M., Narayanan, G., et al. 2008, ApJ, 680, 428Gomez, M., Hartmann, L., Kenyon, S. J., & Hewett, R. 1993, AJ, 105, 1927Gontcharov, G. A. 2006, Astronomy Letters, 32, 759Hacar, A., Tafalla, M., Kau ff mann, J., & Kovács, A. 2013, A&A, 554, A55Hartmann, L., Hewett, R., Stahler, S., & Mathieu, R. D. 1986, ApJ, 309, 275Hartmann, L. W., Soderblom, D. R., & Stau ff er, J. R. 1987, AJ, 93, 907Herbig, G. H. 1977, ApJ, 214, 747Herbig, G. H. & Bell, K. R. 1988, Third Catalog of Emission-Line Stars of theOrion Population : 3 : 1988Hubert, M. & Debruyne, M. 2010, Wiley Interdisciplinary Reviews: Computa-tional Statistics, 2, 36Jackson, J. M., Rathborne, J. M., Shah, R. Y., et al. 2006, ApJS, 163, 145Johnson, D. R. H. & Soderblom, D. R. 1987, AJ, 93, 864Joncour, I., Duchêne, G., & Moraux, E. 2017, A&A, 599, A14Joncour, I., Duchêne, G., Moraux, E., & Motte, F. 2018, A&A, 620, A27Jones, B. F. & Herbig, G. H. 1979, AJ, 84, 1872Kenyon, S. J., Gomez, M., & Whitney, B. A. 2008, Low Mass Star Formation inthe Taurus-Auriga Clouds, ed. B. Reipurth, 405Kharchenko, N. V., Scholz, R.-D., Piskunov, A. E., Röser, S., & Schilbach, E.2007, Astronomische Nachrichten, 328, 889Kounkel, M., Covey, K., Moe, M., et al. 2019, AJ, 157, 196Kounkel, M., Hartmann, L., Loinard, L., et al. 2017, ApJ, 834, 142Kraus, A. L., Herczeg, G. J., Rizzuto, A. C., et al. 2017, ApJ, 838, 150Leinert, C., Zinnecker, H., Weitzel, N., et al. 1993, A&A, 278, 129Lestrade, J.-F., Preston, R. A., Jones, D. L., et al. 1999, A&A, 344, 1014Li, J., Ray, S., & Lindsay, B. G. 2007, J. Mach. Learn. Res., 8, 1687Lindegren, L., Hernandez, J., Bombrun, A., et al. 2018, ArXiv e-prints[ arXiv:1804.09366 ]Lindegren, L., Lammers, U., Bastian, U., et al. 2016, A&A, 595, A4Loinard, L., Mioduszewski, A. J., Torres, R. M., et al. 2011, in Revista Mexicanade Astronomia y Astrofisica, vol. 27, Vol. 40, Revista Mexicana de Astrono-mia y Astrofisica Conference Series, 205–210Loinard, L., Torres, R. M., Mioduszewski, A. J., et al. 2007, ApJ, 671, 546Luhman, K. L. 2018, AJ, 156, 271Luri, X., Brown, A. G. A., Sarro, L. M., et al. 2018, A&A, 616, A9Lynds, B. T. 1962, ApJS, 7, 1MacQueen, J. 1967, in Proceedings of the Fifth Berkeley Symposium on Mathe-matical Statistics and Probability, Volume 1: Statistics (Berkeley, Calif.: Uni-versity of California Press), 281–297Mathieu, R. D., Stassun, K., Basri, G., et al. 1997, AJ, 113, 1841Muzerolle, J., Hillenbrand, L., Calvet, N., Briceño, C., & Hartmann, L. 2003,ApJ, 592, 266Nguyen, D. C., Brandeker, A., van Kerkwijk, M. H., & Jayawardhana, R. 2012,ApJ, 745, 119Ortiz-León, G. N., Dzib, S. A., Kounkel, M. A., et al. 2017a, ApJ, 834, 143 Article number, page 25 of 28 & A proofs: manuscript no. arXiv_version
Table 9.
Comparison of the velocity of the stars and the CO molecular gas. V LS Rgas V LS Rstar
Molecular Cloud(km / s) (km / s)2MASS J04141458 + . ± .
06 6 . ± .
09 L 14952MASS J04141700 + . ± .
02 4 . ± .
10 L 14952MASS J04141760 + . ± .
03 6 . ± .
14 L 14952MASS J04153916 + . ± .
02 6 . ± .
11 L 14952MASS J04161210 + . ± .
04 7 . ± .
14 L 14952MASS J04190110 + . ± .
03 7 . ± .
24 L 14952MASS J04192625 + . ± .
05 7 . ± .
02 L 14952MASS J04194819 + . ± .
03 7 . ± .
11 L 14952MASS J04201611 + . ± .
05 7 . ± .
33 L 14952MASS J04213459 + . ± .
03 7 . ± .
23 B 213, B 2162MASS J04214013 + . ± .
06 6 . ± .
21 L 14952MASS J04222404 + . ± .
03 7 . ± .
23 B 213, B 2162MASS J04224786 + + . ± .
02 7 . ± .
26 B 213, B 2162MASS J04233919 + . ± .
03 7 . ± .
20 B 2152MASS J04262939 + . ± .
11 7 . ± .
26 B 213, B 2162MASS J04272467 + . ± .
08 7 . ± .
12 B 213, B 2162MASS J04295950 + . ± .
05 7 . ± .
24 L 1535, L 1529, L 1531, L 15242MASS J04322329 + . ± .
13 5 . ± .
22 L 1535, L 1529, L 1531, L 15242MASS J04323058 + . ± .
03 5 . ± .
16 L 1535, L 1529, L 1531, L 15242MASS J04323176 + . ± .
03 5 . ± .
35 L 1535, L 1529, L 1531, L 15242MASS J04332621 + . ± .
04 5 . ± .
12 L 15362MASS J04333405 + . ± .
05 6 . ± .
04 L 1535, L 1529, L 1531, L 15242MASS J04341099 + . ± .
07 5 . ± .
17 L 15362MASS J04341527 + . ± .
03 6 . ± .
37 L 15362MASS J04352737 + . ± .
07 5 . ± .
02 L 1535, L 1529, L 1531, L 15242MASS J04382858 + . ± .
04 5 . ± .
17 Heiles Cloud 2 (cluster 14)2MASS J04390396 + . ± .
05 6 . ± .
22 Heiles Cloud 2 (cluster 14)2MASS J04414825 + . ± .
04 4 . ± .
33 Heiles Cloud 2 (cluster 15)
Notes.
We provide for each star its identifier, velocity of the CO emission at the position of the star, radial velocity of the star converted to theLSR, and the molecular cloud to which it belongs.
Ortiz-León, G. N., Loinard, L., Dzib, S. A., et al. 2018, ApJ, 865, 73Ortiz-León, G. N., Loinard, L., Kounkel, M. A., et al. 2017b, ApJ, 834, 141Reipurth, B., Lindgren, H., Nordstrom, B., & Mayor, M. 1990, A&A, 235, 197Rivera, J. L., Loinard, L., Dzib, S. A., et al. 2015, ApJ, 807, 119Rousseeuw, P. J. & Driessen, K. V. 1999, Technometrics, 41, 212Scelsi, L., Sacco, G., A ff er, L., et al. 2008, A&A, 490, 601Schmalzl, M., Kainulainen, J., Quanz, S. P., et al. 2010, ApJ, 725, 1327Schönrich, R., Binney, J., & Dehnen, W. 2010, MNRAS, 403, 1829Torres, C. A. O., Quast, G. R., da Silva, L., et al. 2006, A&A, 460, 695Torres, R. M., Loinard, L., Mioduszewski, A. J., et al. 2012, ApJ, 747, 18Torres, R. M., Loinard, L., Mioduszewski, A. J., & Rodríguez, L. F. 2007, ApJ,671, 1813Torres, R. M., Loinard, L., Mioduszewski, A. J., & Rodríguez, L. F. 2009, ApJ,698, 242Ungerechts, H. & Thaddeus, P. 1987, ApJS, 63, 645Urquhart, J. S., Busfield, A. L., Hoare, M. G., et al. 2007, A&A, 474, 891Wenger, M., Ochsenbein, F., Egret, D., et al. 2000, A&AS, 143, 9White, R. J. & Basri, G. 2003, ApJ, 582, 1109Wichmann, R., Torres, G., Melo, C. H. F., et al. 2000, A&A, 359, 181Wilson, R. E. 1953, Carnegie Institute Washington D.C. PublicationZhang, Z., Liu, M. C., Best, W. M. J., et al. 2018, ApJ, 858, 41 Article number, page 26 of 28. A. B. Galli et al.: Structure and kinematics of the Taurus star-forming region from Gaia-DR2 and VLBI astrometry
Appendix A: Performance assessment of theclustering analysis with simulations
Our clustering analysis with HMAC has identified 21 clusterswhich group 236 stars in our sample, and another 48 outlierswith unique properties (see Sect. 4.2). In this section we analyzethe robustness and dependence of our previous results on the un-certainties of the astrometric parameters used in the clusteringanalysis. We investigate the capability of the HMAC algorithmto distinguish between cluster members and outliers in our sam-ple of stars, and we evaluate the clustering of our sample into the21 clusters derived in our analysis presented in Sect. 4.2 (here-after the true run). The analysis discussed throughout this sectionrefers to the clustering results obtained at the lowest level of theHMAC hierarchical trees that we derived from our simulations,as explained below.First, we constructed 1000 synthetic samples of the Tau-rus association by resampling the five astrometric parameters( α, δ, µ α cos δ, µ δ , (cid:36) ) of each star in the true run from a multivari-ate normal distribution, where mean and standard deviation cor-respond to the individual measurements and their uncertainties.We used the full 5 × ff erent lo-cation in the five-dimensional parameter space. Thus, to identifythe various clusters from the true run in our simulations we firstcomputed their distances to the simulated counterparts, and thenassigned the closest cluster in our simulations to each cluster inthe true run using Euclidean distances in the five-dimensionalspace defined by the observables.Second, we evaluated the robustness of the clustering analy-sis in the true run in terms of the reproducibility of these resultsin our simulations using synthetic data. In each run of our sim-ulations we tracked the membership status (member vs. outlier)and the cluster membership of the synthetic stars produced inour simulations to compare it with the result given in the truerun for each star. In this context, we assigned the classes “mem-ber” (positive) and “outlier” (negative) to describe the member-ship status of the stars in the true run and in our simulations. Itshould be noted that the terminology “outlier” used throughoutthe paper refers to the sources that do not belong to any clusterof members with similar properties identified in this study eventhough they have been identified as YSOs in previous studies andare likely to be associated with the Taurus region. We computedthe number of true positives (TP), false positives (FP), false neg-atives (FN), and true negatives (TN) to quantitatively address thecomparison between the actual and predicted classes, which re-fer to the true run and our simulations, respectively.Our simulations allow us to investigate two important pointsregarding the clustering analysis with HMAC: (i) the dichotomybetween cluster members and outliers, and (ii) the possibility ofstars being assigned to di ff erent clusters in our simulations. Inthe first case, we do not distinguish between the members thathave been assigned to di ff erent clusters in our simulations andin the true run, but we investigate the capability of the HMACalgorithm to distinguish between the two classes. In this context,we define the true positive rate (TPR) and the true negative rate (TNR) as follows: T PR = T PT P + FN , (A.1) T NR = T NT N + FP . (A.2)The mean values of TPR and TNR that we obtain after runningHMAC for the 1000 synthetic samples as described above are0 . ± .
054 and 0 . ± . PPV = T PT P + FP , (A.3) NPV = T NT N + FN . (A.4)The PPV shows whether the sample of members in one clusterobtained from our simulations is contaminated by sources identi-fied as non-members in the true run. Analogously, the NPV mea-sures whether our list of non-members (with respect to a givencluster) obtained in the simulations is polluted by sources iden-tified as cluster members in the true run. In addition, we alsocomputed the F score for the clustering performance within in-dividual clusters which returns the harmonic mean between TPRand PPV. It is given by F = · T PR · PPVT PR + PPV . (A.5)The results of this analysis are shown in Table A1. We note inparticular that clusters 10, 11, and 12 exhibit the lowest perfor-mance of all the clusters (see, e.g., the results for the F score).However, these numbers are a ff ected by small number statistics(i.e., only two stars in each cluster). The early merging of clus-ters 11 and 12 with cluster 7 (see Fig. 3) also explains that thesestars are often associated with di ff erent clusters in our simula-tions. In the specific case of cluster 10 we note that one of itsmembers, namely 2MASS J04312669 + (cid:36) = . ± .
893 mas, see Table 1) that is used inthe resampling procedure described above to generate syntheticstars. Altogether, the results that we obtain in our simulations forthe TPR, TNR, PPV, and NPV support the stability and robust-ness of the clustering results presented in Sect.4.2 for the truerun with respect to the measurement uncertainties.
Article number, page 27 of 28 & A proofs: manuscript no. arXiv_version
Table A1.
Mean values for the TPR, TNR, PPV, NPV, and F score obtained for each cluster from our simulations (after 1000 realizations). Cluster
T PR T NR PPV NPV F -score1 0 . ± .
019 1 . ± .
001 0 . ± .
014 0 . ± .
001 0 . ± . . ± .
011 1 . ± .
001 0 . ± .
080 1 . ± .
000 0 . ± . . ± .
098 1 . ± .
001 0 . ± .
025 0 . ± .
003 0 . ± . . ± .
136 1 . ± .
000 1 . ± .
000 0 . ± .
003 0 . ± . . ± .
035 1 . ± .
000 1 . ± .
000 1 . ± .
000 0 . ± . . ± .
081 0 . ± .
002 0 . ± .
115 1 . ± .
001 0 . ± . . ± .
189 0 . ± .
008 0 . ± .
036 0 . ± .
038 0 . ± . . ± .
075 1 . ± .
001 0 . ± .
012 0 . ± .
004 0 . ± . . ± .
326 0 . ± .
004 0 . ± .
333 0 . ± .
002 0 . ± . . ± .
163 1 . ± .
000 1 . ± .
000 0 . ± .
001 0 . ± . . ± .
479 0 . ± .
004 0 . ± .
453 0 . ± .
003 0 . ± . . ± .
477 0 . ± .
002 0 . ± .
434 0 . ± .
003 0 . ± . . ± .
106 1 . ± .
000 0 . ± .
033 1 . ± .
001 0 . ± . . ± .
227 0 . ± .
004 0 . ± .
096 0 . ± .
007 0 . ± . . ± .
180 0 . ± .
004 0 . ± .
185 0 . ± .
003 0 . ± . . ± .
134 0 . ± .
008 0 . ± .
120 0 . ± .
011 0 . ± . . ± .
188 0 . ± .
007 0 . ± .
156 0 . ± .
007 0 . ± . . ± .
199 0 . ± .
003 0 . ± .
046 0 . ± .
017 0 . ± . . ± .
226 0 . ± .
001 0 . ± .
088 0 . ± .
003 0 . ± . . ± .
037 0 . ± .
002 0 . ± .
016 0 . ± .
005 0 . ± . . ± .
072 1 . ± .
001 0 . ± .
048 0 . ± .