OPEN CLUSTERS AS GALACTIC DISK TRACERS. I. PROJECT MOTIVATION, CLUSTER MEMBERSHIP, AND BULK THREE-DIMENSIONAL KINEMATICS

Open star clusters have long been exploited as tools for understanding Galactic interstellar dust (e.g., Trumpler 1930a, 1930b; Clayton & Fitzpatrick 1987; Dutra & Bica 2000), the age of the Galactic disk (e.g., Janes & Adler 1982; Twarog & Anthony-Twarog 1989; Phelps et al. 1994; Phelps 1997; Chaboyer et al. 1999; Carraro 1999), the Galactic disk metallicity distribution and age–metallicity relation (e.g., Twarog 1980; Friel & Janes 1993; Friel 1995; Twarog et al. 1997), and, of course, stellar evolution (e.g., Sandage 1957; Cannon 1970; Maeder & Mermilliod 1981; Meynet et al. 1993; Koester & Reimers 1996; Prada Moroni & Straniero 2002). The value of open clusters as tracers of the local Galactic rotation curve has also long been recognized (e.g., Hron 1987; Scott et al. 1995; Glushkova et al. 1998; Loktin & Beshenov 2003; Frinchaboy 2006a). It is in this role as a dynamical tracer of the Galactic disk that the present study of open clusters is especially focused.

Star clusters can be effective tracers of the Galactic disk because they offer many advantages over other tracer candidates. First, relative to other tracers, star clusters lend themselves more amenably to age, metallicity, distance, and velocity evaluation. Compared to an isolated field star at the same location in the Galaxy, these quantities are much easier to establish in a star cluster, needing only a properly interpreted color–magnitude diagram (CMD) to establish the first three, while velocities can also be better determined for a star cluster because (1) averaging radial velocity and proper motion data over an ensemble of co-moving stars confers potentially as much as a $\sqrt{N}$ increase in precision for the bulk motion of the ensemble, and (2) better distances allow one to translate proper motions into transverse velocities more accurately. Supplemental knowledge of the age and metallicity of a source confers additional beneficial insights into its proper use as a dynamical tracer with respect to, for example, assumptions about orbit shape and asymmetric drift. Alternatively, one can explore Galactic dynamics as a function of population age and metallicity if all relevant data are available.

On the other hand, there are some complications in the use of open clusters as dynamical tracers. The challenge of proper identification of cluster members can present particular hazards. For example, Frinchaboy (2006b) showed that the UCAC stars used by Dias et al. (2006) to establish the proper motions of at least two particular clusters—Be29 and BH176—in their exhaustive survey of over 400 systems are too bright and cannot be part of these distant systems. Difficulties caused by inaccurate membership censuses are why continued large-scale observational efforts are needed before we can be confident in the use of open clusters as Galactic disk tracers, particularly for more sparse and more distant systems.

To overcome these types of problems, which are typically associated with small number statistics, it is desirable to survey large numbers of potential open cluster members. However, this desire to achieve the largest possible statistical samples often encourages a dangerous reliance on compilations of disparate data. For example, the dynamical study of the Galactic disk using open clusters by (Hron 1987) found that in their compilation of data from the literature ∼50% of the clusters with multiple distance measurements had differences greater than 1 magnitude in determined distance modulus and ∼50% of the clusters also had poor RV qualities.⁴

To help overcome both the membership and homogeneity problems that are often a hindrance to the use of open clusters as tracers of the Galactic disk, we present a new survey of open clusters that will not only take advantage of quality radial velocities to help discriminate cluster members, but also rely on one source of data as much as possible for each independent cluster parameter (e.g., all photometry from one source, all RVs and derived in a uniform manner, all proper motions coming from one catalog, etc). A central objective of this study is the use of these clusters to derive global dynamical properties of the Milky Way disk, with a particular emphasis on the derivation of the full space velocities for the target clusters. In keeping with our philosophy of uniformity of data, and because large numbers of proper motions at present must come from all-sky astrometric surveys, we first investigate the main proper motion catalogs available for investigations of open cluster kinematics, from which we might draw an initial target sample.

A key advance that has propelled a resurgence in the use of open clusters as disk dynamical tracers is the compilation of all-sky proper motion surveys. There have been four surveys to determine bulk Galactic cluster kinematics by averaging the proper motions of presumed cluster stars based on data from the Hipparcos (Baumgardt et al. 2000), Tycho-2 (Dias et al. 2001, 2002a), Four Million Star (4M) (Glushkova et al. 1996), and recently the UCAC-2 (Dias et al. 2006) catalogs. The European Space Agency (ESA) Hipparcos mission has provided critical astrometry for two of these proper motion databases via each of Hipparcos' primary data products: (1) the Hipparcos catalog of ∼118, 000 stars (V ⩽ 11) with proper motion uncertainties of 1–2 mas yr⁻¹ and (2) the Tycho-2 catalog of 2.5 million stars (V ⩽ 13.5) with proper motion uncertainties of 1–3 mas yr⁻¹. The UCAC-2 catalog of 48 million stars is based on Tycho-2 and fainter, ground-based observations (to R = 16) and has proper motion uncertainties of 1–7 mas yr⁻¹. The 4M catalog (Volchkov et al. 1992) was compiled from the Astrographic Catalog and the Hubble Space Telescope guide star catalog (GSC) reduced to the older system of the PPM (Röser & Bastian 1991; Bastian et al. 1993; Röser et al. 1994) survey, with proper motion uncertainties of ∼10 mas yr⁻¹.

Proper motions for hundreds of open clusters have been published using these catalogs. However, a comparison of the derived motions for the clusters in common between surveys reveals substantial discrepancies, as shown in Figure 1, where a cluster-by-cluster comparison of the proper motion differences is illustrated, namely for (a) Tycho-2 versus Hipparcos, (b) Tycho-2 versus 4M, (c) 4M versus Hipparcos, and (d) Tycho-2 versus UCAC-2. As may be seen, differences in derived proper motions typically exceed the quoted uncertainties claimed by each survey. The best correlation of derived proper motions is between surveys using the Tycho-2 and Hipparcos astrometry; remaining differences in derived mean cluster proper motions between these surveys must therefore be due to differences in the adopted samples of presumed cluster members because the actual proper motions, at least for V ≲ 11, are the same (i.e. Hipparcos-based), while the Tycho-2 astrometry used at fainter magnitudes is on the Hipparcos reference system (which means that the system is referenced to background, extra-galactic sources of the International Celestial Reference System). Of course, with its bright magnitude limit, Hipparcos can usually provide useful astrometry for only a small number of stars per cluster (typically less than four). With only a few stars per cluster, a Hipparcos-based survey is far more susceptible to small number statistics as well as the misidentification of true cluster members against the large number of fore/background stars of the Galactic disk.

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Clearly Tycho-2 and Hipparcos, which are currently the most accurate all-sky astrometric surveys, must be considered primary and important sources of proper motion data for our survey. On the other hand, deeper catalogs can provide more cluster members, but typically with worse precision. Thus, it is not immediately obvious that adding additional data from the deeper proper motion catalogs improves or degrades those from Tycho-2 and Hipparcos alone. A reasonable correlation of derived cluster motions is found when either the Tycho-2 and UCAC-2 catalog data are used with a V ⩽ 13 limit, but this is because UCAC-2 adopts Tycho-2 proper motions for stars brighter than about V = 13 (Zacharias et al. 2004). On the other hand, it is clear that there are greater deviations in derived proper motions when we incorporate the fainter stars from UCAC-2. Apart from not knowing whether these differences reflect systematic problems in the fainter UCAC catalog (which allows probing of proper motions with stars to V = 16) or small number statistics in the brighter surveys, some additional concerns about UCAC beyond those suggested by Figure 1 have led us not to adopt this dataset for our own work.

For example, as recently pointed out in Balaguer-Núñez et al. (2007), the UCAC-2 proper motions may have systematic trends with magnitude due to the compiled nature of the UCAC-2 survey (i.e., ground-based proper motions are added to Tycho-2 data). This concern is usefully illustrated by looking at the cluster M67 (NGC 2682). In Figure 2(a), we show the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) CMD for the M67 field plotting only the most probable members based on CMD location. We split the CMD (red: UCAC mag <13.0, blue: UCAC mag ⩾13.0) at a magnitude that represents approximately the transition within the catalog from Tycho-2 to ground-based observations. Substantial proper motion shifts are apparent between the bright and faint samples (Figure 2(b)), and this suggests significant systematic zero-point offsets within the UCAC-2 database.

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The 4M catalog, as well, appears to have systematic proper motion errors. The 4M is not tied to the Hipparcos system, but rather to the PPM (Gulyaev & Nesterov 1992). Glushkova et al. (1996, 1998) have used the 4M catalog to determine the proper motions of about 200 open clusters. Dias et al. (2001) compared their Tycho-2 open cluster proper motions to both those based on Hipparcos (Baumgardt et al. 2000) and the Glushkova et al. 4M work and found that the 4M motions were systematically offset from those in the Hipparcos system by ∼5 mas yr⁻¹ in both μ_αcos δ and μ_δ, an amount that was larger than expected given the quoted errors of both the surveys. While these differences likely reflect both differences in membership as well as astrometric accuracy, this comparison suggests that the deeper proper motions are not necessarily providing better overall accuracy in the open cluster bulk motions, and recommends a strategy based on quality over quantity of cluster star motions.

Therefore, because of uncertainty over the reliability of the UCAC-2 and 4M surveys and our desire to adhere to a "quality over quantity" policy, we have elected to focus on deriving bulk motions using astrometry from the Tycho-2 catalog, but with a dedication to ensuring that we derive a trustworthy membership of the smaller number of available cluster stars available in this shallower database.

The mass and mass distribution of the Galactic disk has been a matter of debate for over a century, and will likely remain so until extremely precise proper motions and trigonometric parallaxes can be obtained for numerous disk tracers, most likely through future space-based studies like the National Aeronautics and Space Administration's (NASA) Space Interferometry Mission (SIM PlanetQuest) and the ESA's Gaia satellites. The new project presented here represents both a preparatory effort in this space-based direction as well as a standalone dynamical study in its own rite. Our goal is to establish a well-constructed, well-studied, baseline tracer population—open clusters—that can not only (1) serve as input targets for Galactic dynamics studies with SIM PlanetQuest (specifically, for the SIM Key Project Taking Measure of the Milky Way, for which SRM is the principal investigator and which has provided support for this project), but which (2) can also be immediately exploited for understanding Galactic dynamics with existing astrometric data.

As mentioned above, the inability to establish a uniform, unbiased tracer sample has been one of the key weaknesses of previous Galactic dynamical surveys (e.g., Fich et al. 1989). To provide a homogeneous set of tracers, we have undertaken a spectroscopic survey to obtain precision RVs of open cluster fields. These RVs will establish cluster membership for individual stars that not only provides a very precise mean RV of each cluster, but, in identifying cluster members having accurate astrometry, can be used to define the bulk cluster proper motion. The combination of the newly found, very precise mean RV of each cluster with its derived bulk proper motion and distance will allow us to determine the space velocities of these clusters. With a large number of cluster space velocities, the rotation curve of the Galactic disk can be constrained over the R_gc range of the sample. Alternatively, through the adoption of an assumed rotation curve (i.e., Galactic potential), the orbital properties of individual clusters can be determined.

Because we are interested in obtaining results before SIM PlanetQuest and Gaia are in service, our RV study will focus on clusters already having available, uniform, and reliable proper motions. As described in Section 1.4, we have elected to focus on the all-sky Tycho-2 proper motion catalog, which provides useful astrometry for typically 50–200 stars per cluster field (⩽0.75 deg²). While selection of Tycho-2 as our source of proper motions limits the depth and thereby the cluster distance that can be explored, it is in keeping with our philosophy of quality over quantity for the astrometric data. The selected proper motion stars for a given cluster field can usually be investigated spectroscopically with a single pointing of the NOAO Hydra multi-fiber spectrographs on the CTIO 4 m and WIYN⁵ 3.5 m telescopes, and the radial velocities derived from these spectroscopic data are the primary results presented here. Our campaign of multi-fiber spectroscopy allows us to check virtually every star in a cluster field having a Tycho-2 proper motion, and leaves additional fibers to (1) expand the RV membership census to fainter stars in anticipation of the future astrometric surveys (e.g., SIM and Gaia), and (2) improve age-dating of the clusters through CMD-isochrone fitting to established member stars. The current study of clusters provides a large uniform database for further open cluster research, as a supplement to the Dias et al. (2002b) and WEBDA (Mermilliod 1995) databases.

The new RVs immediately improve all previous proper motion work on our targeted clusters because of the clarity they bring regarding cluster membership. The improved RVs and proper motions, when combined with new distances we shall derive elsewhere (Paper II), will provide much more reliable space motions of numerous open clusters over a large R_gc range; these space velocities will be at a precision sufficient to make tangible improvements in the determination of the nearby Galactic rotation curve and, in turn, the mass distribution of the Galactic disk. With uncertainties of order ∼1.2 km s⁻¹, the data here yield the best-derived bulk RVs thus far for most of the chosen clusters, This precision is comparable to the uncertainties in transverse velocity that SIM and Gaia will measure for these clusters, and represent a significant improvement over many previous RV surveys of open clusters, which have typical uncertainties of order ∼15 km s⁻¹ (Scott et al. 1995). Our results are more comparable to the RV precisions being obtained for open cluster stars in studies using CORAVEL (e.g., Mermilliod & Mayor 1989, 1990), for example.

Following the work in this paper (Paper I), we will provide uniformly-determined distances and ages derived from isochrone-fitting to 2MASS photometry of these clusters, aided by the cluster membership data derived here (Paper II). With newly-derived kinematics and distances in hand from Papers I and II, we will then use the cluster sample to explore not only the orbital characteristics of the individual clusters (Paper III), but the global properties of the Galactic disk (Paper IV), including: (1) the local Galactic rotation curve and velocity field near the Sun, (2) the kinematics of the disk across the frontier separating R < R₀ and R > R₀, and (3) the validity of the assumption of Galactic dynamical symmetry (e.g., north versus south, Galactic quadrants I/II versus IV/III).

In Section 6 and Table 12 of this paper we present the derived 3D space motions of the clusters that enable these future contributions. In the preceding sections of this paper we explain how we selected our target clusters (Sections 2.1 and 4) and which stars within each cluster field to probe (Section 2.2), the spectroscopic observations and the derivation of radial velocities (Section 3), and the means by which membership within each cluster is established (Section 5).

Our selection of specific open clusters starts with the 205 clusters explored in the Dias et al. (2001, 2002a) catalogs, which derive cluster membership using the statistical method of Sanders (1977). We also adopt the following criteria: (1) the clusters must have at least ten stars with Tycho-2 proper motions in the fields selected by Dias et al. (2001, 2002a), and (2) the cluster diameters cannot be much larger than the Hydra field of view (40': CTIO; 60': WIYN) so that the cluster can be sampled with a significant number of fibers. In addition, to obtain the greatest leverage on the local Galactic rotation curve the selected clusters span a wide area over the Galactic X_gc–Y_gc plane and reach to a heliocentric distance of ⩾2.5 kpc. Neither age, distance from the Galactic plane, nor metallicity was considered as a selection criterion.

Table 1 shows the basic cluster parameters of our sample with data taken from the Dias et al. (2002b) catalog, including coordinates of right ascension and declination (Columns 2 and 3) and Galactic longitude and latitude (Columns 4 and 5), heliocentric distance (Column 6), log(age/years) and visual diameter of the cluster in arcminutes (Columns 7 and 8), and the observing run on which the cluster was observed (see below and Table 3 for definitions). The Galactic distribution of our final cluster sample of 71 clusters is shown in Figure 3. The smaller number of clusters we have sampled in the l = 0–180°half of the Galaxy is result of a smaller amount of observing time obtained for the WIYN observations; however, future work in the research program will aim to remedy this deficiency. Figure 3 also shows the distribution of the selected cluster ages and distances from the Galactic midplane as a function of their Galactic radius (assuming the Sun is at 8.5 kpc). More than half of our final sample have ages less than 200 Myr but older than 10 Myr (Table 1). The large number of relatively young clusters is important for kinematical studies of the Galactic disk because, in general, open clusters should develop increasing deviations from "normal" disk rotation due to the scattering by molecular clouds over time (Spitzer & Schwarzschild 1951, 1953); however, clusters that are too young may still reflect the specific dynamical environment of their birth and may not yet have circular orbits (Lynga & Palous 1987). Figure 3(c) shows that all clusters in our sample are within 500 pc of the Galactic plane, and most are within 200 pc. This supports the notion that most clusters in our sample are likely to be "well behaved" in the sense that they have not been scattered far from the Galactic midplane and therefore are likely to still be on near-circular orbits (of course, we will revisit this question when we examine cluster orbits in detail, in a future contribution).

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Less than 25% of our clusters have estimated metallicities ([Fe/H]), so we have little leverage on this aspect of our sample; however, we hope to derive metallicity estimates for some of our clusters in the future, using not only improved isochrone fits to CMDs aided with our membership data, but the spectra themselves.

Given that bulk 3D motions are our primary goal, the first stellar targets within each cluster selected for observation were those Hipparcos and Tycho-2 stars used in the Dias et al. (2001, 2002a) survey for the clusters. Because constraints on fiber optic placement with the Hydra instrument (i.e., two fibers cannot be closer than 25'' in the Hydra setup) mean that in some cases not all desired stars can be observed in a cluster field, we must prioritize stars within a fiber setup. For this reason, stars were ranked in priority order based on the Dias et al. (2001, 2002a) derived membership probabilities, from highest to lowest probability. Dias et al. (2001, 2002a) derived these probabilities based on the proper motions using the method of Sanders (1977).

Next, additional Tycho-2 stars available in the Hydra field of view, but not used in the Dias et al. (2001, 2002a) study (because they lie beyond the cluster radius studied by these authors) were added as the next priority to the target list. For the WIYN/Hydra runs, no targets beyond the Tycho-2 stars needed to be selected because the combination of a smaller number of available Hydra fibers (90 versus 132 for CTIO/Hydra) and larger field of view (60'versus 40'for CTIO/Hydra) typically meant that nearly all target fibers were filled with Tycho-2 stars.

For the CTIO runs and for fields having less than 50 stars with available Tycho-2 proper motion data, we selected at lowest priority two additional sets of stars; first, stars between V = 13–15 magnitude from the USNO-B1.0 catalog from within the cluster radius (with that value taken from the Dias et al. 2002b catalog), with the goal of searching for additional cluster members fainter than the V ∼ 13.5 magnitude limit of the Tycho-2 survey, and second, we allowed unused "field orientation probe stars" (FOPS; USNO B1.0 stars with 12 < R₂ < 13) to be added to the bottom of the target priority list. At either WIYN or CTIO, fibers that were not assigned to targets were used for sky observations, with at least six (WIYN) or ten (CTIO) fibers positioned on random sky for sky subtraction of the stellar spectra.

We have collected homogeneous spectroscopic observations for 71 open clusters using the HYDRA multi-fiber spectrographs on the Blanco 4 m telescope at Cerro Tololo Inter-American Observatory (CTIO) and the 3.5 m WIYN telescope at Kitt Peak National Observatory (KPNO). This project was conducted using publicly competed NOAO time and was granted long-term status,⁶ which permitted observations in the semesters 2002A–2004A over a total of 14 awarded CTIO 4 m and six WIYN 3.5 m nights. The data for the clusters listed in Table 1 were obtained the nights of UT 2002 March 8–12 ("Run 1"), 2003 March 16–21 ("Run 2"), 2003 July 20–23 ("Run 3"), and 2003 August 2–8 ("Run 4") from CTIO. For more efficient observing, some cluster observations scheduled for two August 2003 CTIO nights were interspersed with other targets for two other observing projects awarded telescope time over the course of eleven CTIO/Hydra nights in 2003 July and August (Runs 3 and 4). The WIYN data were observed on the nights of 2003 September 14–18 ("Run 5").

The CTIO observations made use of 132 Hydra fibers that are simultaneously dispersed onto a 2048 × 4096 pixel, SITe400mm CCD using the 380 grating with 1200 lines mm⁻¹, and with the fiber ends viewed by the spectrograph through the 100 μm slit plate to improve the resolution to a dispersion of 0.68 Å per resolution element (R ∼ 15, 000). The spectral range covered was 7740–8740 Å. Data obtained at WIYN dispersed the 90 Hydra fibers dispersed onto a 2048 × 2048 pixel CCD in the Red Bench Camera using the echelle (316@63.4) grating in sixth order; this yielded a dispersion of 0.82 Å per resolution element (R ∼ 13, 000) which was centered on the 8220–8800 Å spectral range. Typical signal-to-noise ratios (S/N) of 10 or better were obtained; all cluster stars presented have at least S/N ⩾ 5. To aid the RV calibration, multiple RV standards were observed on each run, where each "observation" of an RV standard entails sending the light of the calibrator down 2–12 different fibers, yielding many dozen individual spectra of each RV standard. We present here the results from analysis of spectra for 3436 individual stars out of 3537 with sufficient S/N observed in the fields of 71 open clusters.⁷

Preliminary processing of the two-dimensional data was undertaken using standard IRAF⁸ techniques as described in the IRAF ccdproc documentation. After completing the CCD bias subtraction, overscan correction and trimming, the two-dimensional images were corrected for pixel-to-pixel sensitivity variations and chip cosmetics by applying "milky flats" according to the prescription outlined in the CTIO Hydra manual by N. Suntzeff.⁹

After basic processing the data were run through the IRAF routine dohydra. One-dimensional spectra for each star were extracted from the two-dimensional CCD images and wavelength calibrated with respect to a comparison lamp spectrum. Exposures of the PENRAY (CTIO; He, Ne, Ar, and Xe) or CuAr (WIYN) lamps were taken at each Hydra pointing through all fibers to provide comparison spectra yielding at least 11 prominent emission lines roughly evenly distributed over the observed wavelength range. These comparison spectra provide a wavelength solution (i.e., pixel to wavelength conversion) for each extracted object spectrum.

All radial velocities were derived using IRAF's fxcor package, which we used first to determine RVs for the standard stars. Radial velocity standard stars are used to check for systematics in the data, to determine the measured RV precision, and to calibrate the zero-point of the velocity scale. The reduction to radial velocities employed essentially the classical cross-correlation methodology of Tonry & Davis (1979). The template star input to the correlator is prepared from a high-S/N standard star spectrum from which the stellar continuum is fitted and subtracted. The resulting spectrum is high- and low-pass Fourier-filtered to remove both high-frequency noise (e.g., cosmic rays) and the low-frequency variation cause by difference in instrument throughput.

We first measured the RVs of standard stars by cross-correlating each Fourier-filtered standard star spectrum against every other standard star spectrum from its corresponding observing run over the restricted wavelength range of 8220–8680 Å, which avoided possible contamination from nearby atmospheric lines. The resulting RVs from different cross-correlations for each individual standard star spectrum were averaged and the standard deviations measured; the results are presented in Table 2. The average velocity standard deviation for the individual Hydra standard star spectra is σ_v ≲ 2 km s⁻¹ for spectra with S/N ⩾ 20.

Table 2. RV Standard Observations

UT date	Star	Spec. type	Frame #	Fiber	TDR	Vr (km s−1)	V (km s−1)	Avg. (km s−1)	V,avg (km s−1)	IAU (km s−1)
				2002 March
2002 Mar 11	HD 12605	A0 V	0028	005	34.88	−19.97	2.18
2002 Mar 11	HD 12605	A0 V	0028	029	35.35	−21.50	2.17
2002 Mar 11	HD 12605	A0 V	0028	032	37.84	−20.45	1.86
2002 Mar 11	HD 12605	A0 V	0028	035	37.25	−20.31	2.02
2002 Mar 11	HD 12605	A0 V	0028	082	32.95	−20.98	1.76
2002 Mar 11	HD 12605	A0 V	0028	111	29.99	−19.91	1.87
2002 Mar 11	HD 12605	A0 V	0028	119	31.73	−20.76	1.58
2002 Mar 11	HD 12605	A0 V	0028	124	28.99	−21.13	1.74
2002 Mar 11	HD 12605	A0 V	0028	126	33.70	−21.71	1.91	−20.75	0.64	−18.5 ± 0.4
2002 Mar 11	HD 157457	G8 III	0029	010	59.12	+18.86	1.74

Notes. Stars HR 7773 and HR 675 are not IAU RV standards (see Section 3.3). ^aDue to poor S/N this star was not used as a cross-corelation template.

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VO) versions of the table are available.

Download table as:  Machine-readable (MRT)Virtual Observatory (VOT)Typeset image

We determined the level of the random and any unknown systematic RV errors from a prescription described in Vogt et al. (1995), which is based on the analysis of repeatedly observed stars (Table 2). In this case these stars were typically observed through different Hydra fibers. The Tonry–Davis Ratio (TDR; Tonry & Davis 1979) for each spectrum is measured using fxcor. Since the TDR scales approximately with S/N we can, following the method described in Vogt et al. (1995), determine approximate 1σ errors in the RVs corresponding to a given TDR as

$$\begin{equation} {\rm error}\, V_{r} = \frac{\alpha }{(1+{\rm TDR})}. \end{equation} \tag{ 1 }$$

The parameter α is a constant calibrated by the standard star data using the following formula, which is predicated on the assumption that the TDR is a good measure of the relative S/N, and where autocorrelations are not included:

$$\begin{equation} \alpha ^2 = \frac{\sum _i\!\sum _j(1+{\rm TDR}_{i,j})^2(V_{r,i,j}-\langle V_{r,j}\rangle)^2}{\chi ^2_{50,n}} \end{equation} \tag{ 2 }$$

where V_r,i,j is the ith observation of the jth standard star, and 〈V_r,j〉 is the mean RV of the jth standard star. We obtained the values of χ²₅₀ for our sample's number of degrees of freedom, where χ²_50,nis the critical value of the χ² distribution at the 50% confidence level multiplied by n degrees of freedom, as described fully in Vogt et al. (1995).

Since our target stars were selected based on proper motion criteria, they span a wide range of spectral types, including anything from hot O and Be stars to cool carbon stars. As a result, we observed a range of RV standard star templates. However, due to the lack of International Astronomical Union (IAU) RV standards hotter than spectral type A0, we used B and A stars from Fekel (1999) to provide RV standards for our hot star spectra. For a better match in the spectral types between targets and cross-correlation templates, we divided the observed standard stars into "red" or "blue" subsamples for our cross-correlation templates. Stars were considered "red" stars if the Ca ii infrared triplet (8498 Å, 8542 Å, and 8662 Å) was present in the spectra; this encompasses cool F- through early M-type stars. "Blue" stars have dominant Paschen series lines and virtually no Ca ii triplet (i.e., O- through A-type stars).

Initially we anticipated using primarily late-type stars for our analysis, so that in the earlier runs (2002 March, 2003 March, and 2003 July observations; Table 1—Runs 1, 2, 3) we did not obtain "blue" standards. Later it became clear that good RVs for hotter stars could be derived and we began to collect blue standards. To cover the lack of blue standards in the earlier runs, the "blue" August 2003 standards were used to reduce all CTIO "blue" target stars. This approach was adopted and found to work moderately well because even across observing runs all spectra were taken with the same instrument setup, are dispersion corrected uniformly, and should experience no flexure problems because Hydra uses a bench-mounted spectrograph. In the end we did find some offsets in the RV zero-points for some of the runs—but, ironically these were for the runs where we actually did take blue standards (see Sections 3.6 and 3.7).

The standard star spectra (Table 2) provide a data set for calibration of the RV errors for each run according to Equations (1) and (2). Table 2 lists each observation of a standard star, the UT date of the observation (Column 2), its spectral type (Column 3), which observation frame and fiber were used (Columns 4 and 5), the TDR (Column 6), the mean derived radial velocity (V_r), and the measured standard deviation (Columns 7 and 8), followed by the average V_r and standard deviation for the cluster (Columns 9 and 10), also the IAU or Fekel (1999) RV is shown for comparison in Column 11. Using the Vogt et al. (1995) technique and measurements from Table 2, we find the parameters given in Table 3, which are used to determine errors for each of the runs. The variation in the α values can be due to the effects of focus and small spectrograph setup variations.

To check the reliability of our measurements of radial velocity standard stars, we compare the difference between our measurements (Table 4) and the IAU or Fekel (1999) values, as shown in Figure 4. As may be seen, the derived RVs for the standard stars are all within 2.3 km s⁻¹ of the IAU values. We find that the differences between our measurement and the IAU values are no more than two times larger than the quadrature errors (as shown in Table 4); however, we find that the differences are randomly distributed and that the mean offset is less than 1 km s⁻¹. Therefore we find there are no systematic trends between our measured velocities and the cataloged values for the IAU standards, though we did find an offset for the "blue" Fekel (1999) stars, a situation that is analyzed in more depth below (Section 3.6).

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Target stars were analyzed using the same reduction procedure as the standard stars, with the exception that stars that showed both the Paschen series lines and any hint of the Ca ii triplet were considered "green" stars. As with the RV standards, the targets were sorted into "red," "blue," and "green" sub-samples based on visual inspection of their spectral features in order to match them to the appropriate cross-correlation template. Figure 5(a) shows the 2MASS color distribution of the stars selected for each subsample. The "green" stars were tested against both templates to find the best match. Nearly all "green" stars became part of the "red" sample.

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Each group of target stars was processed through IRAF's fxcor package to cross-correlate them against the standard of the corresponding color class for their respective observing run, as described in Section 3.3. "Green" stars were cross-correlated against both red and blue templates and the derived RV was taken from the template that provided the better result. The final 2MASS color distribution for stars fitted with the "red" and "blue" templates is shown in Figure 5(b). Uncertainties for the stars fitted to the "red" or "blue" templates were determined using the α values from Table 3 and Equation (1).

As an additional check on the measured RVs, we tested the internal consistency delivered by the separate "red" and "blue" reductions for a given run. To do this, stars in our "green" sample were correlated with both the "red" and "blue" standards. For stars with measured uncertainties in their blue measurement of less than 10 km s⁻¹, Figure 6 shows (V_r,blue − V_r,red) versus V_r,red, where stars with the best blue uncertainties (⩽6 km s⁻¹) are denoted with black squares. The subsample of stars with uncertainties of ⩽6 km s⁻¹ was then fitted with a line to determine if any zero point offset was needed between the red and blue samples. The fit to the data in the V_r,red versus V_r,blue plane is given by

$$\begin{equation} V_{r,{\rm adopted}} = a_0 + a_1 * V_{r,{\rm blue}}. \end{equation} \tag{ 3 }$$

The resulting fits for the 2002 March, 2003 March, 2003 August, and 2003 September runs are given in Table 5. We did not find a systematic difference between the ⩽10 km s⁻¹ and ⩽6 km s⁻¹ samples, just a larger scatter for the ⩽10 km s⁻¹ data.

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We find that the blue data are offset from the red data by a significant amount for the August 2003 and September 2003 runs, and a small offset is found for the March 2003 run. To verify that it is the red values that are more reliable and to support the rationale that we shift the blue system RVs to the red system, we next compare our RV measurements from the red sample with those of previously published, high RV resolution studies for a number of open clusters.

As an additional test of the reliability of our RVs, we have found previously published values for stars in nine clusters that we have observed. We undertook a comparison of our velocity measures to those in the following studies: IC 4561 (Mermilliod et al. 1995; Meibom et al. 2002), IC 4756 (Mermilliod & Mayor 1990), NGC 2099 (Mermilliod et al. 1996), NGC 2423 (Mermilliod & Mayor 1990), NGC 2447 and NGC 2539 (Mermilliod & Mayor 1989), NGC 2682 (M67; Mathieu et al. 1986), NGC 5822 (Mermilliod & Mayor 1990), and NGC 6134 (Claria & Mermilliod 1992). In Table 6, we present a direct star-by-star comparison of RV results to the seminal work on M67 by Mathieu et al. (1986). Table 7 provides star-by-star comparison for the other clusters listed above, which include the Tycho-2 star name, the star name from the corresponding photometry reference used for identification in the previous RV studies, the stellar coordinates, our RV (V_r) and its uncertainty, the reference RV and its uncertainty, and the per star difference in these measurements. For stars in common between the surveys, we find overall excellent agreement in the determined per star kinematics.

Table 6. NGC 2682 Comparison to Previous RV Results

Star (Tycho-2)	SAND	FBC	MMJ	ES	α2000 (h)	δ2000 (°)	Vr (km s−1)	$\epsilon _{V_{r}}$ (km s−1)	Vr, Mathieu (km s−1)	$\epsilon _{V_{r}}$ (km s−1)	ΔVr (km s−1)
0813-01125-1	0721	2554	6475	...	8:50:49.65	11:35:08.9	+33.01	0.79	+34.2	0.9	−1.2
0813-02302-1	0727	2425	5158	...	8:50:44.98	11:37:30.4	+21.44	1.82	+16.3	...	5.1
0814-02331-1	0978	3364	6482	...	8:51:17.48	11:45:22.7	+35.17	0.59	+34.7	0.6	0.5
0814-01531-1	1010	3536	6485	1008	8:51:22.81	11:48:01.8	+33.00	0.69	+33.6	0.4	−0.6
0814-01493-1	1016	3349	6484	...	8:51:17.10	11:48:16.2	+35.66	0.59	+34.3	0.7	1.4
0814-01631-1	1023	3668	6487	1001	8:51:26.84	11:48:40.5	+3.54	1.01	+3.6	1.0	−0.1
0814-01119-1	1040	3566	6488	...	8:51:23.78	11:49:49.4	+34.60	0.82	+32.0	6.3	2.6a
0814-01763-1	1054	3347	6489	4020	8:51:17.03	11:50:46.4	+32.63	0.72	+33.5	0.4	−0.9
0814-01099-1	1074	3204	6492	...	8:51:12.70	11:52:42.4	+34.50	0.68	+34.1	3.1	0.4
0814-01823-1	1221	4149	6497	...	8:51:43.56	11:44:26.4	+36.73	0.58	+34.1	3.1	2.6a
0814-01515-1	1250	3755	6499	...	8:51:29.91	11:47:16.8	+31.06	0.99	+34.3	1.4	−3.2
0814-01007-1	1277	4117	6502	3032	8:51:42.32	11:50:07.8	+33.18	0.78	+34.0	0.5	−0.8
0814-01147-1	1279	3726	6503	...	8:51:28.99	11:50:33.1	+33.93	0.66	+33.3	0.4	0.6
0814-01471-1	1288	4118	6505	3034	8:51:42.36	11:51:23.1	+32.25	0.67	+33.3	0.4	−1.0
0814-01225-1	1293	4039	6050	3035	8:51:39.38	11:51:45.4	+33.86	0.97	+34.1	0.5	−0.2
0814-00795-1	1306	...	...	3065	8:51:49.36	11:53:38.9	−2.44	0.63	−1.1	0.4	−1.3
0814-00134-1	1402	4878	6508	2152	8:52:10.97	11:31:49.2	+33.12	0.76	+33.6	0.4	−0.5
0814-00847-1	1327	3979	6507	3086	8:51:37.18	11:59:02.4	+11.62	0.87	+12.0	0.4	−0.4
0814-02313-1	1585	5191	...	...	8:52:26.33	11:41:27.7	+33.25	1.31	+34.1	0.1	−0.9

Notes. References. SAND: Sanders (1977); FBC: Fan et al. (1996); MMJ: Montgomery et al. (1993); ES: Eggen & Sandage (1964); Mathieu: Mathieu et al. (1986). ^aStar listed at spectroscopic binary in Mathieu et al. (1986).

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In Figure 7, we compare differences between our own red data and previously published RVs as a function of photometric parameters (e.g., magnitude and color) of the stars, where the data are color-coded by observing run (red = 2002 March, green = 2003 March, cyan = 2003 August, and blue = 2003 September). We find no systematic trend with magnitude or color, as shown in Figures 7(a)–(d). The bottom two plots in Figure 7 (panels e and f) show a comparison of ΔV_r versus V_r. While there may seem to be an odd trend at −25>V_r > − 40 km s⁻¹ in panel (e), this is due mainly to one cluster—IC 4651—that has a peculiar offset. This is demonstrated by the "disappearance" of that odd trend when IC 4651 is removed from the distribution (Figure 7(f); see Section 6.2.2 for a detailed discussion of IC 4651).

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Therefore, we find that our "red" sample, which we have made our standard reference, is consistent with previous work and this bears out our having corrected the blue sample RVs to the red RV system. The cause of this offset is probably due to a combination of using "blue" standards from different runs, as well as the fact that the two blue Fekel standard stars have only a few good lines for RV determination combined with large rotations with both Fekel stars having Vsin i ∼ 18 km s⁻¹.

To determine cluster membership probabilities for stars based on RV and proper motion, we have chosen to use an empirical, non-parametric technique—modified from that described in Galadí-Enríquez et al. (1998)—that incorporates a kernel estimator (Hand 1982) to isolate the phase space distribution of cluster stars in a field.

While we adopt the basic technique used by Galadí-Enríquez et al. (1998) for proper motions alone, we have generalized it also to operate on a spatially-constrained, 1D RV distribution as well as an RV-constrained, 2D proper motion distribution. In principle, one could use either distribution separately for culling cluster members, but for the most secure assessment of membership we depend on the joint probability distributions. This means, therefore, that we can only use stars having both RV and proper motion data. To improve our results further, we remove stars with large measurement errors in either proper motion or RV, or those stars that clearly have halo-like RVs, using the following constraints applied to the data:

• μ error limit: $\sqrt{\sigma ^2_{\mu _{\alpha }^*} + \sigma ^2_{\mu _\delta }} \le 10$ mas yr⁻¹
• RV limit: −200 < V_r < 200 km s⁻¹
• RV error limit: $\sigma _{V_r} \le 10$ km s⁻¹.

The modified version of the Galadí-Enríquez et al. (1998) formulation is intended to perform better for our particular survey circumstances—i.e., fewer numbers of stars per cluster, but high-quality RV data for these stars. Throughout the following description we will demonstrate the basic features of our analysis via the example processing of the cluster NGC 2682 (M67), for which the raw data are shown in Figure 8.

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For our data, the RV distribution is found to be the most sensitive discriminator of cluster membership because of the small measured relative RV errors. When applying a kernel density estimator the empirical density function (ψ^V_{c + f}) is comprised of both the cluster (c) and the field (f), where here V stands for the RV distribution. Since the observed empirical density function is the sum of two underlying distributions (e.g., ψ^V_{c + f} = ψ^V_f + ψ^V_c), one must decompose the distributions to isolate the cluster function. Because of the accuracy of the RV data and the small intrinsic velocity dispersions of open clusters (0.5–3 km s⁻¹), we expect to be able to discriminate the cluster and field fairly readily. To do so, however, we must first isolate the field population to verify which peak in the ψ^V_{c + f} distribution is due to the cluster. Differences in the cluster versus field distribution should be evident by looking at samples of stars drawn from different radii from the cluster center. A useful initial assumption is that stars outside of the cluster radius are "non-members," and these can provide a reasonable estimate of ψ^V_f.

The RV data kernel analysis is comprised of four steps: (1) all RV data are convolved with a Gaussian kernel to homogenize our errors for a given cluster. This kernel has a width determined by the mean RV errors from all of the observed stars in a given cluster field. Because open clusters have intrinsic velocity dispersions of 1–3 km s⁻¹ in addition to our measurement errors, we limit the Gaussian width to be at least 3 km s⁻¹ and at most 10 km s⁻¹. Applying the Gaussian kernel to smooth our RV data (ψ^V_{c + f}) produces the smoothed field plus cluster distribution Ψ^V_{c + f}; an example for NGC 2682 (M67) is shown in Figure 9(a). (2) We apply the same Gaussian kernel to smooth the RV data of stars that are outside the cluster radius (utilizing the cluster diameters from Dias et al. 2002b). This smoothed RV distribution is used as the field distribution Ψ^V_f (Figure 9(b)). (3) We wish to determine the probability of any particular star with a given RV being a member of the cluster, so we need to determine the normalized probability distribution:

$$\begin{equation} P^V_c (V_{r,i}) = \frac{\Psi ^V_{c+f} (V_{r,i}) - \Psi ^V_{f} (V_{r,i})}{\Psi ^V_{c+f} (V_{r,i})}. \end{equation} \tag{ 4 }$$

The cluster probability distribution P^V_c is shown Figure 9(c); however, we see that a few outliers, which are non-member stars within the cluster radius, are still visible in the distribution. (4) We assume that the strongest peak in the "cluster" probability distribution, P^V_c, belongs to the cluster, and perform a 1D Gaussian fit to this peak (Figure 9(d); dotted line). This Gaussian fit is used to determine RV membership probabilities, P^V_c, for all stars in the field and to exclude non-member RVs that still may appear in Ψ^V_c.

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The proper motion kernel analysis is similarly comprised of four steps, but now applied in 2D. This technique for proper motions is identical to that used in Galadí-Enríquez et al. (1998) with the exception that instead of using a spatial membership separation (which we used for the RV distribution described above) to establish Ψ^K_f, we have chosen to use the RV separation described above (i.e., those stars outside the Gaussian fit to the RV distribution, P^V_c = 0, are considered the "field" population). The proper motion kernel uses the following equation analogous to that used in the RV analysis above:

$$\begin{equation} P^K_c (\mu _{\alpha ^{\prime }, i},\mu _{\delta, j}) = \frac{\Psi ^K_{c+f} (\mu _{\alpha ^{\prime }, i},\mu _{\delta, j}) - \Psi ^K_{f} (\mu _{\alpha ^{\prime }, i},\mu _{\delta, j})}{\Psi ^K_{c+f} (\mu _{\alpha ^{\prime }, i},\mu _{\delta, j})}, \end{equation} \tag{ 5 }$$

where α' is αcos(δ). Continuing our example of NGC 2682, we apply the 2D kernel smoothing to the proper motion distribution as shown in Figures 10(a)–(d). The Gaussian fit to the field-subtracted distribution is used to determine proper motion membership probabilities P^K_c (Figure 10(d)) for stars in each cluster. Both the RV and proper motion kernel analysis was performed on all clusters in Table 6.

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To determine the RV membership "cutoff" criteria, we have chosen to analyze in detail one of our best-sampled clusters, our example NGC 2682. Using techniques standard dynamical techniques from Pryor & Meylan (1993), we performed an iterative 3σ rejection using the full sample of NGC 2682 RV data. We find an intrinsic velocity dispersion of σ_int = 0.96 ± 0.29 km s⁻¹. As a comparison, using proper motions, Girard et al. (1989) found that NGC 2682 (M67) has σ_int = 0.81 ± 0.10 km s⁻¹. Comparing the RV member stars left after applying the iterative 3σ rejection, we find that all of the remaining stars have P^V_c ⩾ 70%. More leniency is given to the proper motions due to the larger average error, and in this regard we follow the criterion used by Dias et al. (2001, 2002a). As a result, we have chosen to define cluster membership as stars that have P^V_c > 70% and P^K_c > 51%.

Cluster membership was determined by jointly assessing the probabilities from the 1D RV distribution (P^V_c) and the 2D proper motion distribution (P^K_c). The probabilities for each star analyzed in the cluster NGC 2682 are included along with the RV and proper motion data in Table 9. This table includes the star name from the Tycho-2 survey, or if not a Tycho-2 star, another identifier (for M67 we have IDs from Eggen & Sandage 1964; Sanders 1977; Montgomery et al. 1993; Fan et al. 1996). The table then lists, in order, the right ascension and declination for each M67 star (Columns 2 and 3), the Tycho-2 proper motions and errors (Columns 4–7), our measured RV and error (Columns 8 and 9), and which spectral cross-correlation template was used to derive these (Column 10). In addition, we have included the membership probability from Dias et al. (2001, 2002a; Column 11) for comparison to our derived membership probabilities P^K_c × 100 (PM; Column 12), P^V_c × 100 (RV; Column 13), and P^tot_c, the joint probability (P^tot_c = P^V_cP^K_c × 100; Column 14). The stars selected as cluster members are presented in boldface type.

Similar probability data are given for the other clusters in our sample in Table 10, which is available in an electronic format. In this table we give for each star observed its Tycho-2 name, or, if a non-Tycho star, an identifier with the format "XXXX_f_####" for the added "filler" candidate FOPS guide stars or "XXXX_u_####," for USNO B-1.0 catalog "filler" stars, categories described in the observational criteria in Section 2.2. In Section 6.2.3 our analysis of the cluster memberships of these stars are compared against the membership analysis by Dias et al. (2001), whose membership probabilities are based only on proper motion.

As shown in Figure 1, with only photometric data the identification of open cluster sequences in the CMD can often be a tricky prospect. Our radial velocity cluster memberships can significantly aid in clarifying the location of these cluster sequences. The 2MASS and Tycho-2 photometry for all stars in our survey with measured RVs are listed in Table 11.

Figure 11 shows the 2MASS CMD for the example cluster NGC 2682 with our spectroscopically-observed stars identified, and with large circles denoting stars selected to be members based on both RV and proper motion. Triangles denote stars that have P^V_c ⩾ 70% but which do not have Tycho-2 proper motion data. For now we present CMDs without reddening corrections applied, because this is a non-trivial process in that not all line-of-sight reddening (the values typically given in catalogs such as Schlegel et al. 1998) is necessarily foreground to the cluster. One can see from the CMD that in this case our membership census yields members that fall primarily along the photometric sequences of M67 apparent in the CMD. Similar 2MASS CMD membership plots for all clusters we have studied are shown in Figures 12–15. As in the case of M67, our identified members typically fall in the expected locations of the main sequence turn-off (MSTO) or giant branches of the clusters, when those are obvious; however, in many cases the CMDs are crowded with field star contamination and our identified members help clarify the cluster sequences. This is particularly useful in the fairly common situation where the giant branches are sparsely populated. As we shall show in another contribution (P. M. Frinchaboy et al. 2008, in preparation), our ability to clarify the CMD locations of cluster giant branches and MSTOs greatly improves the isochrone fitting for these systems.

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The cluster bulk RV is calculated using cluster members (e.g., as shown in Table 9) and techniques from Pryor & Meylan (1993) to determine the cluster mean RV and error in the mean. The cluster mean bulk proper motions are calculated using the following equations (and a symmetrical version for μ_δ):

$$\begin{equation} \langle \mu _{\alpha \cos (\delta)} \rangle = \frac{\sum _{i=1}^{n} \big(\frac{\mu _{i,\alpha \cos (\delta)}}{\sigma _{\mu _{\alpha \cos (\delta)},i}^{2}}\big)}{ \sum _{i=1}^{n} \big(\frac{1}{\sigma _{\mu _{\alpha \cos (\delta)},i}^{2}}\big)} \end{equation} \tag{ 6 }$$

$$\begin{equation} \epsilon _{\mu _{\alpha \cos (\delta)}} = \frac{1}{ \sum _{i=1}^{n} \big(\frac{1}{\sigma _{\mu _{\alpha \cos (\delta)},i}^{2}}\big)}. \end{equation} \tag{ 7 }$$

The derived cluster bulk motions are given in Table 12, where we list the numbers of members with full space motions (Column 2) and the 3D members plus the stars determined to be members by RV criteria alone (3D+RV; Column 3), along with the resulting bulk kinematics and the associated uncertainties (RV from all 3D members; Column 4), RV from 3D and additional "RV only" members (Column 5), and equatorial and Galactic system proper motions (Columns 6–9). We find two clusters NGC 1513 and NGC 7654 with only one star selected for membership (i.e., the membership method found no more than one star with a given RV within the errors); given the uncertainty in selecting among single star subsamples to define the actual "cluster," we remove these two clusters from further analysis.

6.2.1. NGC2682 (M67) Example

6.2.2. Comparison to Previously Derived Bulk Cluster Radial Velocities

A compilation of our derived mean cluster RVs compared to those found previously by other authors is given in Table 14. We have found previous results for 25 of our 71 studied clusters, some with multiple studies. In general, we find consistency with the previous studies to the few km s⁻¹ level, as shown in Figure 16, but in a few cases, there are more substantial differences.

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Table 14. Comparison of Derived Cluster RVs

Cluster	Members		Bulk Vr,3D (km s−1)	Bulk Vr,3D + RV (km s−1)	Other Vr (km s−1)	# stars	ΔVr,3D (km s−1)	ΔVr,3D + RV (km s−1)	Reference
	3D	3D+RV
Berkeley 86	2	...	−25.54 ± 2.64	...	−22.0 ± 7.0	6	+3.5	...	Forbes et al. (1992)
IC 2488	3	...	−1.84 ± 1.52	...	−2.6 ± 0.1	...	−0.8	...	Claria et al. (2003)
IC 4651	9	10	−33.34 ± 0.67	−33.30 ± 0.67	−31.0 ± 0.2	14	+2.3	+2.3	Mermilliod et al. (1995)
					−30.8 ± 0.3	44	+2.5	+2.5	Meibom et al. (2002)
IC 4756	7	13	−24.44 ± 0.75	−25.08 ± 0.64	−25.8 ± 0.6	13	−1.4	−0.7	Mermilliod & Mayor (1990)
					−25.0 ± 0.2	15	−0.6	+0.1	Valitova et al. (1990)
NGC 129	3	...	−39.41 ± 0.54	...	−38.5 ± 0.2	2	+0.9	...	Mermilliod et al. (1987)
NGC 457	2	...	−32.99 ± 0.60	...	−25.1 ± 3.0	4	+7.9	...	Liu et al. (1989)
NGC 884	3	...	−19.35 ± 1.16	...	−42.5 ± 2.8	2	−23.2	...	Liu et al. (1989)
NGC 957	2	...	−34.21 ± 1.22	...	−28.6 ± 13.8	2	−5.6	...	Liu et al. (1989)
NGC 1662	6	20	−12.16 ± 1.35	−11.95 ± 0.86	−13.9 ± 0.5	...	−1.7	−2.0	Grenier et al. (1999)
NGC 2099	3	...	+8.51 ± 0.92	...	+7.7 ± 0.9	30	−0.8	...	Mermilliod et al. (1996)
NGC 2264	1	9	+24.06 ± 2.91	+24.71 ± 0.95	+24.1 ± 8.0	6	+0.0	−0.6	Liu et al. (1989)
NGC 2354	6	7	+32.89 ± 0.39	+32.86 ± 0.38	+33.4 ± 0.3	...	+0.5	+0.5	Claria et al. (1999)
NGC 2447	13	...	+22.38 ± 0.20	...	+21.7 ± 0.7	11	−2.1	...	Mermilliod & Mayor (1989)
NGC 2516	5	57	+23.80 ± 0.71	+23.32 ± 0.26	+22.7 ± 0.4	...	−1.1	+0.6	Robichon et al. (1999)
					+24.2 ± 0.2	57	+0.4	+0.9	Terndrup et al. (2002)
					+23.8 ± 0.3	24	+0.0	+0.5	Jeffries et al. (1998)
					+22.0 ± 0.2	22	−1.8	−1.3	Gonzalez & Lapasset (2001)
NGC 2539	6	8	+28.36 ± 0.41	+28.34 ± 0.39	+29.3 ± 0.1	09	+0.9	+1.0	Mermilliod & Mayor (1989)
NGC 2546	7	9	+18.74 ± 0.57	+21.12 ± 1.32	+16.0 ± 2.0	...	−2.7	−5.1	Hron (1987)
NGC 2547	3	6	+14.22 ± 1.28	+15.65 ± 1.26	+14.4 ± 1.2	...	+0.2	−1.3	Robichon et al. (1999)
NGC 2682	10	33	+33.67 ± 0.42	+33.84 ± 0.33	+33.5 ± 0.5	104	+0.2	+0.3	Mathieu et al. (1986)
					+33.8 ± 1.3	04	−0.1	+0.0	Prichet & Glaspey (1991)
					+32.0 ± 9.0	33	+1.7	+1.8	Scott et al. (1995)
NGC 3680	10	11	+1.06 ± 0.36	+1.04 ± 0.35	+0.9 ± 0.2	6	−0.2	−0.2	Mermilliod et al. (1995)
NGC 5822	13	...	−29.46 ± 0.49	...	−29.0 ± 0.7	...	+0.5	...	Mermilliod & Mayor (1990)
NGC 6067	4	...	−39.83 ± 0.42	...	−39.9 ± 0.2	10	−0.1	...	Mermilliod et al. (1987)
NGC 6134	7	9	−27.30 ± 0.67	−27.41 ± 0.59	−26.0 ± 0.2	14	+1.3	+1.4	Claria & Mermilliod (1992)
NGC 6705	4	6	+30.48 ± 1.42	+30.87 ± 1.14	+34.5 ± 1.4	29	+4.0	+3.6	Mathieu et al. (1986)
NGC 6811	7	...	+6.03 ± 0.30	...	+7.1 ± 0.3	03	+1.1	...	Mermilliod & Mayor (1990)
Trumpler 10	2	8	+27.62 ± 3.10	+31.91 ± 0.73	+25.0 ± 3.5	22	−2.6	−6.9	Robichon et al. (1999)

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Figure 16 shows that the clusters NGC 457, NGC 884, and NGC 957 have discrepant RVs found between our work and any previous study; however all of these clusters, plus NGC 2264, were studied by Liu et al. (1989). The Liu et al. (1989) study is comprised of only a few possible cluster members observed (e.g., for NGC 884 and NGC 957 only two stars each and these clusters also have large mean errors). We believe our results, which incorporate both RV and proper motion membership, are superior to those from Liu et al. (1989). Even with the small numbers of stars in both studies, we find that our results are marginally consistent with Liu et al. (1989) for NGC 2264.

6.2.3. Comparison to Previously Derived Bulk Cluster Proper Motions

In Table 15, we compare our derived open cluster bulk proper motions with the previous results of Dias et al. (2001, 2002a). The latter surveys used only the Tycho-2 proper motions to derive membership and the cluster bulk proper motions. Table 15 compares the numbers of stars used by Dias et al. and their derived mean cluster proper motions (Columns 2–5) to our own sample statistics and derived mean proper motions (Columns 6–9). As shown in Figure 17 (gray histogram), three clusters—Collinder 258, Lynga 1, and NGC 6250—show large inconsistencies (Δμ>5 mas yr⁻¹) between our results and those of Dias et al. We also remind the reader that we have already excluded two other cases (NGC 1513 and NGC 7654; see Section 6.1) from our study, because we identified only one star selected as a possible cluster member. Looking further at the proper motion difference outliers, we find that each Lynga 1 and NGC 6250 have only one star with fully derived 3D kinematics and in the case of Collinder 258 there are only two member stars. Thus, we conclude that our analysis may have settled on the wrong star(s) to represent the cluster in these cases and that the results for Collinder 258, Lynga 1, and NGC 6250 (in addition to NGC 1513 and NGC 7654) may not be reliable. For the remaining 66 of our 71 clusters, our "re-measured" proper motions are within the 1σ errors of those found by Dias et al. (2001, 2002a), though our data generally have comparable or smaller resulting errors in the mean (as shown in Figure 17) of ∼1.5 mas yr⁻¹.

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Table 15. Comparison of Derived Mean Proper Motions to those of Dias et al. (2001, 2002a)

	Dias et al. (2001, 2002a)				This study			Comparison
Cluster	Stars	Memb.	μαcos δ (mas yr−1)	μδ (mas yr−1)	Memb	μαcos δ (mas yr−1)	μδ (mas yr−1)	Δμαcos δ (mas yr−1)	Δμδ (mas yr−1)	Dias Memb.
										Conf.	Rej.
Berkeley 86	99	50	−4.1 ± 2.2	−4.5 ± 2.2	2	−3.8 ± 1.3	−4.6 ± 1.2	−0.3	0.1	2	22
Collinder 205	19	12	−3.9 ± 1.9	6.5 ± 1.9	1	−4.0 ± 2.1	8.0 ± 1.9	0.1	−1.5	1	4
Collinder 258a	25	13	−8.1 ± 2.2	−0.8 ± 2.2	2	−0.9 ± 2.6	−5.0 ± 2.4	−7.2	4.2	0	8
Harvard 10	92	34	−2.8 ± 1.6	−11.2 ± 1.6	3	−3.9 ± 1.1	−11.6 ± 1.1	1.1	0.4	3	11
IC 2488	63	40	−5.6 ± 3.0	8.0 ± 3.0	3	−7.7 ± 1.6	8.9 ± 1.5	2.1	−0.9	3	22
IC 4651	43	19	−1.1 ± 2.1	−2.2 ± 2.1	9	−1.7 ± 0.7	−2.8 ± 0.7	0.6	0.6	7	16
IC 4756	181	30	−0.1 ± 1.3	−3.4 ± 1.3	7	0.7 ± 0.7	−2.0 ± 0.7	−0.8	−1.4	4	8
Kharchenko 1	86	40	2.1 ± 3.6	−3.5 ± 3.6	3	6.1 ± 1.2	−1.9 ± 1.3	−4.0	−1.6	3	14
Lynga 1a	23	9	−7.7 ± 2.9	−2.4 ± 2.9	1	−5.2 ± 4.5	−7.7 ± 4.1	−2.5	5.3	1	11
Lynga 2	33	13	−5.2 ± 3.2	−5.9 ± 3.2	4	−3.9 ± 1.5	−8.6 ± 1.5	−1.3	2.7	2	4
NGC 129	39	10	−1.1 ± 2.8	1.6 ± 2.8	3	−2.4 ± 1.2	−1.3 ± 1.2	1.3	2.9	3	17
NGC 381	25	13	0.9 ± 1.9	−1.3 ± 1.9	2	0.6 ± 2.9	−2.1 ± 3.0	0.3	0.8	2	9
NGC 457	29	14	−0.6 ± 2.5	−1.9 ± 2.5	2	−2.8 ± 1.4	0.0 ± 1.4	2.2	−1.9	2	9
NGC 884	46	18	−1.6 ± 2.5	0.2 ± 2.5	3	−0.6 ± 1.0	0.7 ± 1.0	−1.0	−0.5	3	12
NGC 957	28	12	1.1 ± 3.5	0.3 ± 3.5	2	0.2 ± 1.4	−1.1 ± 1.4	0.9	1.4	2	11
NGC 1513	20	6	5.0 ± 3.8	−3.6 ± 3.8	1	0.1 ± 2.7	−5.4 ± 2.6	4.9	1.8	1	8
NGC 1528	63	20	1.4 ± 1.7	−1.5 ± 1.7	5	1.3 ± 0.8	−0.9 ± 0.8	0.1	−0.6	5	14
NGC 1662	34	18	−1.9 ± 1.2	−2.2 ± 1.2	6	−1.5 ± 0.7	−2.2 ± 0.7	−0.4	0.0	6	5
NGC 1960	49	30	0.1 ± 1.6	−4.0 ± 1.6	18	0.5 ± 0.5	−4.5 ± 0.6	−0.4	0.5	8	18
NGC 2099	84	40	3.8 ± 1.8	−7.1 ± 1.8	3	4.5 ± 1.2	−7.4 ± 1.2	−0.7	0.3	3	23
NGC 2215	17	12	2.6 ± 1.9	−5.6 ± 1.9	3	5.1 ± 1.3	−6.3 ± 1.4	−2.5	0.7	3	8
NGC 2264	81	30	−1.1 ± 2.0	−3.8 ± 1.0	1	−0.4 ± 2.0	−1.2 ± 2.0	−0.7	−2.6	1	7
NGC 2301	89	45	−1.3 ± 1.8	−5.0 ± 1.8	2	−0.6 ± 1.1	−6.2 ± 1.1	−0.7	1.2	2	23
NGC 2323	100	55	0.6 ± 2.0	−1.9 ± 2.0	5	1.5 ± 0.9	−3.9 ± 1.0	−0.9	2.0	3	17
NGC 2353	35	25	−2.5 ± 2.6	0.0 ± 2.6	3	−2.8 ± 0.9	−2.2 ± 0.9	0.3	2.2	3	15
NGC 2354	69	20	−5.8 ± 2.9	−1.5 ± 2.9	6	−9.3 ± 1.2	−2.1 ± 1.1	3.5	0.6	6	19
NGC 2423	93	50	0.6 ± 1.9	−2.6 ± 1.9	20	−0.7 ± 0.4	−3.0 ± 0.4	1.3	0.4	18	22
NGC 2437	144	75	−4.5 ± 1.4	0.6 ± 1.4	18	−4.8 ± 0.5	0.1 ± 0.5	0.3	0.5	18	14
NGC 2447	69	34	−4.8 ± 1.9	4.4 ± 1.9	13	−5.2 ± 0.6	4.3 ± 0.6	0.4	0.1	13	14
NGC 2482	57	32	−4.9 ± 3.0	1.6 ± 3.0	4	−2.0 ± 0.9	4.5 ± 0.8	−2.9	−2.9	2	15
NGC 2516	81	45	−3.2 ± 1.7	10.1 ± 1.7	5	−4.2 ± 0.6	9.7 ± 0.6	1.0	0.4	5	8
NGC 2527	62	32	−4.1 ± 2.9	6.4 ± 2.9	5	−3.9 ± 1.4	6.5 ± 1.2	−0.2	−0.1	5	22
NGC 2539	50	30	−4.1 ± 1.4	−1.8 ± 1.4	6	−3.8 ± 0.8	−3.4 ± 0.8	−0.3	1.6	5	14
NGC 2546	286	80	−4.0 ± 2.2	3.6 ± 2.2	7	−3.8 ± 0.8	3.7 ± 0.7	−0.2	−0.1	7	21
NGC 2547	38	19	−7.7 ± 1.9	3.8 ± 1.9	3	−6.7 ± 0.7	3.5 ± 0.7	−1.0	0.3	3	7
NGC 2548	107	70	−0.8 ± 1.7	1.9 ± 1.7	10	0.6 ± 0.5	1.4 ± 0.5	−1.4	0.5	10	30
NGC 2567	30	17	−3.2 ± 2.6	2.3 ± 2.6	3	−3.8 ± 1.9	1.8 ± 1.7	0.6	0.5	3	8
NGC 2579	14	10	−4.1 ± 1.9	2.9 ± 1.9	2	−2.5 ± 1.4	1.4 ± 1.4	−1.6	1.5	2	5
NGC 2669	32	16	−5.8 ± 3.5	4.1 ± 3.5	1	−3.3 ± 1.3	6.2 ± 1.3	−2.5	−2.1	1	10
NGC 2670	18	9	−8.1 ± 2.2	5.9 ± 2.2	1	−6.1 ± 2.1	4.8 ± 2.0	−2.0	1.1	0	1
NGC 2682	53	30	−8.6 ± 1.5	−6.0 ± 1.5	10	−7.9 ± 0.6	−5.6 ± 0.6	−0.7	−0.4	10	9
NGC 2925	71	32	−8.9 ± 2.5	5.4 ± 2.5	2	−12.8 ± 1.6	3.6 ± 1.4	3.9	1.8	2	14
NGC 3680	24	14	−5.9 ± 2.2	2.0 ± 2.2	10	−5.8 ± 0.6	1.1 ± 0.6	−0.1	0.9	10	9
NGC 5281	29	12	−5.3 ± 2.6	−3.5 ± 2.6	2	−9.3 ± 1.7	−0.3 ± 1.6	4.0	−3.2	0	4
NGC 5316	97	25	−5.0 ± 2.3	0.2 ± 2.3	8	−5.3 ± 1.1	−0.8 ± 1.0	0.3	1.0	8	16
NGC 5460	94	40	−6.6 ± 2.7	−2.6 ± 2.7	5	−5.9 ± 0.6	−2.0 ± 0.6	−0.7	−0.6	5	22
NGC 5617	54	35	−2.0 ± 3.6	−2.3 ± 3.6	3	1.1 ± 3.0	1.8 ± 2.7	−3.1	−4.1	3	16
NGC 5662	109	60	−5.0 ± 2.9	−5.6 ± 2.9	2	−2.2 ± 1.7	−4.8 ± 1.6	−2.8	−0.8	2	26
NGC 5822	257	140	−8.0 ± 2.8	−8.2 ± 2.8	13	−8.6 ± 0.9	−8.8 ± 0.9	0.6	0.6	13	46
NGC 5823	31	10	−3.8 ± 1.9	0.1 ± 1.9	2	−4.7 ± 3.2	−0.6 ± 3.0	0.9	0.7	2	11
NGC 6025	66	30	−3.1 ± 2.0	−3.3 ± 2.0	6	−1.9 ± 0.9	−2.4 ± 0.9	−1.2	−0.9	5	15
NGC 6031	21	11	−2.4 ± 2.4	−7.5 ± 2.4	1	−1.7 ± 2.4	−9.9 ± 2.2	−0.7	2.4	2	6
NGC 6067	114	24	−1.7 ± 2.6	−2.5 ± 2.6	4	−2.7 ± 1.1	−1.8 ± 1.1	1.0	−0.7	4	8
NGC 6124	117	60	−1.3 ± 2.0	−3.1 ± 2.0	10	−0.1 ± 1.1	−3.4 ± 0.5	−1.2	0.3	10	36
NGC 6134	28	15	−0.9 ± 3.3	−4.6 ± 3.3	7	−0.1 ± 1.1	−7.0 ± 1.1	−0.8	2.4	3	3
NGC 6167	22	10	−1.4 ± 2.6	−5.5 ± 2.6	3	−1.9 ± 1.4	−1.6 ± 1.3	0.5	−3.9	0	0
NGC 6250a	23	10	−0.2 ± 1.6	−3.3 ± 1.6	1	13.5 ± 1.7	−11.2 ± 1.7	−13.7	7.9	0	3
NGC 6281	37	21	−3.4 ± 2.5	−3.6 ± 2.5	6	−2.9 ± 0.8	−3.7 ± 0.8	−0.5	0.1	6	10
NGC 6405	60	30	−2.2 ± 2.4	−5.4 ± 2.2	5	−1.5 ± 0.6	−6.1 ± 0.6	−0.7	0.6	6	12
NGC 6416	70	32	−1.4 ± 2.4	0.2 ± 2.4	6	−0.4 ± 0.9	−0.1 ± 1.0	−1.0	0.3	6	8
NGC 6603	44	22	0.7 ± 2.3	0.1 ± 2.3	3	1.0 ± 1.1	0.5 ± 1.2	−0.3	−0.4	2	6
NGC 6705	64	32	−4.6 ± 2.7	−1.1 ± 2.7	4	−5.4 ± 1.2	−0.3 ± 1.2	0.8	−0.8	4	12
NGC 6811	102	51	−5.5 ± 1.9	−7.5 ± 1.9	7	−5.3 ± 0.7	−8.1 ± 0.6	−0.2	0.6	7	26
NGC 6866	89	45	−3.4 ± 2.9	−5.0 ± 2.9	2	−5.5 ± 1.2	−8.0 ± 1.1	2.1	3.0	2	30
NGC 6885	46	20	−2.6 ± 2.6	−4.3 ± 2.6	2	−2.9 ± 1.4	−6.0 ± 1.3	0.3	1.7	2	10
NGC 7209	72	36	1.5 ± 1.9	1.4 ± 1.9	1	1.8 ± 0.7	−0.0 ± 0.6	−0.3	1.4	6	22
NGC 7654	25	10	−0.6 ± 2.7	0.9 ± 2.7	1	0.4 ± 5.0	0.6 ± 5.2	1.0	−0.3	1	8
Platais 1	59	25	−3.7 ± 2.9	−4.0 ± 2.9	3	−4.5 ± 1.1	−3.8 ± 1.1	0.8	−0.2	3	26
Ruprecht 119	31	14	−1.2 ± 1.5	−1.8 ± 1.5	3	0.9 ± 1.5	−1.2 ± 1.4	−2.1	−0.6	2	6
Stock 8	24	15	−1.0 ± 1.7	−5.4 ± 1.7	3	−1.8 ± 1.1	−4.2 ± 1.1	0.8	−1.2	3	7
Trumpler 10	44	22	−12.1 ± 1.5	6.7 ± 1.5	1	−12.2 ± 0.8	8.1 ± 0.8	0.1	−1.4	2	6

Note. ^aCluster excluded from further analysis, due to Δμ_αcos δ or Δμ_δ > 5.0 mas yr⁻¹.

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The direct comparison to the Dias et al. proper motions is shown in Figure 17, with the full sample shown in gray and various subsamples based on the number of members in either survey shown by the colored histograms. A somewhat close agreement with Dias et al. is expected because we are deriving proper motions using a subsample of Dias et al. stars and adopting the same astrometry. A key difference, however, is that a number of Dias et al. "member" stars are excluded by our RV membership criterion so that, while we typically derive approximately the same bulk motions as Dias et al., these authors allow many more actual non-members to enter their sample; nevertheless, that Dias et al. include more actual non-members seems to have relatively small effects because these authors are typically averaging over a large number of stars in each cluster, including, apparently, sufficient numbers of true members to get close to the correct proper motion. We show in Table 15 the numbers of Dias et al. member stars (P_Dias ⩾ 50%) that are confirmed to be members (Column 12) and how many we find to be unlikely members (Column 13) based on the addition of our RV analysis. On average, we find half of the Dias et al. "member" stars to be non-members when we account for the RVs. This suggests that use of proper motion data of the quality of Tycho-2 alone may be insufficient to determine reliable cluster memberships, though, when averaged over many multiple stars and applying the 3σ rejection of outlier proper motions adopted by Dias et al., these proper motions are useful for deriving the cluster bulk proper motion. The Dias et al. membership inaccuracies are likely lessened for closer clusters (e.g., d < 2 kpc) which have more bright Tycho-2 stars. Using the subsamples from Figure 17, we see that when both samples have a lot of "members" there is convergence to a common proper motion, as expected. We also see that as the sample sizes decrease the measured proper motion differences grow. It is clear that, at least in our case, when we have too few stars we may have trouble "finding" the true cluster members (e.g., as in the examples of NGC 1513 and NGC 7654). However, as both our and the Dias et al. also studies drop to a few stars per clusters, it is difficult to determine which study is correct. We argue that given our more restrictive 3D membership criteria that ours is superior, though further study will be needed to confirm this assertion. Thus, while Tycho-2 has the best currently available astrometric data, more strict RV discrimination such as we provide can substantially improve the application of these data for determining cluster motions, given a sufficient number of RV members.