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Up: Astrometric radial velocities


Subsections

   
4 Radial velocities for stars in open clusters

Partial data for astrometric radial velocities and kinematically improved parallaxes of individual stars in more nearby clusters, obtained from Hipparcos data, are in Table 2. However, the complete listing for the more than 1000 stars in all clusters and associations (some with also Tycho-2 solutions), is only in the electronic Table 2.

For some clusters, Fig. 3 shows a comparison between spectroscopic radial velocities compiled from the literature and our currently determined astrometric values. In all cases (also the ones not shown here), the astrometric values agree with the spectroscopic ones within the error limits, verifying the consistency of our method. For several stars (especially rapidly rotating early-type ones with smeared-out spectral lines), the astrometric accuracies are actually substantially better than what has been possible to obtain from spectroscopy. The high accuracies realized for the Hyades enable more detailed comparisons (Sect. 4.2.1).

A subset of known or suspected binary stars for which Hipparcos measurements could be perturbed are defined as stars that are either visual binaries with magnitude difference $\Delta m < 4$ mag and a separation $\rho < 20$ arcsec according to HIC, the Hipparcos Input Catalogue (Turon et al. 1992); known spectroscopic binaries; or flagged as suspected ones (identified in the Hipparcos Catalogue as a solution of type component, acceleration, orbital, variability-induced mover, or stochastic). In Fig. 3 and later, these stars are plotted in gray.

For finite astrometric accuracy, distant clusters of small angular extent basically yield a single astrometric velocity for all stars. This effect is seen in Fig. 3 for Coma Berenices and the Pleiades, and is similar also for Praesepe and the ``HIP 98321'' clusters (not plotted).

   
4.1 The Ursa Major cluster

The initial sample consisted of 81 stars, being the sum of the compilations from Soderblom & Mayor (1993), Dravins et al. (1997) and Montes (2000). A few of the stars identified in a previous kinematic search (Dravins et al. 1997) lacked spectroscopic radial velocities from the literature. Spectroscopic observations of these stars by Gullberg & Dravins (private comm.) made with the ELODIE spectrometer at Observatoire de Haute-Provence confirmed three of them as probable members. The rejection procedure removed four stars, producing a final sample of 77.

We chose to include stars not only from the core but also from the extended halo (the moving group sometimes called the Sirius stream), in order to improve the statistical weight of the solution. Not surprisingly, this led to a relatively high velocity dispersion among individual stars. Ursa Major may thus be viewed as a dissolved cluster moving under influence of the Galactic gravity field. Such a fate may be normal for looser open clusters reaching the age (300 Myr) of Ursa Major (Soderblom & Mayor 1993). For convenience we use the designation ``cluster'' for the entire sample of stars.

One could imagine that moving groups like Ursa Major could be ideal targets for the method since they have great angular extents. Unfortunately, as Ursa Major illustrates, the high velocity dispersion causes the errors of the estimated astrometric radial velocities to be large. However, it should be noted that the core stars have a much lower velocity dispersion. For instance, we get $\sigma_{\rm v}=1.05\pm 0.22$ km s-1 for the 13 core (nucleus) stars defined by Soderblom & Mayor (1993). Wielen (1978) considered six core stars with very well determined proper motions and found the velocity dispersion to be on the order of 0.1 km s-1 (we get $0.09\pm 0.03$ km s-1 for the same six stars), adding that the much larger stream, or moving group, has a dispersion of $\sim$3 km s-1, in good agreement with our value. Since we assume this larger dispersion for all the stars, the standard errors are probably overestimated for the core stars.

In the case of Ursa Major, no real gain results from the kinematically improved parallaxes, simply because the relative accuracy in the Hipparcos parallax values is already very good, given the proximity of this cluster.

The spectroscopic velocity values used for Fig. 3 were taken from Soderblom & Mayor (1993), Duflot et al. (1995), and in a few cases, also the ELODIE observations by Gullberg & Dravins (private comm.). In the case of Duflot et al., no explicit error is quoted, but rather a flag which seems to correspond to a numerical value that is used in the Hipparcos Input Catalogue: those values were adopted here.

   
4.2 The Hyades cluster

The Hyades cluster (Melotte 25) is the classic example of a moving cluster. Its kinematic distance, derived from a combination of proper motions and spectroscopic radial velocities, has been one of the fundamental starting points for the calibration of the photometric distance scale (e.g. Hanson 1975; Gunn et al. 1988; Schwan 1991, and references therein). Of course, the recent availability of accurate trigonometric parallaxes has now superseded this method for distance determination.

The first detailed study of the distance, structure, membership, dynamics and age of the Hyades cluster, using Hipparcos data, was by Perryman et al. (1998). From a combination of astrometric and spectroscopic radial velocity data, using 180 stars within a radius of 20 pc, they derived the space velocity for the cluster centroid, $\vec{v}_0=(-6.32,+45.24,+5.30)$ km s-1. They also estimated that the true internal velocity dispersion, near the centre of the cluster, is in the range 0.2 to 0.3 km s-1.

Our initial sample of stars was selected from the final membership assigned by Perryman et al. (1998), viz. 197 stars classified as probable members (S=1 in their Table 2): this equals our sample Hy0 in Paper II.

In earlier kinematic studies of the Hyades, systematic errors in the proper motions have been of major concern, and the probable cause of discrepant distance estimates. In our application, the solution is also sensitive to such errors, but we expect that the high internal consistency of the Hipparcos proper motion system, and its accurate linking to the (inertial) extragalactic reference frame (Kovalevsky et al. 1997), have effectively eliminated that problem.

Using the methods described in Paper II, the astrometric radial velocity and its standard deviation for each individual star is obtained through Eqs. (1) and (3), even for stars not retained in the final sample. Individual parallaxes follow directly from the estimation procedure, see Table 2.

The analysis was repeated using proper motions from Tycho-2 instead of the Hipparcos Catalogue. Being based on observations covering a much longer time span, the Tycho-2 data are expected to be more precise for binaries with periods from a few years to $\sim$100 years. By coincidence, the procedure of cleaning the sample rejected the same number of stars as in the Hipparcos case, albeit different ones (electronic Table 2). Compared to the Hipparcos solution ( $ 0.49\pm 0.04$ km s-1), we get a smaller velocity dispersion using Tycho-2 ( $0.34\pm 0.03$ km s-1). It can be noted that Makarov et al. (2000) investigated this dispersion in the Hyades as a test of the Tycho-2 proper motions, finding a dispersion close to our latter value. The two solutions for the cluster centroid velocity are equal to within their uncertainties. However, in the radial direction there is a systematic difference of $\simeq$0.9 km s-1, in the sense that the astrometric radial-velocity values from Tycho-2 are smaller than those from the Hipparcos Catalogue (while the kinematically improved parallaxes from Tycho-2 place the stars at slightly greater distances). We have no obvious explanation for this shift, which has analogues for other clusters when comparing Hipparcos and Tycho-2 solutions. Possibly, it reflects the influence of subtle systematic effects in the proper-motion data, which border on the measurement precision. If this is the case, greater confidence should be put on the solution based on the Hipparcos data, as the Tycho-2 system of proper motions was effectively calibrated onto the Hipparcos system. Future space astrometry missions should be able to clarify these matters.

It follows from Eq. (1) that any possible bias in the estimated space velocity $\widehat{\vec{v}}_0$ has only a small influence on the relative astrometric radial velocities in a given cluster, if its angular extent is not too large. Thus the astrophysical differences would still show up as systematic trends when the astrometric radial velocities are compared with spectroscopic values. In such a comparison, the bias in space velocity would mainly introduce a displacement of the zero-point, as mentioned above.

  \begin{figure}
\centering
\includegraphics[width=8.7cm,clip]{H3138F4.eps}\end{figure} Figure 4: The Hyades: Differences between spectroscopic radial-velocity values from the literature, and current astrometric determinations. Systematic differences depend on spectral type, and on the projected stellar rotational velocity $V \sin i$. (These dependences are correlated since rapid rotation dominates for early-type stars.) An increased blueshift of spectral lines in stars somewhat hotter than the Sun ( $B-V\simeq 0.3$-0.5) is theoretically expected due to their more vigorous surface convection, causing greater convective blueshifts. Gravitational redshifts of white-dwarf spectra place them far off main-sequence stars. The error bars show the combined spectroscopic and astrometric errors; stars with errors >3 km s-1 are omitted (except for white dwarfs), as are stars that were not retained by kinematic solutions from both Hipparcos and Tycho-2 data.

   
4.2.1 Hyades: Comparison with spectroscopic data

The astrophysical potential of astrometric radial velocities begins to appear when the accuracy is sufficiently high to detect differences relative to spectroscopic values (e.g., Dravins et al. 1999a; Dravins 2001, and references therein). Such differences are expected due to stellar surface convection (``granulation''): most photons from a stellar surface are emitted by hot and rising (thus locally blueshifted) convective elements, which contribute a greater number of photons than the cool, dark and sinking areas. The resulting statistical bias causes a convective blueshift, theoretically expected to range from some 0.2 km s-1 in red dwarfs, $\simeq$0.4 km s-1 in the Sun, to 1.0 km s-1 in F-type stars with their more vigorous surface convection, the precise amount varying among different spectral lines with dissimilar conditions of formation. Gravitational redshifts are expected to vary greatly between giants (<0.1 km s-1), main-sequence stars (0.5-1 km s-1), and white dwarfs (perhaps 30 km s-1), with almost identical redshifts throughout the spectra. Additional effects enter for pulsating stars, stars with expanding atmospheres, and such with other spectral complexities.

Our current accuracies permit such studies to be made for the Hyades, and perhaps marginally for a few other clusters. In Fig. 4 we show the difference between astrometric radial velocities and spectroscopic measurements from the literature. The latter values are taken from the compilation by Perryman et al. (1998), which mostly are measurements by Griffin et al. (1988). The values used here are their original measurements, i.e. not applying any zero-point or other spectral-type dependent ``corrections'' (such as were later applied in a convergent-point analysis for the Hyades from the same data by Gunn et al. 1988). The plot also includes white dwarfs, whose astrometric velocities are from Eq. (1), and where the spectroscopic data are ``weighted values'' (H$\alpha $ weighted with twice the weight of H$\beta$) from Reid (1996).

The errors for Fig. 4 were calculated as the quadratic sum of the spectroscopic and astrometric uncertainties, where Eq. (3) was used for the latter. Most of the errors are due to the spectroscopic measurements, and it can be noted how the scatter is greater for the [suspected] binary stars.

Over much of the main sequence, convective blueshifts and gravitational redshifts partly cancel one another: an increased convective blueshift in hotter stars is partly balanced by an increased gravitational redshift in these more massive stars. Nevertheless, it is theoretically expected that the strong increase in the vigour of surface convection for middle F-stars ( $B-V\simeq 0.4$) should blueshift their spectra by $\simeq$1 km s-1 relative to those of later-type G or K-type stars ( $B-V\simeq 1.0$). For yet earlier-type stars, there do not yet exist any detailed theoretical models in the literature from which the convective shift can be reliably predicted.

We believe the expected effects are visible in Fig. 4. There is clearly a gradient in the relevant spectral range (B-V between 0.4 and 0.7), with roughly the theoretically expected sign and magnitude of the effect. The trend seems to continue towards even earlier types.

This is not the first time spectral-type dependent radial velocities are seen: a trend of increased spectral blueshift in earlier-type stars was already suggested from residuals in the convergent-point solution by Gunn et al. (1988). A difference between the wavelength scale of giants and dwarfs, suggesting differences in gravitational redshift, was noted from velocity histograms of giants and dwarfs, respectively, in the open cluster NGC 3680 by Nordström et al. (1997).

Both of these works raise an important point relating to the sample selection. Spectroscopic velocities are usually important for the determination of membership probabilities, which are therefore in principle affected by systematics of the kind shown in Fig. 4. Spectral shifts should therefore be taken into account, lest they influence the membership determination and hence the final result, including the spectral shifts themselves. Our initial Hyades sample is based on that of Perryman et al. (1998), who used their compilation of spectroscopic radial velocities to compute membership probabilities. Given the relatively large spectroscopic uncertainties for the early-type stars, this effect probably did not affect the present Hyades sample. However, as long as the mean spectral shifts remain unknown, e.g. as a function of spectral type along the main sequence, it would be necessary to downweight the more precise spectroscopic velocities in order to avoid possible selection effects related to the spectral shifts.

The errors in the spectroscopic velocities in several of the hottest (and often rapidly rotating) stars are large, making conclusions in that part of the diagram difficult. For such stars with often complex spectra and perhaps expanding atmospheres, the concept of spectroscopic radial velocity must be precisely defined, if studies on the sub-km s-1 are to be feasible (cf. Andersen & Nordström 1983; Griffin et al. 2000).

  \begin{figure}
\centering
\includegraphics[width=8.8cm,clip]{H3138F5a.eps}\vspac...
....eps}\vspace*{4mm}
\includegraphics[width=8.8cm,clip]{H3138F5d.eps} \end{figure} Figure 5: The Hyades: Improved definition of the Hertzsprung-Russell diagram from kinematically improved parallaxes. From top: a) apparent magnitudes as measured by Hipparcos; b) absolute magnitudes from Hipparcos parallaxes tighten the main sequence since the cluster depth is resolved; c) absolute magnitudes from kinematically improved parallaxes computed from Hipparcos data greatly improve the definition of the main sequence (especially for the fainter stars), further marginally improved by the use of Tycho-2 data d). This permits searches for fine structure in the HR-diagram, and also confirms the validity of the kinematic solution for the radial-velocity determinations. Only single stars, retained by the kinematic solutions from both Hipparcos and Tycho-2 data, are plotted.

4.2.2 Hyades: The Hertzsprung-Russell diagram

Already the trigonometric parallaxes from Hipparcos yield quite accurate absolute magnitudes, enabling a precise Hertzsprung-Russell diagram to be constructed. Our kinematically improved parallaxes permit this to be carried further, also verifying the working of our mathematical methods.

Figure 5 shows the gradual improvements in the definition of the Hyades main sequence with successively better data. The top frame shows the apparent magnitudes (i.e., effectively placing all stars at the same mean distance); the second frame shows the improvement from Hipparcos having been able to resolve the depth of the cluster; the third frame uses our kinematically improved parallaxes which, especially for the fainter stars, significantly improve the definition of the main sequence. This is further marginally improved by the use of Tycho-2 data in the bottom frame. The plot only shows those stars that were retained in both the Hipparcos and Tycho-2 solutions, and excludes [suspected] binary stars as defined in Sect. 4.

Besides permitting searches for fine structure in the HR diagram, this also confirms the validity of the kinematic solution for the radial-velocity determinations: since no photometric information was used in the solution, such an improvement could hardly be possible unless the underlying physical model is sound. With the kinematically improved parallaxes the error in $M_{\it Hp}$ is typically only $\sim$0.03 mag, much smaller than the symbol size in Fig. 5.

In addition to the two giants retained in the solutions, a few stars lie off the main sequence. Below it is HIP 10672 at B-V = 0.567, a single star quite far (some 30 pc) from the cluster centre; HIP 17962 at B-V = 0.782, an eclipsing binary containing a hot white dwarf (Nelson & Young 1970) which causes a displacement towards the blue; and HIP 19862 at B-V = 0.924, with an uncertain colour index in the Hipparcos Catalogue ( $\sigma_{B-V}=0.301$) - the value $B-V = 1.281 \pm 0.009$given in the Hipparcos Input Catalogue (Turon et al. 1992) would place it exactly on the main sequence. All these stars have an uncertainty in  $M_{\it Hp}$of 0.05 mag or less, meaning that they are not misplaced vertically. Simulations of a Hyades-type cluster by Portegies Zwart et al. (2001) showed that a few stars end up below the main sequence as a result of binary interaction leading to blueward displacements. From Fig. 5 it is difficult to tell where the turnoff point really is: some stars to the far left may be blue stragglers.

The rest of the cluster stars lie practically on a single curve, which can be considered a confirmation of the parallax improvement. It is not clear whether the remaining spread of the main sequence in $M_{\it Hp}$ is real or can be accounted for by uncertainties in B-V, although these are small. Effects such as differential reddening within the cluster seem unlikely: Taylor (1980) found only a very small colour excess $E(B-V)=0.003 \pm 0.002$ mag for the Hyades.

Improved absolute magnitudes were also determined by de Bruijne et al. (2001) based on our original method (Dravins et al. 1997). Lebreton et al. (2001) compared our kinematically improved parallaxes to those by de Bruijne et al., finding excellent agreement in all values, except for one star (HIP 28356). We note that this particular star is the one located the furthest from the cluster centre, and is also one where our cleaning procedure removed it from the Tycho-2 solution (although it was retained in Hipparcos data). It may be a long-period binary whose photocentric motion causes a deviation in the modulus of the measured proper motion, if not in its direction.

For further discussions of the post-Hipparcos HR diagram for the Hyades, see Perryman et al. (1998), Madsen (1999), Castellani et al. (2001), de Bruijne et al. (2001), and Lebreton (2000), where the latter four have used the improved parallaxes.

4.3 The Coma Berenices cluster

The Coma Berenices sample is made up of the 40 Hipparcos stars in Odenkirchen et al. (1998). This sample includes four stars that, while slightly beyond their selected limit for membership, nonetheless were considered to ``very probably also belong to the cluster''. Since the small number of stars made the solution unstable already after rejecting two of them, the results in Table 1 are given for the full sample ( $g_{\rm lim}=\infty$). Although the typical errors in the astrometric radial velocities are only 1.2 km s-1, the precision of published spectroscopic values is generally insufficient for meaningful comparisons.

The kinematically improved parallaxes produce only a slight improvement in the HR diagram at the red end of the main sequence (Fig. 6).

4.4 The Pleiades cluster

The sample contains 60 stars from van Leeuwen (1999, and private comm.). The stars are too few and/or the cluster too distant for the basic cluster model to give a direct estimate for the velocity dispersion. It has instead been estimated by the procedure described in Appendix A.4 of Paper II. No improvements to the parallaxes result from the kinematic solution, since our method is unable to resolve the depth of this cluster; it therefore in essence ascribes the same distance to every star. The small angular extent means that also the astrometric radial velocity is practically the same for all stars (Fig. 3, bottom).

As seen in Fig. 6, the Pleiades main sequence occupies a position at the lower edge of the distribution for the different clusters. The Pleiades cluster is at the focus of an ongoing debate concerning possible localized systematic errors in the Hipparcos parallaxes (see e.g. Pinsonneault et al. 1998, 2000; Robichon et al. 1999; Narayanan & Gould 1999; van Leeuwen 1999, 2000; Paper II; Stello & Nissen 2001). If such errors were present in our input data, they would not be detected by the present maximum-likelihood method, but would affect also the kinematically improved parallaxes. Consequently, the present results provide no direct new information towards the resolution of this issue.

4.5 The Praesepe cluster

The investigated sample was based on 24 stars from van Leeuwen (1999, and private comm.). As for the preceding two clusters, the solution places the stars at practically the same distance. The resulting mean astrometric radial velocity has an error of $\simeq$15 km s-1. While demonstrating the applicability of the method, this present accuracy is insufficient for detailed stellar studies.

  \begin{figure}
\centering
\includegraphics[width=8.8cm,clip]{H3138F6.eps} \end{figure} Figure 6: Hertzsprung-Russell diagram for single stars in the better-defined open clusters, obtained using kinematically improved parallaxes from Hipparcos data. Hp magnitudes are given since these are more precise than ground-based V ones, and since Hp values are available for all stars in this sample (values for $M_{\it Hp}$ fall quite close to those of MV). The random errors in these kinematically improved parallaxes are lower by factors of typically 2 or 3 compared with the original Hipparcos values, and the absolute magnitudes are correspondingly more precise, beginning to reveal fine structures in the HR diagram. For the Hyades, de Bruijne et al. (2000, 2001) suggested the existence of two underpopulated main-sequence segments around $B-V\simeq 0.38$ and 0.5, identified as ``Böhm-Vitense gaps'', theoretically predicted due to changing efficiencies of stellar convection at the corresponding temperatures. However, these gaps are not seen in other clusters, and their ``existence'' is consistent with small-number statistics causing random clustering. This probably also applies to the apparent ``Gap 3'' at $B-V\simeq 0.8$.

4.6 A composite HR diagram

Kinematically improved parallaxes from the different clusters enable a very detailed comparison between the main sequences of different clusters. Such a Hertzsprung-Russell diagram for five nearby clusters is in Fig. 6. We again stress that, while our kinematic solution reduces the random noise, it does not address any possible systematic effects and therefore cannot decide whether, e.g. the systematic shifts in luminosity between different clusters are caused by astrophysical or by instrumental effects.

However, the very low noise level permits to search for morphological fine structures in the HR diagram. From post-Hipparcos data for the Hyades, de Bruijne et al. (2000, 2001) suggested the existence of two underpopulated main-sequence segments around B-V approx 0.38 and 0.5, identified as ``Böhm-Vitense gaps'', theoretically predicted due to changing efficiencies of stellar convection at temperatures corresponding to those particular colours. However, these gaps are not seen in other clusters, and their ``existence'' is consistent with small-number statistics causing random clustering. This probably also applies to the apparent ``Gap 3'' at $B-V\simeq 0.8$. (Of course, the detectability of such gaps depends also on the precision in the other axis, i.e. the colour index.) Although some authors have suggested a possible presence of such ``gaps'' (e.g., Rachford & Canterna 2000), extensive analyses of field stars, using Hipparcos parallaxes, failed to show any (Newberg & Yanny 1998).

A certain fine structure (wiggles, etc.) is theoretically expected in the HR- diagram (e.g., Siess et al. 1997); possible hints of that are becoming visible for the Hyades.


   
Table 2: Data for individual stars for the better-defined clusters. Estimated radial velocities and their standard errors are derived from Eqs. (1) and (3), using the adopted solutions in Table 1 and the corresponding covariances. Columns: HIP = Hipparcos Catalogue number, $\widehat{v}_{{\rm r},\rm Hip}=$ astrometric radial velocity [km s-1] obtained from the kinematic solution using data from the Hipparcos main catalogue; $\widehat{\pi}_{\rm Hip}=$ estimated parallax [mas] from the kinematic solution using data from the Hipparcos main catalogue; $\epsilon(\widehat{\pi}_{\rm Hip})=$ standard error [mas] of this estimated parallax. Part 1: data for Ursa Major and Hyades. The complete table for all clusters and associations, including results and errors obtained from both Hipparcos and Tycho-2 data, is available in electronic form.

HIP
$\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ HIP $\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ HIP $\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ HIP $\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ 

Ursa Major

2213
3.16.60.6 38228-17.745.80.9 61100-12.241.12.9 772332.621.30.8 
84863.842.63.8 42438-15.470.00.7 61481-12.038.11.1 8033712.477.60.9 
84973.742.40.9 43352-6.814.01.1 61621-1.029.00.7 8068612.382.60.6 
10403-7.324.40.9 46298-12.819.10.9 61946-11.843.00.8 80902-8.636.70.6 
10552-1.028.92.7 48341-12.816.10.8 62512-11.640.83.0 827804.07.20.6 
178741.415.80.6 48356-10.611.60.8 62956-11.440.30.6 83988-2.446.51.8 
18512-6.063.32.0 49593-16.635.70.8 63008-8.828.31.5 83996-2.446.12.8 
19655-12.038.51.3 49929-15.115.10.8 63503-11.240.00.6 87079-6.325.10.6 
19855-8.347.81.1 50335-15.912.40.8 64405-9.011.51.2 8869416.057.60.8 
19859-8.347.11.1 51814-15.237.80.6 64532-10.838.90.7 911599.828.91.5 

21818
-11.774.61.2 53910-14.741.10.6 65327-10.539.81.4 94083-6.636.60.5 
23875-9.036.70.8 53985-14.285.71.4 65378-10.341.70.6 962581.239.20.5 
25110-12.047.70.5 55454-6.275.81.7 65477-10.340.20.6 10102717.233.00.9 
27072-6.8111.50.6 56154-7.415.70.8 66459-8.191.71.2 10373817.714.50.8 
27913-14.8115.41.1 57283-5.69.40.7 69989-2.338.20.8 1064812.626.20.5 
28954-14.764.70.9 57548-9.2299.92.2 71876-8.223.50.6 11009112.924.10.9 
30277-5.213.90.6 58001-13.439.00.7 72944-0.6101.71.7 1124601.4198.22.0 
30630-15.668.31.1 59496-12.735.31.2 73996-1.550.90.8      
32349-10.1379.21.6 59514-12.865.61.5 75312-1.653.81.2      
36704-17.750.81.3 59774-12.740.00.6 76267-0.343.60.8      

Hyades

10672
21.3017.00.3 1987037.8820.60.3 2071138.6021.70.3 2147440.5420.60.3 
1270925.7954.00.8 1987738.5121.50.3 2071238.8320.90.3 2148238.6552.00.6 
1360027.7315.30.3 1993437.8019.70.3 2074139.5022.20.4 2154340.6919.70.6 
1380626.8624.50.3 2001938.5621.10.3 2074539.8425.10.8 2158940.9422.30.4 
1383427.9730.50.3 2005638.4621.90.3 2075139.9323.00.5 2163739.6723.30.3 
1397628.6042.80.5 2008238.7222.40.5 2076239.8321.30.5 2165440.9022.80.4 
1497628.3225.00.3 2008738.0318.30.2 2081539.7121.20.3 2167041.1720.40.4 
1530030.0625.50.6 2013038.3421.90.3 2082639.9922.30.4 2168340.7718.30.3 
1556331.7232.10.4 2014638.6621.60.4 2082739.8220.50.4 2172341.0822.90.6 
1572030.6031.00.5 2020538.9122.10.3 2084238.9720.20.3 2174139.7516.60.3 

16529
32.4723.70.3 2021538.8424.30.4 2085039.8921.60.4 2176240.8121.10.8 
1654833.4118.30.6 2021939.0622.30.3 2087339.8622.00.5 2204441.5722.70.4 
1690833.3921.30.3 2023738.5622.20.3 2088939.3921.90.3 2217741.7122.00.7 
1776635.5127.30.5 2026139.0421.00.3 2089039.3220.90.3 2220341.4421.20.4 
1796235.4421.00.3 2028439.1720.60.3 2089439.7822.20.4 2222441.2122.90.5 
1801834.6724.30.7 2034938.4320.20.3 2089939.6521.60.3 2225340.4018.30.4 
1817035.7723.70.3 2035038.8021.40.3 2090140.0221.30.3 2226541.2120.00.4 
1832236.3221.50.4 2035739.2020.40.3 2091639.7918.70.5 2227139.7627.30.5 
1832736.0324.40.4 2040039.2722.30.3 2093539.6721.80.3 2235040.8620.60.4 
1865836.9423.50.5 2041939.4622.10.5 2094839.6521.80.3 2238041.2720.90.4 

18735
36.5822.00.3 2044039.2721.70.5 2094938.1217.30.3 2239440.1820.40.4 
1894636.7621.00.4 2045539.0421.10.3 2095139.6522.30.4 2242241.6520.80.4 
1908236.9620.80.5 2048038.5619.80.3 2097839.8322.00.4 2250541.8121.90.4 
1909837.1622.10.4 2048238.8219.20.3 2099539.9522.30.4 2252441.7220.30.4 
1914837.4420.90.3 2048439.1720.80.3 2100839.4619.10.3 2255042.1521.30.4 
1920737.5621.60.4 2048539.2724.90.5 2102939.9321.80.3 2256541.4319.30.3 
1926137.6522.60.3 2049138.0418.70.3 2103640.1522.40.3 2256641.8516.40.3 
1926337.5321.70.4 2049239.3821.00.4 2103939.9921.70.4 2265441.4819.20.5 
1931637.9120.80.5 2052739.4622.60.6 2106640.3421.90.4 2285041.6115.90.3 
1936535.5714.70.2 2054239.1722.10.3 2109939.5121.70.4 2306942.4818.00.4 

19441
38.1528.30.5 2055738.5923.60.4 2111240.2219.60.3 2321442.4423.30.4 
1950437.6622.50.3 2056339.1222.30.5 2112339.8722.10.4 2331242.9419.30.5 
1955438.2826.50.4 2056739.2419.80.4 2113740.0922.80.3 2349741.8419.10.3 
1959137.0325.20.4 2057739.2721.80.4 2113840.1321.11.0 2349842.9018.40.5 
1978138.4319.80.3 2060539.4020.81.5 2115240.4623.80.4 2370143.3418.50.7 
1978638.5721.60.4 2061439.0621.60.3 2117940.3721.90.6 2375042.6718.80.4 
1978937.5017.60.2 2063538.6021.10.3 2125639.5623.20.4 2398343.5619.00.4 
1979337.3122.40.3 2064138.6222.50.3 2126139.8921.60.5 2401940.8117.90.3 
1979638.6522.00.3 2064839.2521.80.3 2126740.4921.80.4 2411642.5312.40.3 
1980838.5821.90.5 2066139.4821.30.3 2127340.3722.40.5 2492344.1717.70.5 

19834
38.5321.30.8 2067939.2722.90.5 2131740.3822.00.4 2638244.4919.70.5 
1986238.4621.80.5 2068639.1722.10.4 2145939.4323.60.3 2835645.8313.40.6 


 
Table 2: (Continued) Data for individual stars for the better-defined clusters. Part 2: data for Coma Berenices, Pleiades and Praesepe. The complete table for all clusters and associations, including results and errors obtained from both Hipparcos and Tycho-2 data, is available in electronic form.

HIP
$\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ HIP $\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ HIP $\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ HIP $\hat{v}_{{\rm r},\rm Hip}$ $\hat{\pi}_{\rm Hip}$ $\epsilon(\hat{\pi}_{\rm Hip})$ 

Coma Berenices

59364
-1.411.00.6 60123-1.611.50.6 60525-1.510.70.6 61205-2.213.21.0 
59399-1.310.50.8 60206-1.411.30.7 60582-1.510.30.7 61295-1.610.40.5 
59527-1.411.40.6 60266-1.411.00.6 60611-1.311.40.7 61402-1.811.00.7 
59833-1.310.40.6 60293-1.510.90.8 60649-1.612.00.6 62384-1.711.90.7 
59957-1.411.30.6 60304-1.611.10.7 60697-1.613.10.5 62763-2.110.90.6 
60014-1.812.30.6 60347-1.211.20.6 60746-1.611.60.5 62805-2.012.50.8 
60025-1.212.20.7 60351-1.511.40.5 60797-1.610.90.6 63493-2.011.70.7 
60063-1.311.50.7 60406-1.510.60.7 61071-1.511.20.5 64235-2.812.81.0 
60066-1.412.30.5 60458-1.611.60.6 61074-1.711.90.6 65466-2.511.70.6 
60087-1.211.60.5 60490-1.511.80.5 61147-1.911.60.6 65508-2.611.20.8 

Pleiades

16217
9.18.60.2 1728911.27.90.3 1757310.78.50.2 1784711.08.30.2 
164079.68.70.2 1731711.48.40.3 1757910.68.40.2 1785110.98.70.2 
166359.98.20.4 1732512.48.70.2 1758310.28.50.2 1786210.88.30.2 
1663910.28.20.3 1740110.98.50.2 1758810.68.30.2 1789211.78.40.2 
1675310.98.70.3 1748112.28.30.2 1760712.27.90.4 1790011.28.20.2 
1697911.28.10.3 1748910.78.30.2 1760810.98.10.2 1792311.18.20.3 
1700011.18.40.2 1749711.18.40.2 1762510.18.40.2 1799911.18.40.2 
1702010.38.10.3 1749910.88.50.2 1766410.78.60.2 1805010.98.50.2 
1703410.28.60.2 1751111.78.10.3 1769211.08.30.2 1815410.88.30.3 
1704410.48.40.3 175259.88.90.5 1769411.48.50.3 1826311.19.10.4 

17091
10.98.80.3 1752710.58.60.2 1770210.98.10.2 1826612.48.30.4 
171258.98.10.3 1753110.67.90.2 1770410.88.30.2 1843111.78.60.2 
171688.57.50.4 175478.78.90.3 1772910.38.60.2 1854412.89.50.3 
1722510.98.60.3 1755212.19.00.2 1777611.28.70.2 1855911.38.20.2 
1724510.08.00.3 1757211.28.50.2 1779110.88.00.2 1895512.18.50.3 

Praesepe

41788
385.90.3 42327375.70.3 42556365.50.2 42952365.30.3 
42133375.70.3 42485365.70.3 42578365.30.2 42966356.00.3 
42164375.70.3 42516365.40.2 42600365.00.2 42974355.80.3 
42201375.60.3 42518365.80.3 42673365.70.3 43050355.80.3 
42247375.60.3 42523365.70.3 42705365.90.3 43086365.60.3 
42319375.70.3 42549365.70.3 42766365.70.3 43199355.20.4 



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