2 Potential of the moving-cluster method

The achievable accuracies of the moving-cluster method were discussed in Paper I. We recall that the best radial-velocity accuracy is obtained for star-rich nearby clusters with large angular extent, large proper motions, small internal velocity dispersions, and small rates of cluster expansion. The improved astrometric accuracies expected from future space missions will somewhat lessen these constraints, although the intrinsic limitations set by internal velocities cannot be overcome by increasing observational accuracy.

Only about ten clusters and associations can be meaningfully studied already with current astrometric accuracies in the milliarcsecond range. Furthermore, good astrometric data are available only for their relatively brighter stars. The distribution on the sky and the geometries of these nearby clusters are shown in Figs. 1 and 2, together with their stellar populations, and their proper-motion patterns. Only a few among these (Hyades, Pleiades, Coma Berenices, Praesepe) have a utilizable stellar population spanning many spectral types; several of the others are heavily dominated by early-type stars. The main reason for this is of course the limiting magnitude of the Hipparcos mission. The areas subtended on the sky differ greatly: some OB-associations spread out over much of a hemisphere, while some other clusters are very localised. Although the great spatial extents of the Ursa Major cluster and the Scorpius-Centaurus associations in principle are advantageous for the accuracy obtainable, the partly unknown expansion rates and internal velocity patterns of these younger stellar groups actually limit the accuracy in their radial-velocity determinations. For more data on these clusters, see Table 4 in Paper I.

   

Table 1: Estimated space-velocity components and internal velocity dispersions of clusters and associations analyzed with the moving-cluster method, using astrometric data from the Hipparcos main catalogue. $n_{\rm acc}$ is the number of stars retained in the cleaned sample for each cluster, $n_{\rm rej}$ is the number of stars removed in the cleaning process; $\widehat{v}_{0x}$, $\widehat{v}_{0y}$, and $\widehat{v}_{0z}$ are the equatorial (ICRS) components of the estimated space velocity of the cluster centroid; $\widehat{\sigma}_{\rm v}$ is the estimated internal velocity dispersion among individual stars, calculated as described in Paper II, Appendix A.4. The last three columns give the equatorial coordinates $(\alpha_0,\delta_0)$[deg] of the adopted centroid of the cluster (or, in the case of Ursa Major, its core) and the space velocity component $\widehat{v}_{0r}$ toward that direction, i.e. an approximate radial velocity of the cluster as a whole. Uncertainties are given as $\pm 1$ standard error. All velocities are in km s^-1. The electronic version of the table contains, additionally, the six equatorial components of the formal covariance matrix $\mbox{Cov}(\widehat{\vec{v}}_0)$, the spherical equatorial coordinates of the convergence point with standard errors, and the total velocity with its standard error.

Name	$n_{\rm acc}$	$n_{\rm rej}$	$\widehat{v}_{0x}$	$\widehat{v}_{0y}$	$\widehat{v}_{0z}$	$\widehat{\sigma}_{\rm v}$	$\alpha_0$	$\delta_0$	$\widehat{v}_{0r}$
Ursa Major	77	4	$+8.44\pm 0.41$	$-12.19\pm 0.39$	$-10.16\pm 0.43$	$2.82\pm 0.23$	187.3	+56.4	$-12.24\pm 0.46$
Hyades	168	29	$-5.90\pm 0.13$	$+45.65\pm 0.34$	$+5.56\pm 0.10$	$0.49\pm 0.04$	66.5	+16.9	$+39.42\pm 0.36$
Coma Berenices	40	0	$-0.82\pm 0.96$	$+4.57\pm 0.15$	$-4.11\pm 0.48$	$0.47\pm 0.09$	187.5	+26.4	$-1.64\pm 1.07$
Pleiades	60	0	$+1.99\pm 2.20$	$+22.95\pm 3.34$	$-18.73\pm 1.82$	$0.50\pm 0.13$	56.4	+24.0	$+10.85\pm 4.36$
Praesepe	24	0	$-1.46\pm 9.03$	$+48.1\pm 10.9$	$+2.00\pm 5.02$	$0.67\pm 0.23$	130.2	+19.6	$+36.2\pm 15.0$
Lower Cen Crux	179	1	$-0.94\pm 0.29$	$+18.36\pm 0.15$	$-8.59\pm 0.46$	$1.13\pm 0.07$	189.6	-56.2	$+5.95\pm 0.53$
Upper Cen Lupus	218	3	$-4.01\pm 0.27$	$+16.47\pm 0.32$	$-12.91\pm 0.37$	$1.23\pm 0.08$	230.3	-41.6	$+1.01\pm 0.51$
Upper Scorpius	120	0	$-3.73\pm 0.56$	$+9.36\pm 1.09$	$-14.57\pm 0.57$	$1.33\pm 0.12$	243.4	-24.1	$-0.17\pm 1.33$
Sco OB2	510	11	$-1.72\pm 0.15$	$+18.19\pm 0.15$	$-10.43\pm 0.21$	$1.52\pm 0.06$	225.1	-43.9	$-1.17\pm 0.26$
$\alpha$ Per (Per OB3)	78	1	$-3.23\pm 0.89$	$+27.15\pm 1.26$	$-11.76\pm 1.64$	$0.71\pm 0.13$	52.9	+47.8	$+4.53\pm 2.18$
``HIP 98321''	59	0	$-3.45\pm 0.66$	$+15.55\pm 1.26$	$-12.27\pm 1.13$	$2.56\pm 0.26$	297.5	+39.4	$-19.68\pm 1.74$