5 Application to OB associations

The procedures of determining astrometric radial velocities were applied also to a number of nearby associations of young stars. The situation is here somewhat different from that of the previously discussed older clusters because (at least some of) these younger associations may be undergoing significant expansion, or have otherwise complex patterns of stellar motion on levels comparable to our desired accuracies. We recall that the present moving-cluster method is based upon measuring the rate of angular expansion or contraction: it cannot therefore segregate whether a change in angular scale occurs because the cluster is approaching or expanding. While - on the accuracy levels aimed at - this should not be a problem for the older clusters, the likely expansion of young associations may introduce significant biases in the solution. Another complication is that, since some of the associations cover large areas of sky, there is an increased risk for contamination of the samples by field stars. Further, spectroscopic radial velocities often cannot be used to decide membership, both because they do not exist in significant numbers, and because their actual measurement is difficult for the often rapidly rotating O and B-type stars that make up much of these associations. For such reasons, the associations are here being treated separately.

The predictions in Paper I indicate that the accuracies of Hipparcos should enable astrophysically interesting results to be obtained for perhaps half a dozen of the nearer associations. Among these, Lower Centaurus Crux, Upper Centaurus Lupus and Upper Scorpius form part of the larger Scorpius OB2 complex, while the $\alpha$ Persei and ``HIP 98321'' associations are independent entities.

Except for ``HIP 98321'' (Sect. 5.6) the selection of members in the different associations is based on data from de Zeeuw et al. (1999). In their sample selection they combine one method using Hipparcos positions and proper motions (de Bruijne 1999a), and another using Hipparcos positions, proper motions and parallaxes (Hoogerwerf & Aguilar 1999). Although this could cause some contamination by outliers, simulations showed that only 20% of the stars in the first method are expected to be field stars, and only 4% in the second. Although, in principle, our procedure for rejecting outliers does reduce this contamination, actually only few stars were rejected.

De Bruijne (1999b) used an implementation of our original method (Dravins et al. 1997) to obtain kinematically improved parallaxes for the three OB associations in the Scorpius OB2 complex (cf. Sect. 3.6). While the depth of the associations is not fully resolved by the Hipparcos parallaxes, the kinematically improved parallaxes reveal some internal structure. We refer to de Bruijne's work concerning the three-dimensional structure of the complex, although his distance estimates are slightly different from ours (mainly because his selection criterion, $g_{\rm lim}=9$, differs from our $g_{\rm lim}=15$). Based on the kinematically improved parallaxes, we presented the Hertzsprung-Russell diagrams of Upper Centaurus Lupus and Lower Centaurus Crux in Madsen et al. (2000). For additional discussion of the HR diagrams of the complex we again refer to de Bruijne (1999b).

The solutions for the associations as a whole were given in Table 1 (and its electronic version), while the results for the individual stars are given in the electronic version of Table 2.

   
5.1 The Lower Centaurus Crux association

The cleaned sample consists of 179 stars with an estimated internal dispersion of 1.1 km s^-1. Combined with the rather small uncertainty of the cluster velocity, the resulting standard error for the astrometric radial velocities is 1.2 to 1.3 km s^-1. In the corresponding HR diagram, the main sequence becomes somewhat better defined, most noticeably in the A-star regime (Madsen et al. 2000), although there still remains a significant spread.

   
5.2 The Upper Centaurus Lupus association

For Upper Centaurus Lupus, the rejection procedure produces a clean sample with 218 stars with an estimated internal dispersion of 1.2 km s^-1. The resulting standard error of the astrometric radial velocities is 1.3 km s^-1.

The HR diagram clearly shows an improvement across the whole spectral range of the main sequence (Madsen et al. 2000). Probably, the remaining spread is caused by non-detected binaries, some non-members, and pre-main sequence objects moving onto the main sequence. Differential reddening across the association and perhaps also in depth could also cause a spread of the main sequence, although Upper Centaurus Lupus is not believed to be as much affected as the other two associations in the Scorpius OB2 complex (de Zeeuw et al. 1999).

   
5.3 The Upper Scorpius association

The maximum-likelihood solution for the Upper Scorpius association became unstable after rejection of eight stars, at which point the criterion $g_{\rm max}\le 15$ was still not met. We therefore choose to give results for the solution using all 120 stars in the original sample. The internal dispersion is in line with that of the previous two associations, but the larger uncertainty in the cluster velocity gives a higher standard error of about 1.9 km s^-1 for the astrometric radial velocities.

It is difficult to judge whether the main sequence is actually better delineated by the kinematically improved parallaxes. Upper Scorpius appears to be close to the limit of our method, due to its larger distance, smaller angular size and a smaller number of member stars, compared with Lower Centaurus Crux and Upper Centaurus Lupus.

   
5.4 The Scorpius OB2 complex

Lower Centaurus Crux, Upper Centaurus Lupus and Upper Scorpius are all part of a larger OB complex, known as Scorpius OB2, with similar space velocity vectors (Blaauw 1964). Therefore, an attempt was also made to combine the three associations in a single solution assuming a common velocity vector. The resulting vector and internal dispersion are in Table 1, but we give no results for individual stars.

The HR diagram is visibly improved, indicating that Sco OB2 could meaningfully be regarded as one single structure. However, a combination of the HR diagrams from the three separate solutions is even slightly better defined, suggesting that Sco OB2 is, after all, better considered as three separate structures.

When treating Sco OB2 as one complex, the estimated internal velocity dispersion is only slightly larger than for the separate solutions, and the formal uncertainty of the space velocity vector is remarkably small. Nevertheless, when comparing the resulting astrometric radial velocities with those from the previous solutions we find noticeable differences. For Lower Centaurus Crux (LCC) we find $\langle v_{{\rm r}i}({\rm LCC})-v_{{\rm r}i}({\rm Sco~OB2})\rangle\simeq -2$ km s^-1, while for Upper Centaurus Lupus and Upper Scorpius the corresponding mean differences are +4 km s^-1 and +10 km s^-1, respectively. Such a progression of systematic differences could be expected if Sco OB2 is not really one uniform complex, or if there is some internal velocity field. At any rate, the comparison shows that one has to be careful when interpreting the results for young associations: although we get a stable solution with small residuals when considering the whole complex, the resulting velocities are not trustworthy.

Thus both the HR diagrams and the radial-velocity solutions indicate that the Sco OB2 complex has some internal kinematic structure that ultimately will need to be modelled, although it is only marginally discernible in the present data. In Sect. 5.7 we discuss the possible expansion of the associations.

   
5.5 The $\alpha$ Persei association (Per OB3)

This $\alpha$ Per association is sometimes denoted an open cluster. From our sample we obtain a mean astrometric radial velocity of $4.5 \pm 2.2$ km s^-1. A rather modest internal velocity dispersion $\sigma_{\rm v}\simeq$ 0.7 km s^-1 was found using the procedure of Appendix A.4 in Paper II. The value is smaller than for the other OB associations, and indicates that it may be reasonable to look upon the structure as a young open cluster instead. The velocity dispersion, together with the uncertainty in the solution for the cluster velocity, combine to give a standard error of about 2.3 km s^-1 in the astrometric radial velocities of the individual stars. The parallax improvement is not good enough to have a visible impact on the HR diagram.

Our radial-velocity result is close to the spectroscopic values of $\simeq$+2 km s^-1 (Prosser 1992), while somewhat larger than the -0.9 km s^-1 derived from the convergence-point solution by Eggen (1998).

   
5.6 The ``HIP 98321'' association

This possible association was recently discovered in the Cepheus-Cygnus-Lyra-Vulpecula region by Platais et al. (1998), during a search for new star clusters from Hipparcos data. They named it after the central star HIP 98321, and found 59 probable members. Because of the Hipparcos limiting magnitude, only O, B, and A-type stars are utilizable. It was a bit surprising to find that this association gives a good kinematic solution despite its great distance of 307 pc; the reason is probably its large mean radius on the sky of $\sim$12 degrees (Fig. 1).

The mean astrometric radial velocity is $-19.3 \pm 1.6$ km s^-1 for the sample of all 59 stars. Together with the estimated internal dispersion of 2.6 km s^-1, the standard error of the individual astrometric radial velocities is around 3.2 km s^-1. These values are consistent with the somewhat uncertain spectroscopic velocities for these early-type stars. Published values spread around -15 km s^-1, suggesting a possible expansion of the association compatible with its isochrone age (Table 4 in Paper I and next section).

During the cleaning process, the maximum g value was always below $g_{\rm lim}=15$; thus no star was removed from the original sample. Some contamination by outliers may nevertheless be expected due to the lack of spectroscopic information in the selection of the stars. It would have been a nice confirmation of the existence of this new association if the improved parallaxes had given a better-defined main sequence, but unfortunately the improvement is not sufficient to have any visible effect in the HR diagram.

Figure 7: Astrometric versus spectroscopic radial velocities for stars in the Scorpius-Centaurus group of young associations, expected to undergo kinematic expansion. The top three frames show separate solutions for each subgroup. Assuming a rate of isotropic expansion equal to the inverse age of the cluster, a bias in the astrometric radial velocity would result, marked by dashed gray lines (the cluster's increasing angular size would be interpreted as approaching motion; Paper I). The assumed ages are 11, 14 and 5 Myr, respectively (de Geus et al. 1989). The bottom frame shows the solution for all 510 stars in the groups, treated as one entity (only stars with known spectroscopic velocities are plotted). While these data do indicate some expansion of this complex of young associations, the expansion of its individual parts is significantly slower than the naively expected rate.

   
5.7 Expanding associations?

Figure 7 shows the astrometric versus spectroscopic radial velocities for stars in the Scorpius-Centaurus group of young associations, both for each individual subgroup, and for the complex treated as a whole. The spectroscopic values are those compiled in the Hipparcos Input Catalogue HIC (Turon et al. 1992). Because we are dealing with young and rapidly rotating early-type stars, the spectroscopic errors are quite large; some contamination is also expected due to outliers and binaries.

The astrometric radial velocities in OB associations are expected to show a significant bias due to expansion effects (Paper I). Assuming the inverse age of an association to be the upper limit on the relative expansion rate, the resulting maximum bias in the astrometric radial velocity can be computed from Eq. (10) in Paper I. This effect is directly proportional to the distance to the stars in the association and inversely proportional to its age. The expansion causes a positive shift in $v_{\rm r}({\rm spectr})-\widehat{v}_{{\rm r}}({\rm astrom})$: the cluster's increasing angular size is wrongly interpreted as approaching motion. This [upper limit of the] expansion bias is plotted in Fig. 7 together with the spectroscopic and astrometric velocities. We have not been able to observe any correlation between distance and expansion with the present data. The expected effect should be a few km s^-1, but it probably drowns in the noise from spectroscopic measurements that have errors of comparable magnitude, and from a possible anisotropic expansion.

The interpretation of Fig. 7 is not obvious. Stars in Lower Centaurus Crux show a wide spread in the spectroscopic values, while the mean is roughly consistent with an isotropic expansion at about half the rate naively expected from the age of the association. The same can be said for Upper Centaurus Lupus. For these associations the indicated ``kinematic age'' (equal to the inverse of the current expansion rate) is thus around 20-30 Myr, or twice the isochrone ages according to de Geus et al. (1989). Upper Scorpius on the other hand, which is the youngest of the subgroups (5-6 Myr according to de Geus et al.), does not seem to expand at all: taken at face value, the data rather suggest that it contracts. The combined sample again indicates some expansion, roughly consistent with a kinematic age of 20 Myr. We note that already Blaauw (1964) derived such an expansion age of 20 Myr for the Scorpius-Centaurus complex as a whole from the $\simeq$10 km s^-1discrepancy between the spectroscopic radial velocities and the proper motion data combined with photometric distances.

Of the three subgroups in Sco OB2, the result for Upper Scorpius thus stands out as rather puzzling. A detailed study of this association by Preibisch & Zinnecker (1999) suggested that the star formation process was triggered by a giant supernova explosion in the neighbouring Upper Centaurus Lupus. What effect that may have had on the internal kinematics of Upper Scorpius is hard to say. There is a priori no reason to expect Upper Scorpius to be a bound system without expansion. The star formation in Upper Scorpius itself seems to have dispersed the rest of the parent molecular cloud. This result seems to imply the standard picture (see e.g. Mathieu 1986 for a review): the removal of gas leads to loss of binding mass of the system, it becomes unbound and consequently will expand.

From calculations inspired by our method, Makarov & Fabricius (2001) estimated an expansion rate of 0.12 km s^-1 pc^-1 for the TW Hya association of young stars, assuming a uniform expansion. The TW Hya association is dominated by late-type stars and may be an extension of Lower Centaurus Crux. The expansion corresponds to a bias of the centroid radial velocity of $\sim$-9 km s^-1 - comparable to the biases we find for Upper Centaurus Lupus and Lower Centaurus Crux - and to a dynamical age of 8.3 Myr, in agreement with previous age determinations for TW Hya's T Tauri members (Webb et al. 1999).

The results we find here are promising in the sense that it is possible to obtain information about the internal kinematics, formation history and age, but at the same time they confirm the complexity of the kinematics of the associations in the Sco OB2 complex. In the end more accurate spectroscopic observations are also required to answer these questions. These would in particular allow true expansion to be disentangled from the perspective effects of the radial motion.