9. Proper motion
Several proper motion studies of the Trapezium cluster as a whole have been performed, including star P1724 (see Table 6 for details). With only one exception (Fallon 1975) all studies were carried out in a relative rectangular x -y coordinate system, with the zero-point of the proper motions defined by the Trapezium member stars included in the different investigations.
Table 6. Proper motions of P1724. For each study in the first column the table lists the proper motion and mean errors in x and y coordinates relative to the mean motion of the Trapezium cluster. The only absolute proper motions are those by Fallon (FK4 system) and STARNET (HIPPARCOS system). The next columns show the epoch difference, the number of stars investigated, the number of members, and the probability of membership of P1724 to the Trapezium cluster.
Nearly all of these studies find that the proper motion of P1724 in right ascension (or x) is very close to the cluster mean. The proper motion in declination (or y), on the other hand, is fairly larger than the observed velocity dispersion which is believed to be smaller than 1 mas/yr, corresponding to at a distance of 460 pc.
Depending on the membership criterion applied, conclusions regarding the membership of P1724 to the Trapezium cluster differ from author to author: The calculated membership probabilities based on the proper motion range from 0 to , reflecting the fact that the proper motion of P1724 is very close to the boundary chosen to separate members and non-members.
We discuss here a new proper motion from the STARNET Catalogue (Röser 1996), a proper motion catalogue based on a comparison between plates from the Astrographic Catalogue and the Guide Star Catalogue (GSC 1.2, Röser et al. 1996), with an epoch difference of yrs. It contains 4.3 million stars, and provides proper motions in an absolute system with an accuracy of mas/yr. For this study we have selected all stars from the membership list of Parenago (1954), which show no significant offset from the cluster neither in the position nor in the proper motion diagram.
For the center of the Trapezium cluster we adopt the position of Ori, i.e. and . Hence, P1724 is located about from the center of the Trapezium. The mean proper motion of the cluster, using STARNET data converted to the absolute HIPPARCOS system for 38 stars, i.e. all probable members excluding P1724, is mas/yr and mas/yr, while the proper motion of P1724 is mas/yr and mas/yr. This indicates that P1724 is moving north relative to the cluster. Although we see a few more outliers in the proper motion diagram (Fig. 16), the cluster as a whole is not expanding. Not only is the proper motion of P1724 off by from the mean, but the star is also located north of the cluster and is moving north relative to the cluster, so that it seems very likely that it has been ejected.
The errors in STARNET are on average larger than those in relative proper motion studies due to possible errors in the parameters involved in the transformation to the absolute system. But in contrast to the relative studies, proper motions in an absolute astrometric system can provide information on the overall expansion or rotation of a cluster. Indeed, Strand (1958) argued for an overall expansion of the Trapezium cluster, although Vasilevskis (1971) expressed doubts about this conclusion. In contrast to Strand (1958), Fallon et al. (1977) found evidence for a contraction of the Trapezium cluster from an analysis of the proper motions of Fallon (1975) in the FK4-system. From our analysis of the STARNET proper motions, we find no evidence for expansion, contraction, nor rotation of the cluster.
To compare the 3D space motion of P1724 with the mean motion of the Trapezium stars, we note that the mean RV of the Trapezium stars is , with a scatter of (Hartmann et al. 1986). In Sect. 3 we determined the mean radial velocity of P1724 to be .
We conclude from the observed kinematics of P1724 relative to the Trapezium cluster that (a) there is no difference in the mean radial velocity and proper motion in right ascension between P1724 and the cluster mean, and (b) there is a clear difference in the proper motion in declination of about 9 mas/yr, or at a distance of 460 pc. Together with its position 15 arc min north of the center of the Trapezium (Fig. 16), this is compatible with the scenario that P1724 has been ejected from that cluster yrs ago.
© European Southern Observatory (ESO) 1998
Online publication: June 2, 1998