moving clusterAn open cluster, such as the Hyades or the Ursa Major cluster, for which a distance can be derived from the individual radial velocities and proper motions of the member stars. The method is often termed moving-cluster (or expanding-cluster) parallax. The stars in a cluster share a common space motion and, if the system is sufficiently close to Earth, their paths will appear to diverge from or converge towards a point in space (point P in the illustration overleaf). The direction of P is parallel to the space motion of the cluster. Considering each star in turn (illustration B overleaf):
an aggregate of stars that have the same space velocities. If a moving cluster is approaching us, then the directions of the proper motions of the stars in it, because of perspective, look as if they originate from a single point—the radiant of the cluster. But if the moving cluster is receding from us, the proper motions are directed toward a single point—the antiradiant of the cluster. The radial velocity Vr of any star in the cluster is given by Vr = V cos λ, where V is the space velocity of the cluster in km/sec and λ is the angular distance of the star from the radiant. The proper motion of a star in a moving cluster is given by
where r is the distance to the star expressed in parsecs. If the proper motions of the stars in a moving cluster are measured and thus the position of the radiant determined, then it is sufficient to measure the radial velocity of only one of these stars in order to determine the distance to each star in the cluster. Distances determined in this manner are called group distances. They have considerable accuracy.
Certain star clusters, for example, the Hyades, belong to the class of moving clusters. However, stars of one and the same moving cluster often do not form a noticeable concentration of stars and occupy a large area in the sky. Such moving clusters are detected only as a result of their common proper motions. It is impossible to reveal distant moving clusters since the proper motions of distant stars are very small and inaccurately determined. The most well-known moving cluster is the one in Ursa Major, which includes five bright stars out of the seven forming the dipper and eight fainter stars of the constellation with the same space velocity. It is possible that the Ursa Major group includes yet several dozen more stars (in other regions of the sky), which have proper motions directed toward the radiant of the cluster. The stellar density (number of stars per unit volume) of only those stars that belong to the Ursa Major group is very small: it is many times les-s than the average stellar density in the solar neighborhood. Thus the cluster does not form a substantial spatial concentration.
The coincidence of the space velocities of stars belonging to a certain moving cluster cannot be accidental and indicates the common origin of the stars in the cluster.
T. A. AGEKIAN