Velocity Distance of the Open Cluster M11

On the reasonable hypothesis that the internal motions of member stars of a cluster are random and isotropic, a method which can be used to estimate the velocity distance of the cluster and its uncertainty is developed. The velocity distance so determined is an absolute distance estimate, and is completely independent of the (widely used) luminosity distance, which is a relative distance estimate. Using the published high-accuracy observational data of radial velocities and proper motions of the stars in the open cluster M11 region, we have determined the distance of M11 to be 1.89±0.52 kpc. This is in quite good agreement with the published luminosity distances of the cluster. We briefly discuss the problems concerned, including the sources of errors in the method and its applicable range.