Estimating the Ages of Open Star Clusters from Properties of Their Extended Tidal Tails

The most accurate current methods for determining the ages of open star clusters, stellar associations, and stellar streams are based on isochrone fitting or the lithium depletion boundary. We propose another method for dating these objects based on the morphology of their extended tidal tails, which have been recently discovered around several open star clusters. Assuming that the tidal tails originate from the stars released from the cluster during early gas expulsion, or that they form in the same star-forming region as the cluster (i.e., being coeval with the cluster), we derive the analytical formula for the tilt angle beta between the long axis of the tidal tail and the orbital direction for clusters or streams on circular trajectories. Since at a given Galactocentric radius beta is only a function of age t regardless of the initial properties of the cluster, we estimate the cluster age by inverting the analytical formula beta = beta(t). We illustrate the method on a sample of 12 objects, which we compiled from the literature, and we find a reasonable agreement with previous dating methods in approximate to 70% of the cases. This can probably be improved by taking into account the eccentricity of the orbits and by revisiting the dating methods based on stellar evolution. The proposed morphological method is suitable for relatively young clusters (age less than or similar to 300 Myr), where it provides a relative age error of the order of 10%-20% for an error in the observed tilt angle of 5 degrees.