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
early-appearing tidal tails, the so called tidal tails I, 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 $\approx 70$% 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 $\lesssim
300$ Myr), where it provides a relative age error of the order of $10$ to $20$%
for an error in the observed tilt angle of $5 ^\circ$.
