Tidal tails of open star clusters as probes to early gas expulsion I: A
  semi-analytic model
  Star clusters form out of the densest parts of infrared dark clouds. The
emergence of massive stars expels the residual gas, which has not formed stars
yet. Gas expulsion lowers the gravitational potential of the embedded cluster,
unbinding many of the cluster stars. These stars then move on their own
trajectories in the external gravitational field of the Galaxy, forming a tidal
tail. We investigate the formation and evolution of the tidal tail forming due
to expulsion of primordial gas under various scenarios of gas expulsion to
provide predictions for tidal tails around dynamically evolved (age > 100 Myr)
galactic star clusters, which can be possibly detected by the Gaia mission. We
provide a semi-analytical model for the tail evolution. We find that tidal
tails released during gas expulsion have different kinematic properties than
the tails gradually forming due to evaporation. The gas expulsion tidal tail
shows non-monotonic expansion with time, where longer epochs of expansion are
interspersed with shorter epochs of contraction. The tail thickness and
velocity dispersions strongly, but not exactly periodically, vary with time.
The times of minima of tail thickness and velocity dispersions are given only
by the properties of the galactic potential, and not by the properties of the
cluster. The estimates provided by the (semi-)analytical model for the extent
of the tail, the minima of tail thickness, and velocity dispersions are in a
very good agreement with the nbody6 simulations. This implies that the
semi-analytic model can be used for estimating the properties of the gas
expulsion tidal tail for a cluster of a given age and orbital parameters
without the necessity of performing numerical simulations. A study with a more
extended parameter space of the initial conditions is performed in the follow
up paper.
