Tidal tails of open star clusters as probes of early gas expulsion: I. A semi-analytic model

Context. Star clusters form in the densest parts of infrared dark clouds. The emergence of massive stars expels the residual gas that 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.Aims. We investigate, for the first time, the formation and evolution of a tidal tail that forms due to expulsion of primordial gas. We contrast the morphology and kinematics of this tail with that of another tidal tail that forms by gradual dynamical evaporation of the star cluster. We intend to provide predictions that can determine the dynamical origin of possibly observed tidal tails around dynamically evolved (age greater than or similar to 100 Myr) galactic star clusters by the Gaia mission. These observations might estimate the fraction of the initial cluster population that gets released in the gas expulsion event. The severity of the initial gas expulsion is given by the star formation efficiency and the timescale of gas expulsion for the cluster when it was still embedded in its natal gas. A study with a more extended parameter space of the initial conditions is performed in the follow up paper.Methods. We provide a semi-analytical model for the tail evolution. The model is compared against direct numerical simulations using NBODY6.Results. Tidal tails released during gas expulsion have different kinematic properties than the tails gradually forming due to evaporation; the latter kind have been extensively studied. 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 vary strongly, but not exactly periodically, 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 to estimate 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.