Is it possible to reveal the lost siblings of the Sun?

Abstract

We present the results of our numerical experiments on stellar scattering in the galactic disc under the influence of the perturbed galactic gravitation field connected with the spiral density waves and show that the point of view according to which stars do not migrate far from their birthplace, in general, is incorrect. Despite close initial locations and the same velocities after 4.6 Gyrs members of an open cluster are scattered over a very large part of the galactic disc. If we adopt that the parental solar cluster had $\sim 10^3$ stars, it is unlikely to reveal the solar siblings within 100 pc from the Sun. The problem stands a good chance to be solved if the cluster had $\sim 10^4$ stars. We also demonstrate that unbound open clusters disperse off in a short period of time under the influence of spiral gravitation field. Their stars became a part of the galactic disc. We have estimated typical times of the cluster disruption in radial and azimuth directions and the corresponding diffusion coefficients.