Tracking Cluster Debris (TraCD)- I. Dissolution of clusters and
  searching the solar cradle
  The capability to reconstruct dissolved stellar systems in dynamical and
chemical space is a key factor in improving our understanding of the evolution
of the Milky Way. Here we concentrate on the dynamical aspect and given that a
significant portion of the stars in the Milky Way have been born in stellar
associations or clusters that have lived a few Myr up to several Gyr, we
further restrict our attention to the evolution of star clusters. We have
carried out our simulations in two steps: (1) we create a simulation of
dissolution and mixing processes which yields a close fit to the present-day
Milky Way dynamics and (2) we have evolved three sets of stellar clusters with
masses of 400, 1000 and 15000 M$_{\odot}$ to dissolution. The birth location of
these sets was 4, 6, 8 and 10 kpc for the 400 and 1000 M$_{\odot}$ clusters and
4, 6, 8, 10 and 12 kpc for the 15000 M$_{\odot}$. We have focused our efforts
on studying the state of the escapers from these clusters after 4.5 Gyr of
evolution with particular attention to stars that reach the Solar annulus, i.e.
7.5 $\le$ R$_{\rm{gc}}$ $\le$ 8.5 kpc. We give results for Solar twins and
siblings over a wide range of radii and cluster masses for two dissolution
mechanisms. From kinematics alone, we conclude that the Sun was $\sim$50 per
cent more likely to have been born near its current Galactocentric radius,
rather than have migrated (radially) $\sim$2 kpc since birth. We conclude our
analysis by calculating magnitudes and colours of our single stars for
comparison with the samples that the $Gaia$, $Gaia$-ESO and GALAH-AAO surveys
will obtain. In terms of reconstructing dissolved star clusters we find that on
short time-scales we cannot rely on kinematic evolution alone and thus it will
be necessary to extend our study to include information on chemical space.
