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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.