Stellar escapers from M67 can reach solar-like Galactic orbits

We investigate the possibility that the Sun could have been born in M67 by carrying out $N$-body simulations of M67-like clusters in a time-varying Galactic environment, and following the galactic orbits of stars that escape from them. We find that model clusters that occupy similar orbits to M67 today can be divided up into three groups. Hot clusters are born with a high initial $z$-velocity, depleted clusters are born on cold orbits but are destroyed by GMC encounters in the Galactic disc, and scattered clusters are born on cold orbits and survive with more than 1000 stars at an age of 4.6 Gyr. We find that all cluster models in all three cluster groups have stellar escapers that are kinematicaly similar to the Sun. Hot clusters having the lowest such fraction $f_{\odot} = 0.06$ %, whilst depleted clusters have the highest fraction, $f_{\odot} = 6.61$ %. We calculate that clusters that are destroyed in the Galactic disc have a specific frequency of escapers that end up on solar-like orbits that is $\sim$ 2 times that of escapers from clusters that survive their journey.