It is possible that the formation of the Oort Cloud dates back to the earliest epochs of solar system history. At that time, the Sun was almost certainly a member of the stellar cluster, where it was born. Since the solar birth cluster is likely to have been massive (1000--10 000 Msol), and therefore long-lived, an issue concerns the survival of such a primordial Oort Cloud. We have investigated this issue by simulating the orbital evolution of Oort Cloud comets for several hundred Myr, assuming the Sun to start its life as a typical member of such a massive cluster. We have devised a synthetic representation of the relevant dynamics, where the cluster potential is represented by a King model, and about 20 close encounters with individual cluster stars are selected and integrated based on the solar orbit and the cluster structure. Thousands of individual simulations are made, each including 3 000 comets with orbits with three different initial semi-major axes. Practically the entire initial Oort Cloud is found to be lost for our choice of semi-major axes (5 000--20 000 au), independent of the cluster mass, although the chance of survival is better for the smaller cluster, since in a certain fraction of the simulations the Sun orbits at relatively safe distances from the dense cluster centre. For the range of birth cluster sizes that we investigate, a primordial Oort Cloud will likely survive only as a small inner core with semi-major axes < 3 000 au. Such a population of comets would be inert to orbital diffusion into an outer halo and subsequent injection into observable orbits. Some mechanism is therefore needed to accomplish this transfer, in case the Oort Cloud is primordial and the birth cluster did not have a low mass. From this point of view, our results lend some support to a delayed formation of the Oort Cloud, that occurred after the Sun had left its birth cluster.
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