A number of authors have argued that the Sun must have been born in a cluster of no more than several thousand stars, on the basis that, in a larger cluster, close encounters between the Sun and other stars would have truncated the outer solar system or excited the outer planets into eccentric orbits. However, this dynamical limit is in tension with meteoritic evidence that the solar system was exposed to a nearby supernova during or shortly after its formation; a several-thousand-star cluster is much too small to produce a massive star whose lifetime is short enough to have provided the enrichment. In this paper, we revisit the dynamical limit in the light of improved observations of the properties of young clusters. We use a series of scattering simulations to measure the velocity-dependent cross-section for disruption of the outer solar system by stellar encounters, and use this cross-section to compute the probability of a disruptive encounter as a function of birth cluster properties. We find that, contrary to prior work, the probability of disruption is small regardless of the cluster mass, and that it actually decreases rather than increases with cluster mass. Our results differ from prior work for three main reasons: (1) unlike in most previous work, we compute a velocity-dependent cross-section and properly integrate over the cluster mass-dependent velocity distribution of incoming stars; (2) we recognize that ∼90% of clusters have lifetimes of a few crossing times, rather than the 10-100 Myr adopted in many earlier models; and (3) following recent observations, we adopt a mass-independent surface density for embedded clusters, rather than a mass-independent radius as assumed many earlier papers. Our results remove the tension between the dynamical limit and the meteoritic evidence, and suggest that the Sun was born in a massive cluster. A corollary to this result is that close encounters in the Sun's birth cluster are highly unlikely to truncate the Kuiper Belt unless the Sun was born in one of the unusual clusters that survived for tens of Myr. However, we find that encounters could plausibly produce highly eccentric Kuiper Belt objects such as Sedna.
planets and satellites: formation - stars: kinematics and dynamics