  A number of authors have argued that the Sun must have been born in a cluster
of no more than about 1000 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
1000-star cluster is much too small for supernova contamination to be likely.
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 adopt
realistically-short cluster lifetimes of a few crossing times, rather than
assuming lifetimes of 10 to 100 Myr; 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.
