  The Scattered Disk Objects (SDOs) are a population of trans-Neptunian bodies
with semimajor axes $50< a \lesssim 1000$ au and perihelion distances $q
\gtrsim 30$ au. The detached SDOs with orbits beyond the reach of Neptune
(roughly $q>35$~au) are of special interest here as an important constraint on
the early evolution of the outer Solar System. The semimajor axis profile of
detached SDOs at 50--500~au, as characterized from the Dark Energy Survey
(DES), is radially extended, but previous dynamical models of Neptune's early
migration produce a relatively compact profile. This problem is most likely
related to Sun's birth environment in a stellar cluster. We perform new
dynamical simulations that account for cluster effects and show that the
orbital distribution of SDOs can be explained if a particularly close stellar
encounter occurred early on (e.g., M dwarf with the mass $\simeq 0.2$ $M_\odot$
approaching the Sun at $\simeq 200$ au). For such an encounter to happen with a
reasonably high probability the Sun must have formed in a stellar cluster with
$\eta T \gtrsim 10^4$ Myr pc$^{-3}$, where $\eta$ is the stellar number density
and $T$ is the Sun's residence time in the cluster.
