  The problem of accretion in the Trojan 1:1 resonance is akin to the standard
problem of planet formation, transplanted from a star-centered disk to a disk
centered on the Lagrange point. The newly discovered class of Neptune Trojans
promises to test theories of planet formation by coagulation. Neptune Trojans
resembling the prototype 2001 QR322 (``QR'')--whose radius of ~100 km is
comparable to that of the largest Jupiter Trojan--may outnumber their Jovian
counterparts by a factor of ~10. We discover that seeding the 1:1 resonance
with debris from planetesimal collisions and having the seed particles accrete
in situ naturally reproduces the inferred number of QR-sized Trojans. We
analyze accretion in the Trojan sub-disk by applying the two-groups method,
accounting for kinematics specific to the resonance. We find that a Trojan
sub-disk comprising decimeter-sized seed particles and having a surface density
1e-3 that of the local minimum-mass disk produces ~10 QR-sized objects in ~1
Gyr, in accord with observation. Further growth is halted by collisional
diffusion of seed particles out of resonance. In our picture, the number and
sizes of the largest Neptune Trojans represent the unadulterated outcome of
dispersion-dominated, oligarchic accretion. Large Neptune Trojans, perhaps the
most newly accreted objects in our Solar System, may today have a dispersion in
orbital inclination of less than ~10 degrees, despite the existence of niches
of stability at higher inclinations. Such a vertically thin disk, born of a
dynamically cold environment necessary for accretion, and raised in minimal
contact with external perturbations, contrasts with the thick disks of other
minor body belts.
