  A recent examination of K2 lightcurves indicates that ~15% of Jupiter Trojans
have very slow rotation (spin periods Ps>100 h). Here we consider the
possibility that these bodies formed as equal-size binaries in the massive
outer disk at ~20-30 au. Prior to their implantation as Jupiter Trojans, tight
binaries tidally evolved toward a synchronous state with Ps~Pb, where Pb is the
binary orbit period. They may have been subsequently dissociated by impacts and
planetary encounters with at least one binary component retaining its slow
rotation. Surviving binaries on Trojan orbits would continue to evolve by tides
and spin-changing impacts over 4.5 Gyr. To explain the observed fraction of
slow rotators, we find that at least ~15-20% of outer disk bodies with
diameters 15<D<50 km would have to form as equal-size binaries with 12<ab/R<30,
where ab is the binary semimajor axis and R=D/2. The mechanism proposed here
could also explain very slow rotators found in other small body populations.
