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Much of the dynamical structure of the Kuiper belt can be explained ifNeptune migrated over several AU, and/or if Neptune was scattered to aneccentric orbit during planetary instability. An outstanding problem with theexisting formation models is that the distribution of orbital inclinations theypredicted is narrower than the one inferred from observations. Here we performnumerical simulations of Kuiper belt formation starting from an initial statewith Neptune at 20 < a_{N,0} < 30 AU and a dynamically cold outer diskextending from beyond a_{N,0} to 30 AU. Neptune's orbit is migrated into thedisk on an e-folding timescale 1 <= tau <= 100 Myr. A small fraction (~10^{-3})of the disk planetesimals become implanted into the Kuiper belt in thesimulations. By analyzing the orbital distribution of the implanted bodies indifferent cases we find that the inclination constraint implies that tau >= 10Myr and a_{N,0} <= 25 AU. The models with tau < 10 Myr do not satisfy theinclination constraint, because there is not enough time for various dynamicalprocesses to raise inclinations. The slow migration of Neptune is consistentwith other Kuiper belt constraints, and with recently developed models ofplanetary instability/migration. Neptune's eccentricity and inclination arenever large in these models (e_N<0.1, i_N<2 deg), as required to avoidexcessive orbital excitation in the >40 AU region, where the Cold Classicalspresumably formed.

The Evidence for Slow Migration of Neptune from the Inclination Distribution of Kuiper Belt Objects