Neptune has a gaseous envelope with mass larger than that of the Earth. We
examine the possibility that proto-Neptune formed through an initial buildu
p of a core prior to the accretion of a gaseous envelope in the solar nebul
a environment. In thin conventional scenario, the inferred formation timesc
ale of proto-Neptune would be similar to 10(6-7) yr since the signature of
protoplanetary disks are observed to vanish on such a timescale. We show th
at after their emergence through an initial epoch of runaway buildup, proto
-Neptune's core would exert gravitational perturbations On and excite eccen
tricity among the planetesimals near its orbit. In the absence of dissipati
on due to inelastic collisions or gas drag, the planetesimals' velocity dis
persion and the core's growth timescale would increase indefinitely. But cl
ose encounters between planetesimals and the core also lead to orbital drif
t and migration, which would replenish the planetesimals in the core's feed
ing zone and thereby sustain the core's rate of growth. In a subsequent pap
er, we show that when the core has acquired an adequate (comparable to that
of Neptune's present) mass, it may capture those planetesimals along its m
igration path onto its strongest mean-motion resonances. Such a process wou
ld account for the observed distribution of trans-Neptunian objects. Eventu
ally, this resonant barrier would prevent residual planetesimals from reach
ing the core's feeding zone and terminate its mass growth as well as its or
bital migration. We also investigate the process of gas accretion onto the
core. We show that the depletion of nebula gas may be required to limit the
mass of proto-Neptune's gaseous envelope. Such a depletion may either be d
ue to the global viscous evolution of the nebula or to tidally induced gay,
formation near proto-Neptune's orbit. The former process would require a 3
order of magnitude seduction of the surface density from that of the minim
um-mass solar nebula model. The latter process would provide not only a nat
ural mass limit for the gaseous envelope in both Neptune and Uranus but als
o a mechanism for Neptune's outward orbital migration on its formation time
scale. The necessary conditions for gap formation are that the outer parts
of the disk have a very low viscosity and a small thickness.