  Stochastic impacts by large bodies are, at present, the usually accepted
mechanisms able to account for the obliquity of the ice giants. We attempt to
set constraints on giant impacts as the cause of Neptune's current obliquity in
the framework of modern theories. We also use the present orbital properties of
the Neptunian irregular satellites (with the exception of Triton) to set
constraints on the scenario of giant impacts at the end of Neptune formation.
We model the angular momentum transfer to proto-Neptune and the impulse
transfer to its irregular satellites by the last stochastic collision (GC)
between the protoplanet and an oligarchic mass at the end of Neptune's
formation. We obtain that an impactor mass greather than 4 Earth masses is not
possible since it cannot reproduce the present rotational properties of the
planet, unless the impact parameter of the collision were very small. On the
other hand, if the impactor mass was greather than 1.4 Earth masses, the
present Neptunian irregular satellites had to be formed or captured after the
end of stochastic impacts. The upper bounds on the oligarchic masses (4 Earth
masses from the obliquity of Neptune and 1.4 earth masses from the Neptunian
irregular satellites) are independent of unknown parameters, such as the mass
and distribution of the planetesimals, the location at which Uranus and Neptune
were formed, the Solar Nebula initial surface mass density, and the growth
regime. If stochastic impacts had occurred, these results should be understood
as upper constraints on the oligarchic masses in the trans-Saturnian region at
the end of ice planet formation and may be used to set constraints on planetary
formation scenarios.
