  Since the Voyager fly-bys of Uranus and Neptune, improved gravity field data
have been derived from long-term observations of the planets' satellite
motions, and modified shape and solid-body rotation periods were suggested. A
faster rotation period (-40 min) for Uranus and a slower rotation period
(+1h20) of Neptune compared to the Voyager data were found to minimize the
dynamical heights and wind speeds. We apply the improved gravity data, the
modified shape and rotation data, and the physical LM-R equation of state to
compute adiabatic three-layer structure models, where rocks are confined to the
core, and homogeneous thermal evolution models of Uranus and Neptune. We
present the full range of structure models for both the Voyager and the
modified shape and rotation data. In contrast to previous studies based solely
on the Voyager data or on empirical EOS, we find that Uranus and Neptune may
differ to an observationally significant level in their atmospheric heavy
element mass fraction Z1 and nondimensional moment of inertia, nI. For Uranus,
we find Z1 < 8% and nI=0.2224(1), while for Neptune Z1 < 65% and nI=0.2555(2)
when applying the modified shape and rotation data, while for the unmodified
data we compute Z1 < 17% and nI=0.230(1) for Uranus and Z1 < 54% and
nI=0.2410(8) for Neptune. In each of these cases, solar metallicity models
(Z1=0.015) are still possible. The cooling times obtained for each planet are
similar to recent calculations with the Voyager rotation periods: Neptune's
luminosity can be explained by assuming an adiabatic interior while Uranus
cools far too slowly. More accurate determinations of these planets' gravity
fields, shapes, rotation periods, atmospheric heavy element abundances, and
intrinsic luminosities are essential for improving our understanding of the
internal structure and evolution of icy planets.
