  The amount and distribution of heavy elements in Jupiter gives indications on
the process of its formation and evolution. Core mass and metallicity
predictions however depend on the equations of state used, and on model
assumptions. We present an improved ab initio hydrogen equation of state,
H-REOS.2 and compute the internal structure and thermal evolution of Jupiter
within the standard three-layer approach. The advance over our previous Jupiter
models with H-REOS.1 by Nettelmann et al.(2008) is that the new models are also
consistent with the observed 2 or more times solar heavy element abundances in
Jupiter's atmosphere. Such models have a rock core mass Mcore=0-8 ME, total
mass of heavy elements MZ=28-32 ME, a deep internal layer boundary at 4 or more
Mbar, and a cooling time of 4.4-5.0 Gyrs when assuming homogeneous evolution.
We also calculate two-layer models in the manner of Militzer et al.(2008) and
find a comparable large core of 16-21 ME, out of which ~11 ME is helium, but a
significantly higher envelope metallicity of 4.5 times solar. According to our
preferred three-layer models, neither the characteristic frequency (nu0 ~156
microHz) nor the normalized moment of inertia (~0.276) are sensitive to the
core mass but accurate measurements could well help to rule out some classes of
models.
