Constraints on Jupiter's (upper panel) and Saturn's (lower
panel) core masses ($M_{\rm core}$) and total masses of heavy elements
($M_{Z\rm tot}$), expressed in Earth masses ($M_\oplus$). The dashed
regions correspond to the constraints
obtained from static models only. The shaded regions are those which
also satisfy the
condition that the model ages should be close to the age of the Solar
System (see text). Within those, darker regions corresponds to
calculations that ignore uncertainties on the equation of state of
heavy elements. Models calculated with the PPT-EOS are to the left,
models using the $i$-EOS to the right. The region surrounded by the
thick line corresponds to the most plausible ($M_{\rm core}$, $M_{Z\rm
tot}$) region given all possible constraints and uncertainties. In the
case of Saturn, the horizontally-dashed region and the region
surrounded by dashed lines correspond to constraints using the Voyager
helium mixing ratios $Y=0.06\pm 0.05$, whereas other models assume
$Y=0.16\pm 0.05$. Arrows indicate the direction and magnitude of the
assumed uncertainties, if $J_4$ or $Y_{\rm proto}$ are increased by
$1\sigma$, rotation is assumed to be solid (``$\Omega$''), the core is
assumed to be composed of ices only (``$f_{\rm ice}$''), if Jupiter's
interior becomes fully adiabatic (``$\nabla_T$''), and if Saturn's
surface temperature is increased from 135 to 145 K (``$T_{\rm
1bar}$'').
(From Guillot 1999; Plan. Space Sci. 47, 1183)