All Figures

$\begin{figure} \par\includegraphics[width=12cm,clip]{9321fig1.ps} \end{figure}$ Figure 1: EOS for water, rock and iron for two temperatures: T=300 K for ANEOS (red solid line) and SESAME (blue dash-dotted curve); T=6000 K for ANEOS (red short-dashed curve) and SESAME (blue dotted curve). The long-dashed (magenta) curves correspond to the zero-temperature EOS of Seager et al. (2007; their Table 3). The inset in the lower panel (water) shows a zoom of the $P(\rho )$ relation for $\log P < 0.5$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9321fig2.ps}\end{figure}$ Figure 2: Pressure (in dyne cm^-2) and temperature (in K) dependence of the entropy (in erg/g/s), as obtained for water for the ANEOS EOS (solid line) and the SESAME EOS (dash-line). The entropy for a H/He fluid, with Y=0.275 obtained with the SCVH EOS is shown for comparison (dash-dotted line). Upper panel: for each EOS, three isobars are displayed (the corresponding pressure is given on the right hand side of the figure). Lower panel: three isotherms are shown for each EOS (corresponding temperatures given on the right hand side of the figure). The T and P domains characteristic of Neptune-like and Jupiter-like planet interiors are indicated.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9321fig3.ps} \end{figure}$ Figure 3: Effect of the composition and internal distribution of heavy elements on the radius evolution for a planet of mass $M_{\rm P}=20~{M}_\oplus$ with a total heavy element mass fraction $Z=(M_Z/M_{\rm P})=50$ %. a) Models with $~{M}_{\rm core}= 10~{M}_\oplus$ of water (solid line), rock (dashed-line) and iron (dotted line), and $~{Z}_{\rm env}=0$ . b) Models with no core and heavy elements distributed over the entire planet. Dash-dotted line: mixture of H/He + Z described by the SCVH EOS with $~{Y}_{\rm equiv}=0.275 + 0.5=0.775$ . Long-dashed line: mixture of H/He + water (SESAME EOS) using the additive volume law. Short-dashed line: mixture of H/He + water (ANEOS EOS) using the additive volume law. For comparison, the model with $~{M}_{\rm core}= 10~{M}_\oplus$ of water and $~{Z}_{\rm env}=0$ is shown by the solid line. c) More realistic models with a 8 ${M}_\oplus$ core of water (ANEOS EOS) and a $~{Z}_{\rm env}= 16.6$ % heavy element enrichment in the envelope. Dash-dotted line: mixture of H/He + $~{Z}_{\rm env}$ described by the SCVH EOS with $~{Y}_{\rm equiv}= 0.275 + 0.166 = 0.441$ . Long-dashed line: mixture of H/He + water (SESAME EOS) using the additive volume law. Short-dashed line: mixture of H/He + water (ANEOS EOS) using the additive volume law. Also displayed is the model with $~{M}_{\rm core}= 10~{M}_\oplus$ of water and $~{Z}_{\rm env}=0$ (solid line).
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9321fig4.ps} \end{figure}$ Figure 4: Effect of the EOS on the inner profile as a function of fractional mass for a planet of 20 ${M}_\oplus$ with a mass fraction Z=50% of heavy elements distributed over the entire planet. In all panels, the curves correspond to: a mixture of H/He + Z described by: the SCVH EOS with $~{Y}_{\rm equiv}=0.275 + 0.5=0.775$ (solid line); a mixture of H/He + water (SESAME EOS) using the additive volume law (dash-dotted line); a mixture of H/He + water (ANEOS EOS) using the additive volume law (dashed line). Upper panel: inner profile of the local gravothermal energy, $-T{\rm d}S/{\rm d}t$ (in erg/g/s), at the beginning of the evolution. Middle panel: pressure profile (in dyne/cm²) at 1 Gyr. Lower panel: specific entropy profile (in erg/g/K) at 1 Gyr.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9321fig5.ps}\end{figure}$ Figure 5: Internal temperature (K) and density (g cm^-3) profiles for a 20 ${M}_\oplus$ planet, irradiated by a Sun at 0.045 AU, at an age of 4 Gyr. Solid line: $M_{\rm core}=0.5~ M_{\rm p}$ , $~{Z}_{\rm env}=0$ ; long-dash line: $M_{\rm core}=0$ , Z=0.5, AVL SESAME EOS; short-dash line: $M_{\rm core}=0$ , Z=0.5, AVL ANEOS EOS.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{9321fig6.ps}\end{figure}$ Figure 6: Effect of the composition and the distribution of heavy elements on the radius evolution of a planet of 1 $M_{\rm J}$ (318 ${M}_\oplus$ ). a) Total heavy element enrichment Z=50%. Models with $~{M}_{\rm core}= 159~{M}_\oplus$ of water (solid line), rock (dashed-line) and iron (dotted line), and $~{Z}_{\rm env}=0$ . b) Total heavy element enrichment Z=50%. The solid line corresponds to a model with $~{M}_{\rm core}= 159~{M}_\oplus$ of water and $~{Z}_{\rm env}=0$ . The other curves correspond to models with no core and heavy elements distributed over the entire planet: mixture of H/He + Z described by the SCVH EOS with $~{Y}_{\rm equiv}=0.275 + 0.5=0.775$ (dash-dotted line); mixture of H/He + water (SESAME EOS) using the additive volume law (long-dashed line); mixture of H/He + water (ANEOS EOS) using the additive volume law (short-dashed line). c) Total heavy element enrichment Z=20%. Solid line: model with $~{M}_{\rm core}= 63.6~{M}_\oplus$ of water and $~{Z}_{\rm env}=0$ ; dash-dotted-line: no core and mixture of H/He + Z described by the SCVH EOS with $~{Y}_{\rm equiv}=0.275 + 0.2 = 0.475$ ; long-dashed line: no core and mixture of H/He + water (SESAME EOS) with the AVL and $~{Z}_{\rm env}=0.20$ ; short-dashed line: no core and mixture of H/He + water (ANEOS EOS) using the AVL and $~{Z}_{\rm env}=0.20$ .
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{9321fig7.ps} \end{figure}$ Figure 7: Internal temperature and density profiles for a 1 $M_{\rm J}$ planet at an age of 4 Gyr. Solid line: $M_{\rm core}=0.5~ M_{\rm p}$ ; long-dash line: $M_{\rm core}=0$ , Z=0.5, AVL SESAME EOS; short-dash line: $M_{\rm core}=0$ , Z=0.5, AVL ANEOS EOS.
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9321fig8.ps}\end{figure}$ Figure 8: Evolution of a planet with the characteristics of HD 149206b ( $m_{\rm P}=116$ ${M}_\oplus\sim 0.36~M_{\rm J}$ ) with different heavy element distributions. Solid line: model with $~{M}_{\rm core}= 80~{M}_\oplus$ of water (ANEOS EOS) and $~{Z}_{\rm env}=0$ . The other curves correspond to models with heavy elements distributed over the entire planet. Dash-dot line: mixture of H/He + Z described by the SCVH EOS with an effective helium abundance, $~{Y}_{\rm equiv}=0.275+0.69=0.965$ , which corresponds to Z=0.69, i.e. $80~{M}_\oplus$ of heavy elements. Long-dash line: mixture of H/He + water (SESAME EOS) using the AVL with Z=69%. Short-dash line: mixture of H/He + water (ANEOS EOS) using the AVL with Z=69%. Dotted line: mixture of H/He + water (ANEOS EOS) using the AVL with Z=51%, i.e. 60 ${M}_\oplus$ of heavy elements.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{9321fig9.ps}\end{figure}$ Figure 9: Evolution of a planet characteristic of GJ 436b ( $M_{\rm P}=22.6~{M}_\oplus$ ,) with different heavy element distributions. Models with no irradiation: Solid line: model with $~{M}_{\rm core}= 21~{M}_\oplus$ of water (ANEOS EOS) and $~{Z}_{\rm env}=0$ ; short-dash line: model with $~{M}_{\rm core}= 21~{M}_\oplus$ of water (SESAME EOS) and $~{Z}_{\rm env}=0$ ; dotted line: test model with $~{M}_{\rm core}= 21~{M}_\oplus$ of water (SESAME EOS) and $~{Z}_{\rm env}=0$ , assuming an uniform temperature of 300 K in the core. Effect of irradiation, with $F_{\rm inc}=6\times F_{\rm inc}$ for GJ 436b (see text): long-dash line: same as short-dash line with irradiated atmosphere models; dash-dot line: same as dotted line with irradiated atmosphere models.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{9321fig10.ps}\end{figure}$ Figure 10: Various contributions to the gravothermal energy, $E_{\rm g}=-T{\rm d}S/{\rm d}t$ , normalized to the total value, for a planet characteristic of GJ 436b ( $M_{\rm P}=22.6~{M}_\oplus$ ), with a 21 ${M}_\oplus$ core of water with the SESAME EOS. Solid line: global contribution from the core; dash-dot line: contraction work contribution from the core; long-dash line: thermal contribution from the core; short-dash line: global contribution from the H/He 1.6 ${M}_\oplus$ envelope.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{9321fig11.ps}\end{figure}$ Figure 11: Evolution of a super-Jupiter planet with the characteristics of HAT-P-2b ( $M_{\rm p}= 9~M_{\rm J}$ ) for different distributions of heavy elements. Irradiation effects from the parent star are taken into account, adopting a time-average orbital distance a=0.077 AU, for the proper eccentricity e=0.52and semimajor axis of the relative orbit $a_{\rm rel}=0.0677$ AU. Solid line: $~{M}_{\rm core}= 600~{M}_\oplus$ of water (ANEOS EOS) and $~{Z}_{\rm env}=0$ . Long-dashed line: $~{M}_{\rm core}= 350~{M}_\oplus$ of water (ANEOS EOS) and $~{Z}_{\rm env}=0$ . Dash-dotted line: 600 ${M}_\oplus$ of heavy elements with 100 ${M}_\oplus$ in the core (water, with ANEOS EOS) and 500 ${M}_\oplus$ in the envelope, i.e. $Z_{\rm env}=0.18$ , mimicked by an $~{Y}_{\rm equiv}=0.275 + 0.18$ . Short-dashed line: H/He brown dwarf with $Z=Z_\odot$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9321fig12.ps}\end{figure}$ Figure 12: Mass-radius relationships for planets in the mass range 10 ${M}_\oplus$ -1 $M_{\rm J}$ at different ages, as indicated in the panels, and different levels of heavy element enrichment: $Z=Z_\odot$ (solid lines); $Z=10\%$ (short-dash lines); $Z=50\%$ (dash-dot lines); Z=90% (long-dash lines). Left panels: without irradiation; right panels: with irradiation from a Sun at 0.045 AU. Symbols indicate the observed data for transiting Neptune-mass to Jupiter mass planets, taken from F. Pont's website (www.inscience.ch/transits).
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{9321fig5.ps}\end{figure}$	Figure 5: Internal temperature (K) and density (g cm^-3) profiles for a 20 ${M}_\oplus$ planet, irradiated by a Sun at 0.045 AU, at an age of 4 Gyr. Solid line: $M_{\rm core}=0.5~ M_{\rm p}$ , $~{Z}_{\rm env}=0$ ; long-dash line: $M_{\rm core}=0$ , Z=0.5, AVL SESAME EOS; short-dash line: $M_{\rm core}=0$ , Z=0.5, AVL ANEOS EOS.
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$\begin{figure} \par\includegraphics[width=7cm,clip]{9321fig7.ps} \end{figure}$	Figure 7: Internal temperature and density profiles for a 1 $M_{\rm J}$ planet at an age of 4 Gyr. Solid line: $M_{\rm core}=0.5~ M_{\rm p}$ ; long-dash line: $M_{\rm core}=0$ , Z=0.5, AVL SESAME EOS; short-dash line: $M_{\rm core}=0$ , Z=0.5, AVL ANEOS EOS.
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