All Figures

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2656fig1.eps} \end{figure}$ Figure 1: Planetary mass ratio, M₁/M₂, average orbital eccentricities, $\langle e_1 \rangle$ and $\langle e_2 \rangle$ , and the ratio of eccentricity damping rate to migration rate, K, for the GJ 876 best-fit solutions of Laughlin et al. (2004) with coplanar inclination $i > 35^\circ$ . The value of $K = \vert{\dot e}_2/e_2\vert/\vert{\dot a}_2/a_2\vert$ is for the equilibrium eccentricities to match $\langle e_j \rangle$ if there is inward migration and damping of the outer planet only.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig2.eps} \end{figure}$ Figure 2: The global grid structure with gray-shaded initial surface density superimposed. Every second grid points is shown. The dots denote the location of the star and the two planets and the oval line refers to the Roche lobe of the outer planet.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig3.eps} \end{figure}$ Figure 3: The azimuthally averaged density profile for the relaxed configurations for three different masses of the outer planet: $q_2 = 1.0 \times 10^{-3}, q_2 = 3.5 \times 10^{-3}$ and $5.9\times 10^{-3}$ . The planet is located at a₂ = 0.35 with a fixed semi-major axis, and is allowed to accrete. In these models the mass of the inner planet has been switched off. The density is given in dimensionless units.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{2656fg4a.eps}\vspace*{3mm} \includegraphics[width=7.4cm,clip]{2656fg4b.eps} \end{figure}$ Figure 4: Gray scale plots of the surface density $\Sigma$ for the relaxed state with no inner planet for two different masses: top: $q_2 = 3.5 \times 10^{-3}$ and bottom: $q_2 = 5.9\times 10^{-3}$ . Due to the higher planetary mass much stronger wave-like disturbances are created in the density, and the disk becomes eccentric with very small pattern speed in the inertial frame.
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{2656fig5.eps} \end{figure}$ Figure 5: The time evolution of the semi-major axis and eccentricity for three models with different masses of the outer planet, and zero mass inner planet.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig6.eps} \end{figure}$ Figure 6: The time evolution of the periastron for three models with different masses of the outer planet. The thick dashed line is a fit corresponding to a 1 deg yr^-1 shift.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig7.eps} \end{figure}$ Figure 7: The relaxed azimuthally averaged density profile for two isothermal models with and without considering the inner planet (solid, dotted lines), and two radiative models including only heating and cooling (short-dashed), and additionally radiative diffusion (long-dashed). The mass of the inner planet is $q_1 = 1.75 \times 10^{-3}$ and that of the outer $q_2 = 5.9\times 10^{-3}$ . The gray short-dashed line is identical to the corresponding line in Fig. 3 (labeled 5.9).
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig8.eps} \end{figure}$ Figure 8: The relaxed azimuthally averaged temperature profile for the isothermal (solid line) and two radiative models including only heating and cooling (short-dashed), and additionally radiative diffusion (long-dashed). The mass of the inner planet is $q_1 = 1.75 \times 10^{-3}$ and that of the outer $q_2 = 5.9\times 10^{-3}$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig9.eps} \end{figure}$ Figure 9: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h4) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 3.5 \times 10^{-3}$ (test case with lower outer planet mass).
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg10.eps} \end{figure}$ Figure 10: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h2) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ (as GJ 876 edge on).
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg11.eps} \end{figure}$ Figure 11: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h9) with $q_1 = 2.10\times 10^{-3}$ and $q_2 = 7.1\times 10^{-3}$ (as GJ 876 at $55\deg$ inclination).
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg12.eps} \end{figure}$ Figure 12: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for a radiative model including heating and cooling (m1) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ (as GJ 876 edge on). Note that at around t=380 the outer planet leaves the computational grid and the results are not reliable anymore.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg13.eps} \end{figure}$ Figure 13: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (k3b) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ , including disk dispersal.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg14.eps} \end{figure}$ Figure 14: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h8a) with $q_1 = 2.10\times 10^{-3}$ and a growing outer planet $q_2 = 5.9\rightarrow 6.9\times 10^{-3}$ . The model includes disk dispersal.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg15.eps} \end{figure}$ Figure 15: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for a radiative model (m2) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ , including disk dispersal.
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{2656fg16.eps} \end{figure}$ Figure 16: Time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for the baseline three-body model with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ . The planets are initially on coplanar circular orbits. The outer planet is forced to migrate inward at the rate ${\dot a_2}/a_2 = -4.8 \times 10^{-4}~(0.35 {\rm~AU}/a_2)^{3/2} {\rm~yr}^{-1}$ , and there is no eccentricity damping or additional apsidal precession.
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{2656fg17.eps} \end{figure}$ Figure 17: Time evolution of the orbital eccentricities for the three-body models with additional apsidal precession ${\dot \varpi}_{{\rm disk},2} = p~(0.35 {\rm~AU}/a_2)^{3/2} ~^\circ {\rm~yr}^{-1}$ and p = 1 and 10, compared to the case without additional apsidal precession (p = 0) from Fig. 16.
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In the text

$\begin{figure} \par\includegraphics[width=8.1cm,clip]{2656fg18.eps} \end{figure}$ Figure 18: Same as Fig. 16, but for the three-body model with the following initial conditions: e₁ = 0.01, e₂ = 0.05, and the orbits are antialigned, with the inner planet at periapse and the outer planet at apoapse.
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In the text

$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig2.eps} \end{figure}$	Figure 2: The global grid structure with gray-shaded initial surface density superimposed. Every second grid points is shown. The dots denote the location of the star and the two planets and the oval line refers to the Roche lobe of the outer planet.
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$\begin{figure} \par\includegraphics[width=7.4cm,clip]{2656fg4a.eps}\vspace*{3mm} \includegraphics[width=7.4cm,clip]{2656fg4b.eps} \end{figure}$	Figure 4: Gray scale plots of the surface density $\Sigma$ for the relaxed state with no inner planet for two different masses: top: $q_2 = 3.5 \times 10^{-3}$ and bottom: $q_2 = 5.9\times 10^{-3}$ . Due to the higher planetary mass much stronger wave-like disturbances are created in the density, and the disk becomes eccentric with very small pattern speed in the inertial frame.
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$\begin{figure} \par\includegraphics[width=14cm,clip]{2656fig5.eps} \end{figure}$	Figure 5: The time evolution of the semi-major axis and eccentricity for three models with different masses of the outer planet, and zero mass inner planet.
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig6.eps} \end{figure}$	Figure 6: The time evolution of the periastron for three models with different masses of the outer planet. The thick dashed line is a fit corresponding to a 1 deg yr^-1 shift.
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig8.eps} \end{figure}$	Figure 8: The relaxed azimuthally averaged temperature profile for the isothermal (solid line) and two radiative models including only heating and cooling (short-dashed), and additionally radiative diffusion (long-dashed). The mass of the inner planet is $q_1 = 1.75 \times 10^{-3}$ and that of the outer $q_2 = 5.9\times 10^{-3}$ .
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fig9.eps} \end{figure}$	Figure 9: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h4) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 3.5 \times 10^{-3}$ (test case with lower outer planet mass).
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg10.eps} \end{figure}$	Figure 10: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h2) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ (as GJ 876 edge on).
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg11.eps} \end{figure}$	Figure 11: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h9) with $q_1 = 2.10\times 10^{-3}$ and $q_2 = 7.1\times 10^{-3}$ (as GJ 876 at $55\deg$ inclination).
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg12.eps} \end{figure}$	Figure 12: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for a radiative model including heating and cooling (m1) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ (as GJ 876 edge on). Note that at around t=380 the outer planet leaves the computational grid and the results are not reliable anymore.
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg13.eps} \end{figure}$	Figure 13: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (k3b) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ , including disk dispersal.
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg14.eps} \end{figure}$	Figure 14: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for an isothermal model (h8a) with $q_1 = 2.10\times 10^{-3}$ and a growing outer planet $q_2 = 5.9\rightarrow 6.9\times 10^{-3}$ . The model includes disk dispersal.
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$\begin{figure} \par\includegraphics[width=7.9cm,clip]{2656fg15.eps} \end{figure}$	Figure 15: The time evolution of the orbital elements ( $a, e, \theta _1, \Delta {\varpi }$ ) for a radiative model (m2) with $q_1 = 1.75 \times 10^{-3}$ and $q_2 = 5.9\times 10^{-3}$ , including disk dispersal.
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$\begin{figure} \par\includegraphics[width=8.1cm,clip]{2656fg17.eps} \end{figure}$	Figure 17: Time evolution of the orbital eccentricities for the three-body models with additional apsidal precession ${\dot \varpi}_{{\rm disk},2} = p~(0.35 {\rm~AU}/a_2)^{3/2} ~^\circ {\rm~yr}^{-1}$ and p = 1 and 10, compared to the case without additional apsidal precession (p = 0) from Fig. 16.
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$\begin{figure} \par\includegraphics[width=8.1cm,clip]{2656fg18.eps} \end{figure}$	Figure 18: Same as Fig. 16, but for the three-body model with the following initial conditions: e₁ = 0.01, e₂ = 0.05, and the orbits are antialigned, with the inner planet at periapse and the outer planet at apoapse.
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