All Figures

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6582fig1.eps} \end{figure}$ Figure 1: Typical simulation of the accretion process of a Trojan-like planet in a gas-free scenario. Size of the initial population was N₀=1000 and total mass was $M_{\rm T}=3~M_{\oplus}$ . Top plot shows the number of surviving planetesimals N as function of time, as well as the cumulative number of collisions $n_{\rm col}$ and escapes $n_{\rm esc}$ . The middle graph shows the evolution of the average mass of the swarm $\langle m \rangle$ and it largest value $m_{\rm max}$ , while the bottom plot gives the average eccentricity $\langle e \rangle$ (black) and inclination $\langle I \rangle$ (grey). Recall that we are using inflated physical radii for the planetesimals, so the time axis must be scaled accordingly.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6582fig2.eps} \end{figure}$ Figure 2: Same as previous figure, but with N₀=300 and $M_{\rm T}=1.5~M_{\oplus}$ . Note that the time axis is now in linear scale.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6582fig3.eps} \end{figure}$ Figure 3: Osculating eccentricity and semimajor axis of the Trojan swarm in four different time frames during the accretional process. The area of the circles are proportional to the planetesimal's mass.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6582fig4.eps} \end{figure}$ Figure 4: The size of the stability region as a function of the mass of a Trojan planetesimal placed to L₄ calculated by the RLI chaos indicator. Light colors indicate stable, while dark colors indicate unstable orbits. It can be seen that a $0.15~M_{\oplus}$ Trojan planetesimal can seriously destabilize the region around L₄.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6582fig5.eps}\par\vspace*{2mm} \includegraphics[width=7.8cm,clip]{6582fig6.eps} \end{figure}$ Figure 5: Same as previous figure, now showing the logarithm of the maximum eccentricity attained by each initial condition during the complete integration timespan T. Top: T = 10³ orbital periods. Bottom: T = 10⁴ orbital periods. Note that the region in black corresponds to a change in the eccentricity of the order of unity; consequently the orbit is unstable over the timespan T.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6582fig7.eps}\par\vspace*{2mm} \par\includegraphics[width=8cm,clip]{6582fig8.eps} \end{figure}$ Figure 6: Hydrodynamical simulations of a gaseous disk with two embedded planets, performed with FARGO. Top: gas density plots. Darker (lighter) regions correspond to smaller (larger) surface density values. Left plot corresponds to a giant planet with mass $M_1=30~M_{\oplus}$ , while the right graph was obtained with $M_1=300~M_{\oplus}$ . In both frames the location of the giant planet is shown with a white circle in the X axis, while the position of the Trojan body can be seen in the vicinity of the L₄ point. Bottom: surface density of the gaseous disk, as function of the distance from the star, for an azimuthal angle crossing the L₄ point. The three curves correspond to simulations with masses of the giant planet equal to 30, 100 and $300~M_{\oplus}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{6582fig9.eps} \end{figure}$ Figure 7: Black: results of three hydrodynamical simulations of a system consisting of a massive planet of mass m₁ and a small Trojan-like body near the L₄ Lagrange point. Left frames show the evolution of the Trojan's orbital eccentricity, while the right frames correspond to the amplitude of libration $\lambda - \lambda _1$ . Top graphs were obtained with a massive planet of mass $M_1=30~M_{\oplus}$ , middle graphs with $M_1 = 100~M_{\oplus}$ , and bottom plots with $M_1=300~M_{\oplus}$ . Grey: temporal variation of the eccentricity and libration amplitude obtained from a 3-body model where the gas effects on the Trojan body are modeled with Stokes gas drag with C = 10^-5.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{6582fg10.eps} \end{figure}$ Figure 8: Typical simulation of the accretion process of a Trojan-like planetary body in a gas-rich scenario. The size of the initial population was N₀=300, the total mass was $M_{\rm T}=1.5~M_{\oplus}$ and the initial drag coefficient was set to C=10^-5.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{6582fg11.eps} \end{figure}$ Figure 9: Top: histogram of the mass of the final Trojan body obtained from two different sets of simulations in a gas-rich scenario. The continuous lines correspond to 50 runs with C=10^-5, and the broken lines to 50 simulations with a drag five times greater. The mass of the giant planet was set to $M_1=300~M_{\oplus}$ , and the initial mass of the swarm was $M_{\rm T}=1~M_{\oplus}$ . Bottom: distribution of the orbital eccentricity of the final bodies.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{6582fg12.eps} \end{figure}$ Figure 10: Decay in semimajor axis of the giant planet (black) and a Trojan body (grey) obtained with a FARGO hydro-simulation of a type II migration. Planetary masses were $M_1=300~M_{\oplus}$ and $M_{\rm p}=0.001~M_{\oplus}$ . Note that the semimajor axis of the Trojan body oscillates about the giant planet, and follows the orbital decay.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{6582fg13.eps} \end{figure}$ Figure 11: N-body simulation of the accretional evolution of a Trojan swarm coinciding with an inward type II migration of the giant planet. After $t \sim 10^4$ years, only a single exotrojan remains, and follows the giant planet towards a stable tadpole orbit in the habitable region of the system.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6582fig2.eps} \end{figure}$	Figure 2: Same as previous figure, but with N₀=300 and $M_{\rm T}=1.5~M_{\oplus}$ . Note that the time axis is now in linear scale.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{6582fig3.eps} \end{figure}$	Figure 3: Osculating eccentricity and semimajor axis of the Trojan swarm in four different time frames during the accretional process. The area of the circles are proportional to the planetesimal's mass.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{6582fig4.eps} \end{figure}$	Figure 4: The size of the stability region as a function of the mass of a Trojan planetesimal placed to L₄ calculated by the RLI chaos indicator. Light colors indicate stable, while dark colors indicate unstable orbits. It can be seen that a $0.15~M_{\oplus}$ Trojan planetesimal can seriously destabilize the region around L₄.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6582fig5.eps}\par\vspace*{2mm} \includegraphics[width=7.8cm,clip]{6582fig6.eps} \end{figure}$	Figure 5: Same as previous figure, now showing the logarithm of the maximum eccentricity attained by each initial condition during the complete integration timespan T. Top: T = 10³ orbital periods. Bottom: T = 10⁴ orbital periods. Note that the region in black corresponds to a change in the eccentricity of the order of unity; consequently the orbit is unstable over the timespan T.
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$\begin{figure} \par\includegraphics[width=8.2cm,clip]{6582fg10.eps} \end{figure}$	Figure 8: Typical simulation of the accretion process of a Trojan-like planetary body in a gas-rich scenario. The size of the initial population was N₀=300, the total mass was $M_{\rm T}=1.5~M_{\oplus}$ and the initial drag coefficient was set to C=10^-5.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{6582fg12.eps} \end{figure}$	Figure 10: Decay in semimajor axis of the giant planet (black) and a Trojan body (grey) obtained with a FARGO hydro-simulation of a type II migration. Planetary masses were $M_1=300~M_{\oplus}$ and $M_{\rm p}=0.001~M_{\oplus}$ . Note that the semimajor axis of the Trojan body oscillates about the giant planet, and follows the orbital decay.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{6582fg13.eps} \end{figure}$	Figure 11: N-body simulation of the accretional evolution of a Trojan swarm coinciding with an inward type II migration of the giant planet. After $t \sim 10^4$ years, only a single exotrojan remains, and follows the giant planet towards a stable tadpole orbit in the habitable region of the system.
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