All Figures

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9178fig1.ps}\end{figure}$ Figure 1: ( Top) Eccentricity evolution of a 10 $M_{\oplus }$ protoplanet on a variety of eccentric orbits. Solid lines are the results from NIRVANA, crosses from the N-body code. ( Bottom) The corresponding migration rates. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9178fig2.ps}\end{figure}$ Figure 2: ( Top) Inclination evolution of a 10 $M_{\oplus }$ protoplanet on a variety of inclined orbits. Solid lines are the results from NIRVANA, crosses from the N-body code. ( Bottom) The corresponding migration rates. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9178fig3.ps}\end{figure}$ Figure 3: ( Top) Eccentricity evolution of a 10 $M_{\oplus }$ protoplanet on a variety of eccentric and inclined orbits. Solid lines are the results from NIRVANA, crosses from the N-body code. ( Bottom) Inclination evolution of the same orbits. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9178fig4.ps} \end{figure}$ Figure 4: Orbital elements for the 3D NIRVANA model, similar to Fig. 5 but with eight protoplanets (run H1). Behaviour is similar to the early stages of the N-body models, with scattering and collisions among the inner population. A co-orbital system is formed, which remains stable for the remainder of the integrations. Note only the smallest protoplanet achieves e>0.1 or $i>0.5^{\circ }$ after the initial values have been damped. The 6 and 10 $M_{\oplus }$ protoplanets collide at $t=6.7\times 10^3$ yrs, and the 4 and 8 $M_{\oplus }$ protoplanets collide at $t=1.20\times 10^4$ yrs. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9178fig5.ps} \end{figure}$ Figure 5: Evolution of a 10 planet N-body model with ordered masses and the fiducial set-up (O1). ( Top) Semi-major axes of the migrating embryos. Short periods of activity are followed by long periods of migration between bodies in first order mean-motion resonances. The 4 and 18 $M_{\oplus }$ planets collide at $t=6.76\times 10^4$ yrs. ( Middle) The embryos' eccentricities over the same time. ( Bottom) The embryos' inclinations. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=14.5cm,clip]{9178fig6.ps} \end{figure}$ Figure 6: The first order mean-motion resonances between the planets in Fig. 5, during the longest resonant migration phase. Each plot is labelled (P_i,P_j)-p:q, where P_i and P_j are the exterior and interior protoplanets in each resonance respectively, and p:q is the commensurability between them. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{9178fig7.ps} \end{figure}$ Figure 7: Evolution of a 10 planet N-body model with randomised masses and the fiducial set-up (R1). ( Top) Semi-major axes of the migrating embryos. Short periods of activity are followed by long periods of migration of bodies in first order mean-motion resonances. ( Middle) The embryos' eccentricities over the same time. ( Bottom) The embryos' inclinations. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{9178fig8.ps} \end{figure}$ Figure 8: Snapshots of two randomly selected simulations from the model classes shown, with the exception of the first (R1) and fourth (R2) rows, which correspond to Figs. 7 and 9 respectively. The snapshots are taken at $t=2\times 10^5$ yrs. The area of each planet is linearly proportional to its mass; the smallest body (in the top row) is of 2 $M_{\oplus }$ , and the largest (formed from multiple collisions) is of 39 $M_{\oplus }$ . The co-orbitals of Fig. 9 are clearly visible as concentric circles. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{9178fig9.ps} \end{figure}$ Figure 9: Evolution of a co-orbital system (class R2) migrating inwards: two co-orbital pairs, locked in a 3:2 MMR. The size of each planet is proportional to its mass, while the open triangles display each primary body's L₄ and L₅ points. The other protoplanets present in the model are not displayed, but those shown are part of a resonant group encompassing nine bodies. ( Top) Initially the co-orbital planets' motions cover the whole horseshoe region. ( Middle) The disc's action causes the planets to shift into tadpole orbits. ( Bottom) The planets migrate inwards under small librations. (The figure is available in colour in the online version.)
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In the text

$\begin{figure} \par\includegraphics[width=5.7cm,clip]{9178fig10.ps} \end{figure}$ Figure 10: Frequency of N-body models displaying stable horseshoe or tadpole planets. On the left, N-body data from Paper I is shown for comparison. Left-right: 2D ordered, 2D randomised, 3D ordered, 3D randomised.
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In the text

$\begin{figure} \par\includegraphics[width=5.7cm,clip]{9178fig11.ps} \end{figure}$ Figure 11: Frequency of collisions per simulation for the ordered mass models ( left) and randomised mass models ( right). The open bars show the corresponding 2D data of Paper I.
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In the text

$\begin{figure} \par\includegraphics[width=5.7cm,clip]{9178fig12.ps} \end{figure}$ Figure 12: Frequency of resonant group size per simulation for the ordered mass models ( left) and randomised mass models ( right).
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In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9178fig1.ps}\end{figure}$	Figure 1: ( Top) Eccentricity evolution of a 10 $M_{\oplus }$ protoplanet on a variety of eccentric orbits. Solid lines are the results from NIRVANA, crosses from the N-body code. ( Bottom) The corresponding migration rates. (The figure is available in colour in the online version.)
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9178fig2.ps}\end{figure}$	Figure 2: ( Top) Inclination evolution of a 10 $M_{\oplus }$ protoplanet on a variety of inclined orbits. Solid lines are the results from NIRVANA, crosses from the N-body code. ( Bottom) The corresponding migration rates. (The figure is available in colour in the online version.)
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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{9178fig3.ps}\end{figure}$	Figure 3: ( Top) Eccentricity evolution of a 10 $M_{\oplus }$ protoplanet on a variety of eccentric and inclined orbits. Solid lines are the results from NIRVANA, crosses from the N-body code. ( Bottom) Inclination evolution of the same orbits. (The figure is available in colour in the online version.)
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$\begin{figure} \par\includegraphics[width=14.5cm,clip]{9178fig6.ps} \end{figure}$	Figure 6: The first order mean-motion resonances between the planets in Fig. 5, during the longest resonant migration phase. Each plot is labelled (P_i,P_j)-p:q, where P_i and P_j are the exterior and interior protoplanets in each resonance respectively, and p:q is the commensurability between them. (The figure is available in colour in the online version.)
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$\begin{figure} \par\includegraphics[width=5.7cm,clip]{9178fig10.ps} \end{figure}$	Figure 10: Frequency of N-body models displaying stable horseshoe or tadpole planets. On the left, N-body data from Paper I is shown for comparison. Left-right: 2D ordered, 2D randomised, 3D ordered, 3D randomised.
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$\begin{figure} \par\includegraphics[width=5.7cm,clip]{9178fig11.ps} \end{figure}$	Figure 11: Frequency of collisions per simulation for the ordered mass models ( left) and randomised mass models ( right). The open bars show the corresponding 2D data of Paper I.
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$\begin{figure} \par\includegraphics[width=5.7cm,clip]{9178fig12.ps} \end{figure}$	Figure 12: Frequency of resonant group size per simulation for the ordered mass models ( left) and randomised mass models ( right).
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