Astronomy & Astrophysics

All Figures

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[angle=-90]{7934f01.eps}} \end{figure}$ Figure 1: Example of a planetesimal disk without outward planet migration, nor inward P-R drag migration of the test particles, according to our numerical simulations as explained in Sect. 2. The star and planet locations, projected onto the orbital plane of the planet, are represented by large red points, and the planet orbit by a thin green line. The initial planetesimal disk consists of 50 000 planetesimals distributed between 40 and 75 AU, with the surface density distribution proportional to r^-1. Although some planetesimals are trapped in MMRs with the planet, they are not sufficiently numerous to generate spatial structures (besides the 1:1 MMR). (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \par\makebox[\textwidth] { \includegraphics[angle=-90,width=0.33\... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f13.eps} } \\\end{figure}$ Figure 2: Spatial distribution of planetesimals for a planet on a strictly circular orbit. The star and planet locations, projected onto the orbital plane of the planet, are represented by larger red points, and the planet orbit by a thin green line. Green (resp. red) points represent planetesimals trapped in 3:2 (resp. 2:1) resonance. The 4 rows correspond respectively to Earth mass, Neptune mass, Saturn mass and 3 Jupiter mass planets, from top to bottom. The 3 columns show the disk after 5, 15 and 40 Myr. The initial planetesimal disk consists of 50 000 planetesimals distributed between 40 and 75 AU, with the surface density distribution proportional to r^-1. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \par\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\t... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f25.eps} } \\\end{figure}$ Figure 3: Same simulations as in Fig. 2, with the planetesimals represented in a (semi-major axis, eccentricity) plane. The plotting conventions are the same as in Fig. 2. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \par\makebox[12truecm]{ \includegraphics[width=5.9truecm]{7934f74.eps}\hfil \includegraphics[width=5.9truecm]{7934f75.eps} }\end{figure}$ Figure 8: Phase portraits (Hamiltonian level curves in an $(\nu , e)$ plane) of the secular non-resonant dynamics in the planar restricted three body problem, for a fixed semi-major axis $a=1.3a_{\rm p}$ , and planet eccentricities $e_{\rm p}=0.5$ ( left plot) and $e_{\rm p}=0.1$ ( right plot). The red line separates regions where the planetesimal orbit does not cross that of the planet (low eccentricities for $e_{\rm p}=0.1$ and a small island around $\nu =0$ for $e_{\rm p}=0.5$ ) from regions where both orbits cross each other. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics[angle=-90]{7934f76.eps}} \end{figure}$ Figure 9: An Earth mass planet on a very eccentric orbit ( $e_{\rm p}=0.6$ ). The plotting conventions are the same that Fig. 1. The disk structure does not rotate with the planet and is spatially fixed. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=12cm,origin=br]{7934f77.eps} \end{figure}$ Figure 10: Overview of the simulation outputs for planetesimal disks, in a (planet mass, planet eccentricity) plane. All simulations shown in this figure concern a planet with a constant migration rate of 0.5 AU Myr^-1. Color scale indicates the fraction of planetesimals still bound after 40 Myr. The fraction of surviving planetesimals is linearly interpolated between the simulations of the Table 2. In zones I and II, observable structures in the disk are generated by MMRs while in zone III, transient structures are generated by non-resonant mechanisms. In the remaining region, the disk does not show any structure. In zone I, MMRs create clumpy disks while in zone II they generate a smooth disk with a hole at the planet location. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[angle=-90,width=0.48\te... ...}{!}{\includegraphics[angle=-90,width=0.48\textwidth]{7934f79.eps}} \end{figure}$ Figure 11: A Saturn mass planet on a circular orbit migrating outward a dynamically warm disk. Initial eccentricities of planetesimals are uniformly distributed between 0 and 0.2. The plotting conventions are the same as in Figs. 2 and 3. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \par\begin{tabular}{c} \resizebox{8.5cm}{!}{\includegraphics[angl... ...graphics[angle=-90,width=0.48\textwidth]{7934f82.eps}}\end{tabular} \end{figure}$ Figure 12: Capture in the 2:1 resonance for a Neptune mass planet ( top), en Earth mass planet ( middle) and a Saturn mass planet ( bottom), all on a circular orbit, after 5 Myr. Dashed lines show the position of the resonance at the beginning and at the end of the simulations. In those simulations, an Earth mass planet does not capture at all planetesimals while a Saturn mass planet traps all of them. A Neptune mass planet only traps a fraction of the planetesimals but gives a small kick in eccentricity for the others. The plotting conventions are the same as in Fig. 3. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[angle=-90,width=0.48\textwidth]{7934f83.eps}}\\\end{figure}$ Figure 13: Projection on the (semi-major axis, eccentricity) plane of the trajectory of 40 planetesimals near the 2:1 resonance of a Neptune mass planet, migrating on a circular orbit. The semi-major axis is in units of the planet semi-major axis. Green lines are for permanently trapped planetesimals while the red lines are for the temporarily perturbed planetesimals. (See the electronic edition of the Journal for a color version of this figure.)
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In the text

$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...il \includegraphics[angle=-90,width=0.33\textwidth]{7934f37.eps} }\end{figure}$ Figure 4: Same as Fig. 2, for similar planets, but on a low-eccentricity orbit ( $e_{\rm p}=0.05$ ).
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In the text

$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f49.eps} } \\\end{figure}$ Figure 5: Same as Fig. 3, for similar planets, but on a low-eccentricity orbit ( $e_{\rm p}=0.05$ ).
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In the text

$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f61.eps} } \\\end{figure}$ Figure 6: Same as Fig. 2, for similar planets, but on a moderate eccentricity orbit ( $e_{\rm p}=0.3$ ).
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In the text

$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f73.eps} } \\\end{figure}$ Figure 7: Same as Fig. 3, for similar planets, but on a moderate eccentricity orbit ( $e_{\rm p}=0.3$ ).
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In the text

$\begin{figure} \par\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\t... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f25.eps} } \\\end{figure}$	Figure 3: Same simulations as in Fig. 2, with the planetesimals represented in a (semi-major axis, eccentricity) plane. The plotting conventions are the same as in Fig. 2. (See the electronic edition of the Journal for a color version of this figure.)
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$\begin{figure} \resizebox{8.8cm}{!}{\includegraphics[angle=-90]{7934f76.eps}} \end{figure}$	Figure 9: An Earth mass planet on a very eccentric orbit ( $e_{\rm p}=0.6$ ). The plotting conventions are the same that Fig. 1. The disk structure does not rotate with the planet and is spatially fixed. (See the electronic edition of the Journal for a color version of this figure.)
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[angle=-90,width=0.48\te... ...}{!}{\includegraphics[angle=-90,width=0.48\textwidth]{7934f79.eps}} \end{figure}$	Figure 11: A Saturn mass planet on a circular orbit migrating outward a dynamically warm disk. Initial eccentricities of planetesimals are uniformly distributed between 0 and 0.2. The plotting conventions are the same as in Figs. 2 and 3. (See the electronic edition of the Journal for a color version of this figure.)
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$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...il \includegraphics[angle=-90,width=0.33\textwidth]{7934f37.eps} }\end{figure}$	Figure 4: Same as Fig. 2, for similar planets, but on a low-eccentricity orbit ( $e_{\rm p}=0.05$ ).
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$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f49.eps} } \\\end{figure}$	Figure 5: Same as Fig. 3, for similar planets, but on a low-eccentricity orbit ( $e_{\rm p}=0.05$ ).
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$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f61.eps} } \\\end{figure}$	Figure 6: Same as Fig. 2, for similar planets, but on a moderate eccentricity orbit ( $e_{\rm p}=0.3$ ).
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$\begin{figure}\makebox[\textwidth]{ \includegraphics[angle=-90,width=0.33\textwi... ...includegraphics[angle=-90,width=0.33\textwidth]{7934f73.eps} } \\\end{figure}$	Figure 7: Same as Fig. 3, for similar planets, but on a moderate eccentricity orbit ( $e_{\rm p}=0.3$ ).
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