All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{3391f1.ps} \end{figure}$ Figure 1: The secular precession timescale relative to that at a semimajor axis corresponding to the planet's outer 3:2 mean motion resonance (i.e., $a = 1.31a_{{\rm pl}}$ ).
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In the text

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{3391f2.ps} \end{figure}$ Figure 2: The secular evolution of the complex eccentricity, $z = e\ast \exp{{\rm i}\tilde{w}}$ , of planetesimals orbiting at semimajor axes of 1.4, 1.45 and $1.5a_{{\rm pl}}$ . Their eccentricities are shown relative to the eccentricity of the planet, $e_{{\rm pl}}$ . The large symbols on the x axis show the forced eccentricity about which these complex eccentricities are precessing. The precession is anticlockwise, and each point is advanced by a timestep of $0.05t_{{\rm sec}(3:2)}$ . The total evolution is $1t_{{\rm sec}(3:2)}$ .
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In the text

$\begin{figure} \par\begin{tabular}{cccccc} $0.1t_{sec(3:2)}$\space & $0.3t_{sec... ...ce{-0.45in} \includegraphics[width=1.4in]{3391f3l.ps} \end{tabular} \end{figure}$ Figure 3: The eccentricities ( top) and pericentre orientations ( bottom) of planetesimals in an initially dynamically cold planetesimal disk at times from left to right of 0.1, 0.3, 1, 3, 10 and 100 $t_{{\rm sec}(3:2)}$ after the introduction of a planet on an eccentric orbit. The eccentricities are shown relative to that of the planet, and the dotted lines on these plots indicate the maximum planetesimal eccentricity at a given distance from the star, $e_{{\rm max}} = 2e_{\rm f}$ . The minima in the eccentricity plots occur at locations corresponding to an integer number of precession timescales; there is also a jump of pericentre orientation from $+90^\circ$ to $-90^\circ$ at these locations. In the region close to the planet, several precession timescales have taken place leading to random eccentricities and pericentre orientations, although these still lie within the range -90 to $+90^\circ$ . Movies showing the evolution of the planetesimals' eccentricities and pericentre orientations are available in the electronic edition of the journal.
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In the text

$\begin{figure} \par\hspace*{1.2cm} \begin{tabular}{cccccc} \hspace{-0.4in} $0.1... ...\includegraphics[width=1.5in]{3391f4r.ps}\\ [-0.1in] \end{tabular} \end{figure}$ Figure 4: The response of the spatial distribution of planetesimals orbiting with semimajor axes in the range $1-3a_{{\rm pl}}$ to the introduction of a planet on an eccentric orbit. The different panels show the response for planet eccentricities of 0.05, 0.1, and 0.2 ( top to bottom), and at times of 0.1, 0.3, 1, 3, 10 and $100t_{{\rm sec}(3:2)}$ ( left to right). The x and y axes are scaled to the semimajor axis of the planet. The planet's orbit is shown by the white line with the pericentre direction to the right. The planetesimals are orbiting anticlockwise, but the direction of the planet's motion is unconstrained. The star is marked by the plus. The colour scale indicates the number of planetesimals in a given pixel (i.e., the surface density), and this number is also quantified by the black contours which indicate where the density is 0.33 and 0.67 times the maximum value. A movie showing the evolution of the planetesimal distribution for $e_{{\rm pl}} = 0.1$ is available in the electronic edition of the journal.
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In the text

$\begin{figure} \par\hspace*{1.4cm} \begin{tabular}{cccccc} \hspace{-0.4in} $0.1... ...\includegraphics[width=1.5in]{3391f5r.ps}\\ [-0.1in] \end{tabular} \end{figure}$ Figure 5: The same as Fig. 4 except for planetesimals orbiting with semimajor axes in the range $0.3-1a_{{\rm pl}}$ . Again, a movie showing the evolution of the planetesimal distribution for $e_{{\rm pl}} = 0.1$ is available in the electronic edition of the journal.
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In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{3391f6.ps} \end{figure}$ Figure 6: The orbits of planetesimals at semimajor axes of 1.4, 1.45 and $1.5a_{{\rm pl}}$ at a time of $1t_{{\rm sec}(3:2)}$ after a planet is introduced with $e_{{\rm pl}} = 0.1$ . The x direction denotes the orientation of the planet's pericentre and the axes are scaled in units of the planet's semimajor axis. The 10 symbols for each orbit are distributed at equal timesteps around the orbit with the pericentre denoted by a filled circle. Orbital motion is anticlockwise.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{3391f7.ps} \end{figure}$ Figure 7: The semimajor axes of planetesimals which have completed 0.5, 1.5, and 2.5 precession periods (solid lines) and 1.0 and 2.0 precession periods (dotted lines) at any given time after the introduction of an eccentric planet into a disk; lower numbers of precession periods correspond to planetesimals further from the planet. Times are given relative to the secular precession time at the 3:2 resonance, $t_{{\rm sec}(3:2)}$ . The most prominent spiral in the images is associated with planetesimals which have completed half a precession period. The spirals from planetesimals at 1.5 and 2.5 precession periods are so close that they often appear as an asymmetric ring.
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In the text

$\begin{figure} \par\begin{tabular}{rl} \textbf{(a)} & \includegraphics[width=3i... ...textbf{(b)} & \includegraphics[width=3in]{3391f8b.ps} \end{tabular} \end{figure}$ Figure 8: Orbits of planetesimals determined using a full numerical integration involving 1000 planetesimals distributed between 110 and 200 AU from a $2.5~M_\odot$ star: a) eccentricities, and b) pericentre orientations. The planetesimals were started on circular orbits and a $80~M_\oplus$ planet was introduced at 100 AU with an eccentricity of 0.08. These plots show the distribution at 15 Myr ( $\sim$ $3.5t_{{\rm sec}(3:2)}$ ). The solid lines show the distribution predicted from the analytical theory and the dotted lines show the locations of the planet's resonances. The dashed line delineates planet-crossing orbits.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{3391f9.ps} \end{figure}$ Figure 9: Width of the empty region, $abs(a/a_{{\rm pl}}-1)$ , caused by planets of different eccentricities and masses. Planetesimals on planet crossing orbits are shown with a solid line for external orbits and a dashed line for internal orbits. Planetesimals on chaotic orbits due to resonance overlap are shown with dotted lines for planet masses defined by $\mu =M_{{\rm pl}}/M_\star =10^{-2}$ , 10^-3, 10^-4, and 10^-5.
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In the text

$\begin{figure} \par\hspace*{0.6cm} \begin{tabular}{rl} \textbf{(a)} & \includeg... ...e{-0.0in} \includegraphics[width=3.05in]{3391f10c.ps} \end{tabular} \end{figure}$ Figure 10: Surface density image of the HD 141569 disk: a) observed density distribution reproduced from Fig. 8b of Clampin et al. (2003), but cropped so that the length of each side measures 800 AU; b) model density distribution (i) which fits the spiral at 325 AU assuming its structure is as outlined in Fig. 8a of Clampin et al., but assumes the star is at the centre of the disk and not where it was inferred to be from the images (the plus in a)); c) model density distribution (ii) which fits the spiral at 325 AU assuming that the position of the star is as inferred by Clampin et al. (2003). The two models (i) and (ii) are described in more detail in the text. The planet's orbit in these models is shown with a white line, the axes are in AU, and the position of the star shown with a plus. The orientation of all images is such that N is to the left, E is down.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{3391f1.ps} \end{figure}$	Figure 1: The secular precession timescale relative to that at a semimajor axis corresponding to the planet's outer 3:2 mean motion resonance (i.e., $a = 1.31a_{{\rm pl}}$ ).
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$\begin{figure} \par\hspace*{1.4cm} \begin{tabular}{cccccc} \hspace{-0.4in} $0.1... ...\includegraphics[width=1.5in]{3391f5r.ps}\\ [-0.1in] \end{tabular} \end{figure}$	Figure 5: The same as Fig. 4 except for planetesimals orbiting with semimajor axes in the range $0.3-1a_{{\rm pl}}$ . Again, a movie showing the evolution of the planetesimal distribution for $e_{{\rm pl}} = 0.1$ is available in the electronic edition of the journal.
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