All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{aa0034f1.eps} \end{figure}$ Figure 1: Greyscale plot of the surface density in the disc in the case of the reference model after 10 orbits of the protoplanet in the disc. The gap clearing has already started, and the spiral density wave pattern is visible throughout the disc. The circle represents the Roche lobe of the protoplanet according to Eggleton's formula.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f002.eps} \end{figure}$ Figure 2: Evolution of the azimuthally averaged surface density for five different times in the case of the reference model. The planet has a fixed orbit at 5.2 AU.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f003.eps} \end{figure}$ Figure 3: Influence of the kinematic viscosity parameter on the gap size. The azimuthally averaged surface density is plotted for three different viscosities in units of $\nu_0=10^{15}~{\rm cm^2/s}$ after 100 orbits of the protoplanet. The planet has a fixed orbit with a radial distance of 5.2 AU.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{aa0034f4.eps} \end{figure}$ Figure 4: Influence of the scale height of the disc. The greyscale plot shows the surface density in the disc after 100 orbits of the protoplanet for three different scale heights.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f005.eps} \end{figure}$ Figure 5: Evolution of the radial distance of the planet to the central object. The planet is initially located at a radial distance of $5.2~{\rm AU}$ . In one model, the accreted mass is added to the planet's mass, in the other the mass of the planet remains fixed.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f006.eps} \end{figure}$ Figure 6: Evolution of the accretion rate on the planet for a planet with fixed mass and a planet with increasing mass. The planet is originally located at a radial distance of 5.2 ${\rm AU}$ , and migrates inwards as shown in Fig. 5.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f007.eps} \end{figure}$ Figure 7: Evolution of the azimuthally averaged surface density in the case of two protoplanets in the disc. The number of orbits of the inner planet is indicated. The inner planet is located at $5.2~{\rm AU}$ , the outer planet at twice that distance from the central object.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f008.eps} \end{figure}$ Figure 8: Evolution of the semi-major axis of the two protoplanets. The initial parameters of the planets are the same as in Fig. 7, but now the trajectories of the planets are integrated.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f009.eps} \end{figure}$ Figure 9: Evolution of the eccentricities of the two protoplanets during the migration, same simulation as presented in Fig. 8.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f0a1.eps} \end{figure}$ Figure A.1: Evolution of the azimuthally averaged surface density of the viscous ring at three different times, using only physical viscosity in the simulation. Dotted lines denote the analytic solutions.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f0a2.eps} \end{figure}$ Figure A.2: Evolution of the azimuthally averaged surface density of the viscous ring at three different times, additionally using artificial bulk viscosity and XSPH together with the physical viscosity. Dotted lines denote the analytic solutions.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f0a3.eps} \end{figure}$ Figure A.3: Evolution of the azimuthally averaged surface density of the viscous ring at three different times, applying only artificial bulk viscosity. The dotted line represents the initial analytic solution.

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{aa0034fa4.eps} \end{figure}$ Figure A.4: Greyscale plots of the surface density of the inner part of the protoplanetary disc in the case of the reference model similar to Fig. 1 but in Cartesian coordinates, with ( upper panel) and without ( lower panel) using the XSPH-algorithm. Note that the planet cannot be seen on these plots, since it is located at a radial distance of $5.2~{\rm AU}$ .

In the text

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{0034f0a5.eps} \end{figure}$ Figure A.5: Evolution of the azimuthally averaged surface density of the viscous ring at three different times, applying only the usual artificial viscosity. The dotted line represents the initial analytic solution.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{aa0034f1.eps} \end{figure}$	Figure 1: Greyscale plot of the surface density in the disc in the case of the reference model after 10 orbits of the protoplanet in the disc. The gap clearing has already started, and the spiral density wave pattern is visible throughout the disc. The circle represents the Roche lobe of the protoplanet according to Eggleton's formula.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f002.eps} \end{figure}$	Figure 2: Evolution of the azimuthally averaged surface density for five different times in the case of the reference model. The planet has a fixed orbit at 5.2 AU.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f003.eps} \end{figure}$	Figure 3: Influence of the kinematic viscosity parameter on the gap size. The azimuthally averaged surface density is plotted for three different viscosities in units of $\nu_0=10^{15}~{\rm cm^2/s}$ after 100 orbits of the protoplanet. The planet has a fixed orbit with a radial distance of 5.2 AU.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{aa0034f4.eps} \end{figure}$	Figure 4: Influence of the scale height of the disc. The greyscale plot shows the surface density in the disc after 100 orbits of the protoplanet for three different scale heights.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f005.eps} \end{figure}$	Figure 5: Evolution of the radial distance of the planet to the central object. The planet is initially located at a radial distance of $5.2~{\rm AU}$ . In one model, the accreted mass is added to the planet's mass, in the other the mass of the planet remains fixed.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f006.eps} \end{figure}$	Figure 6: Evolution of the accretion rate on the planet for a planet with fixed mass and a planet with increasing mass. The planet is originally located at a radial distance of 5.2 ${\rm AU}$ , and migrates inwards as shown in Fig. 5.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f007.eps} \end{figure}$	Figure 7: Evolution of the azimuthally averaged surface density in the case of two protoplanets in the disc. The number of orbits of the inner planet is indicated. The inner planet is located at $5.2~{\rm AU}$ , the outer planet at twice that distance from the central object.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f008.eps} \end{figure}$	Figure 8: Evolution of the semi-major axis of the two protoplanets. The initial parameters of the planets are the same as in Fig. 7, but now the trajectories of the planets are integrated.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0034f009.eps} \end{figure}$	Figure 9: Evolution of the eccentricities of the two protoplanets during the migration, same simulation as presented in Fig. 8.
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