All Figures

$\begin{figure} \par\resizebox{11cm}{!}{\includegraphics[clip]{MS3608f1.eps}}\end{figure}$ Figure 1: Gas density of the atmosphere is plotted as a function of distance from the center of the planet. The solid and dashed lines are the numerical and analytical solutions, respectively. The detail of the former is described in the Sect. 2.2 and that of the latter in Appendix. a) The dependence on the core mass, $M_{\rm core}$ , and b) the dependences on the luminosity, L and the grain depletion factor, f, are shown.
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In the text

$\begin{figure} \par\resizebox{11cm}{!}{\includegraphics[clip]{MS3608f2.eps}}\end{figure}$ Figure 2: a) The enhanced radii of the protoplanet with $M_{\mbox{\scriptsize core}} = 1~ M_{\oplus}$ , $L = 1 \times 10^{-8} ~L_{\odot}$ , and f=0.01 when the velocities of planetesimals are $1 r_{\mbox{\scriptsize H}} \Omega_{\mbox{\scriptsize K}}$ and b) the dynamical pressure the planetesimals take. The cases without and with ablation are shown by the solid lines and the filled circles. The strength of the planetesimal given by Benz & Asphaug (1999) is shown by the dashed curve as well. Planetesimals with the radii larger than $5\times 10^8$ cm cannot be captured in the atmosphere.
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In the text

$\begin{figure} \par\resizebox{11cm}{!}{\includegraphics[clip]{MS3608f3.eps}}\end{figure}$ Figure 3: The enhanced radii of protoplanets with various parameters. a) The enhanced radii of the protoplanets for the case with $L = 1 \times 10^{-8} ~L_{\odot}$ , $v = 1 r_{\mbox{\scriptsize H}} \Omega_{\mbox{\scriptsize K}}$ , and $M_{\mbox{\scriptsize core}} = 4, 2, 1, 0.1 ~M_{\oplus}$ . b) Those for the cases with $M_{\mbox{\scriptsize core}} = 1~ M_{\oplus}$ , $L = 1 \times 10^{-8} ~L_{\odot}$ , and $v = 0.1, 1, 10 r_{\mbox{\scriptsize H}} \Omega_{\mbox{\scriptsize K}}$ , c) those for the cases with $M_{\mbox{\scriptsize core}} = 1~ M_{\oplus}$ , $v = 1 r_{\mbox{\scriptsize H}} \Omega_{\mbox{\scriptsize K}}$ , and $L = 1\times 10^{-7}, 1\times 10^{-8}, 1\times 10^{-9} ~L_{\odot}$ . In every cases, the grain depletion factor is f=0.01. Comparison between the enhanced radii obtained from the numerical simulation (solid lines) and the analytical formula (dashed lines) is shown as well.
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In the text

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics*[clip]{MS3608f5.eps}}\end{figure}$ Figure 4: The enhanced radii of the protoplanet normalized by the core radius given by case J1 of Pollack et al. (1996) (dashed curve) and this study (solid curve). The radius of the planetesimal is 100 km.
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In the text

$\begin{figure} \par\resizebox{11cm}{!}{\includegraphics[clip]{MS3608f4.eps}}\end{figure}$ Figure 5: The closest distances of the planetesimals with radius of 100 m from the protoplanet with $M_{\mbox{\scriptsize core}} = 1~ M_{\oplus}$ , $L = 1 \times 10^{-8} ~L_{\odot}$ , and f=0.01for the cases without the atmosphere (the dashed line) and with the atmosphere (the solid line). The enhanced radius, $R_{\mbox{\scriptsize c}}$ , obtained from Fig. 2 and the radius of the core, $R_{\mbox{\scriptsize core}}$ , are shown by the horizontal dotted lines.
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In the text

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{MS3608f6.eps}}\end{figure}$ Figure 6: The growth time, $T_{\mbox{\scriptsize g}}$ , of the protoplanet with $10 ~M_{\oplus}$ by accumulation of uniform planetesimals with radius of $r_{\mbox{\scriptsize p}}$ without (dashed curve) and with (solid curve) the effect of enhanced radius.
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In the text

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics*[clip]{MS3608f5.eps}}\end{figure}$	Figure 4: The enhanced radii of the protoplanet normalized by the core radius given by case J1 of Pollack et al. (1996) (dashed curve) and this study (solid curve). The radius of the planetesimal is 100 km.
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$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{MS3608f6.eps}}\end{figure}$	Figure 6: The growth time, $T_{\mbox{\scriptsize g}}$ , of the protoplanet with $10 ~M_{\oplus}$ by accumulation of uniform planetesimals with radius of $r_{\mbox{\scriptsize p}}$ without (dashed curve) and with (solid curve) the effect of enhanced radius.
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