All Figures

$\begin{figure} \par\includegraphics[width=4.1cm,clip]{9483fig1.eps}\hspace*{2mm} \includegraphics[width=4cm,clip]{9483fig2.eps}\end{figure}$ Figure 1: Orbital evolution tracks in the eccentricity (e)-periastron distance( $r_{\rm p}$ ) plane. Different types of evolution are displayed. Arrows indicate the direction of time. The left panel shows tidal evolution toward stable corotating circular orbits at $r_0^\prime$ = $450~r_{\rm g}$ . The right panel is an enlargement of the left bottom part. It shows the evolution of very low orbital angular momentum orbits. (See text for details.) In this example, intended to show the topology of small $\alpha$ tidal evolution, the value of $\alpha$ is arbitrarily taken to be 0.05. Different curves correspond to initial $\tilde r_{\rm p}=25, 50, 100, 200, 250, 400, 600, 800, 1000$ ( left panel) and $\tilde r_{\rm p}=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.85, 0.9$ ( right panel).
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In the text

$\begin{figure} \par\includegraphics[width=6.3cm,clip]{9483fig3.eps}\end{figure}$ Figure 2: Angular momentum ( $\lambda ={h\over 2 m r_{\rm g} c}$ ) - orbital energy (E) during the tidal evolution of the orbit for the evolution tracks shown in the right panel of Fig. 1.
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{9483fig4.eps}\includegraphics[width=4.1cm,clip]{9483fig5.eps}\end{figure}$ Figure 3: The evolution of radial turning points in the Kepler (red) and Schwarzschild effective potentials (black) for the case of a highly eccentric orbit starting with periastron at $9.5~r_{\rm g}$ and apoastron at $110~r_{\rm g}$ . The right figure is an enlargement of the final evolution. The gray line indicates the third root of the effective potential equation (Misner et al. 1971).
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In the text

$\begin{figure} \par\includegraphics[width=7.55cm,clip]{9483fig6.eps}\end{figure}$ Figure 4: Resonant and non-resonant timescales as a function of $\beta$ for $\rho =\rho _0$ , R=10 km, and Q=100 (see Eqs. (21), (22)).
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In the text

$\begin{figure} \par\includegraphics[width=6.3cm,clip]{9483fig3.eps}\end{figure}$	Figure 2: Angular momentum ( $\lambda ={h\over 2 m r_{\rm g} c}$ ) - orbital energy (E) during the tidal evolution of the orbit for the evolution tracks shown in the right panel of Fig. 1.
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$\begin{figure} \par\includegraphics[width=4.2cm,clip]{9483fig4.eps}\includegraphics[width=4.1cm,clip]{9483fig5.eps}\end{figure}$	Figure 3: The evolution of radial turning points in the Kepler (red) and Schwarzschild effective potentials (black) for the case of a highly eccentric orbit starting with periastron at $9.5~r_{\rm g}$ and apoastron at $110~r_{\rm g}$ . The right figure is an enlargement of the final evolution. The gray line indicates the third root of the effective potential equation (Misner et al. 1971).
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$\begin{figure} \par\includegraphics[width=7.55cm,clip]{9483fig6.eps}\end{figure}$	Figure 4: Resonant and non-resonant timescales as a function of $\beta$ for $\rho =\rho _0$ , R=10 km, and Q=100 (see Eqs. (21), (22)).
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