All Figures

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{2260f1a.eps} \end{figure}$ Figure 1: Cooling curves for material of solar abundance assuming collisional ionization equilibrium (solid) or non-equilibrium ionization (dashed). The former was calculated using the MEKAL thermal plasma code (Mewe et al.1985; Kaastra 1992) distributed in XSPEC (v11.2.0), while the latter was taken from data in Sutherland & Dopita (1993). These curves are normalized so that the net cooling rate per unit volume, $\dot{E} = n_{\rm e} n_{\rm i} \Lambda(T)$ , where $n_{\rm e}$ is the electron number density and $n_{\rm i}$ is the total number density of all of the ions.
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In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{2260f1b.eps} \end{figure}$ Figure 2: The slope, $\alpha$ , of the respective cooling curves in Fig. 1 (CIE - solid; NEI - dashed).
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{2260f2.eps} \end{figure}$ Figure 3: Schematic of the grid set up for implusive shock generation. Supersonic flow with density $\rho _{\rm0}$ and flow speed $v_{\rm0}$ collides with a subsonic CDL with density $\gamma M^{2} \rho _{\rm0}$ and flow speed $v_{\rm0}/\gamma M^{2}$ . The upstream boundary condition is inflow, while the downstream boundary condition is outflow. All simulations are 1-D.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{2260f3a.eps}\par\i... ...f3b.eps}\par\includegraphics[angle=-90,width=8cm,clip]{2260f3c.eps} \end{figure}$ Figure 4: Time-space diagrams of the density evolution of a 1-dimensional Mach 1.4 radiative shock with different cooling exponents $\alpha$ . Supersonic flow enters the grid from the top, and the cooled postshock gas flows off the grid at the bottom. Lighter shades indicate lower densities. Distances are marked in units of $L_{\rm c}$ (the value of this is different in each panel - see Eq. (4) and Table 2) while time is shown in units of $L_{\rm c}/v_{\rm0}$ ( $v_{\rm0} = 1$ ). The value of $\alpha$ is -2.5, -2.0, and -1.5 in the top, middle, and bottom panels respectively.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.1cm,clip]{2260f4a.eps}\par... ...c.eps}\par\includegraphics[angle=-90,width=8.1cm,clip]{2260f4d.eps} \end{figure}$ Figure 5: Time-space diagrams of the density evolution of a 1-dimensional radiative shock with cooling exponents $\alpha =-1.5$ and different Mach numbers. M is varied from 1.4, 2, 3 and 5 from the top to bottom panels. Note that the axis and density scaling changes from panel to panel, unlike in Fig. 4 where the scaling is kept constant.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{2260f5a.eps}\par\includegr... ...ip]{2260f5c.eps}\par\includegraphics[width=7.4cm,clip]{2260f5d.eps} \end{figure}$ Figure 6: Power spectra (mean square amplitude) for the simulations shown in Fig. 5 where $\alpha =-1.5$ . M varies from 1.4, 2, 3, 5 from the top to bottom panels respectively.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{2260f6a.eps}\par\i... ...clip]{2260f6b.eps}\par\includegraphics[width=8cm,clip]{2260f6c.eps} \end{figure}$ Figure 7: Time-space diagrams of the density evolution of a 1-dimensional radiative shock with M=3 and cooling exponent $\alpha =-1.5$ . In the top panel the flow is initialized to the steady state solution. In the middle panel the shock is impulsively generated. In the bottom panel the downstream boundary condition is reflecting.
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In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{2260f7.eps} \end{figure}$ Figure 8: The shock position as a function of time for simulations with M=3 and $\alpha =-1.5$ . The set up with an isolated steady-state shock as the initial condition is shown at the top, the set up with impulsive shock generation is shown in the middle, and the set up with a reflecting downstream boundary ( i.e. "flow into a wall'') is shown at the bottom. In the latter case the growth in width of the cold dense layer has been removed to aid comparison with the other scenarios, and each dataset is offset with respect to the others.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{2260f8a.eps}\par\includegraphics[angle=-90,width=8cm,clip]{2260f8b.eps} \end{figure}$ Figure 9: Time-space diagrams of the density evolution of a 1-dimensional radiative shock with cooling exponent $\alpha =-1.5$ and M=5 ( top) and M=10 ( bottom).
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2260f9.eps} \end{figure}$ Figure 10: The time-evolution of the shock position as a function of $\chi$ when M=1.4 and $\alpha =-2.5$ .
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{2260f10a.eps}\par\includegraphics[width=7.7cm,clip]{2260f10b.eps} \end{figure}$ Figure 11: The shock position as a function of time when M=1.4 and $\alpha =-1.5$ . The ratio of the temperature of the CDL to the pre-shock temperature, $\chi$ , is noted in each panel.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2260f11.eps} \end{figure}$ Figure 12: The value of $\alpha _{\rm cr}$ , the critical value for damping of the overstability, as a function of the reflection coefficient, R, for four different values of $\chi$ . The lines are only meant to guide the eye.
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In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{2260f1b.eps} \end{figure}$	Figure 2: The slope, $\alpha$ , of the respective cooling curves in Fig. 1 (CIE - solid; NEI - dashed).
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$\begin{figure} \par\includegraphics[width=6cm,clip]{2260f2.eps} \end{figure}$	Figure 3: Schematic of the grid set up for implusive shock generation. Supersonic flow with density $\rho _{\rm0}$ and flow speed $v_{\rm0}$ collides with a subsonic CDL with density $\gamma M^{2} \rho _{\rm0}$ and flow speed $v_{\rm0}/\gamma M^{2}$ . The upstream boundary condition is inflow, while the downstream boundary condition is outflow. All simulations are 1-D.
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$\begin{figure} \par\includegraphics[angle=-90,width=8.1cm,clip]{2260f4a.eps}\par... ...c.eps}\par\includegraphics[angle=-90,width=8.1cm,clip]{2260f4d.eps} \end{figure}$	Figure 5: Time-space diagrams of the density evolution of a 1-dimensional radiative shock with cooling exponents $\alpha =-1.5$ and different Mach numbers. M is varied from 1.4, 2, 3 and 5 from the top to bottom panels. Note that the axis and density scaling changes from panel to panel, unlike in Fig. 4 where the scaling is kept constant.
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$\begin{figure} \par\includegraphics[width=7.4cm,clip]{2260f5a.eps}\par\includegr... ...ip]{2260f5c.eps}\par\includegraphics[width=7.4cm,clip]{2260f5d.eps} \end{figure}$	Figure 6: Power spectra (mean square amplitude) for the simulations shown in Fig. 5 where $\alpha =-1.5$ . M varies from 1.4, 2, 3, 5 from the top to bottom panels respectively.
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$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{2260f6a.eps}\par\i... ...clip]{2260f6b.eps}\par\includegraphics[width=8cm,clip]{2260f6c.eps} \end{figure}$	Figure 7: Time-space diagrams of the density evolution of a 1-dimensional radiative shock with M=3 and cooling exponent $\alpha =-1.5$ . In the top panel the flow is initialized to the steady state solution. In the middle panel the shock is impulsively generated. In the bottom panel the downstream boundary condition is reflecting.
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$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{2260f8a.eps}\par\includegraphics[angle=-90,width=8cm,clip]{2260f8b.eps} \end{figure}$	Figure 9: Time-space diagrams of the density evolution of a 1-dimensional radiative shock with cooling exponent $\alpha =-1.5$ and M=5 ( top) and M=10 ( bottom).
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$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2260f9.eps} \end{figure}$	Figure 10: The time-evolution of the shock position as a function of $\chi$ when M=1.4 and $\alpha =-2.5$ .
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$\begin{figure} \par\includegraphics[width=7.7cm,clip]{2260f10a.eps}\par\includegraphics[width=7.7cm,clip]{2260f10b.eps} \end{figure}$	Figure 11: The shock position as a function of time when M=1.4 and $\alpha =-1.5$ . The ratio of the temperature of the CDL to the pre-shock temperature, $\chi$ , is noted in each panel.
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$\begin{figure} \par\includegraphics[width=7.6cm,clip]{2260f11.eps} \end{figure}$	Figure 12: The value of $\alpha _{\rm cr}$ , the critical value for damping of the overstability, as a function of the reflection coefficient, R, for four different values of $\chi$ . The lines are only meant to guide the eye.
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