All Figures

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{H4150F1.ps} \end{figure}$ Figure 1: Simulated X-ray fluxes in the 0.1-4 keV band for the M=120 cases. The rows refer from top to bottom to the $\nu =0.1,0.01,0.001$ cases respectively. In the first two columns on the left the X-ray images are shown in logarithmic scale at times corresponding to cocoon lengths of $l_{\rm c}\sim 1$ and 2 core radii. In the two columns on the right longitudinal cuts along to the jet axis corresponding to the images on the left are plotted with a solid line. The dashed line represents the emission from the undisturbed atmosphere. The fluxes are given in unity of the central flux of the unperturbed atmosphere.
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In the text

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{H4150F2.ps} \end{figure}$ Figure 2: Simulated X-ray fluxes, in logarithmic scale, in the 0.1-4 keV band for the M=60 cases. The rows refer from top to bottom to the $\nu =0.1,0.01,0.001$ cases respectively. The quantities represented are the same as in Fig. 1.
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In the text

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{H4150F3.ps} \end{figure}$ Figure 3: Simulated X-ray fluxes, in logarithmic scale, in the 0.1-4 keV band for the M=10, $\nu =0.1$ case. The quantities represented are the same as in Figs. 1, 2.
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In the text

$\begin{figure} \par\includegraphics[width=17cm,clip]{H4150F4.ps} \end{figure}$ Figure 4: Density maps for the M=60 cases. The scale is logarithmic. The rows refer from top to bottom to the $\nu =0.1,0.01,0.001$ cases respectively. In the columns density maps are shown at times corresponding to a cocoon length $l_{\rm c} \sim 1,1.5$ and 2 core radii. The densities are given in unity of the central density of the unperturbed atmosphere.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F5.ps} \end{figure}$ Figure 5: (Upper panels) Plot of the integrated flux deficit as a function of cocoon length in the 0.1-4 keV band (left) and in the 4-10 keV band ( right) for the M=60 cases. This quantity is defined in Eq. (9). (Lower panels) Plot of the excess emission as a function of cocoon length in the 0.1-4 keV band (left) and in the 4-10 keV band (right) for the M=60 cases. This quantity is defined in Eq. (10). In the four panels the three lines refer to the $\nu =0.1$ (solid), $\nu =0.01$ (dashed) and $\nu =0.001$ (dash-dotted) cases.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F6.ps} \end{figure}$ Figure 6: Temperature plots for the M=120 cases ( $\nu =0.1,0.01,0.001$ from left to right respectively) at a time corresponding to a cocoon length of 2 core radii. (Upper panels) Plot of the quantity E(T) as defined in Eq. (11). It represents the energy emitted in the 0.1-10 keV band by the gas at the temperature T. The vertical line marks the temperature of the ambient isothermal medium while the peak correponds to the compressed shell emission. The emission is normalized to the total emission from the unperturbed atmosphere. ( Lower panels) Plot of the shell average temperature as a function of the angle with origin in r=0, z=0. The $0^\circ$ angle corresponds to the direction of the jet axis. The ambient temperature is taken 2.3 keV.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F7.ps} \end{figure}$ Figure 7: Temperature plots for the M=60 cases ( $\nu =0.1,0.01,0.001$ from left to right respectively) at a time corresponding to a cocoon length of 2 core radii. The quantities plotted are the same as in Fig. 6.
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In the text

$\begin{figure} \par\includegraphics[width=3.5cm]{H4150F8.ps} \end{figure}$ Figure 8: Temperature plots for the M=10, $\nu =0.1$ case at a time corresponding to a cocoon length of 2 core radii. The quantities plotted are the same as in Figs. 6 and 7.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F9.ps} \end{figure}$ Figure 9: Plot of the internal and external radii vs time. The rows refer to the different Mach cases while columns to the different $\nu$ values. The solid lines show the extended and internal cocoon radii as determined in the simulations taking an average value between 1/8 and 1/4 of the total length of the cocoon. The dashed lines show the same quantities as determined by our analytical model assuming that the expansion of the cocoon is driven by the average pressure of the cocoon.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F10.ps} \end{figure}$ Figure 10: Plot of the pressure vs. cocoon length. The rows refer to the different Mach numbers while columns to the different $\nu$ values. The solid line shows the evolution of the average cocoon pressure with time in the different cases. The dashed one represents the external pressure averaged on the cocoon volume as defined in Eq. (A.7).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F11.ps} \end{figure}$ Figure 11: Plot of the values of $(P_{\rm c} - P^*)/P^*$ at a cocoon length $l_{\rm c} = 0.3$ (see Table 3) against jet kinetic luminosity $L_{\rm j}/L_{\rm k}=M^3\nu$ . The solid line is a $(P_{\rm c} - P^*)/P^* \propto (L_{\rm j}/L_{\rm k})^{0.62}$ , that is also the best fit, excluding the value of the case M=10, $\nu =0.1$ that is in a weakly overpressured regime already.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F12.ps} \end{figure}$ Figure 12: Representation of the different regimes of the cocoon expansion in the $M{-}\nu$ plane. Inside the dashed area the jet becomes subsonic with respect to its internal sound speed. The solid lines correspond to a constant kinetic jet power $L_{\rm j}/L_{\rm k}=M^3\nu$ given in unit of the power $L_{\rm k}$ defined in Eq. (5). The fragmented curves separate strongly and weakly overpressured regimes for different lengths of the cocoon given in core radii units. It can be seen that these lines correspond to lines of constant kinetic jet power. The diamonds correspond to the simulated cases.
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In the text

$\begin{figure} \par\includegraphics[width=15.5cm,clip]{H4150F2.ps} \end{figure}$	Figure 2: Simulated X-ray fluxes, in logarithmic scale, in the 0.1-4 keV band for the M=60 cases. The rows refer from top to bottom to the $\nu =0.1,0.01,0.001$ cases respectively. The quantities represented are the same as in Fig. 1.
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$\begin{figure} \par\includegraphics[width=15.5cm,clip]{H4150F3.ps} \end{figure}$	Figure 3: Simulated X-ray fluxes, in logarithmic scale, in the 0.1-4 keV band for the M=10, $\nu =0.1$ case. The quantities represented are the same as in Figs. 1, 2.
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$\begin{figure} \par\includegraphics[width=17cm,clip]{H4150F4.ps} \end{figure}$	Figure 4: Density maps for the M=60 cases. The scale is logarithmic. The rows refer from top to bottom to the $\nu =0.1,0.01,0.001$ cases respectively. In the columns density maps are shown at times corresponding to a cocoon length $l_{\rm c} \sim 1,1.5$ and 2 core radii. The densities are given in unity of the central density of the unperturbed atmosphere.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F7.ps} \end{figure}$	Figure 7: Temperature plots for the M=60 cases ( $\nu =0.1,0.01,0.001$ from left to right respectively) at a time corresponding to a cocoon length of 2 core radii. The quantities plotted are the same as in Fig. 6.
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$\begin{figure} \par\includegraphics[width=3.5cm]{H4150F8.ps} \end{figure}$	Figure 8: Temperature plots for the M=10, $\nu =0.1$ case at a time corresponding to a cocoon length of 2 core radii. The quantities plotted are the same as in Figs. 6 and 7.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F10.ps} \end{figure}$	Figure 10: Plot of the pressure vs. cocoon length. The rows refer to the different Mach numbers while columns to the different $\nu$ values. The solid line shows the evolution of the average cocoon pressure with time in the different cases. The dashed one represents the external pressure averaged on the cocoon volume as defined in Eq. (A.7).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{H4150F11.ps} \end{figure}$	Figure 11: Plot of the values of $(P_{\rm c} - P^)/P^$ at a cocoon length $l_{\rm c} = 0.3$ (see Table 3) against jet kinetic luminosity $L_{\rm j}/L_{\rm k}=M^3\nu$ . The solid line is a $(P_{\rm c} - P^)/P^ \propto (L_{\rm j}/L_{\rm k})^{0.62}$ , that is also the best fit, excluding the value of the case M=10, $\nu =0.1$ that is in a weakly overpressured regime already.
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