All Figures

$\begin{figure} \par\includegraphics[angle=90,width=8.8cm,clip]{1291f1.eps}\end{figure}$ Figure 1: Comparison between our baseline model ( dashed line) and and the results of the adiabatic simulation by Tornatore et al. (2003) ( solid line) of a cluster with a mass $M_{\rm vir}=39.4$ $\times$ $10^{13}~M_\odot$ , taken at z=0. We show the radial dependencies for the following quantities: (Upper panels) gas density $\rho$ , dark matter density $\rho _{\rm dm}$ , total mass $M_{\rm tot}$ ; (Lower panels) gas pressure P, gas temperature T and gas entropy $S=T/n_{\rm e}^{2/3}$ .
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=8.8cm,clip]{1291f2.eps}\end{figure}$ Figure 2: Same comparison as Fig. 1, for a group with a mass $M_{\rm vir}=2.52$ $\times$ $10^{13}~M_\odot$ .
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In the text

$\begin{figure} \par\includegraphics[width=15cm,clip]{1291f3.eps}\end{figure}$ Figure 3: Time evolution of the M=150 case. First row: density maps in logarithmic scale. Second row: specific entropy S=T/n^2/3 (logarithmic scale) which shows clearly the contribution of the entrainment by the high entropy material of the jet. Third row: entropy per unit volume ( $n \log(T/n^{2/3})$ ), which shows the contribution of the bow shock propagating into the medium. These quantities are shown in the columns at different times being $\tau =0.1$ the time at which the jet is switched off and $\tau =3.9$ the final simulated time. Notice the different spatial scale represented in the three columns. The density and temperature are given in units of their values in the center of the undisturbed medium.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f4.eps}\end{figure}$ Figure 4: Temporal evolution of the variation of the ambient energy. Left panel: temporal behavior of the total ambient energy at the beginning of the cocoon evolution ( t/t₀ < 0.4). We show plots of the total injected energy ( solid line), total ambient energy $E_{\rm tot}$ ( dotted line), total energy acquired by the shocked compressed material $E_{\rm tot,\; comp}$ ( dashed line) and by the entrained material $E_{\rm tot,\; entr}$ ( dot-dashed line). Right panel: plotted here are the ambient internal energy $E_{\rm int}$ ( solid line), the ambient kinetic energy $E_{\rm kin}$ ( long-dashed line) and the ambient gravitational potential energy $E_{\rm pot}$ ( triple-dot-dashed line). Values of the energy are given in units of the total injected energy while time is given in units of t₀.
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In the text

$\begin{figure} \par\includegraphics[width=8.7cm,clip]{1291f5.eps}\end{figure}$ Figure 5: Left panel: temporal evolution of the average entropy per particle S = T/n^2/3 of the ambient material marked by the innermost three tracers: $\mathcal{T}_1$ ( $r/r_{\rm s} \in \; [0,1]$ , dashed line), $\mathcal{T}_2$ ( $r/r_{\rm s} \in \; ]1,3]$ , dot-dashed line) and $\mathcal{T}_3$ ( $r/r_{\rm s} \in \; ]3,6]$ , solid line). Right panel: temporal evolution of the total entropy increase $S_{\rm tot}$ (Eq. (18)) of the innermost tracer $\mathcal{T}_1$ : plotted are the total entropy increase of the ambient medium ( dashed line), the entropy increase of the shocked material ( triple-dot-dashed line) and the entropy increase of the entrained material ( dotted line). Time is given in units of t₀.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f6.eps}\end{figure}$ Figure 6: Entropy S=T/n^2/3 profiles as a function of Lagrangian (mass) coordinate at the beginning and at the end of the simulation. The panels refer to the simulations performed with the $T_{\rm ew}$ = 2 keV ( left panel), $T_{\rm ew}$ = 1 keV ( central panel) and $T_{\rm ew}$ = 0.5 keV ( right panel) clusters. In each panel are shown the initial entropy profile ( dotted line), the profiles determined by the interaction with the jets characterized by a luminosity $L_{\rm j}= 10^{46}$ erg s^-1 ( lower solid line) and $L_{\rm j}= 5$ $\times$ 10⁴⁶ erg s^-1 ( upper solid line) and analytical extrapolations of the profile up to the virial radius ( dashed line). The mass coordinate is given in units of the total gas mass content of the clusters $f_{\rm bar} M_{\rm vir}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f7.eps}\end{figure}$ Figure 7: Plot of the heating energy per particle $E_{\rm h}$ needed to obtain the entropy profiles of Fig. 6 as a function of mass coordinate. The panels refer to the $T_{\rm ew}$ = 2 keV ( left panel), $T_{\rm ew}$ = 1 keV ( central panel) and $T_{\rm ew}$ = 0.5 keV ( right panel) clusters. In each panel we plot the heating energy per particle given by the $L_{\rm j}= 10^{46}$ erg s^-1 ( lower solid line) and $L_{\rm j}= 5$ $\times$ 10⁴⁶ erg s^-1 jets ( upper solid line) and analytical approximations up to the virial radius ( dashed line) obtained from the extrapolated entropy profiles. The mass coordinate is given in units of the total gas mass content of the clusters $f_{\rm bar} M_{\rm vir}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f8.eps}\end{figure}$ Figure 8: Plot of the total heating energy dissipated by the jet in units of the total injected energy as a function of time. The curves refer to the cases characterized by M=105 ( solid line), M=150 ( dotted line), M=211 ( dashed line), M=180 ( dot-dashed line), M=255 ( double dot-dashed line) and M=361 ( long dashed line). It is important to notice that the lines are divided in three groups characterized by different ratios $E_{\rm j}/E_{\rm th}$ between the total injected energy and the thermal energy of the cluster: $E_{\rm j}/E_{\rm th}$ = 10.9, 2.2, 1.9 (upper lines), $E_{\rm j}/E_{\rm th}$ = 0.39, 0.34 (middle lines) and $E_{\rm j}/E_{\rm th}$ = 0.068 (lower line). See Table 1 for the correspondence between $E_{\rm j}/E_{\rm th}$ and Mach number.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f9.eps}\end{figure}$ Figure 9: Radial density profiles of the clusters defined in the initial conditions (Eq. (3)) and obtained by calculating the hydrostatic equilibrium determined by the entropy profiles of Fig. 6. The panels refer to the $T_{\rm ew}$ = 2 keV ( left panel), $T_{\rm ew}$ = 1 keV ( central panel) and $T_{\rm ew}$ = 0.5 keV ( right panel) clusters. Plotted are the profiles of our baseline model ( solid line) and the profiles determined by taking into account the energy dissipated by the $L_{\rm j}= 10^{46}$ erg s^-1 ( dot-dashed line) and $L_{\rm j}= 5$ $\times$ 10⁴⁶ erg s^-1 jets ( dashed line). The density is given in units of the central density in the initial conditions while the radial coordinate is normalized with the virial radius $R_{\rm vir}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f10.eps}\end{figure}$ Figure 10: Plot of the difference between the average energy per particle of the final and initial hydrostatic equilibrium as a function of the final emission-weighted temperature of the clusters. The average of the energy excess is calculated over the particles contained inside the virial radius in the final hydrostatic conditions. Left panel: plot of the average energy excess per particle determined by the $L_{\rm j}= 10^{46}$ erg s^-1 jets: plotted are the total energy ( crosses), the gravitational potential energy ( asterisks) and the internal energy ( diamonds). Right panel: plot of the total energy excess per particle determined by the $L_{\rm j}= 10^{46}$ erg s^-1 ( crosses) and the $L_{\rm j}= 5$ $\times$ 10⁴⁶ erg s^-1 jets ( asterisks).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f11.eps}\end{figure}$ Figure 11: Bolometric luminosity-emission weighted temperature relation for our simulations characterized by $L_{\rm j}= 10^{46}$ erg s^-1 ( empty squares) and $L_{\rm j}= 5$ $\times$ 10⁴⁶ erg s^-1 ( crosses) in comparison with observational data ( pluses: Helsdon & Ponman 2000; filled squares: Arnaud & Evrard 1999; filled triangles Markevitch 1999). Plotted are also the scaling of the bremsstrahlung luminosity ( dashed line) and the X-ray luminosity with a correction for line emissivity (metallicity $0.3~Z_\odot$ ) ( solid line) of our initial model. The bolometric luminosities of the three initial unperturbed clusters ( asterisks) and of the four Tornatore et al. (2003) simulations ( diamonds) from which our initial conditions were derived are shown for comparison.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f12.eps}\end{figure}$ Figure 12: Comparison between the X-ray luminosity - M₂₀₀ relation obtained from our simulations with $L_{\rm j}= 10^{46}$ erg s^-1 ( empty squares) and $L_{\rm j}= 5$ $\times$ 10⁴⁶ erg s^-1 ( crosses) and the observational data ( triangles: Reiprich & Böhringer 2002). Plotted are also the scaling of the bremsstrahlung luminosity ( dashed line) and the X-ray luminosity with a correction for line emissivity (metallicity $0.3~Z_\odot$ ) ( solid line) of our initial model. The bolometric luminosities of the three initial unperturbed clusters ( asterisks) are also plotted.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f13.eps}\end{figure}$ Figure 13: Entropy (at 0.1R₂₀₀) emission weighted temperature relation for our simulations ( $L_{\rm j}= 10^{46}$ erg s^-1, empty squares and $L_{\rm j}= 5$ $\times$ 10⁴⁶ erg s^-1, crosses), in comparison with observational data ( pluses: Ponman et al. 2003). The observational data represent averages in different bins of temperature. The dotted line represents the scaling of the initial model (Eq. (5)). The dotted-dashed line represents the constant floor 125 (h/0.7)^-1/3 keV cm² ( crosses) determined by Lloyd-Davies et al. (2000).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1291f14.eps}\end{figure}$ Figure 14: Entropy S=T/n^2/3 profiles as a function of Lagrangian (mass) coordinate. Plotted are the initial conditions ( dotted line) and the results obtained with the M=211 simulation ( dashed line) which represents a $L_{\rm j}= 10^{46}$ erg s^-1 jet injected in a $T_{\rm ew}$ = 0.5 keV cluster for a time $t\sim 2$ $\times$ 10⁷ years and with the case in the third line of Table 2 ( solid line)which is a jet with half the kinetic power (lower density) injected for twice the time. The mass coordinate is given in units of the total gas mass content of the clusters $f_{\rm bar} M_{\rm vir}$ .
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=8.8cm,clip]{1291f2.eps}\end{figure}$	Figure 2: Same comparison as Fig. 1, for a group with a mass $M_{\rm vir}=2.52$ $\times$ $10^{13}~M_\odot$ .
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