All Figures

$\begin{figure} \par\psfig{figure=0134.f1.ps,width=5.5cm,clip=} \end{figure}$ Figure 1: The radiative overstability of a spherical accretion shock with cooling and conductively-driven mass-loading. The dimensionless parameters for this calculation were: $T_{\rm m}' = 1$ , $t_{\rm c}' = 1$ , $q_{\rm c}' = 1$ , which correspond to the temperature at minimum cooling, the cooling time, and the mass-loading coefficient respectively - see Sect. 2. The top panel shows the time evolution of the shock radius, while the bottom panel shows the ratio of the injected mass to the accreted ( i.e. non-injected) mass (in all our figures this ratio is integrated over radii from the inner boundary to the outermost shock, i.e. the accretion shock). Once the system is steadily oscillating, the injected mass is about 1/5 of the accreted mass. The initial bounce in such runs is always higher than subsequent bounces (see, e.g., Imamura et al.1984). There is no sign of higher order modes.
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In the text

$\begin{figure} \par\psfig{figure=0134.f2.ps,width=5.5cm,clip=} \end{figure}$ Figure 2: As Fig. 1 but with $T_{\rm m}' = 1$ , $t_{\rm c}' = 1$ , and $q_{\rm c}' = 10$ . Here the cooling timescale exceeds the mass-loading timescale and the radiative overstability is largely damped. At late times the injected mass is about 2/3 of the accreted mass ( i.e. the injected mass is not quite the dominant component).
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In the text

$\begin{figure} \par\psfig{figure=0134.f3.ps,width=11.2cm,clip=} \end{figure}$ Figure 3: Radial profiles at t = 24 for the run shown in Fig. 2. The bottom right panel shows the fraction of injected mass to the total mass, as a function of radius. If the density of injected material is equal to the density of accreted material this parameter would have a value of 0.5, whereas if the density of injected material significantly exceeds the density of accreted material this parameter approaches unity. The flow is from right to left in these figures.
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In the text

$\begin{figure} \par\psfig{figure=0134.f4.ps,width=5.0cm,clip=} \end{figure}$ Figure 4: As Fig. 1 but for $T_{\rm m}' = 1$ , $t_{\rm c}' = 10$ , and $q_{\rm c}' = 10$ . Here the radiative overstability is completely damped, and at late times there is 15% more injected mass than accreted mass behind the shock front.
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In the text

$\begin{figure} \par\psfig{figure=0134.f5.ps,width=5.0cm,clip=} \end{figure}$ Figure 5: As Fig. 1 but for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 10$ , and $q_{\rm c}' = 100$ . The radiative overstability is completely damped, and at late times the injected mass is about 50% greater than the accreted mass.
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In the text

$\begin{figure} \par\psfig{figure=0134.f6.ps,width=13.9cm,clip=} \end{figure}$ Figure 6: Radial profiles at t = 100 for the run shown in Fig. 5. Note that the inflow becomes supersonic shortly after passing through the accretion shock, before encountering another shock much closer to the inner boundary. The density of injected material exceeds the density of accreted material for $r \mathrel {\hbox to 0pt{\lower 3pt\hbox {$\sim $ }\hss } \raise 2.0pt\hbox {$<$ }}2$ .
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In the text

$\begin{figure} \par\psfig{figure=0134.f7.ps,width=13.9cm,clip=} \end{figure}$ Figure 7: Radial profiles at t=55 for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 1$ , and $q_{\rm c}' = 3162$ . The accretion shock at $r \approx 4.7$ has a perfectly stable position at late times. As in the Fig. 6 case the inflow again becomes supersonic between the accretion shock and the inner boundary, and passes through another shock at small radii. The dotted lines show the initial conditions.
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In the text

$\begin{figure} \par\psfig{figure=0134.f8.ps,width=13.9cm,clip=} \end{figure}$ Figure 8: Radial profiles at t = 200 for the model with $T_{\rm m}' = 1$ , $t_{\rm c}' = 10$ , and $q_{\rm c}' = 3162$ . After passing through each shock the flow reaccelerates towards the central mass. The heavy mass-loading that it experiences leads to its rapid cooling to the ambient temperature. These combine to cause the flow to become highly supersonic before it encounters the next mass-loading shell. The density enhancement of the flow increases through each of these encounters, such that near the inner boundary the flow is almost completely dominated by injected mass.
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In the text

$\begin{figure} \par\psfig{figure=0134.f9.ps,width=13.7cm} \end{figure}$ Figure 9: Radial profiles at t=47 for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 100$ , and $q_{\rm a}' = 1.0$ . The mass loading in this calculation occurs through hydrodynamic ablation. The dotted lines illustrate the initial conditions.
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In the text

$\begin{figure} \par\psfig{figure=0134.f10.ps,width=11cm,clip} \end{figure}$ Figure 10: Radial profiles at t = 16 for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 100$ , and $q_{\rm a}' = 10$ . Mass loading occurs through hydrodynamic ablation. The dotted lines show the initial conditions.
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In the text

$\begin{figure} \par\includegraphics[width=8.3cm,clip]{0134.f11.ps} \end{figure}$ Figure 11: The differential luminosity distribution at t = 24 for the model with $T_{\rm m}' = 1$ , $t_{\rm c}' = 1$ , and $q_{\rm c}' = 10$ (see also Figs. 2 and 3). The isobaric multiphase cooling flow model predicts that this function should be independent of temperature, though recent observations have revealed a dearth of low-temperature emission. We have smoothed our data with a boxcar of width 3 bins.
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In the text

$\begin{figure} \par\psfig{figure=0134.f2.ps,width=5.5cm,clip=} \end{figure}$	Figure 2: As Fig. 1 but with $T_{\rm m}' = 1$ , $t_{\rm c}' = 1$ , and $q_{\rm c}' = 10$ . Here the cooling timescale exceeds the mass-loading timescale and the radiative overstability is largely damped. At late times the injected mass is about 2/3 of the accreted mass ( i.e. the injected mass is not quite the dominant component).
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$\begin{figure} \par\psfig{figure=0134.f4.ps,width=5.0cm,clip=} \end{figure}$	Figure 4: As Fig. 1 but for $T_{\rm m}' = 1$ , $t_{\rm c}' = 10$ , and $q_{\rm c}' = 10$ . Here the radiative overstability is completely damped, and at late times there is 15% more injected mass than accreted mass behind the shock front.
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$\begin{figure} \par\psfig{figure=0134.f5.ps,width=5.0cm,clip=} \end{figure}$	Figure 5: As Fig. 1 but for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 10$ , and $q_{\rm c}' = 100$ . The radiative overstability is completely damped, and at late times the injected mass is about 50% greater than the accreted mass.
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$\begin{figure} \par\psfig{figure=0134.f6.ps,width=13.9cm,clip=} \end{figure}$	Figure 6: Radial profiles at t = 100 for the run shown in Fig. 5. Note that the inflow becomes supersonic shortly after passing through the accretion shock, before encountering another shock much closer to the inner boundary. The density of injected material exceeds the density of accreted material for $r \mathrel {\hbox to 0pt{\lower 3pt\hbox {$\sim $ }\hss } \raise 2.0pt\hbox {$<$ }}2$ .
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$\begin{figure} \par\psfig{figure=0134.f7.ps,width=13.9cm,clip=} \end{figure}$	Figure 7: Radial profiles at t=55 for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 1$ , and $q_{\rm c}' = 3162$ . The accretion shock at $r \approx 4.7$ has a perfectly stable position at late times. As in the Fig. 6 case the inflow again becomes supersonic between the accretion shock and the inner boundary, and passes through another shock at small radii. The dotted lines show the initial conditions.
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$\begin{figure} \par\psfig{figure=0134.f9.ps,width=13.7cm} \end{figure}$	Figure 9: Radial profiles at t=47 for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 100$ , and $q_{\rm a}' = 1.0$ . The mass loading in this calculation occurs through hydrodynamic ablation. The dotted lines illustrate the initial conditions.
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$\begin{figure} \par\psfig{figure=0134.f10.ps,width=11cm,clip} \end{figure}$	Figure 10: Radial profiles at t = 16 for $T_{\rm m}' = 0.1$ , $t_{\rm c}' = 100$ , and $q_{\rm a}' = 10$ . Mass loading occurs through hydrodynamic ablation. The dotted lines show the initial conditions.
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