Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f1.eps}\end{figure}$ Figure 1: Radial profile of the Mach number in the unperturbed flow, for which l=1.87 and $c_{\rm s}=0.1$ . The two circles denote the inner and the outer sonic points, respectively. The dashed arrow shows the shock at $r_{\rm sh}= 6.8$ .
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f2.eps}\end{figure}$ Figure 2: Eigenspectrum of the flow l=1.87 and $c_{\rm s}=0.1$ , showing the instability of the modes $1\le m\le 5$ . The empty triangles correspond to the stable axisymmetric eigenmodes found by Nobuta & Hanawa (1994).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f3.eps}\end{figure}$ Figure 3: The maximum growth rate of the non radial modes is reached for $m\sim 10$ in the flow l=1.87 and $c_{\rm s}=0.1$ . The pattern frequency $\omega _r/m$ of these unstable modes is concentrated in a limited band.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f4.eps}\end{figure}$ Figure 4: The two thick solid lines are the threshold for shock-included solutions. The dotted lines measure the shock strength by the value of ${\cal M}_{\rm sh}$ indicated on the left. The thin solid lines correspond to the value of the minimum Mach number ${\cal M}_{\rm min}$ indicated on the right. The 19 filled circles correspond to unstable outer shock solutions, andthe 5 empty squares correspond to stable ones.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f5.eps}\end{figure}$ Figure 5: Growth rates compared to three timescales: advection $\tau _{\rm adv}$ (squares), acoustic $\tau _{\rm ac}$ (circles), and rotation $\Omega (r_{\rm son})$ (crosses).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f6.eps}\end{figure}$ Figure 6: The position of the corotation radius is indicated for 19 unstable flows (circles) and 5 stable ones (squares).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f7.eps}\end{figure}$ Figure 7: The value of the ratio $c_{\rm s}/\Omega _{\rm K}r$ at the sonic point (dotted lines) and at the shock (full lines) is indicated on the lines.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f8.eps}\end{figure}$ Figure 8: Growth rate measured in units of the total acoustic time $\tau _{\rm ac}$ (circles) compared to the acoustic time $\tau _{\rm out}$ between the corotation and the shock (stars).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f9.eps}\end{figure}$ Figure 9: Incidence of advection on the PPI for weak shocks ( ${\cal M}_{\rm sh}=0.9$ ). The growth rate of the instability is measured in units of the acoustic time $\tau _{\rm out}$ between the corotation and the shock.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f1.eps}\end{figure}$	Figure 1: Radial profile of the Mach number in the unperturbed flow, for which l=1.87 and $c_{\rm s}=0.1$ . The two circles denote the inner and the outer sonic points, respectively. The dashed arrow shows the shock at $r_{\rm sh}= 6.8$ .
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f2.eps}\end{figure}$	Figure 2: Eigenspectrum of the flow l=1.87 and $c_{\rm s}=0.1$ , showing the instability of the modes $1\le m\le 5$ . The empty triangles correspond to the stable axisymmetric eigenmodes found by Nobuta & Hanawa (1994).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f3.eps}\end{figure}$	Figure 3: The maximum growth rate of the non radial modes is reached for $m\sim 10$ in the flow l=1.87 and $c_{\rm s}=0.1$ . The pattern frequency $\omega _r/m$ of these unstable modes is concentrated in a limited band.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f5.eps}\end{figure}$	Figure 5: Growth rates compared to three timescales: advection $\tau _{\rm adv}$ (squares), acoustic $\tau _{\rm ac}$ (circles), and rotation $\Omega (r_{\rm son})$ (crosses).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f6.eps}\end{figure}$	Figure 6: The position of the corotation radius is indicated for 19 unstable flows (circles) and 5 stable ones (squares).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f7.eps}\end{figure}$	Figure 7: The value of the ratio $c_{\rm s}/\Omega _{\rm K}r$ at the sonic point (dotted lines) and at the shock (full lines) is indicated on the lines.
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f8.eps}\end{figure}$	Figure 8: Growth rate measured in units of the total acoustic time $\tau _{\rm ac}$ (circles) compared to the acoustic time $\tau _{\rm out}$ between the corotation and the shock (stars).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{3844f9.eps}\end{figure}$	Figure 9: Incidence of advection on the PPI for weak shocks ( ${\cal M}_{\rm sh}=0.9$ ). The growth rate of the instability is measured in units of the acoustic time $\tau _{\rm out}$ between the corotation and the shock.
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