Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{0047f01.ps}\end{figure}$ Figure 1: Temporal evolution of the Fourier amplitudes of the m=0,1,2,6,8,10-modes for a single component model with the mass distribution of the gaseous component in the reference model. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=5.8cm,clip]{0047f02a.ps}\hspa... ...e*{2.8cm} \includegraphics[angle=90,width=5.8cm,clip]{0047f02d.ps} \end{figure}$ Figure 2: Spatial distribution of the surface density perturbations (normalized to the their initial values) of the single component gaseous nuclear disk ( $Q_{\rm min} = 1.54$ ) at different times: during the linear growth regime (t=16, upper left), saturation of the higher-order moments (t=24, upper right), saturation of the lower-order moments (t=32, lower left) and at the end of the simulation (t=40 $\sim$ 600 Myr, lower right). Areas devoid of material are white, areas with a density enhancement of a factor of 2 or more are black. The grey area seen at the outer edges correspond to no deviation from the initial surface density. Note that the data inside the inner boundary of the computational grid ( $\vert x\vert,\vert y\vert \leq 0.03 = 30$ pc) are artificial. They are created by the graphics software when converting from the polar grid to the Cartesian grid of the image.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=7.2cm,clip]{0047f03a.ps}\vspace*{3mm} \includegraphics[angle=90,width=7.2cm,clip]{0047f03b.ps} \end{figure}$ Figure 3: Temporal evolution of the spatially resolved Fourier amplitudes for the m = 2-mode ( upper diagram) and the m = 8-mode ( lower diagram) for a single component model with the mass distribution of the gaseous component in the reference model. The amplitudes are calculated according to Eq. (18) integrating over small radial annuli defined by the numerical grid resolution. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f04.eps}\end{figure}$ Figure 4: Radial profile of the initial rotation curve and the different contributions to the gaseous azimuthal velocity of the reference model: rotation curve, i.e. circular velocity $v_{\rm c}$ (solid), azimuthal velocity of gas $v_{\rm rot}$ (triangles), pressure contribution to rotational equilibrium v_P (dot-dashed), halo (and stellar) contribution to rotational equilibrium $v_{\rm halo,stars}$ (short-dashed) and contribution form the self-gravity of the disk $v_{\rm disk}$ (long-dashed).
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In the text

$\begin{figure} \par\includegraphics[width=15.2cm,clip]{0047f05.ps}\end{figure}$ Figure 5: Surface density of the gas component of the reference model at different times. A white area corresponds to surface densities of $10^2~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or lower, whereas black means $10^3~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or higher. The length unit is kpc and the time is given in $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[width=15.2cm,clip]{0047f06.ps} \end{figure}$ Figure 6: Surface density of the dust component of the reference model at different times. A white area corresponds to surface densities of $1~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or lower, whereas black means $10~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or higher. The length unit is kpc and the time is given in $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{0047f07.ps}\end{figure}$ Figure 7: Temporal evolution of the Fourier amplitudes of the m=0,1,2,6,8,10-modes of the dust component in the reference model. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{0047f08.ps}\end{figure}$ Figure 8: Temporal evolution of the Fourier amplitudes of the m=0,1,2,6,8,10-modes of the gas component in the reference model. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=7.2cm,clip]{0047f09a.ps}\vspace*{3mm} \includegraphics[angle=90,width=7.2cm,clip]{0047f09b.ps} \end{figure}$ Figure 9: Temporal evolution of the spatially resolved Fourier amplitudes for the m= 2-mode (upper diagram) and the m= 8-mode (lower diagram) for gaseous component of the reference model. The amplitudes are calculated according to Eq. (18) integrating over small radial annuli defined by the numerical grid resolution. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{0047f10.eps} \end{figure}$ Figure 10: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the dust component for different coupling timescales ( $\tau _{\rm d}=10^5$ yr (open boxes), $\tau _{\rm d}=10^6$ yr (plus), $\tau _{\rm d}=10^7$ yr (triangles) and 10⁸ yr (filled boxes)) and the reference model (thin disk friction; solid line). The dust-to-gas mass fraction is 2%. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f11.eps} \end{figure}$ Figure 11: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas component for different coupling timescales ( $\tau _{\rm d}=10^6$ yr (plus) and 10⁸ yr (filled boxes)), the reference model (thin disk friction; solid line), the single-component model (no friction; dashed line) and a model with the "thick disk friction'' (open boxes). The dust-to-gas mass fraction is 2%. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{0047f12.eps}\end{figure}$ Figure 12: Temporal evolution of the logarithmic Fourier amplitudes of the dominant m= 8-mode of the dust component for different dust-to-gas mass fractions: 0.5% (open boxes), 1% (crosses), 2% (reference model, solid line), 10% (plus), 20% (triangle) and the purely gaseous model (dashed line). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=5.3cm,clip]{0047f13a.ps}\hspa... ...e*{3.3cm} \includegraphics[angle=90,width=5.3cm,clip]{0047f13d.ps} \end{figure}$ Figure 13: Spatial distribution of the surface density and its perturbations (normalized to their initial values) of the gas and dust component after t= 6 $\sim$ 90 Myr for a model with a 10% dust mass fraction (relative to gas): $\Sigma _{\rm g}$ ( upper left; white: $10^{1.5}~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ , black: $10^3~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ ), $\Sigma _{\rm d}$ ( upper right; white: $10^{0.5}~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ , black: $10^2~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ ), $\Delta \Sigma _{{\rm g,d}} / \Sigma _{{\rm g,d}}$ for gas ( lower left) and dust ( lower right). The latter are coded as follows: areas devoid of material are white, areas with a density enhancement of a factor of 2 or more are black. The grey area seen at the outer edges correspond to no deviation from the initial surface density.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f14.eps}\end{figure}$ Figure 14: Radial profile of the surface density of gas (solid) and dust (dashed) along a radial line at t=5 for the 10% dust fraction model. The surface densities are given in $10^3~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ , the radius in kpc.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.6cm,clip]{0047f15.ps}\end{figure}$ Figure 15: Temporal evolution of the logarithmic Fourier amplitudes of the m= 8-mode of the gas component for different initial (minimum) Toomre parameters of the disk: Q=1.1 (triangle), Q=1.2 ( $\times$ ), Q=1.54 (reference, solid line), Q=1.8 (dashed line), Q=2.0 (boxes) and Q=3.0 (dot-dashed). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f16.ps}\end{figure}$ Figure 16: Temporal evolution of the logarithmic Fourier amplitudes of the m= 8-mode of the dust component for different initial (minimum) Toomre parameters of the disk: Q=1.1 (triangle), Q=1.2 ( $\times$ ), Q=1.54 (reference, solid line), Q=1.8 (dashed line), Q=2.0 (boxes) and Q=3.0 (dot-dashed). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{0047f17a.ps}\hspace*{5mm} \includegraphics[width=8cm,clip]{0047f17b.ps} \end{figure}$ Figure 17: Spatial distribution of the surface density perturbations (normalized to the their initial values) at t=16 $\sim$ 240 Myr of the Q= 1.2-disk: gas component ( left), dust ( right). Areas devoid of material are white, areas with a density enhancement of a factor of 2 or more are black. The grey area seen at the outer edges correspond to no deviation from the initial surface density.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f18.eps}\end{figure}$ Figure 18: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas and dust component for different equations of state (of the gas phase): $\gamma = 5/3$ , reference model (gas: solid; dust: dashed) and isothermal (gas: crosses; dust: triangles). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{0047f19.eps}\end{figure}$ Figure 19: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas component for different initial perturbations: reference model (solid), another set of random numbers, otherwise identical to reference model (dashed), locally identical relative overdensities for dust and gas (boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[% width=8.7cm,clip]{0047f20.eps}\end{figure}$ Figure 20: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas component for different artificial viscosity: reference model: no artificial viscosity (solid), $C_{\rm vis} = 1.0$ (dashed), 2.0 (boxes), 3.0 (plus). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f21.eps}\end{figure}$ Figure 21: Temporal evolution of the logarithmic Fourier amplitudes of the m= 8-mode of the dust component for different transition positions $R_{\rm flat}$ of the rotation curve: reference model, $R_{\rm flat} = 100$ pc (solid) and $R_{\rm flat} = 200$ pc (open boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{0047f22.eps}\end{figure}$ Figure 22: Temporal evolution of the azimuthally averaged surface density of the dust component at two neighbouring radial cells ( $R\sim 140$ pc) for the hot gaseous disk model with $Q_{\rm min}=3.0$ . The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr, the surface densities are given in $10^3~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ .
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f23.eps}\end{figure}$ Figure 23: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the dust component for different treatments of the dust component: reference (pressureless self-gravitating dust; solid), no dust self-gravity (dashed) and non-vanishing pressure (boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f24.eps}\end{figure}$ Figure 24: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas component for different treatments of the dust component: reference (pressureless self-gravitating dust; solid), no dust self-gravity (dashed) and non-vanishing pressure (boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{0047f01.ps}\end{figure}$	Figure 1: Temporal evolution of the Fourier amplitudes of the m=0,1,2,6,8,10-modes for a single component model with the mass distribution of the gaseous component in the reference model. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[width=15.2cm,clip]{0047f05.ps}\end{figure}$	Figure 5: Surface density of the gas component of the reference model at different times. A white area corresponds to surface densities of $10^2~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or lower, whereas black means $10^3~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or higher. The length unit is kpc and the time is given in $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[width=15.2cm,clip]{0047f06.ps} \end{figure}$	Figure 6: Surface density of the dust component of the reference model at different times. A white area corresponds to surface densities of $1~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or lower, whereas black means $10~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ or higher. The length unit is kpc and the time is given in $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{0047f07.ps}\end{figure}$	Figure 7: Temporal evolution of the Fourier amplitudes of the m=0,1,2,6,8,10-modes of the dust component in the reference model. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{0047f08.ps}\end{figure}$	Figure 8: Temporal evolution of the Fourier amplitudes of the m=0,1,2,6,8,10-modes of the gas component in the reference model. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=90,width=7.2cm,clip]{0047f09a.ps}\vspace*{3mm} \includegraphics[angle=90,width=7.2cm,clip]{0047f09b.ps} \end{figure}$	Figure 9: Temporal evolution of the spatially resolved Fourier amplitudes for the m= 2-mode (upper diagram) and the m= 8-mode (lower diagram) for gaseous component of the reference model. The amplitudes are calculated according to Eq. (18) integrating over small radial annuli defined by the numerical grid resolution. The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{0047f12.eps}\end{figure}$	Figure 12: Temporal evolution of the logarithmic Fourier amplitudes of the dominant m= 8-mode of the dust component for different dust-to-gas mass fractions: 0.5% (open boxes), 1% (crosses), 2% (reference model, solid line), 10% (plus), 20% (triangle) and the purely gaseous model (dashed line). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f14.eps}\end{figure}$	Figure 14: Radial profile of the surface density of gas (solid) and dust (dashed) along a radial line at t=5 for the 10% dust fraction model. The surface densities are given in $10^3~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ , the radius in kpc.
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$\begin{figure} \par\includegraphics[angle=270,width=8.6cm,clip]{0047f15.ps}\end{figure}$	Figure 15: Temporal evolution of the logarithmic Fourier amplitudes of the m= 8-mode of the gas component for different initial (minimum) Toomre parameters of the disk: Q=1.1 (triangle), Q=1.2 ( $\times$ ), Q=1.54 (reference, solid line), Q=1.8 (dashed line), Q=2.0 (boxes) and Q=3.0 (dot-dashed). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f16.ps}\end{figure}$	Figure 16: Temporal evolution of the logarithmic Fourier amplitudes of the m= 8-mode of the dust component for different initial (minimum) Toomre parameters of the disk: Q=1.1 (triangle), Q=1.2 ( $\times$ ), Q=1.54 (reference, solid line), Q=1.8 (dashed line), Q=2.0 (boxes) and Q=3.0 (dot-dashed). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f18.eps}\end{figure}$	Figure 18: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas and dust component for different equations of state (of the gas phase): $\gamma = 5/3$ , reference model (gas: solid; dust: dashed) and isothermal (gas: crosses; dust: triangles). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{0047f19.eps}\end{figure}$	Figure 19: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas component for different initial perturbations: reference model (solid), another set of random numbers, otherwise identical to reference model (dashed), locally identical relative overdensities for dust and gas (boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[% width=8.7cm,clip]{0047f20.eps}\end{figure}$	Figure 20: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas component for different artificial viscosity: reference model: no artificial viscosity (solid), $C_{\rm vis} = 1.0$ (dashed), 2.0 (boxes), 3.0 (plus). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f21.eps}\end{figure}$	Figure 21: Temporal evolution of the logarithmic Fourier amplitudes of the m= 8-mode of the dust component for different transition positions $R_{\rm flat}$ of the rotation curve: reference model, $R_{\rm flat} = 100$ pc (solid) and $R_{\rm flat} = 200$ pc (open boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.8cm,clip]{0047f22.eps}\end{figure}$	Figure 22: Temporal evolution of the azimuthally averaged surface density of the dust component at two neighbouring radial cells ( $R\sim 140$ pc) for the hot gaseous disk model with $Q_{\rm min}=3.0$ . The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr, the surface densities are given in $10^3~\mbox{$M_{\odot}~{\rm pc}^{-2}$ }$ .
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$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f23.eps}\end{figure}$	Figure 23: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the dust component for different treatments of the dust component: reference (pressureless self-gravitating dust; solid), no dust self-gravity (dashed) and non-vanishing pressure (boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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$\begin{figure} \par\includegraphics[angle=270,width=8.7cm,clip]{0047f24.eps}\end{figure}$	Figure 24: Temporal evolution of the logarithmic Fourier amplitudes for the m= 8-mode of the gas component for different treatments of the dust component: reference (pressureless self-gravitating dust; solid), no dust self-gravity (dashed) and non-vanishing pressure (boxes). The time unit is $\mbox{$1.5 \times 10^{7}$ }$ yr.
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