Astronomy & Astrophysics

All Figures

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f1.eps}} % \end{figure}$ Figure 1: The cut of the spherical particles by the plane. The models of composite grains containing the same amount of carbon and silicate are shown. The 3- and 9-layered spheres consist of equivolume spherical layers with the total volume fractions of carbon, silicate and vacuum equal to 33.33%. The core-mantle particle includes the same mass of carbon and silicate but is free of vacuum.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f2.eps}}\end{figure}$ Figure 2: The cut of the pseudospherical particles with the maximum size $d_{\rm max}=45$ by the plane. The models of very porous particles with small single size ( left) and different size ( right) cubic inclusions are shown. The volume fractions of carbon and silicate are equal to 5%.
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In the text

$\begin{figure} \par\resizebox{8.7cm}{!}{\includegraphics[clip]{3679f3.eps}} \par\end{figure}$ Figure 3: Size dependence of the extinction efficiency factors for layered spherical particles. Each particle contains an equal fraction of amorphous carbon (AC1), astrosil and vacuum (the porosity ${\cal P}=1/3$ ) separated in equivolume layers. The cyclic order of the different material layers is indicated (starting from the core). The effect of the increase of the number of layers is illustrated. The thick line at the lowest panel corresponds to compact spheres consisting of AC1 and astrosil. For a given value of the size parameter, the compact and porous particles have the same mass.
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In the text

$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f4.eps}}\end{figure}$ Figure 4: Size dependence of the scattering and absorption efficiency factors, albedo and asymmetry parameter for multi-layered spheres. The parameters of particles are the same as in Fig. 3.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f5.eps}} \par\end{figure}$ Figure 5: Size dependence of the extinction efficiency factors for pseudospheres with inclusions of the same single size after averaging of three different targets. Each particle contains an equal volume fraction (33.33%) of AC1, astrosil and vacuum. The effect of variations of the size of inclusions is illustrated.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f6.eps}}\end{figure}$ Figure 6: Size dependence of the extinction efficiency factors for pseudospheres with a size distribution of inclusions. Each particle contains an equal volume fraction (33.33%) of AC1, astrosil and vacuum. The volume fractions of inclusions of different sizes are approximately the same.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f7.eps}}\end{figure}$ Figure 7: The average extinction efficiencies for particles with single size inclusions (from Fig. 5) and particles with size distribution of inclusions (from Fig. 6). Each particle contains an equal volume fraction (33.33%) of AC1, astrosil and vacuum. The thick solid line corresponds to compact spheres consisting of AC1 and astrosil. For a given value of the size parameter, the compact and porous particles have the same mass. The thick dashed line shows the extinction for layered spheres after averaging over four samples presented at the bottom panel of Fig. 3.
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In the text

$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f8.eps}}\end{figure}$ Figure 8: Size dependence of the scattering and absorption efficiency factors, albedo and the asymmetry parameter for pseudospheres with inclusions. The parameters of particles are the same as in Fig. 7.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f9.eps}}\par\end{figure}$ Figure 9: Size dependence of the extinction efficiency factors for very porous pseudospheres with inclusions of different size. Each particle contains volume fractions of AC1 and astrosil equal to about 5%, the porosity ${\cal P}=0.9$ . The particles are similar to those presented in Fig. 5 but have larger porosity.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f10.eps}}\par\end{figure}$ Figure 10: Size dependence of the extinction efficiency factors for very porous pseudospheres with a size distribution of inclusions. Each particle contains volume fractions of AC1 and astrosil equal to about 5%, the porosity ${\cal P}=0.9$ . The particles are similar to those presented in Fig. 6 but have larger porosity.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f11.eps}}\par\end{figure}$ Figure 11: Averaged extinction efficiencies for particles with single size inclusions (from Fig. 9) and particles with a size distribution of inclusions (from Fig. 10). Each particle contains volume fractions of AC1 and astrosil equal to about 5%, the porosity ${\cal P}=0.9$ . The particles are similar to those presented in Fig. 7 but have larger porosity. The thick dashed line shows the extinction for layered spheres.
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In the text

$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f12.eps}}\end{figure}$ Figure 12: Size dependence of the scattering and absorption efficiency factors, albedo and the asymmetry parameter for pseudospheres with inclusions. The parameters of particles are the same as in Fig. 11.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f13.eps}}\end{figure}$ Figure 13: The normalized extinction cross sections for multi-layered spheres of different porosity. Open circles show the normalized extinction for pseudospheres with a size distribution of inclusions (see Fig. 10).
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In the text

$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f14.eps}}\end{figure}$ Figure 14: Size dependence of the scattering and absorption normalized cross sections for multi-layered porous spheres and pseudospheres with a size distribution of inclusions. The parameters of particles are the same as in Fig. 13.
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In the text

$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f15.eps}}\end{figure}$ Figure 15: Size dependence of the efficiency factors ( left panel) and their relative errors ( right panel) calculated with the exact theory for multi-layered spheres and with the Mie theory using four different EMT rules. Multi-layered particles contain an equal volume fraction of amorphous carbon (AC1), astrosil and vacuum. The cyclic order of the 18 layers is indicated.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f16.eps}}\end{figure}$ Figure 16: Size dependence of the extinction efficiency factors calculated for multi-layered spheres, pseudospheres with inclusions and with the Mie theory using three different EMT rules. The porosity of particles is ${\cal P}=0.9$ .
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f1.eps}} % \end{figure}$	Figure 1: The cut of the spherical particles by the plane. The models of composite grains containing the same amount of carbon and silicate are shown. The 3- and 9-layered spheres consist of equivolume spherical layers with the total volume fractions of carbon, silicate and vacuum equal to 33.33%. The core-mantle particle includes the same mass of carbon and silicate but is free of vacuum.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f2.eps}}\end{figure}$	Figure 2: The cut of the pseudospherical particles with the maximum size $d_{\rm max}=45$ by the plane. The models of very porous particles with small single size ( left) and different size ( right) cubic inclusions are shown. The volume fractions of carbon and silicate are equal to 5%.
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$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f4.eps}}\end{figure}$	Figure 4: Size dependence of the scattering and absorption efficiency factors, albedo and asymmetry parameter for multi-layered spheres. The parameters of particles are the same as in Fig. 3.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f5.eps}} \par\end{figure}$	Figure 5: Size dependence of the extinction efficiency factors for pseudospheres with inclusions of the same single size after averaging of three different targets. Each particle contains an equal volume fraction (33.33%) of AC1, astrosil and vacuum. The effect of variations of the size of inclusions is illustrated.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f6.eps}}\end{figure}$	Figure 6: Size dependence of the extinction efficiency factors for pseudospheres with a size distribution of inclusions. Each particle contains an equal volume fraction (33.33%) of AC1, astrosil and vacuum. The volume fractions of inclusions of different sizes are approximately the same.
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$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f8.eps}}\end{figure}$	Figure 8: Size dependence of the scattering and absorption efficiency factors, albedo and the asymmetry parameter for pseudospheres with inclusions. The parameters of particles are the same as in Fig. 7.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f9.eps}}\par\end{figure}$	Figure 9: Size dependence of the extinction efficiency factors for very porous pseudospheres with inclusions of different size. Each particle contains volume fractions of AC1 and astrosil equal to about 5%, the porosity ${\cal P}=0.9$ . The particles are similar to those presented in Fig. 5 but have larger porosity.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f10.eps}}\par\end{figure}$	Figure 10: Size dependence of the extinction efficiency factors for very porous pseudospheres with a size distribution of inclusions. Each particle contains volume fractions of AC1 and astrosil equal to about 5%, the porosity ${\cal P}=0.9$ . The particles are similar to those presented in Fig. 6 but have larger porosity.
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$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f12.eps}}\end{figure}$	Figure 12: Size dependence of the scattering and absorption efficiency factors, albedo and the asymmetry parameter for pseudospheres with inclusions. The parameters of particles are the same as in Fig. 11.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f13.eps}}\end{figure}$	Figure 13: The normalized extinction cross sections for multi-layered spheres of different porosity. Open circles show the normalized extinction for pseudospheres with a size distribution of inclusions (see Fig. 10).
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$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f14.eps}}\end{figure}$	Figure 14: Size dependence of the scattering and absorption normalized cross sections for multi-layered porous spheres and pseudospheres with a size distribution of inclusions. The parameters of particles are the same as in Fig. 13.
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$\begin{figure} \par\resizebox{16cm}{!}{\includegraphics[clip]{3679f15.eps}}\end{figure}$	Figure 15: Size dependence of the efficiency factors ( left panel) and their relative errors ( right panel) calculated with the exact theory for multi-layered spheres and with the Mie theory using four different EMT rules. Multi-layered particles contain an equal volume fraction of amorphous carbon (AC1), astrosil and vacuum. The cyclic order of the 18 layers is indicated.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{3679f16.eps}}\end{figure}$	Figure 16: Size dependence of the extinction efficiency factors calculated for multi-layered spheres, pseudospheres with inclusions and with the Mie theory using three different EMT rules. The porosity of particles is ${\cal P}=0.9$ .
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