All Figures

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{6777f1_a.ps}\hspace*{4mm} ... ...1_c.ps}\hspace*{4mm} \includegraphics[width=4.3cm,clip]{6777f1_d.ps}\end{figure}$ Figure 1: Comparison of the magnetic field at the source surface for CR 1907 ( left column) and CR 1913 ( right column) calculated from NSO and WSO magnetograms. The two neutral lines are compared in the top panel and the differences NSO-WSO are displayed in the bottom panel.
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{6777f2_a.ps}\vspace*{5mm} \includegraphics[width=8.6cm,clip]{6777f2_b.ps}\end{figure}$ Figure 2: Two different methods of computing the neutral sheet to simulate its time evolution. The sliding window method ( top panel) centers a window on concatened magnetograms with a time shift corresponding to the selected date (here three days after the begining of CR1913). The interpolation method consists in interpolating the magnetic field at the source surface between two successive Carrington maps centered at their mid-points ( bottom panel). In this example, the field map at time $t_{i}+\Delta {t}$ is interpolated between the maps obtained at times t_i and t_i+1, the mid-points of CR_i and CR_i+1.
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In the text

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{6777f3_a.ps}\hspace*{4mm} \includegraphics[width=4.3cm,clip]{6777f3_b.ps}\end{figure}$ Figure 3: Comparison of the results given by the interpolation and the sliding window methods when generating the neutral line three days after the beginning of CR1913: direct comparison ( right panel) and difference ( left panel).
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In the text

$\begin{figure} \par\includegraphics[width=4.45cm,clip]{6777f4_a.ps}\includegraphics[width=4.45cm,clip]{6777f4_b.ps}\end{figure}$ Figure 4: Illustration of the two methods of calculating the distance to the neutral sheet: analytic ( left diagram) for the simple case of a rather flat neutral line, and using an image representation for complex configurations of the neutral line ( right diagram).
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{6777f5.ps}\end{figure}$ Figure 5: Illustration of the construction of the octree representing the electron density. The division process produces nodes (intermediate stage) represented by filled circles, and leaves (final stage) represented by open circles. In this example, cubes 1 and 2 have reached their final states and are not divided further.
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{6777f6.ps}\end{figure}$ Figure 6: 3D representation of the electron density using octree compression and corresponding to the neutral sheet of CR 1913 (an iso-density surface is displayed).
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,clip]{6777f7.ps}\end{figure}$ Figure 7: An example of a synthetic image of coronal radiance of 512 $\times$ 512 pixels generated with the adapted HERO algorithm. The $\log_{10}$ of the radiance is displayed in units of $10^{-10}~B_{\rm sun}$ , and the dotted circle represents the solar disk.
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In the text

$\begin{figure} \includegraphics[width=8.5cm,clip]{6777f8_a.ps}\hspace*{0.5cm} \includegraphics[width=8.5cm,clip]{6777f8_b.ps}\end{figure}$ Figure 8: Synthetic images of the coronal radiance based on the Saito model of a homogeneous K corona. The left image is calculated with the analytic integration and the right image with the method of octree compression. The $\log_{10}$ of the radiance is displayed in unit of $10^{-10}~B_{\rm sun}$ , and the dotted circle represents the solar disk.
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In the text

$\begin{figure} \includegraphics[width=7.65cm,clip]{6777f9.ps}\end{figure}$ Figure 9: The ratios between the equatorial radiance profiles from the octree models with different outer boundaries (from 24 to $30~R_{\rm sun}$ ) and the analytic model.
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In the text

$\begin{figure} \includegraphics[width=6.65cm,clip]{6777f10.eps}\end{figure}$ Figure 10: Illustration of the origin of the radiance's overestimation in the simple case of 1D sampling. The concavity of the analytic function clearly shows that the averaged sampling process tends to overestimate the electron density.
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In the text

$\begin{figure} \par\includegraphics[width=7.65cm,clip]{6777f11a.eps} \includegra... ...clip]{6777f11b.ps} \includegraphics[width=7.65cm,clip]{6777f11c.ps} \end{figure}$ Figure 11: Illustration of the simulation of the temporal evolution of the neutral sheet. The top panel a) displays the individual magnetograms and the corresponding calculated neutral lines at times t_i-1, t_i, and t_i+1. The middle panel b) illustrates the interpolation process of the neutral line at 9 equally-spaced time intervals. The octree representation of the electron density (similar to Fig. 8) is therefore updated every 3 days, and two examples corresponding to the 1st and 9th interpolations are displayed. The bottom panel c) summarizes the global process: a given octree is rotated during 3 days and then updated.
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In the text

$\begin{figure} \par\includegraphics[width=8.15cm,clip]{6777f12.ps}\end{figure}$ Figure 12: Comparison of the radial profiles of the radiance: the sheet streamer model (solid line), the axial streamer model (dotted line), and the observation of 31 March 1996 (dash-dot line).
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In the text

$\begin{figure} \par\includegraphics[width=16.5cm,clip]{6777f13a.ps}\par\includeg... ...13b.ps}\hspace*{0.8cm} \includegraphics[width=8cm,clip]{6777f13c.ps}\end{figure}$ Figure 13: Examples of the tangential function N_t(d) for two values of d₀ (0.2 and 0.5 $R_{\rm sun}$ ) and four values of k (0.5, 1, 2, 4) in the upper panels, and corresponding visual appearances of the streamer belt on synoptic maps in the lower panels.
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In the text

$\begin{figure} \par\includegraphics[width=4.1cm,clip]{6777f14a.ps}\hspace*{6mm} \includegraphics[width=4.3cm,clip]{6777f14b.ps}\end{figure}$ Figure 14: Results of numerical simulation illustrating the relationships between the parameters of the tangential function for the electron density (k, d₀) and for the coronal radiance ( $k_{\rm phot}$ , $d_{\rm phot}$ ). The dashed lines correspond, respectively, to $k_{\rm phot}=k$ ( left diagram) and $d_{\rm phot}=0.35~R_{\rm sun}$ ( right diagram).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6777f15a.ps}\includegraphics... ...=8cm,clip]{6777f15c.ps}\includegraphics[width=8cm,clip]{6777f15d.ps}\end{figure}$ Figure 15: Synoptic maps at $2.5~R_{\rm sun}$ , calculated from LASCO-C2 images ( top panels) and from simulations ( bottom panels). The left panels correspond to CR 1910 and the right ones to CR 1913.
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In the text

$\begin{figure} \par\includegraphics[width=7.3cm,clip]{6777f16.ps}\end{figure}$ Figure 16: Comparison of our model of radial function of the electron density to some published models: Van de Hulst (1950), Saito (1970), and Koutchmy & Livshits (1992).
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In the text

$\begin{figure} \par\hspace*{-1.5mm}\includegraphics[width=16.45cm,clip]{6777f17a.ps}\vspace*{3mm} \includegraphics[width=16.3cm,clip]{6777f17b.ps}\end{figure}$ Figure 17: Comparison of radiance profiles extracted at a constant longitude from observed (dashed line) and simulated (solid line) synoptic maps corresponding to CR1910 ( top panels) and CR1913 ( bottom panels). The origin of the latitude is at the south pole and the radiance is given in unit of 10^-10 of the mean solar brightness.
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In the text

$\begin{figure} \par\includegraphics[width=11.6cm,clip]{6777f18a.ps}\hspace*{0.7c... ...18e.ps}\hspace*{0.7cm} \includegraphics[width=5cm,clip]{6777f18f.ps}\end{figure}$ Figure 18: Examples of simulated Cor-2 A and B and LASCO-C2 images. The white circle represents the solar disk. The configurations of the STEREO and SOHO spacecrafts in space are shown in the right panels).
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In the text

$\begin{figure} \par\includegraphics[width=3.4cm,clip]{6777f19a.ps}\hspace*{-1mm}... ...9i.ps}\hspace*{-1mm} \includegraphics[width=3.4cm,clip]{6777f19j.ps}\end{figure}$ Figure 19: Simulated images of the streamer belt based on the configurations of the solar corona for CR 1956 ( top panel) and CR 1885 ( bottom panel) for five heliographic latitudes of the observer.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6777f20.ps}\end{figure}$ Figure 20: Example of simulated polar plumes (over exposed for better visibility) combined with a streamer belt. The white circle represents the solar disk.
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In the text

$\begin{figure} \par\includegraphics[width=4.4cm,clip]{6777f21a.ps}\includegraphics[width=4.3cm,clip]{6777f21b.ps}\end{figure}$ Figure 21: Simple model of a flux rope CME: geometric parameters ( left diagram) and octree representation ( right diagram).
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{6777f22a.ps}\par\includegrap... ...,clip]{6777f22b.ps}\par\includegraphics[width=8cm,clip]{6777f22c.ps}\end{figure}$ Figure 22: Temporal evolution of a simulated flux rope CME as seen by the LASCO-C2 and the Cor-2 A and B coronagraphs at angular separation of $\pm 10^{\circ }$ with respect to SOHO. The origin of this CME has a heliospheric longitude of $45^{\circ }$ and a latitude of $45^{\circ }$ .
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In the text

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{6777f1_a.ps}\hspace{4mm} ... ...1_c.ps}\hspace{4mm} \includegraphics[width=4.3cm,clip]{6777f1_d.ps}\end{figure}$	Figure 1: Comparison of the magnetic field at the source surface for CR 1907 ( left column) and CR 1913 ( right column) calculated from NSO and WSO magnetograms. The two neutral lines are compared in the top panel and the differences NSO-WSO are displayed in the bottom panel.
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$\begin{figure} \par\includegraphics[width=4.3cm,clip]{6777f3_a.ps}\hspace*{4mm} \includegraphics[width=4.3cm,clip]{6777f3_b.ps}\end{figure}$	Figure 3: Comparison of the results given by the interpolation and the sliding window methods when generating the neutral line three days after the beginning of CR1913: direct comparison ( right panel) and difference ( left panel).
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$\begin{figure} \par\includegraphics[width=4.45cm,clip]{6777f4_a.ps}\includegraphics[width=4.45cm,clip]{6777f4_b.ps}\end{figure}$	Figure 4: Illustration of the two methods of calculating the distance to the neutral sheet: analytic ( left diagram) for the simple case of a rather flat neutral line, and using an image representation for complex configurations of the neutral line ( right diagram).
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$\begin{figure} \par\includegraphics[width=6cm,clip]{6777f5.ps}\end{figure}$	Figure 5: Illustration of the construction of the octree representing the electron density. The division process produces nodes (intermediate stage) represented by filled circles, and leaves (final stage) represented by open circles. In this example, cubes 1 and 2 have reached their final states and are not divided further.
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$\begin{figure} \par\includegraphics[width=7.7cm,clip]{6777f6.ps}\end{figure}$	Figure 6: 3D representation of the electron density using octree compression and corresponding to the neutral sheet of CR 1913 (an iso-density surface is displayed).
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$\begin{figure} \par\includegraphics[width=7.7cm,clip]{6777f7.ps}\end{figure}$	Figure 7: An example of a synthetic image of coronal radiance of 512 $\times$ 512 pixels generated with the adapted HERO algorithm. The $\log_{10}$ of the radiance is displayed in units of $10^{-10}~B_{\rm sun}$ , and the dotted circle represents the solar disk.
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$\begin{figure} \includegraphics[width=8.5cm,clip]{6777f8_a.ps}\hspace*{0.5cm} \includegraphics[width=8.5cm,clip]{6777f8_b.ps}\end{figure}$	Figure 8: Synthetic images of the coronal radiance based on the Saito model of a homogeneous K corona. The left image is calculated with the analytic integration and the right image with the method of octree compression. The $\log_{10}$ of the radiance is displayed in unit of $10^{-10}~B_{\rm sun}$ , and the dotted circle represents the solar disk.
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$\begin{figure} \includegraphics[width=7.65cm,clip]{6777f9.ps}\end{figure}$	Figure 9: The ratios between the equatorial radiance profiles from the octree models with different outer boundaries (from 24 to $30~R_{\rm sun}$ ) and the analytic model.
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$\begin{figure} \includegraphics[width=6.65cm,clip]{6777f10.eps}\end{figure}$	Figure 10: Illustration of the origin of the radiance's overestimation in the simple case of 1D sampling. The concavity of the analytic function clearly shows that the averaged sampling process tends to overestimate the electron density.
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$\begin{figure} \par\includegraphics[width=8.15cm,clip]{6777f12.ps}\end{figure}$	Figure 12: Comparison of the radial profiles of the radiance: the sheet streamer model (solid line), the axial streamer model (dotted line), and the observation of 31 March 1996 (dash-dot line).
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$\begin{figure} \par\includegraphics[width=16.5cm,clip]{6777f13a.ps}\par\includeg... ...13b.ps}\hspace*{0.8cm} \includegraphics[width=8cm,clip]{6777f13c.ps}\end{figure}$	Figure 13: Examples of the tangential function N_t(d) for two values of d₀ (0.2 and 0.5 $R_{\rm sun}$ ) and four values of k (0.5, 1, 2, 4) in the upper panels, and corresponding visual appearances of the streamer belt on synoptic maps in the lower panels.
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$\begin{figure} \par\includegraphics[width=4.1cm,clip]{6777f14a.ps}\hspace*{6mm} \includegraphics[width=4.3cm,clip]{6777f14b.ps}\end{figure}$	Figure 14: Results of numerical simulation illustrating the relationships between the parameters of the tangential function for the electron density (k, d₀) and for the coronal radiance ( $k_{\rm phot}$ , $d_{\rm phot}$ ). The dashed lines correspond, respectively, to $k_{\rm phot}=k$ ( left diagram) and $d_{\rm phot}=0.35~R_{\rm sun}$ ( right diagram).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{6777f15a.ps}\includegraphics... ...=8cm,clip]{6777f15c.ps}\includegraphics[width=8cm,clip]{6777f15d.ps}\end{figure}$	Figure 15: Synoptic maps at $2.5~R_{\rm sun}$ , calculated from LASCO-C2 images ( top panels) and from simulations ( bottom panels). The left panels correspond to CR 1910 and the right ones to CR 1913.
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$\begin{figure} \par\includegraphics[width=7.3cm,clip]{6777f16.ps}\end{figure}$	Figure 16: Comparison of our model of radial function of the electron density to some published models: Van de Hulst (1950), Saito (1970), and Koutchmy & Livshits (1992).
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$\begin{figure} \par\hspace{-1.5mm}\includegraphics[width=16.45cm,clip]{6777f17a.ps}\vspace{3mm} \includegraphics[width=16.3cm,clip]{6777f17b.ps}\end{figure}$	Figure 17: Comparison of radiance profiles extracted at a constant longitude from observed (dashed line) and simulated (solid line) synoptic maps corresponding to CR1910 ( top panels) and CR1913 ( bottom panels). The origin of the latitude is at the south pole and the radiance is given in unit of 10^-10 of the mean solar brightness.
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$\begin{figure} \par\includegraphics[width=11.6cm,clip]{6777f18a.ps}\hspace{0.7c... ...18e.ps}\hspace{0.7cm} \includegraphics[width=5cm,clip]{6777f18f.ps}\end{figure}$	Figure 18: Examples of simulated Cor-2 A and B and LASCO-C2 images. The white circle represents the solar disk. The configurations of the STEREO and SOHO spacecrafts in space are shown in the right panels).
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$\begin{figure} \par\includegraphics[width=3.4cm,clip]{6777f19a.ps}\hspace{-1mm}... ...9i.ps}\hspace{-1mm} \includegraphics[width=3.4cm,clip]{6777f19j.ps}\end{figure}$	Figure 19: Simulated images of the streamer belt based on the configurations of the solar corona for CR 1956 ( top panel) and CR 1885 ( bottom panel) for five heliographic latitudes of the observer.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{6777f20.ps}\end{figure}$	Figure 20: Example of simulated polar plumes (over exposed for better visibility) combined with a streamer belt. The white circle represents the solar disk.
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$\begin{figure} \par\includegraphics[width=4.4cm,clip]{6777f21a.ps}\includegraphics[width=4.3cm,clip]{6777f21b.ps}\end{figure}$	Figure 21: Simple model of a flux rope CME: geometric parameters ( left diagram) and octree representation ( right diagram).
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$\begin{figure} \par\includegraphics[width=8cm,clip]{6777f22a.ps}\par\includegrap... ...,clip]{6777f22b.ps}\par\includegraphics[width=8cm,clip]{6777f22c.ps}\end{figure}$	Figure 22: Temporal evolution of a simulated flux rope CME as seen by the LASCO-C2 and the Cor-2 A and B coronagraphs at angular separation of $\pm 10^{\circ }$ with respect to SOHO. The origin of this CME has a heliospheric longitude of $45^{\circ }$ and a latitude of $45^{\circ }$ .
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