Astronomy & Astrophysics

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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f1.eps} \end{figure}$ Figure 1: Projection on the sky plane (x-y plane) of the column density of the LMC disk and bar. The numerical values on the contours are in $10^{7}~M_{\odot}~{\rm kpc}^{-2}$ units. The three innermost contours correspond to 10, 20 and $30\times 10^{7}~M_{\odot}~{\rm kpc}^{-2}$ . The locations of the MACHO (black stars and empty diamonds) and EROS (triangles) microlensing candidates are also shown.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f2.eps} \end{figure}$ Figure 2: Plot of the interpolating function ${\cal E}({\hat t})$ of the MACHO detection efficiency.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f3.eps} \end{figure}$ Figure 3: Contour map of the optical depth for lenses in the Galactic halo. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f4.eps} \end{figure}$ Figure 4: Model S: contour map of the optical depth for lenses in the LMC halo. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f5.eps} \end{figure}$ Figure 5: Model E: contour map of the optical depth for lenses in the LMC halo. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f6.eps}\end{figure}$ Figure 6: Contour map of the optical depth for self-lensing. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units. The innermost contours correspond to values $2.4\times 10^{-8}$ , $3.2\times 10^{-8}$ , $4.0\times 10^{-8}$ and $4.6\times 10^{-8}$ respectively.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f7.eps} \end{figure}$ Figure 7: Contour map of the difference between the self-lensing optical depth calculated in the case of $+ 40^{\circ }$ rotated bar and the one with coplanar bar and disk. Going from the outer to the inner part, the contours correspond to increasing values of the difference: $0.1, ~ 0.6, ~ 1.1 ~ {\rm and}~ 1.6 \times 10^{-8}$ . The difference is null outside the barregion.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f8.eps} \end{figure}$ Figure 8: Contour map of the difference between the self-lensing optical depth calculated in the case of a shift of 0.5 kpc of the bar and the one with coplanar bar and disk. Going from the outer to the inner part, the black contours correspond to increasing positive values of the difference: $+0.1, ~ +0.5, ~ +0.9, ~ {\rm and}~ +1.3 \times 10^{-8}$ ; the lighter contours to negative values of the difference: $-0.1, ~ {\rm and}~ -0.2 \times 10^{-8}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f9.eps}\end{figure}$ Figure 9: Differential rate of the microlensing events with respect to the Einstein time $T_{{\rm E}}$ , along the lines of sight pointing towards the events LMC-8 (dashed red line), LMC-1 (solid black line) and LMC-23 (dot dashed blue line). The y-axis values are in 10^-12 units.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f10.eps} { } \end{figure}$ Figure 10: Scatter plot of the observed (empty boxes) values of the Einstein time and of the expected values of the median $T_{{\rm E},50~ \%}$ (filled stars), with respect to the self-lensing optical depth evaluated along the directions of the events. The $T_{{\rm E},50~ \%}$ for the Galactic disk event LMC-5 is represented by a filled box.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f11.eps}\end{figure}$ Figure 11: Differential rate of the microlensing events with respect to the mass of the lens in the direction of events LMC-4 and LMC-6. The dashed vertical line is at $\mu =0.08$ . The y-axis values are in 10^-3 units.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f12.eps}\end{figure}$ Figure 12: Scatter plot of the modal value of $\mu$ (y-axis) with respect to the measured Einstein time (x-axis) of each event. The label identifies the event. Filled (empty) triangles represent points with $\tau_{{\rm SL}}~ >~ 2\times 10^{-8} ({<}2\times 10^{-8})$ . The horizontal line indicates the lower limit of the lens mass for self-lensing, $\mu =0.08$ . The four events LMC-1, LMC-4, LMC-15 and LMC-27 have a modal value of the lens mass smaller than the lower limit and therefore are not shown. The dashed line represents the correlation line for the 6 events with $\tau_{{\rm SL}}~ <~ 2\times 10^{-8}$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f13.eps}\end{figure}$ Figure 13: Correlation plot of the median value (square boxes) of $\delta={\frac{D_{{\rm os}}-D_{{\rm ol}}}{D_{{\rm os}}}}$ (y-axis) with respect to the measured Einstein time (x-axis) of each event. The label identifies the event. The dashed line is the correlation straight line of the cluster of 10 events.
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In the text

$\begin{figure} \par\includegraphics[width=16cm,clip]{0535f14.eps} \end{figure}$ Figure 14: Locations of the 30 MACHO fields with respect to post-Van der Marel LMC geometry (black reference axes) and with respect to pre-Van der Marel LMC geometry (light blue reference axes). Also shown are the locations of the MACHO and EROS microlensing candidates. The distances on the axes are in kpc. For each field, inside brackets, we report the expected number of self-lensing event as discussed in Sect. 4.4.
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In the text

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f2.eps} \end{figure}$	Figure 2: Plot of the interpolating function ${\cal E}({\hat t})$ of the MACHO detection efficiency.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f3.eps} \end{figure}$	Figure 3: Contour map of the optical depth for lenses in the Galactic halo. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f4.eps} \end{figure}$	Figure 4: Model S: contour map of the optical depth for lenses in the LMC halo. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f5.eps} \end{figure}$	Figure 5: Model E: contour map of the optical depth for lenses in the LMC halo. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f6.eps}\end{figure}$	Figure 6: Contour map of the optical depth for self-lensing. The locations of the MACHO fields and of the microlensing candidates are also shown. The numerical values are in 10^-8 units. The innermost contours correspond to values $2.4\times 10^{-8}$ , $3.2\times 10^{-8}$ , $4.0\times 10^{-8}$ and $4.6\times 10^{-8}$ respectively.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{0535f7.eps} \end{figure}$	Figure 7: Contour map of the difference between the self-lensing optical depth calculated in the case of $+ 40^{\circ }$ rotated bar and the one with coplanar bar and disk. Going from the outer to the inner part, the contours correspond to increasing values of the difference: $0.1, ~ 0.6, ~ 1.1 ~ {\rm and}~ 1.6 \times 10^{-8}$ . The difference is null outside the barregion.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f9.eps}\end{figure}$	Figure 9: Differential rate of the microlensing events with respect to the Einstein time $T_{{\rm E}}$ , along the lines of sight pointing towards the events LMC-8 (dashed red line), LMC-1 (solid black line) and LMC-23 (dot dashed blue line). The y-axis values are in 10^-12 units.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f10.eps} { } \end{figure}$	Figure 10: Scatter plot of the observed (empty boxes) values of the Einstein time and of the expected values of the median $T_{{\rm E},50~ \%}$ (filled stars), with respect to the self-lensing optical depth evaluated along the directions of the events. The $T_{{\rm E},50~ \%}$ for the Galactic disk event LMC-5 is represented by a filled box.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f11.eps}\end{figure}$	Figure 11: Differential rate of the microlensing events with respect to the mass of the lens in the direction of events LMC-4 and LMC-6. The dashed vertical line is at $\mu =0.08$ . The y-axis values are in 10^-3 units.
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$\begin{figure} \par\includegraphics[width=8.5cm,clip]{0535f13.eps}\end{figure}$	Figure 13: Correlation plot of the median value (square boxes) of $\delta={\frac{D_{{\rm os}}-D_{{\rm ol}}}{D_{{\rm os}}}}$ (y-axis) with respect to the measured Einstein time (x-axis) of each event. The label identifies the event. The dashed line is the correlation straight line of the cluster of 10 events.
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