Astronomy & Astrophysics

All Figures

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{figgeometria.ps} \end{figure}$ Figure 1: The geometry of a retro-lensing event is shown in the case of a general configuration for the lens, source and observer positions. Photons emitted by the Sun S, in the center of the reference frame, move towards the retro-MACHO L (a Schwarzschild or a Kerr black hole) which, for simplicity, is placed on the Z-Y plane. Light rays, which interact with the black hole strong gravitational field, may suffer a path deflection to bending angle multiples of $\pi$ and reach the observer O'. The arrow on the lens represents the black hole spin vector which lies perpendicular to the lens-observer-source plane.
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,height=5.5cm,clip]{plot0rot.ps} \end{figure}$ Figure 2: The expected visual magnitude mof the arcs forming close to a $10 ~M_{\odot}$ Schwarzschild black hole (with a=0 at 0.01 pc from the Earth) as a function of time (i.e of the Earth position) is shown. The curves correspond to different displacement angles $\beta$ . In particular, from top to bottom, we set $\beta =1\hbox {$^\circ $ }$ , $\beta =R_{\odot }/1$ AU and $\beta =0\hbox {$^\circ $ }$ , respectively. Note that t=0 means, referring to Fig. 1, that the Earth is on the Y axis.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,height=5.7cm,clip]{photonsphere.ps} \end{figure}$ Figure 3: The radius of the photosphere as a function of the black hole spin parameter a is shown. As expected, for positive values of a (i.e. for light rays co-rotating with the black hole) photons are allowed to get closer to the black hole. For $a\rightarrow 0$ the photosphere radius approaches the last stable orbit radius value for a Schwarzschild black hole (x_m=3/2).
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In the text

$\begin{figure} \par$\begin{array}{c} \includegraphics[width=7cm,height=5.7cm,cli... ...ncludegraphics[width=7.4cm,height=5.7cm,clip]{bbarra.ps}\end{array}$\end{figure}$ Figure 4: The coefficients $\overline {k}_1$ (upper panel) and $\overline {k}_2$ (bottom panel) appearing in Eq. (20) are plotted as functions of the black hole spin parameter a. For details see text.
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In the text

$\begin{figure} \par\includegraphics[width=7.7cm,height=5.7cm,clip]{parametroimpatto.ps} \end{figure}$ Figure 5: The impact parameter b, evaluated for the deflection angle $\alpha _{\rm d}=\pi$ , is shown as a function of the black hole spin parameter a. Note that for $a\rightarrow 0$ the impact parameter approaches the result b=5.34664 for a Schwarzschild black hole given by Chandrasekhar (1983).
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In the text

$\begin{figure} \par\includegraphics[width=16.7cm,clip]{graficototale01.ps} \end{figure}$ Figure 6: The expected retro-lensing light curves for a Kerr black hole with mass $10 ~M_{\odot}$ and spin parameter a=0.1 is given as a function of the time (i.e. of the Earth position in its orbit). The solid red line corresponds to the magnitude of the image formed by co-rotating photons while the dashed red line is the magnitude of the image formed by counter-rotating photons. The central black line corresponds to a retro-lensing event involving a Schwarzschild black hole with the same mass. The light source is the Sun and the black hole is placed at 0.01 pc from Earth.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,height=5.7cm,clip]{photonsphere.ps} \end{figure}$	Figure 3: The radius of the photosphere as a function of the black hole spin parameter a is shown. As expected, for positive values of a (i.e. for light rays co-rotating with the black hole) photons are allowed to get closer to the black hole. For $a\rightarrow 0$ the photosphere radius approaches the last stable orbit radius value for a Schwarzschild black hole (x_m=3/2).
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$\begin{figure} \par$\begin{array}{c} \includegraphics[width=7cm,height=5.7cm,cli... ...ncludegraphics[width=7.4cm,height=5.7cm,clip]{bbarra.ps}\end{array}$\end{figure}$	Figure 4: The coefficients $\overline {k}_1$ (upper panel) and $\overline {k}_2$ (bottom panel) appearing in Eq. (20) are plotted as functions of the black hole spin parameter a. For details see text.
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$\begin{figure} \par\includegraphics[width=7.7cm,height=5.7cm,clip]{parametroimpatto.ps} \end{figure}$	Figure 5: The impact parameter b, evaluated for the deflection angle $\alpha _{\rm d}=\pi$ , is shown as a function of the black hole spin parameter a. Note that for $a\rightarrow 0$ the impact parameter approaches the result b=5.34664 for a Schwarzschild black hole given by Chandrasekhar (1983).
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