All Figures

$\begin{figure} \par\includegraphics[width=13.3cm,clip]{H4037F1.PS} \end{figure}$ Figure 1: The critical geodesics (heavy lines) through P_f divide the orbital plane in three regions. Some geodesics of type Athrough P_f are also shown (gray lines).
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In the text

$\begin{figure} \par\includegraphics[width=17cm]{H4037f2.eps} \end{figure}$ Figure 2: Images of a mildly warped disk (a₁=0.1, b=3, $R_{\rm out}=40M$ ), illuminated by two point sources at $h=\pm 10M$ , seen from the inclination $\iota = 30^\circ$ for $\Omega =0^\circ$ (top left) to $\Omega =330^\circ$ (bottom right) in steps of $30^\circ$ . The hue of the color corresponds to the redshift (blueshift) and the intensity of the colors is in a semi-log scale. The corresponding line profiles are also shown as intensity vs. redshift g with $0 \le \ g\ \le 2$ .
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In the text

$\begin{figure} \par\includegraphics[width=15.2cm,clip]{H4037F3.PS} \end{figure}$ Figure 3: An array of line profiles of a moderately warped disk (a₁=0.1, b=3, $R_{\rm out}=100M$ ) together with flat disk line profiles (in light gray) at the same inclination. X-axis scale is Energy in keV. Y-scale is observed flux in arbitrary units.
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In the text

$\begin{figure} \par\includegraphics[width=15cm]{H4037F4.PS} \end{figure}$ Figure 4: An array of twisted disk (a₂=0.3, $R_{\rm out}=100M$ ) line profiles together with flat disk line profiles (in light gray). X-axis scale is Energy in keV. Y-scale is observed flux in arbitrary units.
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In the text

$\begin{figure} \par\includegraphics[width=11.5cm,clip]{H4037F5.PS} \end{figure}$ Figure 5: Fitting the flat disk (at inclination $\iota _0=30^\circ$ ) noisy line profiles. The $\chi ^2$ of the fit is shown as function of $\iota _m$ and the $\sigma$ of the noise, where $\sigma$ is measured in % of the maximum signal value. Note that the minimum is always at $30^\circ$ , but its depth decreases rapidly with $\sigma$ .
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In the text

$\begin{figure} \par\includegraphics[width=17cm,clip]{H4037f6.eps} \end{figure}$ Figure 6: The line profile and the fit (above) and the calculated emissivity profile (below). Left: theoretical line profile, right: line profile contaminated by 3% noise. The right top figure shows one random realization of a noisy line; the error bars properly indicate the noise dispersion. The noise free profile is also indicated in light gray. A number of emissivity profiles obtained for different realizations of noise are shown in the right bottom part of the picture, where the heaviest line corresponds to the above line profile.
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In the text

$\begin{figure} \par\includegraphics[width=12.5cm,clip]{H4037F7.PS} \end{figure}$ Figure 7: Line profiles of the Fe K $_\alpha$ line from a warped disk with $R_{\rm out}=100M$ , $a_{\rm rot}=0$ , a₁=0.06, b=3seen at the inclination $\iota = 30^\circ$ as a function of $\Omega$ .
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In the text

$\begin{figure} \par\includegraphics[width=11.7cm,clip]{H4037F8.PS} \end{figure}$ Figure 8: Line profiles obtained by fitting line profiles shown in Fig. 7 with the flat disk model.
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In the text

$\begin{figure} \par\includegraphics[width=7.5cm,clip]{H4037F9.PS} \end{figure}$ Figure 9: Flat disk model fits to the line profiles shown in Fig. 7.
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In the text

$\begin{figure} \par\includegraphics[width=13cm,clip]{H4037F10.PS} \end{figure}$ Figure 10: Emissivity profiles derived for the line profiles shown in Fig. 7.
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{H4037F11.PS} \end{figure}$ Figure 11: The effect of increasing warp on the line profile for a disk with $R_{\rm out}=100M$ , b=3, $\iota = 30^\circ$ and $\Omega =0$ . The warp a₁ is increased in steps of 0.1.
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In the text

$\begin{figure} \par\includegraphics[width=14.8cm,clip]{H4037F12.PS} \end{figure}$ Figure 12: Line profiles obtained by fitting the profiles shown in Fig. 11 with the flat disk model.
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In the text

$\begin{figure} \par\includegraphics[width=10.8cm,clip]{H4037F13.PS} \end{figure}$ Figure 13: Flat disk model fits to the line profiles shown in Fig. 11.
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In the text

$\begin{figure} \par\includegraphics[width=13.2cm,clip]{H4037F14.PS} \end{figure}$ Figure 14: Emissivity profiles derived for the line profiles shown in Fig. 11.
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In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{H4037F15.PS} \end{figure}$ Figure 15: Some examples of line profiles for warped disks around a rotating (Kerr) black hole with a/M = 0.009981. All profiles (thick lines) are computed for $\iota = 40^\circ$ , $R_{\rm out}=100M$ . Top row: twist free disk; bottom row: twisted disk. In each row, profiles are arranged in order of increasing $\Omega$ , from $\Omega =0^\circ$ to $\Omega = 300^\circ$ in steps of $60^\circ$ . The emissivity law is $\epsilon (r)\propto r^{-2}$ . The thin line represents, for comparison, the line profile for an equatorial (flat) disk for the same inclination and outer radius. X-axis scale is Energy in keV. Y-scale is observed flux in arbitrary units.
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In the text

$\begin{figure} \par\includegraphics[width=13.3cm,clip]{H4037F1.PS} \end{figure}$	Figure 1: The critical geodesics (heavy lines) through P_f divide the orbital plane in three regions. Some geodesics of type Athrough P_f are also shown (gray lines).
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$\begin{figure} \par\includegraphics[width=15.2cm,clip]{H4037F3.PS} \end{figure}$	Figure 3: An array of line profiles of a moderately warped disk (a₁=0.1, b=3, $R_{\rm out}=100M$ ) together with flat disk line profiles (in light gray) at the same inclination. X-axis scale is Energy in keV. Y-scale is observed flux in arbitrary units.
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$\begin{figure} \par\includegraphics[width=15cm]{H4037F4.PS} \end{figure}$	Figure 4: An array of twisted disk (a₂=0.3, $R_{\rm out}=100M$ ) line profiles together with flat disk line profiles (in light gray). X-axis scale is Energy in keV. Y-scale is observed flux in arbitrary units.
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$\begin{figure} \par\includegraphics[width=11.5cm,clip]{H4037F5.PS} \end{figure}$	Figure 5: Fitting the flat disk (at inclination $\iota _0=30^\circ$ ) noisy line profiles. The $\chi ^2$ of the fit is shown as function of $\iota _m$ and the $\sigma$ of the noise, where $\sigma$ is measured in % of the maximum signal value. Note that the minimum is always at $30^\circ$ , but its depth decreases rapidly with $\sigma$ .
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$\begin{figure} \par\includegraphics[width=12.5cm,clip]{H4037F7.PS} \end{figure}$	Figure 7: Line profiles of the Fe K $_\alpha$ line from a warped disk with $R_{\rm out}=100M$ , $a_{\rm rot}=0$ , a₁=0.06, b=3seen at the inclination $\iota = 30^\circ$ as a function of $\Omega$ .
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$\begin{figure} \par\includegraphics[width=11.7cm,clip]{H4037F8.PS} \end{figure}$	Figure 8: Line profiles obtained by fitting line profiles shown in Fig. 7 with the flat disk model.
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$\begin{figure} \par\includegraphics[width=7.5cm,clip]{H4037F9.PS} \end{figure}$	Figure 9: Flat disk model fits to the line profiles shown in Fig. 7.
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$\begin{figure} \par\includegraphics[width=13cm,clip]{H4037F10.PS} \end{figure}$	Figure 10: Emissivity profiles derived for the line profiles shown in Fig. 7.
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$\begin{figure} \par\includegraphics[width=14cm,clip]{H4037F11.PS} \end{figure}$	Figure 11: The effect of increasing warp on the line profile for a disk with $R_{\rm out}=100M$ , b=3, $\iota = 30^\circ$ and $\Omega =0$ . The warp a₁ is increased in steps of 0.1.
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$\begin{figure} \par\includegraphics[width=14.8cm,clip]{H4037F12.PS} \end{figure}$	Figure 12: Line profiles obtained by fitting the profiles shown in Fig. 11 with the flat disk model.
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$\begin{figure} \par\includegraphics[width=10.8cm,clip]{H4037F13.PS} \end{figure}$	Figure 13: Flat disk model fits to the line profiles shown in Fig. 11.
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$\begin{figure} \par\includegraphics[width=13.2cm,clip]{H4037F14.PS} \end{figure}$	Figure 14: Emissivity profiles derived for the line profiles shown in Fig. 11.
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