All Figures

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=6.62cm,width=8.8cm,clip]{H4692F1.ps}} \end{figure}$ Figure 1: Prototype X-ray spectrum of a type-1 AGN (illustration idea taken from Fabian 1998). The spectrum is dominated by the global Comptonized continuum. At low energies, there is the soft excess, in principle a composition of some black bodies belonging to the disk divided into rings. At energies around 1 keV, one can recognize a complex of absorption dips, originating from the warm absorbers. The reflection component consists of a broad bump peaking around 20 keV and the prominent fluorescence emission line complex around 6.4 keV.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.8cm,width=8.8cm,clip]{H4692F2.ps}} \end{figure}$ Figure 2: Illustration of topological elements in the innermost region of accreting black hole systems. The size and morphology of these elements depend on accretion rate, black hole mass and radiative cooling.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=5.09cm,width=8.8cm,clip]{H4692F3.ps}} \end{figure}$ Figure 3: Radial behaviour of the Boyer-Lindquist functions at extreme Kerr (a=1.0) in the equatorial plane. Relativistic units were used.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.82cm,width=8.8cm,clip]{H4692F4.ps}} \end{figure}$ Figure 4: Schematical representation of a Kerr ray tracer. The light rays start at the screen ( back tracking) and hit the disk surface in the equatorial plane. On the screen the lensed image is formed as seen by a distant observer. Our solver folds directly from equatorial plane to screen.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=6.9cm,width=8.8cm,clip]{H4692F5.ps}} \end{figure}$ Figure 5: Simulated disk image at inclination of $30^{\circ }$ and extreme Kerr a=0.999999 with color-coded distribution of generalized Doppler factor g (white corresponds to g=1). The beamed blue approaching left side is clearly seen (triangular segment, g>1). Gravitational redshift (dark colors, g<1) darkens the inner edge until g vanishes at the horizon.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=6cm,width=8.8cm,clip]{H4692F6.ps}} \end{figure}$ Figure 6: Radial dependence of the velocity component $v^{\rm (\Phi )}$ in the equatorial plane for Kerr parameter a=0.8. Prograde case is shown in the upper curve; retrograde case is illustrated in the lower curve. The matter starts in free-fall from a drift radius of $R_{\rm t}=3.0~r_{\rm g}$ . $v^{\rm (\Phi )}$ vanishes self-consistently (for ZAMOs) at the horizon at $r_{\rm H}=1.6~r_{\rm g}$ .
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=7.63cm,width=8.8cm,clip]{H4692F7.ps}} \end{figure}$ Figure 7: Distribution of the Doppler factor g⁴ over the disk. The inner disk edge touches at $r_{\rm in}=1.0015~r_{\rm g}$ the horizon of the black hole with a=0.999999. The inclination angle is $30^{\circ }$ and the outer edge is at $r_{\rm out}=30.0~r_{\rm g}$ . The shadow of the black hole is clearly seen. Beaming on the left approaching side brightens any emission originating there. The right receeding part of the disk is darkened. This distribution is always folded in the flux integral and therefore important for any emission near black holes.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.96cm,width=8.8cm,clip]{H4692F8.ps}} \end{figure}$ Figure 8: Distribution of specific angular momentum, $\lambda {(r)}$ , for Kerr parameter a=0.8. Fixing a constant specific angular momentum, $\lambda _{\rm t}$ , is only allowed inbetween the two levels: the lower one, $\lambda _{\rm ms}$ , and the upper one, $\lambda _{\rm mb}$ .
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=5.26cm,width=8.8cm,clip]{H4692F9.ps}} \end{figure}$ Figure 9: Radial distribution of prograde (solid curve), $\Omega _{+}$ , and retrograde (dashed curve) angular velocity limit, $\Omega _{-}$ , for Kerr parameter a=0.8. The dotted curve illustrates the frame-dragging potential, $\omega$ . At the horizon, here at $r_{\rm H}=1.6~r_{\rm g}$ , all curves coincide. This is the visualization of the frame-dragging effect.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=5.82cm,width=8.8cm,clip]{H4692F10.ps}} \end{figure}$ Figure 10: Radial velocity component in the ZAMO for different radial drift models, that means different rotation state of black hole, a, and drift radius, $R_{\rm t}$ . In all cases, the radial drift becomes light speed at the horizon radii.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=6.98cm,width=8cm,clip]{H4692F11.ps}} \end{figure}$ Figure 11: Illustration of different radial emissivity models.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=6.28cm,width=8.8cm,clip]{H4692F12.ps}} \end{figure}$ Figure 12: Influence of radial drift. Upper hemisphere: pure Keplerian rotation $v^{\rm (\Phi )}\not =0, \ v^{\rm (r)}=0$ . Bottom hemisphere: Keplerian rotation plus radial drift $v^{\rm (\Phi )}\not =0, \ v^{\rm (r)}\not =0$ . Enhanced gravitional redshift is clearly seen by darkening near the horizon indicated by an arrow. Parameters were a=0.1, $i=40^{\circ }$ , $r_{\rm in}=r_{\rm H}=1.996 \ r_{\rm g}$ , $r_{\rm out}=10.0 \ r_{\rm g}$ . The radial drift starts at $R_{\rm t}=5.0 \ r_{\rm g}$ .
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=9cm,width=8.8cm,clip]{H4692F13.ps}} \end{figure}$ Figure 13: The upper disk shows the distribution of the g-factor over a narrow ring with radial drift starting at $R_{\rm t}=3.0 \ r_{\rm g}$ . White color indicates no net photon energy shift (g=1), the left side is beamed (g>1) whereas the right side and the regions near the horizon are strongly redshifted (g<1). The inclination angle is $80^{\circ }$ , the black hole rotation is fast, a=0.8, inner edge is the horizon at $r_{\rm in}=r_{\rm H}=1.6 \ r_{\rm g}$ and outer edge is only at $r_{\rm out}=4.6 \ r_{\rm g}$ . The lower disk indicates the associated distribution of the emission of the same narrow ring. White indicates high emission, black low emission. Here, the emissivity follows a broad Gaussian profile with $R_{\rm t}=3.0 \ r_{\rm g}$ and constant Gaussian width $\sigma _{\rm r}=3.0$ .
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In the text

$\begin{figure} \par\includegraphics[height=6cm,width=6cm,clip]{H4692F14.ps} \end{figure}$ Figure 14: Three effects form the line profile. This simulated profile of an iron K line has typical parameters for Seyfert-1 s. The observer is intermediately inclined, the plasma rotates only Keplerian and typical disk sizes $r_{\rm in} = r_{\rm ms}$ , $r_{\rm out} = 50 \ r_{\rm g}$ were taken.
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In the text

$\begin{figure} \par\rotatebox{-90}{\includegraphics[height=8.8cm,width=4cm,clip]... ...{-90}{\includegraphics[height=8.8cm,width=4cm,clip]{H4692F15e.ps}} \end{figure}$ Figure 15: A selection of topology types of relativistic emission lines. From top to bottom: triangular, double-horned, double-peaked, bumpy and shoulder-like. Line flux in normalized arbitrary units is plotted over g-factor.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=8cm,width=8cm,clip]{H4692F16.ps}} \end{figure}$ Figure 16: Illustration of line criteria to determine characteristics of a typical emission line profile. The position of the relic Doppler peaks (if existing) can be used to fix their flux ratio (Doppler Peak Ratio, ${\rm DPR}$ ) and energetic distance (Doppler Peak Spacing, ${\rm DPS}$ ). Other specific quantities are the maximal flux, $F_{\rm max}$ , and the minimum and maximum energy of a line, $E_{\rm min}$ and $E_{\rm max}$ . These criteria can be used to describe a line shape, observed or theoretically derived, with a few numerical values.
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In the text

$\begin{figure} \par\rotatebox{-90}{\includegraphics[height=8.8cm,width=5.7cm,clip]{H4692F17.ps}} \end{figure}$ Figure 17: Relativistic emission line forming directly in front of the horizon. The parameters were chosen to $i=30^{\circ }$ , Kerr parameter a=0.998, disk size $r_{\rm in}=r_{\rm H}=1.0633 \ r_{\rm g}$ , $r_{\rm out}=30.0 \ r_{\rm g}$ , radial drift starting at $R_{\rm t}=1.5 \ r_{\rm g}$ and a localized emissivity by means of a Gaussian profile with $R_{\rm t}=1.5 \ r_{\rm g}$ and $\sigma _{\rm r}=0.4$ . This more or less unphysical example for line emission should demonstrate the strongly suppressed emission due to the shadow of the black hole. Even if emission lines could form in the direct vicinity of black holes, the high power of the generalized Doppler factor g reduces the flux and shifts the line significantly to lower energies due to gravitational redshift effects.
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In the text

$\begin{figure} \par\rotatebox{-90}{\includegraphics[height=8.8cm,width=5.7cm,clip]{H4692F18.ps}} \end{figure}$ Figure 18: Investigation of the dependence on the Kerr parameter a. The plasma motion is only Keplerian, the inclination is $40^{\circ }$ . The black hole spin decreases from top to bottom line profile, $a=0.999999, \ 0.5, \ 0.1$ . The inner disk edge is equal to the corresponding black hole horizon, $r_{\rm in}=r_{\rm H}(a)$ , and the disk edges are chosen so that the total disk surface remains constant.
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In the text

$\begin{figure} \par\rotatebox{-90}{\includegraphics[height=8.8cm,width=5.7cm,clip]{H4692F19.ps}} \end{figure}$ Figure 19: Reproduction of the line set with variable inclination, $i=10^{\circ }, \ 30^{\circ }, \ 60^{\circ }$ in Schwarzschild (Fabian et al. 2000). The main difference is that here an additional radial drift is adapted whereas Fabian et al. (2000) only assumed Keplerian motion. In both cases the emissivity follows a standard single power law. For better comparison, the abscissa is scaled to the iron K $\alpha$ line with 6.4 keV rest frame energy.
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In the text

$\begin{figure} \par\rotatebox{-90}{\includegraphics[height=8.8cm,width=5.79cm,clip]{H4692F20.ps}} \end{figure}$ Figure 20: Relativistic emission lines with radial drift model and Gaussian emissivity. The drift radius $R_{\rm t}$ from the plasma velocity field couples to the emissivity. From bottom to top, the drift radius increases, $R_{\rm t}=4.0, \ 5.0, \ 6.0$ . The black hole rotates slowly, a=0.1, the inclination angle is $40^{\circ }$ , $r_{\rm in}=r_{\rm H}=1.995 \ r_{\rm g}$ and $r_{\rm out}=30.0 \ r_{\rm g}$ . The emissivity is modelled with constant $\sigma _{\rm r}=3.0$ .
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.5cm,width=8.8cm,clip]{H4692F21.ps}} \end{figure}$ Figure 21: Cut-emissivity with $\alpha =\beta =3.0$ for different truncation radii. From bottom to top, the drift radius increases, $R_{\rm t}=4.0, \ 5.0, \ 6.0$ . With this choice of $\alpha$ and $\beta$ , the emissivity peaks naturally at $R_{\rm t}$ . For $r\leq R_{\rm t}$ the emissivity decreases exponentially.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.5cm,width=8.8cm,clip]{H4692F22.ps}} \end{figure}$ Figure 22: Relativistic emission lines with radial drift model and cut-power law emissivity. The drift radius $R_{\rm t}$ from the plasma velocity field couples to the emissivity. From bottom to top, the drift radius increases, $R_{\rm t}=4.0, \ 5.0, \ 6.0$ . The black hole rotates slowly, a=0.1, the inclination angle is $40^{\circ }$ , $r_{\rm in}=r_{\rm H}=1.995 \ r_{\rm g}$ and $r_{\rm out}=30.0 \ r_{\rm g}$ . The emissivity is modelled with constant $\alpha =\beta =3.0$ .
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In the text

$\begin{figure} \par\rotatebox{-90}{\includegraphics[height=8.8cm,width=5.17cm,clip]{H4692F23.ps}} \end{figure}$ Figure 23: Direct confrontation of relativistic emission lines with and without radial drift model. A single-power law emissivity with $\beta =3.0$ is chosen. The black hole spin parameter is a=0.8, the inclination angle is $40^{\circ }$ , $r_{\rm in}=r_{\rm H}=1.6 \ r_{\rm g}$ and $r_{\rm out}=20.0 \ r_{\rm g}$ . The pure Keplerian case, top line, is modelled by constant specific angular momentum for $r\leq r_{\rm ms}=2.91 \ r_{\rm g}$ . The non-Keplerian case, bottom line, includes drift starting at $R_{\rm t}=4.5 \ r_{\rm g}$ .
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.6cm,width=8.8cm,clip]{H4692F24.ps}} \end{figure}$ Figure 24: Suggestion of a multi-species line system fitting the XMM-Newton observation of MCG-6-30-15 (Fabian et al. 2002). A line complex consisting of Fe K $\alpha$ at 6.4 keV, Fe K $\beta$ at 7.06 keV, Ni K $\alpha$ at 7.48 keV and one weak contribution of Cr K $\alpha$ at 5.41 keV (all energies measured in the rest frame) is simulated.
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In the text

$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.8cm,width=8.8cm,clip]{H4692F2.ps}} \end{figure}$	Figure 2: Illustration of topological elements in the innermost region of accreting black hole systems. The size and morphology of these elements depend on accretion rate, black hole mass and radiative cooling.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=5.09cm,width=8.8cm,clip]{H4692F3.ps}} \end{figure}$	Figure 3: Radial behaviour of the Boyer-Lindquist functions at extreme Kerr (a=1.0) in the equatorial plane. Relativistic units were used.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.82cm,width=8.8cm,clip]{H4692F4.ps}} \end{figure}$	Figure 4: Schematical representation of a Kerr ray tracer. The light rays start at the screen ( back tracking) and hit the disk surface in the equatorial plane. On the screen the lensed image is formed as seen by a distant observer. Our solver folds directly from equatorial plane to screen.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=6.9cm,width=8.8cm,clip]{H4692F5.ps}} \end{figure}$	Figure 5: Simulated disk image at inclination of $30^{\circ }$ and extreme Kerr a=0.999999 with color-coded distribution of generalized Doppler factor g (white corresponds to g=1). The beamed blue approaching left side is clearly seen (triangular segment, g>1). Gravitational redshift (dark colors, g<1) darkens the inner edge until g vanishes at the horizon.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.96cm,width=8.8cm,clip]{H4692F8.ps}} \end{figure}$	Figure 8: Distribution of specific angular momentum, $\lambda {(r)}$ , for Kerr parameter a=0.8. Fixing a constant specific angular momentum, $\lambda _{\rm t}$ , is only allowed inbetween the two levels: the lower one, $\lambda _{\rm ms}$ , and the upper one, $\lambda _{\rm mb}$ .
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=5.26cm,width=8.8cm,clip]{H4692F9.ps}} \end{figure}$	Figure 9: Radial distribution of prograde (solid curve), $\Omega _{+}$ , and retrograde (dashed curve) angular velocity limit, $\Omega _{-}$ , for Kerr parameter a=0.8. The dotted curve illustrates the frame-dragging potential, $\omega$ . At the horizon, here at $r_{\rm H}=1.6~r_{\rm g}$ , all curves coincide. This is the visualization of the frame-dragging effect.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=5.82cm,width=8.8cm,clip]{H4692F10.ps}} \end{figure}$	Figure 10: Radial velocity component in the ZAMO for different radial drift models, that means different rotation state of black hole, a, and drift radius, $R_{\rm t}$ . In all cases, the radial drift becomes light speed at the horizon radii.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=6.98cm,width=8cm,clip]{H4692F11.ps}} \end{figure}$	Figure 11: Illustration of different radial emissivity models.
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$\begin{figure} \par\includegraphics[height=6cm,width=6cm,clip]{H4692F14.ps} \end{figure}$	Figure 14: Three effects form the line profile. This simulated profile of an iron K line has typical parameters for Seyfert-1 s. The observer is intermediately inclined, the plasma rotates only Keplerian and typical disk sizes $r_{\rm in} = r_{\rm ms}$ , $r_{\rm out} = 50 \ r_{\rm g}$ were taken.
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$\begin{figure} \par\rotatebox{-90}{\includegraphics[height=8.8cm,width=4cm,clip]... ...{-90}{\includegraphics[height=8.8cm,width=4cm,clip]{H4692F15e.ps}} \end{figure}$	Figure 15: A selection of topology types of relativistic emission lines. From top to bottom: triangular, double-horned, double-peaked, bumpy and shoulder-like. Line flux in normalized arbitrary units is plotted over g-factor.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.5cm,width=8.8cm,clip]{H4692F21.ps}} \end{figure}$	Figure 21: Cut-emissivity with $\alpha =\beta =3.0$ for different truncation radii. From bottom to top, the drift radius increases, $R_{\rm t}=4.0, \ 5.0, \ 6.0$ . With this choice of $\alpha$ and $\beta$ , the emissivity peaks naturally at $R_{\rm t}$ . For $r\leq R_{\rm t}$ the emissivity decreases exponentially.
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$\begin{figure} \par\rotatebox{0}{\includegraphics[height=4.6cm,width=8.8cm,clip]{H4692F24.ps}} \end{figure}$	Figure 24: Suggestion of a multi-species line system fitting the XMM-Newton observation of MCG-6-30-15 (Fabian et al. 2002). A line complex consisting of Fe K $\alpha$ at 6.4 keV, Fe K $\beta$ at 7.06 keV, Ni K $\alpha$ at 7.48 keV and one weak contribution of Cr K $\alpha$ at 5.41 keV (all energies measured in the rest frame) is simulated.
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