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Astron. Astrophys. 348, 71-76 (1999)

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3. Results

The main difference between the line emission from planar disks and warped ones is that in the latter case only a part of each disk ring is irradiated and respectively emits lines. A schemathic 2D map of the disk emission flux is given in Fig. 3. Profiles for different lines of sight are presented in Fig. 4. Here the bolometric luminosity is [FORMULA], the black hole mass is [FORMULA], and the initial inclination angle is [FORMULA]. The Kerr parameter [FORMULA] and the viscosity parameter [FORMULA], so [FORMULA].

[FIGURE] Fig. 3a-c. A schematic map of the HFI - emission line flux from an irradiated nonplanar disk ab . The flux values are expressed in relative logarithmic units. The initial inclination of the flow is [FORMULA]. [FORMULA], [FORMULA], [FORMULA]. Maps for two values of [FORMULA], [FORMULA] a and [FORMULA] b  are shown. The inner ([FORMULA]) part of the disk, where the lines are emitted predominantly, is shown in the figure. The height (in [FORMULA]) of the disk surface in respect to the X-Y plane (an izo-Z map) is shown in c .

[FIGURE] Fig. 4a-f. Line profiles of HFI emission from the disk, shown in Fig. 3a, for different viewing angles. The observer is tilted at an angle [FORMULA] with respect to the black hole equatorial plane. The azimuthal angle along the X-Y plane ([FORMULA]) is respectively [FORMULA] - a -f  The inner and the outer radii of the disk are 10 and [FORMULA] respectively. Abscissa is in [FORMULA].

The most important result of this work is that the profiles of the disk emission (Fig. 4) are nonsymmetrical and red or blue frequency shifted, as expected if only about a half of the disk emits in the direction towards the observer (Fig. 3). Only for special viewing angles, these profiles could be almost symmetric, double or single-peaked and non frequency-shifted. In Fig. 5 the profile dependence of various quantities is presented. [FORMULA] is an important parameter, affecting significantly the disk shape and respectively the line profiles. In Fig. 5a the profiles for [FORMULA] (for instance [FORMULA], [FORMULA]); 130 ([FORMULA], [FORMULA]) and 400 (the upper limit - [FORMULA], [FORMULA]) are shown. In Fig. 5b the profile dependence on the source height [FORMULA] is shown. Increasing [FORMULA], a larger part of the central disk region is irradiated and the profiles approach those from the planar disks - the second, symmetrically displaced peak increases its intensity. We do not see any physical reason, however, to put the source far above the central object. The dependence of the profiles on the hard X-ray luminosity is also significant, because of the effect of the saturation of the lines, which limits the emission line flux at small distances (high velocities), independent of an increase of [FORMULA]. For higher [FORMULA], the lines should become narrower (Fig. 5c). One should keep in mind, however, that [FORMULA] should be [FORMULA] to match the observed line intensities. Profile shapes are almost independent of the initial disk tilt (Fig. 5d). The FWHM and the shift slightly decrease with increasing tilt. Note that the profiles are also not dependent directly on the black hole mass and the accretion rate (of course, the mass and the accretion rate may affect the incident flux at a given distance and [FORMULA] respectively).

[FIGURE] Fig. 5a-d. The profile dependence for different factors: the value of [FORMULA] - a ; the source height - b ([FORMULA] is measured in [FORMULA]); the central hard luminosity - c ([FORMULA], with [FORMULA] in [FORMULA]) and the initial tilt angle - d ([FORMULA] is in degrees). [FORMULA], [FORMULA]. Abscissa is in [FORMULA]. All profiles are normalized to the maximal value.

Weaker emission from the opposite side of the disk may appear in case the disk is not fully opaque at visual wavelengths. This might be the case for the outer regions, where the optical depth is probably not significant if no dust is present (Collin-Souffrin & Dumont 1990). Profiles should then be double-peaked and more or less symmetric. Although this case is not considered here, one can easily reproduce such profiles. A similar situation occurs when the disk is transparent to the hard radiation, which is then absorbed within the whole vertical structure of the disk.

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© European Southern Observatory (ESO) 1999

Online publication: July 16, 1999