The line profiles like that of the fluorescent Fe K or Co K lines in the X-ray spectra of the active galactic nuclei (AGN) reflect characteristics of the central regions of these objects. These lines can be formed in the accretion disks around central supermassive black holes and their shapes are connected with the central black hole spin and the accretion disk inclination angle to the line-of-the-sight. If an AGN is a source of a gravitational lens system with microlensing events, one can get an additional important information about both the accretion disk parameters and gravitational lens parameters as well. Microlensing processes were observed in such gravitational lens systems, as PKS 1830-211, B0218+357, RX J1131-1231 i HE1104-1805, Q2237+0305 and we can suspect to observe there also the spectral appearances of microlensing. Here we performed the numerical simulations of the microlensed relativistic spectral line profiles formed in the AGN accretion disks. Using the inear caustic model we show that the time dependence of the profile is determined essentially by the angle between to the disk axis and the caustic. This gives us an opportunity to assess this orientation. Microlens caustics magnify some parts of the accretion disk more prominently than others. Due to the Doppler effects and differences in the rotation direction this leads to the frequency-dependent magnification which distorts the profile of a relativistic spectral line. Such deformations are variable with time due to relative motions of the source and the microlens, and they can give us possibility to obtain some additional information about the disk brightness profile and caustic orientation relatively to the disk. Here we consider the thin disk model, Schwarzschild black hole, and the linear caustic approximation as well. The numerical simulations of the relativistic emission line profiles distorted by strong gravitational microlensing effect were performed for several different orientations of the linear caustic relatively to the disk, as well as several inclinations of the disk to the line-of-the-sight. Basic presumptions for the numerical modeling were the following: (a) AGN is a source in the gravitational lens system and it its inner parts the luminescent emission lines with relativistic profiles are being emitted; (b) this line is formed in the thin accretion disk quite far away from the central black hole and can be calculated with no taking into account the relativistic effects; (c) the caustic can be considered as a linear one. We show that the relative orientation of the caustic and the disk can be determined from emission lines profiles. Our numerical simulations demonstrate that the difference between profiles corresponding to different caustic orientations appears to be more prominent during the first half of the strong microlensing event, namely, before the crossing the disk center, and this dependence is irrespective to the accretion disk brightness profile. We show that for the spectral accuracy level high enough we have a perspective to determine the caustic orientation from the observational data.
Measuring the supermassive black hole parameters with space missions
