We study the variability mechanism of active galactic nuclei (AGN) within the framework of the flare model. To this end we examine the case of Seyfert/LINER galaxy NGC 4258, which is observed at high inclination angle and exhibits rapid fluctuations
of the X-ray light curve. We construct a model light curve based on the assumption of magnetic flares localized in the equatorial plane and orbiting with Keplerian speed at each given radius. We calculate the level of variability as a function of the inclination of an observer, taking into account all effects of general relativity near a rotating supermassive black hole. The variability level is a monotonic function of the source inclination. It rises more rapidly for larger values of the black hole spin (Kerr parameter) and for steeper emissivity (index beta of the radial profile). We compare the expected level of variability for the viewing angle 81.6 deg, as inferred for NGC 4258, with the case of moderate viewing angles about 30 deg, typical for Seyfert type-1 galaxies. Highly inclined sources such as this one are particularly suitable to test the flare model because the effects of orbital motion, Doppler boosting and light bending are all expected to have maximum when the accretion disk is seen almost edge-on. The model is consistent with the NGC 4258 variability, where the obscuring material is thought to be localized mainly towards the equatorial plane rather than forming a geometrically thick torus. Once the intrinsic time-scales of the flare duration are determined to better precision, this kind of highly inclined objects with a precisely known mass of the black hole can be used to set independent constraints on the spin parameter.
Episodically accreting black holes are thought to produce flares when a chunk of particles is accelerated to high velocity near the black hole horizon. This also seems to be the case of Sagittarius A* in the Galactic Center, where the broad-band radi
ation is produced, likely via the synchrotron self-Compton mechanism. It has been proposed that strong-field gravitational lensing magnifies the flares. The effect of lensing is generally weak and requires a fine-tuned geometrical arrangement, which occurs with only a low probability. However, there are several aspects that make Sagittarius A* a promising target to reveal strong gravity effects. Unlike type II (obscured) active galaxies, chances are that a flare is detected at high inclination, which would be favourable for lensing. Time delays can then significantly influence the observed flare duration and the form of light-curve profiles. Here we discuss an idea that the impact of lensing amplification should be considerably enhanced when the shape of the flaring clump is appropriately elongated in the form of a spiral wave or a narrow filament, rather than a simple (circular) spot which we employed previously within the phenomenological `orbiting spot model. By parameterizing the emission region in terms of the spiral shape and contrast, we are able to extend the spot model to more complicated sources. In the case of spirals, we notice a possibility that more photons reach a distant observer at the same moment because of interplay between lensing and light-travel time. The effect is not symmetrical with respect to leading versus trailing spirals, so in principle the source geometry can be constrained. In spite of this, the spot model seems to provide entirely adequate framework to study the currently available data.
