We address a question whether the observed light curves of X-ray flares originating deep in galactic cores can give us independent constraints on the mass of the central supermassive black hole. To this end we study four brightest flares that have been recorded from Sagittarius A*. They all exhibit an asymmetric shape consistent with a combination of two intrinsically separate peaks that occur at a certain time-delay with respect to each other, and are characterized by their mutual flux ratio and the profile of raising/declining parts. Such asymmetric shapes arise naturally in the scenario of a temporary flash from a source orbiting near a super- massive black hole, at radius of only 10-20 gravitational radii. An interplay of relativistic effects is responsible for the modulation of the observed light curves: Doppler boosting, gravitational redshift, light focusing, and light-travel time delays. We find the flare properties to be in agreement with the simulations (our ray-tracing code sim5lib). The inferred mass for each of the flares comes out in agreement with previous estimates based on orbits of stars; the latter have been observed at radii and over time-scales two orders of magnitude larger than those typical for the X-ray flares, so the two methods are genuinely different. We test the reliability of the method by applying it to another object, namely, the Seyfert I galaxy RE J1034+396.
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