Probing the spin of the central black hole in the galactic centre with secondary images

Abstract

This paper explores the possibility of determining the spin of the supermassive black hole (SMBH) in Sgr A*, by using secondary images of stars orbiting the SMBH. The photons propagate close to the SMBH and their trajectories probe the space time in a region where the spin of the SMBH is important. We find the appearance of spikes in the secondary image, which depends on the angular momentum and spin axis of the SMBH and study the specific case of the star S2 in detail. The spikes has a magnitude of $\sim 29$ in the K-band and the required angular resolution is of order 15-20 $\mu$as. The combination of these two requirements poses an extreme observational challenge, but might be possible with interferometric observations in the sub-mm regime. The next possible time frame for observing this effect on the star S2 is in the late 2017 and then it repeats with the period of the star.