Possibility of measuring spin precession of the nearest supermassive black hole by using S stars

The supermassive black hole(SMBH) with a mass of 4 million M inside the radio source Sgr A* in our Galactic center is the nearest SMBH. Once S stars with a shorter period are observed, relativistic precessions especially the Lense-Thirring effect can be measured by astronomical observations at the 10 μas level in the future.An interesting but so far unaddressed problem is that the SMBH not only has spin but also spin precession like similar objects. We study the effect of such spin precession on the orbital precessions of orbiting stars. Our results show that the spin precession can produce a periodic oscillation in the precession of the star’s orbital plane, but has no obvious effect on the periapse shift. For stars with an orbital period of O(0.1) yr or less, such visible oscillations occur when the SMBH’s spin-precession period ranges from about a few tens of years to hundreds of years. The period of oscillation is the same as the one of the spin precession. In principle, the precession of this oscillating orbital plane can be observed and then the spin and spin precession of the nearest SMBH can be determined.