The Short-period S-stars S4711, S62, S4714 and the Lense–Thirring Effect due to the Spin of Sgr A*

Abstract

Abstract Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black hole (SMBH) in Sgr A* with short orbital periods (7.6 yr ≤ P b ≤ 12 yr) were discovered. It was suggested that they may be used to measure the general relativistic Lense–Thirring (LT) precessions of their longitudes of ascending node Ω induced by the SMBH's angular momentum J •. In fact, the proposed numerical estimates hold only in the particular case of a perfect alignment of J • with the line of sight, which does not seem to be the case. Moreover, the inclination I and the argument of perinigricon ω also undergo LT precessions for an arbitrary orientation of J • in space. We explicitly show the analytical expressions of in terms of the SMBH's spin polar angles i •, ε •. It turns out that the LT precessions, in arcseconds per year , range within , , and for S4714, , , and for S62, and , , and for S4711. For each star, the corresponding values of , and are determined as well, along with those that cancel the LT precessions. The LT perinigricon precessions are overwhelmed by the systematic uncertainties in the Schwarzschild ones due to the current errors in the stars’ orbital parameters and the mass of Sgr A* itself.