2020ApJ...904..186I

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 {dot}I^LT,{dot}Ω^LT,ω^LT in terms of the SMBH's spin polar angles i^*, ε^*. It turns out that the LT precessions, in arcseconds per year (^′′ yr^–1), range within {dot}I^LT|≲7^′′^yr-1^, |{dot}Ω^LT|≲9^′′^yr-1^, and -13^′′^yr-1^≲{dot}ω^LT≲14^′′^yr-1^ for S4714, |{dot}I^LT|≲5^′′^yr-1^, |{dot}Ω^LT|≲5^′′^yr-1^, and {dot}ω^LT|≲10^′′^yr-1^ for S62, and |{dot}I^LT|≲0.3^′′^yr-1^, |{dot}Ω^LT|≲0.3^′′^yr-1^, and |{dot}ω^LT|≲0.7^′′^yr-1^ for S4711. For each star, the corresponding values of i_{max}^•, ε_{max}^• , and i_{min}^• ,ε_{min}^•^ are determined as well, along with those i₀•,ε₀^• that cancel the LT precessions. The LT perinigricon precessions {dot}ω^LT 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.