Is It Possible to Measure the Lense–Thirring Orbital Shifts of the Short-period S Star S4716 Orbiting Sgr A*?

Abstract

The maximal values of the general relativistic Lense–Thirring (LT) orbital shifts ΔI LT, ΔΩLT, and Δω LT of the inclination I, the longitude of the ascending node Ω, and the perinigricon ω, respectively, of the recently discovered star S4716, which has the shortest orbital period of all the S stars that orbit the supermassive black hole (SMBH) in Sgr A*, are of the order of ≃5–16 arcseconds per revolution . Given the current error σ ω = 0.°02 in determining ω, which is the most accurate orbital parameter of S4716 among all those affected by the SMBH's gravitomagnetic field through its angular momentum J •, about 48 yr would be needed to reduce σ ω to ≃10% of the cumulative LT perinigricon shift over the same time span. Measuring ΔI LT and ΔΩLT to the same level of accuracy would take much longer. Instead, after just 16 yr, a percent measurement of the larger gravitoelectric (GE) Schwarzschild-like perinigricon shift Δω GE, which depends only on the SMBH's mass M •, would be possible. On the other hand, the uncertainties in the physical and orbital parameters entering Δω GE would cause a huge systematic bias of Δω LT itself. The SMBH's quadrupole mass moment induces orbital shifts as little as ≃0.01–0.05″ rev−1.