Is it possible to measure the Lense-Thirring orbital shifts of the short-period S-star S4716 orbiting Sgr A${}^{\ast }$?

Abstract

The maximal values of the general relativistic Lense-Thirring (LT) orbital shifts $\Delta I^{\mathrm{LT}},\Delta {\Omega }^{\mathrm{LT}}$ and $\Delta {\omega }^{\mathrm{LT}}$ of the inclination $I$, the longitude of the ascending node $\Omega$ and the perinigricon $\omega$ of the recently discovered star S4716, which has the shortest orbital period $\left(P_{\mathrm{b}}=4.02\mathrm{yr}\right)$ of all the S-stars that orbit the supermassive black hole (SMBH) in Sgr A${}^{\ast }$, are of the order of $\simeq 5-16$ arcseconds per revolution $\left({}^{\prime \prime }{\mathrm{rev}}^{-1}\right)$. Given the current error ${\sigma }_{\omega }=0.02^{\circ }$ in determining $\omega$, which is the most accurate orbital parameter of S4716 among all those affected by the SMBH's gravitomagnetic field through its angular momentum ${\mathbf{J}}_{\bullet }$, about 48 yr would be needed to reduce ${\sigma }_{\omega }$ to $\simeq 10\%$ of the cumulative LT perinigricon shift over the same time span. Measuring $\Delta I^{\mathrm{LT}}$ and $\Delta {\Omega }^{\mathrm{LT}}$ to the same level of accuracy would take even much longer. Instead, after just 16 yr, a per cent measurement of the larger gravitoelectric (GE) Schwarzschild-like perinigricon shift $\Delta {\omega }^{\mathrm{GE}}$, which depends only on the SMBH's mass $M_{\bullet }$, would be possible. On the other hand, the uncertainties in the physical and orbital parameters entering $\Delta {\omega }^{\mathrm{GE}}$ would cause a huge systematic bias of $\Delta {\omega }^{\mathrm{LT}}$ itself. The SMBH's quadrupole mass moment $Q_2^{\bullet }$ induces orbital shifts as little as $\simeq 0.01-0.05{}^{\prime \prime }{\mathrm{rev}}^{-1}$.

LaTex2e, 13 pages, 4 tables, 1 figure. Accepted for publication in The Astrophysical Journal

References in corpus (12)

• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Testing the general relativistic ''no-hair'' theorems using the galactic center black hole SgrA*
• Periapsis and gravitomagnetic precessions of stellar orbits in Kerr and Kerr-de Sitter black hole spacetimes
• S62 and S4711: Indications of a population of faint fast moving stars inside the S2 orbit -- S4711 on a 7.6 year orbit around Sgr~A*
• An upper limit on the spin of SgrA${}^{\ast }$ based on stellar orbits in its vicinity
• On post-Newtonian orbits and the Galactic-center stars
• On the orientation of the Sagittarius A* system
• Kinematic Structure of the Galactic Center S-cluster
• Observation of S4716 -- a Star with a 4 yr Orbit around Sgr A*
• On the Newtonian and Spin-induced Perturbations felt by the Stars Orbiting around the Massive Black Hole in the Galactic Center
• Possibility of Measuring spin precession of the nearest supermassive black hole by S stars
• Revisiting Stellar Orbits and the Sgr A${}^{\ast }$ Quadrupole Moment

Cited by in corpus (2)

• On the parameters of the spherically symmetric parametrized Rezzolla-Zhidenko spacetime through solar system tests, orbit of S2 star about Sgr A${}^{\star }$, and quasiperiodic oscillations
• Candidate Young Stellar Objects in the S-cluster: The Kinematic Analysis of a Sub-population of the Low-mass G-objects close to Sgr A*