The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A${}^{\ast }$

Abstract

Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black hole (SMBH) in Sgr A${}^{\ast }$ with short orbital periods ($7.6\mathrm{yr}\le P_{\mathrm{b}}\le 12\mathrm{yr}$) 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 $\Omega$ induced by the SMBH's angular momentum ${\mathbf{J}}_{\bullet }$. In fact, the proposed numerical estimates hold only in the particular case of a perfect alignment of ${\mathbf{J}}_{\bullet }$ with the line of sight, which does not seem to be the case. Moreover, also the inclination $I$ and the argument of perinigricon $\omega$ undergo LT precessions for an arbitrary orientation of ${\mathbf{J}}_{\bullet }$ in space. We explicitly show the analytical expressions of ${\dot{I}}^{\mathrm{LT}},{\dot{\Omega }}^{\mathrm{LT}},{\omega }^{\mathrm{LT}}$ in terms of the SMBH's spin polar angles $i^{\bullet },{\epsilon }^{\bullet }$ by finding the range of values for each of them in arcseconds per year (${}^{\prime \prime }{\mathrm{yr}}^{-1}$). For each star, the corresponding values of $i_{\max }^{\bullet },{\epsilon }_{\max }^{\bullet }$ and $i_{\min }^{\bullet },{\epsilon }_{\min }^{\bullet }$ are determined as well, along with those $i_0^{\bullet },{\epsilon }_0^{\bullet }$ that cancel the LT precessions. The LT perinigricon precessions ${\dot{\omega }}^{\mathrm{LT}}$ 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${}^{\ast }$ itself. [Abridged]

LateX2e, 14 pages, 5 tables, 3 figures. Sign in front of the periastron precession corrected in Equation (4) and Equation (10). Pictures for the periastron precessions replaced in Figures (1) to (3). Table 4 for the periastron precessions corrected

References in corpus (13)

• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• An Update on Monitoring Stellar Orbits in the Galactic Center
• 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
• On the nature of the fast moving star S2 in the Galactic Center
• 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
• General Relativistic Flux Modulations from Disk Instabilities in Sagittarius A*
• On the Newtonian and Spin-induced Perturbations felt by the Stars Orbiting around the Massive Black Hole in the Galactic Center
• What Would Happen If We Were About 1 pc Away from a Supermassive Black Hole?
• Possibility of Measuring spin precession of the nearest supermassive black hole by S stars

Cited by in corpus (7)

• Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star
• 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
• Multi-scale Constraints on Scalar-Field couplings to Matter: The Geodetic and Frame-Dragging Effects
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• On the 2PN pericentre precession in the general theory of relativity and the recently discovered fast orbiting S-stars in Sgr A${}^{\ast }$
• Relativistic effects in orbital motion of the S-stars at the Galactic Center
• Revisiting Stellar Orbits and the Sgr A${}^{\ast }$ Quadrupole Moment