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]

arXiv commentLateX2e, 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

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