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arXiv · 2009.01158

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

Lorenzo Iorio
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Abstract

Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black hole (SMBH) in Sgr A$^\ast$ with short orbital periods ($7.6\,\mathrm{yr}\leq P_\mathrm{b}\leq 12\,\mathrm{yr}$) 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 $\mathitΩ$ induced by the SMBH's angular momentum $\boldsymbol{J}_\bullet$. In fact, the proposed numerical estimates hold only in the particular case of a perfect alignment of $\boldsymbol{J}_\bullet$ with the line of sight, which does not seem to be the case. Moreover, also the inclination $I$ and the argument of perinigricon $ω$ undergo LT precessions for an arbitrary orientation of $\boldsymbol{J}_\bullet$ in space. We explicitly show the analytical expressions of $\dot I^\mathrm{LT},\,\dot{\mathitΩ}^\mathrm{LT},\,ω^\mathrm{LT}$ in terms of the SMBH's spin polar angles $i^\bullet,\,\varepsilon^\bullet$ 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 $i^\bullet_\mathrm{max},\,\varepsilon^\bullet_\mathrm{max}$ and $i^\bullet_\mathrm{min},\,\varepsilon^\bullet_\mathrm{min}$ are determined as well, along with those $i_0^\bullet,\,\varepsilon_0^\bullet$ that cancel the LT precessions. The LT perinigricon precessions $\dotω^\mathrm{LT}$ 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]

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Lorenzo Iorio. 2022-12-14. The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A$^\ast$. https://doi.org/10.3847/1538-4357%2Fabbfb5

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