论文标题
短期S-Stars S4711，S62，S4714和由于Sgr a $^\ ast $的旋转而导致的透镜效应
The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A$^\ast$
论文作者
论文摘要
最近，一些S-Star（S4711，S62，S4714）在sgr a $^\ ast $中绕具有短轨道时期的$^\ ast $运行（$ 7.6 \，\ Mathrm {yrm {yr} \ leq p_ p_ \ leq p_ \ mathrm {b} b} \ leq 12 \ \ nre有人建议它们可以用来测量其上升节点的纵向$ \mathitΩ$ the SMBH的角动量$ \ boldsymbol {j} _ \ bullet $引起的一般相对论透镜（LT）预读。实际上，所提出的数值估计仅在特定情况下与$ \ boldsymbol {j} _ \ bullet $与视线的完美对齐情况下，这似乎并非如此。此外，倾斜度$ i $和Perinigricon $ω$的参数进行了LT预呼吸，以在太空中的$ \ boldsymbol {J} _ \ bullet $的任意方向。我们明确显示了$ \ dot i^\ mathrm {lt}，\，\ dot {\mathitΩ}^\ mathrm {lt}，\，\，ω^\ mathrm {lt} $的分析表达对于每个人，每年都有每年的弧度（$^{\ prime \ prime} \，\ mathrm {yr}^{ - 1} $）。对于每个恒星，$ i^\ bullet_ \ mathrm {max}，\，\，\ varepsilon^\ bullet_ \ mathrm {max} $和$ i^\ buleart_ \ mathrm {minrm {min}，\，\ varepsilon^varepsilon^\ buleast_ \ mathrm} $ i_0^\ bullet，\，\ varepsilon_0^\ bullet $取消LT预络。 lt Perinigricon预读$ \dotΩ^\ mathrm {lt} $由于恒星轨道参数的当前错误和sgr a $^\ ast $本身的质量而被Schwarzschild的系统不确定性所淹没。 [简略]
Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black hole (SMBH) in Sgr A$^\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]
