短周期S星S4711、S62、S4714和Sgr A $^\ast$自旋引起的Lense-Thirring效应
The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A$^\ast$
Lorenzo Iorio
备注：
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
最近，在Sgr A $7.6\,\mathrm{yr}\leq P_\mathrm{b}\leq 12\,\mathrm{yr}$中发现了一些围绕超大质量黑洞（SMBH）运行的短轨道周期S星（S4711，S62，S4714）。它们可以用来测量由SMBH的角动量$\boldsymbol{J}_\bullet$引起的升交点$\mathitΩ$轨道的广义相对论Lense-Thirring（LT）进动。事实上，所提出的数值估计仅在$\boldsymbol{J}_\bullet$与视线完美对齐的特定情况下才成立，但情况似乎并非如此。此外，还倾角$I$和围黑子$ω$的论点进行LT进动的任意取向的$\boldsymbol{J}_\bullet$在空间中。我们明确地显示了解析表达式的$\dot I^\mathrm{LT},\,\dot{\mathitΩ}^\mathrm{LT},\,ω^\mathrm{LT}$在SMBH的自旋极角$i^\bullet,\,\varepsilon^\bullet$通过找到的范围内的值为他们每个人在弧秒每年（$^{\prime\prime}\,\mathrm{yr}^{-1}$）。对于每一颗恒星，相应的$i^\bullet_\mathrm{max},\,\varepsilon^\bullet_\mathrm{max}$和$i^\bullet_\mathrm{min},\,\varepsilon^\bullet_\mathrm{min}$的值也被确定，连同那些抵消LT岁差的$i_0^\bullet,\,\varepsilon_0^\bullet$。由于恒星轨道参数和Sgr A $^\ast$本身的质量的当前误差，LT围日珥进动$\dotω^\mathrm{LT}$被史瓦西进动中的系统不确定性所淹没。[摘要]
英文摘要：
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]
On the Measurement of the Lense-Thirring effect Using the Nodes of the LAGEOS Satellites in reply to "On the reliability of the so-far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites" by L. Iorio
The meaning of systematic errors, a comment to "Reply to On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter", by Lorenzo Iorio
An assessment of the measurement of the Lense-Thirring effect in the Earth gravity field, in reply to: ``On the measurement of the Lense-Thirring effect using the nodes of the LAGEOS satellites, in reply to ``On the reliability of the so far performed tests for measuring the Lense-Thirring effect with the LAGEOS satellites'' by L. Iorio,'' by I. Ciufolini and E. Pavlis
Prospects of constraining the dense matter equation of state from the timing analysis of pulsars in double neutron star binaries: the cases of PSR J0737-3039A and PSR J1757-1854
Reply to ``On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter '', by Giampiero Sindoni, Claudio Paris and Paolo Ialongo
Reply to "The meaning of systematic errors, a comment to "Reply to On the Systematic Errors in the Detection of the Lense-Thirring Effect with a Mars Orbiter", by Lorenzo Iorio'', by G. Felici
Some comments on the recent results about the measurement of the Lense-Thirring effect in the gravitational field of the Earth with the LAGEOS and LAGEOS II satellites
The impact of the new CHAMP and GRACE Earth gravity models on the measurement of the general relativistic Lense--Thirring effect with the LAGEOS and LAGEOS II satellites
Lense-Thirring precession of neutron-star accretion flows: Relativistic versus classical precession
Silesian University in Opava（奥帕瓦西里西亚大学）；Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）
