Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
GRAVITY Collaboration, R. Abuter, A. Amorim, M. Bauboeck, J. P. Berger, H. Bonnet, W. Brandner, V. Cardoso, Y. Clenet, P. T. de Zeeuw, J. Dexter, A. Eckart, F. … 展开作者
GRAVITY Collaboration, R. Abuter, A. Amorim, M. Bauboeck, J. P. Berger, H. Bonnet, W. Brandner, V. Cardoso, Y. Clenet, P. T. de Zeeuw, J. Dexter, A. Eckart, F. Eisenhauer, N. M. Foerster Schreiber, P. Garcia, F. Gao, E. Gendron, R. Genzel, S. Gillessen, M. Habibi, X. Haubois, T. Henning, S. Hippler, M. Horrobin, A. Jimenez-Rosales, L. Jochum, L. Jocou, A. Kaufer, P. Kervella, S. Lacour, V. Lapeyrere, J. -B. Le Bouquin, P. Lena, M. Nowak, T. Ott, T. Paumard, K. Perraut, G. Perrin, O. Pfuhl, G. Rodriguez-Coira, J. Shangguan, S. Scheithauer, J. Stadler, O. Straub, C. Straubmeier, E. Sturm, L. J. Tacconi, F. Vincent, S. von Fellenberg, I. Waisberg, F. Widmann, E. Wieprecht, E. Wiezorrek, J. Woillez, S. Yazici, G. Zins
The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole (candidate). Over the last 2.7 decades we have monitored the star's radial velocity and motion on the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on the ESO VLT, and since 2017, with the four-telescope interferometric beam combiner instrument GRAVITY. In this paper we report the first detection of the General Relativity (GR) Schwarzschild Precession (SP) in S2's orbit. Owing to its highly elliptical orbit (e = 0.88), S2's SP is mainly a kink between the pre-and post-pericentre directions of motion ~ +- 1 year around pericentre passage, relative to the corresponding Kepler orbit. The superb 2017-2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction. The incoming direction is anchored by 118 NACO-AO measurements of S2's position in the infrared reference frame, with an additional 75 direct measurements of the S2-Sgr A* separation during bright states ('flares') of Sgr A*. Our 14-parameter model fits for the distance, central mass, the position and motion of the reference frame of the AO astrometry relative to the mass, the six parameters of the orbit, as well as a dimensionless parameter f_SP for the SP (f_SP = 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2, del phi = 12' per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find f_SP = 1.10 +- 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2's orbit cannot exceed ~ 0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000 M_sun.
Universitat Politècnica de València（瓦伦西亚理工大学）；Max Planck Institute for Extraterrestrial Physics（马克斯·普朗克地外物理研究所）；Kavli Institute for Astronomy and Astrophysics at Peking University（北京大学科维理天文与天体物理研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；University of California, Berkeley（加州大学伯克利分校）；Technical University of Munich（慕尼黑工业大学）
Schwarzschild dynamical model of the Fornax dwarf spheroidal galaxy
我们提出了一个完整的动力学模型的天炉座矮球状星系获得的球对称史瓦西轨道叠加方法适用于目前最大的运动学数据集。我们用随半径变化的质光比$Υ$模拟了矮星的总质量含量，发现天炉座很有可能嵌在一个巨大的和扩展的暗物质晕中。我们估计1个$\,$ kpc中包含的总质量为$M(<1\,$ kpc $)=1.25^{+0.06}_{-0.13} \times 10^8\,$ M $_{\odot}$。仅在3 $σ$水平，数据与恒定质光比一致，即质随光模型，但仍需要高值的$Υ\approx 11.2\,$ M $_{\odot}/$ L $_{\odot}$。我们的结果与以前估计的天炉座的动态质量分布基本一致。由于史瓦西方法不需要对恒星的轨道各向异性进行任何假设，因此我们获得了各向异性参数$β$的分布作为我们建模的输出。导出的各向异性接近于零的中心的星系和半径减小，但保持一致的各向同性轨道在所有半径在1 $σ$置信水平。
