Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole

Article
Report number	arXiv:2004.07187
Title	Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
Author(s)	Abuter, R. (European Southern Observ.) ; Amorim, A. (Lisbon U. ; Lisbon, CENTRA) ; Bauböck, M. (Garching, Max Planck Inst., MPE) ; Berger, J.P. (IPAG ; European Southern Observ.) ; Bonnet, H. (European Southern Observ.) ; Brandner, W. (Heidelberg, Max Planck Inst. Astron.) ; Cardoso, V. (Lisbon, CENTRA ; CERN) ; Clénet, Y. (LESIA, Meudon) ; de Zeeuw, P.T. (Leiden Observ. ; Garching, Max Planck Inst., MPE) ; Dexter, J. (Colorado U. ; JILA, Boulder ; Garching, Max Planck Inst., MPE) ; Eckart, A. (Cologne U. ; Bonn, Max Planck Inst., Radioastron.) ; Eisenhauer, F. (Garching, Max Planck Inst., MPE) ; Förster Schreiber, N.M. (Garching, Max Planck Inst., MPE) ; Garcia, P. (Porto U. ; Lisbon, CENTRA) ; Gao, F. (Garching, Max Planck Inst., MPE) ; Gendron, E. (LESIA, Meudon) ; Genzel, R. (Garching, Max Planck Inst., MPE ; UC, Berkeley) ; Gillessen, S. (Garching, Max Planck Inst., MPE) ; Habibi, M. (Garching, Max Planck Inst., MPE) ; Haubois, X. (European Southern Obs., Chile) ; Henning, T. (Heidelberg, Max Planck Inst. Astron.) ; Hippler, S. (Heidelberg, Max Planck Inst. Astron.) ; Horrobin, M. (Cologne U.) ; Jiménez-Rosales, A. (Garching, Max Planck Inst., MPE) ; Jochum, L. (European Southern Obs., Chile) ; Jocou, L. (IPAG) ; Kaufer, A. (European Southern Obs., Chile) ; Kervella, P. (LESIA, Meudon) ; Lacour, S. (LESIA, Meudon) ; Lapeyrère, V. (LESIA, Meudon) ; Le Bouquin, J.B. (IPAG) ; Léna, P. (LESIA, Meudon) ; Nowak, M. (Cambridge U., Inst. of Astron. ; LESIA, Meudon) ; Ott, T. (Garching, Max Planck Inst., MPE) ; Paumard, T. (LESIA, Meudon) ; Perraut, K. (IPAG) ; Perrin, G. (LESIA, Meudon) ; Pfuhl, O. (European Southern Observ. ; Garching, Max Planck Inst., MPE) ; Rodríguez-Coira, G. (LESIA, Meudon) ; Shangguan, J. (Garching, Max Planck Inst., MPE) ; Scheithauer, S. (Heidelberg, Max Planck Inst. Astron.) ; Stadler, J. (Garching, Max Planck Inst., MPE) ; Straub, O. (Garching, Max Planck Inst., MPE) ; Straubmeier, C. (Cologne U.) ; Sturm, E. (Garching, Max Planck Inst., MPE) ; Tacconi, L.J. (Garching, Max Planck Inst., MPE) ; Vincent, F. (LESIA, Meudon) ; von Fellenberg, S. (Garching, Max Planck Inst., MPE) ; Waisberg, I. (Weizmann Inst. ; Garching, Max Planck Inst., MPE) ; Widmann, F. (Garching, Max Planck Inst., MPE) ; Wieprecht, E. (Garching, Max Planck Inst., MPE) ; Wiezorrek, E. (Garching, Max Planck Inst., MPE) ; Woillez, J. (European Southern Observ.) ; Yazici, S. (Garching, Max Planck Inst., MPE ; Cologne U.) ; Zins, G. (European Southern Obs., Chile)
Publication	2020-04-01
Imprint	2020-04-15
Number of pages	14
Note	accepted to A&A
In:	Astron. Astrophys. 636 (2020) L5
DOI	10.1051/0004-6361/202037813 (publication)
Subject category	gr-qc ; General Relativity and Cosmology ; astro-ph.IM ; Astrophysics and Astronomy ; astro-ph.GA ; Astrophysics and Astronomy
Accelerator/Facility, Experiment	GRAVITY
Abstract	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.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2020-2024 GRAVITY Collaboration (License: CC-BY-4.0)

$Summary of the observational results of monitoring the S2-Sgr~A* orbit from 1992 to the end of 2019. Left: SHARP, NACO (black points), and GRAVITY (blue points) astrometric positions of the star S2, along with the best-fitting GR orbit (grey line). The orbit does not close as a result of the SP. The mass centre is at (0,0), marked by the cross. All NACO and SHARP points were corrected for a zero-point offset and drift in RA and Dec. The red data points mark the positions of the infrared emission from Sgr~A* during bright states, where the separation of S2 and Sgr~A* can be directly inferred from differential imaging. Right: RA (top) and Dec (middle) offset of S2 (black and blue) and of the infrared emission from Sgr~A* (red) relative to the position of Sgr~A* (assumed to be identical with the mass centre). Grey is the best-fitting GR-orbit including the R{\o}mer effect (finite speed of light), SRT, and GR to PPN1. We assumed $f_\mathrm{RS}=1$ and fitted for $f_\mathrm{SP}$. Bottom right: Same for the line-of-sight velocity of the star.$ $Posterior analysis of all data by fitting for $f_\mathrm{SP}$ simultaneously with all other parameters. As in Figure~\ref{fig:figB2}, the bottom panels show the residuals in RA (left) and Dec (right) between the data and the best-fitting GR (thick red curve, $f_\mathrm{SP} =1.1$), relative to the same orbit for $f_\mathrm{SP}=0$ (Newton, plus R{\o}mer effect, plus SRT, plus RS). Grey crosses denote individual NACO or SINFONI data, cyan filled black circles show averaged GRAVITY data, and grey rectangles denote averages of the NACO data. The top right panel shows the same for $\delta \varphi$, and the top left panel for $\delta vz$. Blue filled black circles are averages of the SINFONI residuals, with all residuals shown as grey crosses. The best fit (red curve) including the flare data (Figure~\ref{fig:fig1}) has $f_\mathrm{SP}=1.1$, with a $1\sigma$ uncertainty of $0.19$. The overall reduced $\chi^2_r$ of this fit is $1.5$.$ $As Figure~\ref{fig:fig2}, but now zooming into the critical 2018 pericentre residuals (best-fit $f_\mathrm{SP}=1.1$ minus $f_\mathrm{SP}=0$, with all other parameters fixed). In the bottom two and the top right panels, blue filled, open black circles (with $1\sigma$ uncertainties) are averages of GRAVITY data. The grey bar on the left denotes the constraints obtained from NACO imagery of S2 and Sgr~A* flares on the location of the apocentre value (2010.35). Averages (and $1\sigma$ uncertainties) of the radial velocity residuals from SINFONI are open black, blue filled circles (top left). The residuals of the best-fitting $f_\mathrm{SP}=1.1$ minus $f_\mathrm{SP}=0$ curves are plotted in red.$ Show more plots

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