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

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.

• The paper confirms Schwarzschild Precession in S2's orbit, measuring a 12' precession angle that aligns closely with General Relativity predictions.
• The study utilizes 54 high-precision GRAVITY measurements along with adaptive optics and spectroscopy to robustly delineate S2's orbital dynamics.
• The paper constrains extended mass within S2's orbit to about 0.1% of Sgr A*'s mass, tightening limits on dark matter and alternative mass distribution models.

Detection of Schwarzschild Precession in the Orbit of Star S2

The paper by the GRAVITY Collaboration presents a significant observational confirmation of a key relativistic effect in the orbit of the star S2, orbiting the massive black hole candidate at the Galactic center, Sagittarius A* (Sgr A*). The research elucidates the Schwarzschild Precession (SP) of S2, a critical prediction of General Relativity (GR), which had hitherto remained unobserved in this context.

Summary of Findings

S2 follows an elliptical trajectory around Sgr A*, characterized by a high eccentricity (e=0.88). Over nearly three decades, the star's motion has been meticulously monitored, which, when combined with high-precision instruments like the GRAVITY beam combiner on the ESO VLT, has enabled the detection of General Relativity effects.

• Schwarzschild Precession Detection: The measurement of SP in S2's orbit provides compelling consistency with GR. The observed precession amounts to approximately 12' per orbital period, with a dimensionless fitting parameter $f_\mathrm{SP} = 1.10 \pm 0.19$, signifying close alignment with GR (where $f_\mathrm{SP} = 1$).
• Precision Measurements: The combination of GRAVITY's unprecedented astrometric precision and extensive historical data allows for the robust delineation of SP. Key contributors include 54 GRAVITY measurements achieving a root mean square (RMS) uncertainty of about 65 µas, along with adaptive optics and spectroscopy measurements to establish a coherent orbital model.
• Consistency with Extended Mass Constraints: The data rules out significant extended mass within S2's orbit, with upper limits on such a mass at around 0.1% of the central mass. This implies stringent constraints on potential mass distribution models around the Galactic center’s massive black hole.

Implications and Future Prospects

The implications of this study are multifaceted, impacting both practical astronomical methodologies and our broader understanding of GR in strong-field regimes.

• Validation of GR in a New Regime: Observationally confirming SP in the highly curved spacetime near a massive black hole presents GR's applicability in environments vastly different from those previously tested, such as the solar system or binary pulsars.
• Constraints on Theoretical Models: This work limits allowable deviations from GR within the central parsec of the Milky Way. The findings bear on models of dark matter distribution, potential intermediate black holes, and the stellar content within the inner regions.
• Instrumentation and Methodology: The success of this observation underscores the continuing importance of advancements in high-precision astrometry and interferometry. Instruments of comparable or superior sensitivity will be pivotal for probing gravitational effects in even more extreme environments, such as around near-star entities or other galactic nuclei.

In conclusion, the detection of Schwarzschild Precession in S2 enriches the catalog of empirical tests supporting GR. As astrometric and interferometric techniques progress, further elucidation of stellar dynamics around massive black holes will likely provide additional insights into both the nature of gravitation and the characteristics of supermassive black holes themselves.