Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole

Abstract: The highly elliptical, 16-year-period orbit of the star S2 around the massive black hole candidate Sgr A* is a sensitive probe of the gravitational field in the Galactic centre. Near pericentre at 120 AU, ~1400 Schwarzschild radii, the star has an orbital speed of ~7650 km/s, such that the first-order effects of Special and General Relativity have now become detectable with current capabilities. Over the past 26 years, we have monitored the radial velocity and motion on the sky of S2, mainly with the SINFONI and NACO adaptive optics instruments on the ESO Very Large Telescope, and since 2016 and leading up to the pericentre approach in May 2018, with the four-telescope interferometric beam-combiner instrument GRAVITY. From data up to and including pericentre, we robustly detect the combined gravitational redshift and relativistic transverse Doppler effect for S2 of z ~ 200 km/s / c with different statistical analysis methods. When parameterising the post-Newtonian contribution from these effects by a factor f, with f = 0 and f = 1 corresponding to the Newtonian and general relativistic limits, respectively, we find from posterior fitting with different weighting schemes f = 0.90 +/- 0.09 (stat) +- 0.15 (sys). The S2 data are inconsistent with pure Newtonian dynamics.

• The paper detects gravitational redshift and Doppler effects in S2's orbit, revealing a combined redshift of approximately 200 km/s.
• The study uses 26 years of observations from VLT instruments, achieving a precision of 30 μas and enabling daily tracking of S2's motion.
• The orbital analysis via a Markov Chain Monte Carlo framework provides a robust ~10σ support for General Relativity near Sagittarius A*.

Analyzing the Detection of Gravitational Redshift in the Orbit of S2 Near the Galactic Center's Massive Black Hole

The paper presented by the GRAVITY Collaboration, entitled "Detection of the Gravitational Redshift in the Orbit of the Star S2 Near the Galactic Centre Massive Black Hole," provides a robust empirical analysis of the relativistic effects observed in the orbit of the star S2 around Sagittarius A* (SgrA*), the supermassive black hole at the center of the Milky Way. This study leverages 26 years of observational data and focuses on detecting first-order relativistic effects, specifically the gravitational redshift and transverse Doppler effect, as predicted by General Relativity (GR).

Summary of Key Findings

The highly elliptical 16-year orbital period of S2 around SgrA* offers a unique opportunity to probe the gravitational field's strength. Observations were primarily conducted using the ESO Very Large Telescope, featuring adaptive optics instruments SINFONI and NACO, and later the interferometric instrument GRAVITY.

Results and Analysis:

• Detection of Gravitational Redshift & Doppler Effect: The study demonstrates a combined redshift effect of approximately 200 km/s, computed using various statistical methods. When expressed in post-Newtonian terms, the parameter $f$, which defines the contribution of relativistic effects relative to Newtonian physics, was found to be $f = 0.90 \pm 0.09$ (statistical) ± $0.15$ (systematic). These results significantly deviate from Newtonian predictions, providing robust support for the detection of GR effects.
• Precision of Measurements: GRAVITY's high-resolution data improved the observational precision to as fine as 30 micro-arcseconds (μas), a significant enhancement over past measurements. This allowed daily detection of S2's motion instead of the monthly tracking previously achievable.
• Posterior Analysis and Parameters: Inclusion of the S2-SgrA* orbital data into a Markov Chain Monte Carlo framework affirmed the preference for GR over Newtonian physics with considerable statistical significance ($\sim 10\sigma$ level). The modeling also accounted for systemic errors predominant in different measurement techniques, notably NACO's correlation errors.
• Implications for Stellar Dynamics and Black Hole Studies: The results provide a comprehensive test of GR at high masses, adding significant empirical backing within this regime. Furthermore, the GRAVITY instrument's continued applicability enhances prospects for detecting future gravitational effects, such as Schwarzschild precession and potentially even Lense-Thirring precession, as the observational campaign proceeds and more data accumulate post-pericenter.

Theoretical and Practical Implications

The foundational knowledge bestowed by this observational study secures further confidence in GR's validity in strong gravitational fields, such as those surrounding supermassive black holes. This improves our theoretical understanding and informs models of stellar dynamics near massive black holes, influencing both theoretical astrophysics and cosmology.

In practical terms, the paper's methodologies illustrate the potent capabilities of current instruments like the VLT and GRAVITY in testing relativistic physics and pave the way for innovating adaptive optics and interferometry methodologies.

Future Outlooks and Considerations

Future work focusing on the GRAVITY Collaboration's long-term observational campaign around the Galactic Center could further enhance these findings, potentially detecting secondary relativistic phenomena like Schwarzschild and Lense-Thirring precessions. There is an intriguing opportunity here for observing stars even closer to Sagittarius A*, which could provide new insights into the spacetime properties of the vicinity around a supermassive black hole.

As these methodologies refine and data precision improves, the astrophysics community may witness nuanced tests of GR with a level of precision unconceived a few decades ago, fostering opportunities for novel discoveries in this critical area of fundamental physics.