A geometric distance measurement to the Galactic Center black hole with 0.3% uncertainty

Abstract: We present a 0.16% precise and 0.27% accurate determination of R0, the distance to the Galactic Center. Our measurement uses the star S2 on its 16-year orbit around the massive black hole Sgr A* that we followed astrometrically and spectroscopically for 27 years. Since 2017, we added near-infrared interferometry with the VLTI beam combiner GRAVITY, yielding a direct measurement of the separation vector between S2 and Sgr A* with an accuracy as good as 20 micro-arcsec in the best cases. S2 passed the pericenter of its highly eccentric orbit in May 2018, and we followed the passage with dense sampling throughout the year. Together with our spectroscopy, in the best cases with an error of 7 km/s, this yields a geometric distance estimate: R0 = 8178 +- 13(stat.) +- 22(sys.) pc. This work updates our previous publication in which we reported the first detection of the gravitational redshift in the S2 data. The redshift term is now detected with a significance level of 20 sigma with f_redshift = 1.04 +- 0.05.

• The paper achieves a groundbreaking 0.3% uncertainty in measuring the Galactic Center distance to Sgr A*.
• It combines 27 years of astrometry and spectroscopy with VLTI’s GRAVITY to achieve sub-20 μas precision.
• The findings refine Milky Way dynamics models and confirm General Relativity through observed gravitational redshift effects.

A Geometric Distance Measurement to the Galactic Center Black Hole with 0.3% Uncertainty

The paper presents a precision measurement of the distance to the Galactic Center (GC), specifically to the supermassive black hole Sagittarius A* (Sgr A*), with an uncertainty of only 0.3%. The authors employ a method combining astrometric and spectroscopic observations of the star S2, which orbits Sgr A* in a highly eccentric 16-year orbit. This study capitalizes on a long-term observation campaign that spans 27 years, integrated with data from the Very Large Telescope Interferometer (VLTI) starting in 2017 for improved astrometric precision using the GRAVITY instrument.

Key Findings

• Measurement Precision: The distance to the GC, denoted as $R_0$, is determined to be $8178 \pm 13_{\text{stat.}} \pm 22_{\text{sys.}}$ parsecs. This represents a remarkable precision, with a statistical error of 0.16% and a total systematic uncertainty of 0.27%, attributed primarily to astrometric uncertainties.
• GRAVITY Instrumentation: The use of GRAVITY enabled direct measurement of the vector separation between S2 and Sgr A*, with angular precision better than $20\,\mu \text{as}$. This instrument, by interfacing large telescopes in the infrared spectrum, overcame limitations from dust obscuration and stellar crowding near the GC.
• Gravitational Redshift and Relativity: The study also measures gravitational redshift effects with a significance of $20\sigma$, detecting it with $f_{\text{redshift}} = 1.04 \pm 0.05$, in agreement with General Relativity. This confirms relativistic predictions for the orbit of S2 near Sgr A*.

Study Implications

This level of precision in measuring $R_0$ holds significant implications for various areas of astrophysics:

1. Galaxy Dynamics: An accurately determined $R_0$ refines models of the Milky Way's dynamics, including the motion of stars and gas in the central region of the Galaxy.
2. Cosmic Calibration: Providing a solid benchmark for distance scales, this work aids calibration across the cosmic distance ladder, especially in contexts where Sgr A* orbits serve as reference points.
3. Black Hole Studies: Understanding precise distances at the Galaxy's core supports deeper insights into black hole physics, accretion processes, and the interplay with nearby stellar environments.
4. Astrometry and Instrumentation Advancements: The methodology demonstrates the utility of VLTI and similar instruments for ultra-precise astrometry, encouraging further enhancements in the field.

Future Directions

This pivotal work suggests several pathways for forthcoming research:

• Further Refinements in Astrometry: With upcoming enhancements in interferometry and telescope technology, further reduction in systematic uncertainties could be achieved.
• Synoptic Papers about Stellar Dynamics: Extending similar measurement techniques to other stars in proximity to Sgr A* could expand our knowledge on stellar populations' dynamics and star formation history near supermassive black holes.
• Cross-field Applications: The techniques refined here could be adapted for use in the study of other galaxies, facilitating precise distance measurements to their central black holes and enhancing our understanding of galactic structures across the universe.

In conclusion, this paper exemplifies how interdisciplinary coordination and technological advances can substantially contribute to high-precision measurements in astronomy, aligning observational data with theoretical predictions, and enabling enhanced models of our galaxy's structure and dynamics.