The Massive Black Hole


These images illustrate the orbit of the star S2. Left: NTT/VLT (red) and GRAVITY measurements (blue) of the positions of S2 from 1992 to 2021 show that the star is orbiting Sgr A* every 16 years on a Keplerian ellipse (best fit: black line). Right: Here, you can see the measured radial velocities and the best-fitting orbit.

By following the motions of individual stars we have measured the mass associated with the radio source Sgr A* – we see stars on Keplerian ellipses surrounding an object of four million times the mass of the Sun. The physics at play is extremely simple: it is Newton's law of gravity. The precision of these measurements is stunning – see the orbit of the star S2 (Gillessen et al 2009, Gillessen et al 2013, GRAVITY Collaboration 2018, 2019, 2020, 2021).


S2 is the best example of the orbits, and constrains the mass most. Overall, we can measure the mass with a precision of well below 1% (GRAVITY Collaboration 2019, 2021). Furthermore, we can locate the mass and show that its position agrees to better than 1 milliarcseond with the location of the radio source Sgr A* (Plewa et al. 2015). This measurement relies on a few SiO maser stars, which are visible both in the infrared and at radio wavelengths.

These images illustrate the differences between the radio and infrared coordinate system derived from SiO maser star observations in the Galactic Center. The radio system is centered on the black point with an uncertainty given by the gray area. The hatched area indicates the infrared system. Left: in position space. Right: in velocity space. The single-hatched region shows the values used in Gillessen et al. 2009, the double-hatched region denotes the improvement due to the distortion correction from Plewa et al. 2015.


This picture shows the positions and proper motions of the SiO maser stars in the Galactic Center.
This figure shows the 1-, 2-, and 3-σ likelihood contours for the mass of the black hole and its distance to Earth (GRAVITY Collaboration et al. 2021).





Since we can determine both the proper motion of S2 on the sky as well as its radial velocity along the line of sight, our measurements allow us to calculate both the mass of the black hole as well as the distance R0 to the Galactic Center. The GRAVITY instrument has allowed us to measure these two quantities with unprecedented precision and accuracy. By combining the precise astrometry from GRAVITY with the spectral measurements of SINFONI, we found out that the distance to the Galactic Center is 8,275 parsecs ±9 stat ±33 sys (GRAVITY Collaboration  et al. 2021). The statistical error is dominated by the uncertainty in measuring the radial velocity, while the systematic error stems from the astrometry of GRAVITY.


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