The massive black hole

 

<p><em>The orbit of the star S2. Left: NTT/VLT (blue) and Keck measurements (red) of the positions of S2 from 1992 to 2016 show that the star is orbiting Sgr A* every 16 years on a Keplerian ellipse (best fit: black line). Right: The measured radial velocities and the best-fitting orbit.</em></p> Zoom Image

The orbit of the star S2. Left: NTT/VLT (blue) and Keck measurements (red) of the positions of S2 from 1992 to 2016 show that the star is orbiting Sgr A* every 16 years on a Keplerian ellipse (best fit: black line). Right: The measured radial velocities and the best-fitting orbit.

 By following the motions of individual stars we have measured the mass associated with radio source Sgr A* - we see stars on Keplerian ellipses surrounding an object of 4 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)

 

S2 is the best example of the orbits, and constraints the mass most. Overall, we can measure the mass with a precision of around 1%. Furthermore, we can locate the mass and show that its position agrees to better than 1mas with where the radio source Sgr A* is located (Plewa et al. 2015). This measurement uses a few SiO maser stars, which are visible both in the infrared, and at radio wavelengths.

<p><em>The positions and motions of the SiO maser stars in the Galactic Center.</em></p> Zoom Image

The positions and motions of the SiO maser stars in the Galactic Center.

<em>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 areas. The hatched areas indicate infrared system. Left: in position space. Right: in velocity space. The single-hatched regions are the values used in Gillessen et al. 2009, the double-hatched region denotes the improvement due to the recent distortion correction achieved in Plewa et al. 2015</em>. Zoom Image
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 areas. The hatched areas indicate infrared system. Left: in position space. Right: in velocity space. The single-hatched regions are the values used in Gillessen et al. 2009, the double-hatched region denotes the improvement due to the recent distortion correction achieved in Plewa et al. 2015.

<p><em>Mass of and distance to Sgr A* from the orbit of S2. The plot shows a projection of a Markov chain into the mass-distance plane, indicating the 1, 2, and 3-sigma uncertainties.</em></p> Zoom Image

Mass of and distance to Sgr A* from the orbit of S2. The plot shows a projection of a Markov chain into the mass-distance plane, indicating the 1, 2, and 3-sigma uncertainties.

Since we measure proper motions (angle on sky per time) and radial velocity (km/s) for the stars, we actually can constrain geometrically the distance R0 to the Galactic Center. The following figure shows that we reach a precision of few percent (Gillessen et al. 2013).

 
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