Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center

Abstract

The S-star cluster in the Galactic center allows us to study the physics close to a supermassive black hole, including distinctive dynamical tests of general relativity. Our best estimates for the mass of and the distance to Sgr A* using the three stars with the shortest period (S2, S38, and S55/S0-102) and Newtonian models are M BH = (4.15 ± 0.13 ± 0.57) × 10 6 M and R 0 = 8.19 ± 0.11 ± 0.34 kpc. Additionally, we aim at a new and practical method to investigate the relativistic orbits of stars in the gravitational field near Sgr A*. We use a first-order post-Newtonian approximation to calculate the stellar orbits with a broad range of periapse distance r p . We present a method that employs the changes in orbital elements derived from elliptical fits to different sections of the orbit. These changes are correlated with the relativistic parameter defined as Υ ≡ r s /r p (with r s being the Schwarzschild radius) and can be used to derive Υ from observational data. For S2 we find a value of Υ = 0.00088 ± 0.00080, which is consistent, within the uncertainty, with the expected value of Υ = 0.00065 derived from M BH and the orbit of S2. We argue that the derived quantity is unlikely to be dominated by perturbing influences such as noise on the derived stellar positions, field rotation, and drifts in black hole mass.

A stellar fly‐by close to the Galactic center: Can we detect stars on highly relativistic orbits?

“…One of the brightest stars, S2, has the orbital period of ∼16 years, and it was possible to take measurements of its proper motions and radial velocities along its whole orbit. Thanks to the long-term monitoring of S2 and other two stars (S38 and S55/S0-102), it was possible to put the first weak constraints on the periastron shift of S2, which so far agrees with the relativistic prediction (Parsa et al 2017). It should be noted that the first-order post-Newtonian effects can also be revealed in the orbital radial velocities when the near-infrared spectroscopic data is available.…”

“…For practical purposes, the eccentric anomaly expressed at the distance R (when the star crosses the sphere of radius R ), may be expressed as where we expressed the radius of the field of view in Schwarzschild radii and introduced the relativistic parameter Υ = r p / r s (Parsa et al ), which basically represents the term on which the post‐Newtonian corrections depend. In particular, the smaller the parameter Υ, the larger the periastron shift.…”

The Milky Way’s Supermassive Black Hole: How Good a Case Is It?

“…the object about which the stars are in orbit. This seems to be within reach even with the the currently observable stars S2, S02-1, and S38 (Boehle et al, 2016;Parsa et al, 2017).…”

“…The most recent quite consistent combined estimates of mass and distance have been obtained by Boehle et al (2016) with M = 4.0 ± 0.2 × 10 6 M ⊙ and 7.9 ± 0.2 kpc based on a combined orbital fit of S2 and S38 data, and by Parsa et al (2017) with M = 4.29 ± 0.02 × 10 6 M ⊙ and 8.25 ± 0.02 kpc based on a combined orbital fit of three stars closest to SgrA*: S2, S0-102 and S38. From Fig.5, we see that the measurements (as a function of time) started off from higher values of up to 10 kpc and have now settled to a value of about 8 kpc with total uncertainties of the order of 0.2 kpc.…”

“…While the early measurements using stellar radial velocities and proper motions all depend on modeling the volume mass density and the three dimensional distant dependency of the velocity dispersion, the more recent measurements rely on the orbital analysis of the innermost stars (predominantly S2). Using the closest stars possible, the mass estimate may now be expected to settle around a value of 4.0 million solar masses with an uncertainty of about 0.2 million solar masses (Boehle et al, 2016;Parsa et al, 2017). As mass and distance are determined simultaneously from stellar orbits, future improvements of the uncertainties must involve further improvements of the positional and spectroscopic measurement accuracy.…”