# 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 {sub BH} = (4.15 ± 0.13 ± 0.57) × 10{sup 6} M {sub ⊙} and R {sub 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 {sub 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 {sub s} / r {sub p} (with r {sub 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, withinmore »

- Authors:

- I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln (Germany)
- Astronomical Institute, Academy of Science, Boční II 1401, CZ-14131 Prague (Czech Republic)
- Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn (Germany)

- Publication Date:

- OSTI Identifier:
- 22663278

- Resource Type:
- Journal Article

- Journal Name:
- Astrophysical Journal

- Additional Journal Information:
- Journal Volume: 845; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0004-637X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; BLACK HOLES; GALAXIES; GALAXY NUCLEI; GENERAL RELATIVITY THEORY; GRAVITATIONAL FIELDS; MASS; ORBITS; RELATIVISTIC RANGE; ROTATION; SCHWARZSCHILD RADIUS; STAR CLUSTERS; STARS; SUPERMASSIVE STARS

### Citation Formats

```
Parsa, M., Eckart, A., Shahzamanian, B., Zajaček, M., Straubmeier, C., Karas, V., and Zensus, J. A., E-mail: parsa@ph1.uni-koeln.de.
```*Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA7BF0.

```
Parsa, M., Eckart, A., Shahzamanian, B., Zajaček, M., Straubmeier, C., Karas, V., & Zensus, J. A., E-mail: parsa@ph1.uni-koeln.de.
```*Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center*. United States. doi:10.3847/1538-4357/AA7BF0.

```
Parsa, M., Eckart, A., Shahzamanian, B., Zajaček, M., Straubmeier, C., Karas, V., and Zensus, J. A., E-mail: parsa@ph1.uni-koeln.de. Thu .
"Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center". United States. doi:10.3847/1538-4357/AA7BF0.
```

```
@article{osti_22663278,
```

title = {Investigating the Relativistic Motion of the Stars Near the Supermassive Black Hole in the Galactic Center},

author = {Parsa, M. and Eckart, A. and Shahzamanian, B. and Zajaček, M. and Straubmeier, C. and Karas, V. and Zensus, J. A., E-mail: parsa@ph1.uni-koeln.de},

abstractNote = {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 {sub BH} = (4.15 ± 0.13 ± 0.57) × 10{sup 6} M {sub ⊙} and R {sub 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 {sub 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 {sub s} / r {sub p} (with r {sub 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 {sub 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.},

doi = {10.3847/1538-4357/AA7BF0},

journal = {Astrophysical Journal},

issn = {0004-637X},

number = 1,

volume = 845,

place = {United States},

year = {2017},

month = {8}

}