# Constraining a companion of the galactic center black hole, Sgr A*

**Authors:** Clifford M. Will, Smadar Naoz, Aurélien Hees, Alexandria Tucker, Eric Zhang, Tuan Do, Andrea Ghez  
**arXiv:** [2307.16646](https://arxiv.org/abs/2307.16646)  
**Date:** 2023-07-31  
**Summary page:** https://www.summarizepaper.com/en/paper/2307.16646v1/

## Key points

- Authors utilize 23 years of astrometric and radial velocity data on the orbit of star S0-2
- Investigate existence of a hypothetical intermediate-mass black hole (IMBH) orbiting massive black hole Sgr A* at Galactic center
- Upper limits on variations in S0-2's stellar orbit are between 0.02 and 0.07 degrees per year
- Exclusion bounds for IMBH companion with semi-major axis larger than S0-2's are between 1000 and 4000 astronomical units
- Exclusion bounds for IMBH companion with semi-major axis smaller than S0-2's are derived from quadrupolar perturbations on S0-2's orbit caused by interaction with IMBH
- Stronger constraints on mass of inner companion derived from measuring location of S0-2 relative to bright emission from Sgr A*
- Bounds as small as $400 M_\odot$ at 200 astronomical units derived from analysis
- Comparison made with findings from other groups such as GRAVITY collaboration

## Summary

In this study, the authors utilize 23 years of astrometric and radial velocity data on the orbit of the star S0-2 to investigate the existence of a hypothetical intermediate-mass black hole (IMBH) orbiting the massive black hole Sgr A* at the Galactic center. By analyzing variations in the orientation of S0-2's stellar orbit, including inclination, nodal angle, and pericenter, they are able to place upper limits on these variations at levels between 0.02 and 0.07 degrees per year. To explore the potential presence of an IMBH companion, they employ a combination of analytic estimates and full numerical integrations of S0-2's orbit in the presence of a black-hole binary. They find that for a companion IMBH with a semi-major axis larger than that of S0-2 (1020 astronomical units), a companion black hole with mass between $10^3$ and $10^5 M_\odot$ is excluded in the region between 1000 and 4000 astronomical units. The boundary behavior is described by $a_c \sim m_c^{1/3}$. For a companion with a semi-major axis smaller than that of S0-2 (1020 astronomical units), they find that a black hole with mass between $10^3$ and $10^5 M_\odot$ is again excluded, with a boundary behaving as $a_c \sim m_c^{-1/2}$. These exclusion bounds arise from quadrupolar perturbations on S0-2's orbit caused by its interaction with an IMBH. Moreover, measuring the location of S0-2 relative to the bright emission from Sgr A* leads to even stronger constraints on the mass of an inner companion. The "wobble" motion exhibited by Sgr A* around its center of mass with respect to its companion results in apparent perturbations in S0-2's orbit, including a dipole component. As such, bounds as small as $400 M_\odot$ at 200 astronomical units are derived from this analysis. Numerical simulations suggest that these effects lead to exclusion boundaries varying as $a_c \sim m_c^{-1}$. The authors compare their findings with those from recent analyses conducted by other groups such as GRAVITY collaboration. Overall, this study provides valuable insights into the potential presence of an IMBH companion to Sgr A* at the Galactic center, shedding light on dynamics related to black hole binaries and their influence on stellar orbits.