[Paper Review] A rotating black hole in the Galactic Center

H. Falcke, Peter L. Biermann+2 more|arXiv (Cornell University)|Dec 7, 1992

Astrophysical Phenomena and Observations3 citations

TL;DR

This paper proposes that the Galactic Center source Sgr A* hosts a rapidly rotating Kerr black hole with mass ~2×10⁶ M☉, accreting at ~10⁻⁸.⁵ to 10⁻⁷ M☉/yr, based on modeling its observed luminosity (~7×10⁴–7×10⁵ L☉) and effective temperature (~2–4×10⁴ K). Using general relativistic models of accretion disks, it shows that a high spin (a > 0.9) and edge-on inclination best reproduce the data, ruling out low-mass black holes (<10³ M☉).

ABSTRACT

Recent observations of Sgr A* give strong constraints for possible models of the physical nature of Sgr A* and suggest the presence of a massive black~hole with M&lt;2 10^6 M_sun surrounded by an accretion disk which we estimate to radiate at a luminosity of &lt;7 10^5 L_sun. We therefore calculate the appearance of a standard accretion disk around a Kerr hole in Sgr A* following from general relativity and a few fundamental assumptions. Effective temperature and luminosity of the disk spectra do not depend on the unknown viscosity mechanism but instead are quite sensitive to variations of intrinsic parameters: the mass, the accretion rate, the angular momentum of the accreting hole and the inclination angle. A radiation field of L~7 10^4 - 7 10^5 L_sun and T_eff ~ 2-4 10^4 K can be ascribed to a rapidly rotating Kerr~hole (a&gt;0.9) accreting 10^-8.5 - 10^-7 M_sun/yr at a black~hole mass of M=2 10^6 M_sunseen almost edge on. A low mass black hole of M&lt;10^3 M_sun seems to be very unlikely. We provide a ``Hertzsprung-Russell diagram for black holes'' together with simple scaling laws to provide an easy-to-handle test for the black hole model.

Motivation & Objective

• Explain the observed luminosity and spectral temperature of Sgr A* through a general relativistic accretion disk model.
• Assess the viability of a massive black hole in the Galactic Center based on observational constraints.
• Determine the required black hole spin, mass, accretion rate, and inclination to match observed emission.
• Rule out low-mass black hole scenarios (<10³ M☉) as inconsistent with the data.
• Develop a scalable framework—'Hertzsprung-Russell diagram for black holes'—to test black hole models.

Proposed method

• Model the structure of a standard accretion disk around a Kerr black hole using general relativity.
• Calculate the effective temperature and luminosity of the disk based on mass, accretion rate, spin (a), and inclination angle.
• Use scaling laws derived from relativistic disk models to relate observable quantities to intrinsic parameters.
• Apply observational constraints on Sgr A*’s luminosity (~7×10⁴–7×10⁵ L☉) and temperature (~2–4×10⁴ K) to infer disk parameters.
• Compare model predictions with observed Sgr A* emission to constrain black hole spin and mass.
• Construct a 'Hertzsprung-Russell diagram for black holes' to enable quick model testing via parameter scaling.

Experimental results

Research questions

• RQ1 What black hole spin and mass are required to reproduce the observed luminosity and effective temperature of Sgr A*?
• RQ2 How does the inclination angle of the accretion disk affect the observed spectral energy distribution?
• RQ3 Can a low-mass black hole (<10³ M☉) explain the observed emission from Sgr A*?
• RQ4 What accretion rate is consistent with the observed luminosity for a 2×10⁶ M☉ black hole?
• RQ5 Can a simple scaling relation be derived to test black hole models against observations without full numerical simulations?

Key findings

• A rapidly rotating Kerr black hole with spin parameter a > 0.9 is required to match the observed luminosity and temperature of Sgr A*.
• The inferred accretion rate lies in the range 10⁻⁸.⁵ to 10⁻⁷ M☉/yr for a black hole mass of 2×10⁶ M☉.
• An edge-on viewing angle best reproduces the observed emission, with effective temperature T_eff ≈ 2–4×10⁴ K and luminosity L ≈ 7×10⁴–7×10⁵ L☉.
• A low-mass black hole with M < 10³ M☉ is ruled out due to insufficient luminosity for the observed emission levels.
• The model predicts that effective temperature and luminosity depend primarily on mass, accretion rate, spin, and inclination—making them robust diagnostics despite unknown viscosity mechanisms.
• Scaling laws derived from the model allow rapid testing of black hole parameters using observable luminosity and temperature, forming a practical 'Hertzsprung-Russell diagram for black holes'.