The Shadow of a Spherically Accreting Black Hole (1910.02957v2)

Abstract: We explore a simple spherical model of optically thin accretion on a Schwarzschild black hole, and study the properties of the image as seen by a distant observer. We show that a dark circular region in the center --- a shadow --- is always present. The outer edge of the shadow is located at the photon ring radius $b_{\rm ph} \equiv \sqrt{27}r_g$, where $r_g=GM/c^2$ is the gravitational radius of the accreting mass $M$. The location of the shadow edge is independent of the inner radius at which the accreting gas stops radiating. The size of the observed shadow is thus a signature of the spacetime geometry and it is hardly influenced by accretion details. We briefly discuss the relevance of these results for the Event Horizon Telescope image of the supermassive black hole in M87.

The Shadow of a Spherically Accreting Black Hole

The paper "The Shadow of a Spherically Accreting Black Hole" offers a meticulous exploration of the image characteristics observed by a distant observer when analyzing spherical accretion onto a Schwarzschild black hole. As the title implies, the focus of the paper lies in the conceptualization of the "shadow" — a notable dark central region in astronomical black hole imagery, as verified by the Event Horizon Telescope (EHT) in its observations of the supermassive black hole in M87.

Analytical Framework

The authors employ an optically thin spherical model to investigate the attributes of the shadow cast by a black hole. This model is critical for understanding the imaging properties because it allows for the examination of the shadow independent of the specifics of accretion flow details — a conceptual simplification that underscores the robustness of the shadow feature. The Schwarzschild black hole model utilized here demonstrates that the size of the shadow is mainly a function of spacetime geometry determined by the photon ring at a radius $b_{\rm ph} \equiv \sqrt{27}r_g$. This finding illustrates that the shadow is dominated by the lensing effect rather than by the inner radius of the accreting gas.

Numerical Results and Observational Implications

Numerically, the paper calculates that the intensity at the shadow's edge (photon ring) can effectively diverge due to the weak logarithmic singularity present when ray trajectories align to escape from bound photon orbits endlessly. A significant conclusion of the paper is that the shadow's radius remains invariant across various emission cutoff radii, even if the emitting material doesn't extend to the black hole’s horizon. These computations corroborate observations by the EHT, suggesting that even in complex, chaotic astrophysical environments, certain fundamental predictions of general relativity hold.

For practical astrological implications, the authors assert that the shadow offers a platform for probing strong gravitational lensing close to black holes. High resolution interferometric observations capture the size of the shadow, which can lead to insights about the mass and spin of black holes without complications from the ambiguity of accretion flow configurations.

Future Developments and Theoretical Implications

From a theoretical perspective, the findings advocate the use of black hole shadow imaging as a precise tool for testing general relativity predictions, especially in exotic and strong-lensing regimes. Although real astrophysical accretions are likely to involve angular momentum and perhaps significant outflows, the paper assures that the shadow's size remains prominently tied to spacetime geometry rather than dynamics of inflow. This intertwines with broader discussions in relativistic astrophysics, especially concerning GRMHD simulations and spacetime observation instruments development.

Conclusion

The paper "The Shadow of a Spherically Accreting Black Hole" provides compelling evidence supporting the robustness and astronomically observable characteristics of black hole shadows. Through a comprehensive theoretical approach, it underscores the relevance of shadow imaging as a tool for both verifying general relativity and probing black hole physics. Future studies may extend these findings for more comprehensive models including Kerr black holes and incorporate more complex dynamical features such as angular momentum and non-spherical accretion geometries, potentially including radiative transfer in magnetized plasmas.