How does the shadow size relate to the black hole’s properties?

How does the shadow size relate to the black hole’s properties?

• A. The shadow size observed depends mainly on the black hole’s mass and distance, with spin having a smaller effect.
• B. The shadow size depends only on spin.
• C. The shadow size is independent of mass and distance.
• D. The shadow size is determined solely by the accretion disk brightness.

Answer: (A)

The key idea is that the shadow’s apparent size is set by the gravitational scale of the black hole and how far away you are. The angular size you observe roughly scales with the mass of the black hole divided by its distance from you, so bigger mass or closer distance makes the shadow appear larger. Spin mainly changes the shape of the silhouette, causing some asymmetry, but it doesn’t drastically change the overall size in the first approximation. The brightness or structure of the surrounding accretion disk doesn’t determine the shadow’s boundary—it affects how clearly you can see it, not how big it is.

The key idea is that the shadow’s apparent size is set by the gravitational scale of the black hole and how far away you are. The angular size you observe roughly scales with the mass of the black hole divided by its distance from you, so bigger mass or closer distance makes the shadow appear larger. Spin mainly changes the shape of the silhouette, causing some asymmetry, but it doesn’t drastically change the overall size in the first approximation. The brightness or structure of the surrounding accretion disk doesn’t determine the shadow’s boundary—it affects how clearly you can see it, not how big it is.