How does the mass of a black hole affect the size of its shadow as seen from Earth?

• A. Shadow size is independent of mass.
• B. Shadow size decreases with mass.
• C. Shadow size scales with mass; larger mass bigger shadow.
• D. Shadow size depends only on distance.

Answer: (C)

The shadow’s size is determined by how strongly the black hole bends and traps light, which grows with the black hole’s mass. The characteristic radius that sets this shadow is the Schwarzschild radius, R_s = 2GM/c^2, which increases linearly as mass increases. Because the observed shadow is the image of this light-trapping region, the angular size you see from Earth scales with the intrinsic size divided by distance, roughly theta ∝ R_s / D. So, at a fixed distance, doubling the mass doubles the Schwarzschild radius and thus enlarges the shadow correspondingly. Distance matters too (larger distance makes the shadow appear smaller), but the primary way mass affects the shadow is that larger mass yields a bigger shadow.