What angular scale is needed to resolve a black hole shadow with Earth-based interferometry?

What angular scale is needed to resolve a black hole shadow with Earth-based interferometry?

• A. Degrees
• B. Microarcseconds
• C. Arcseconds
• D. Nanoradians

Answer: (B)

The needed angular scale is microarcseconds. The shadow of a supermassive black hole is only about tens of microarcseconds across on the sky. Earth-based very long baseline interferometry reaches such tiny angles by using the entire Earth as a baseline at millimeter wavelengths. Roughly, the angular resolution is set by theta ≈ lambda / B. With lambda ≈ 1.3 mm and B roughly the Earth’s diameter (~12,700 km), you get theta ≈ 1.3e-3 / 1.27e7 ≈ 1e-10 radians, which converts to about 20 microarcseconds. Degrees or arcseconds are far too coarse to resolve this feature, and nanoradians isn’t the standard unit used in this context, whereas microarcseconds directly describe the needed precision.

The needed angular scale is microarcseconds. The shadow of a supermassive black hole is only about tens of microarcseconds across on the sky. Earth-based very long baseline interferometry reaches such tiny angles by using the entire Earth as a baseline at millimeter wavelengths. Roughly, the angular resolution is set by theta ≈ lambda / B. With lambda ≈ 1.3 mm and B roughly the Earth’s diameter (~12,700 km), you get theta ≈ 1.3e-3 / 1.27e7 ≈ 1e-10 radians, which converts to about 20 microarcseconds. Degrees or arcseconds are far too coarse to resolve this feature, and nanoradians isn’t the standard unit used in this context, whereas microarcseconds directly describe the needed precision.