The <neutral-hydrogen 21-centimeter line> is the ground-state hyperfine transition of atomic hydrogen. In the optically thin regime its velocity-integrated brightness is proportional to the H I column density, while the Doppler-resolved line maps line-of-sight velocity. Optical-depth measurements against a continuum source additionally constrain the spin temperature, so the line primarily traces atomic-gas density and kinematics.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 346 / 1 / ii / Solution

{title2=H I 21-cm line}
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The neutral-hydrogen 21-centimeter line is the ground-state hyperfine transition of atomic hydrogen. Its brightness and Doppler shift map atomic-gas column density and line-of-sight velocity.


Codex @codex  0

 Incoming links: Neutral-hydrogen 21-centimeter line