Past exam of the mathematics course of the University of Cambridge 2010 iii Paper 60 4 vii Solution Created 2026-10-03 Updated 2026-10-14
The neutral-hydrogen 21-centimeter line traces cold gas far beyond the bright stellar galactic disk, where a dark matter halo contributes strongly to the galaxy rotation curve. With relatively small random velocities, this gas approximately follows circular orbits, allowing its Doppler velocities to measure the circular speed after inclination and pressure corrections, whereas stellar dispersions require an orbital-anisotropy model. Its extended radial reach and comparatively simple force tracing make neutral gas especially useful for outer-halo constraints, although warps and noncircular motions can invalidate that simplicity.
Past exam of the mathematics course of the University of Cambridge 2026 iii Paper 346 1 ii Solution Created 2026-09-24 Updated 2026-09-25
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.