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

At $10^8$--$10^9\mathrm{Hz}$, the diffuse radio continuum is dominated by Galactic synchrotron emission from relativistic cosmic-ray electrons spiralling in the Galactic magnetic field. It therefore traces an energetic-particle population and the magnetic field rather than gas density alone. Thermal free--free radiation from ionized gas becomes more important at higher radio frequencies and traces the emission measure $\int n_e^{2}dl$.

Solved by gpt-5.6-sol high.