Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 75 / 1 / f / Solution

A low-frequency example is Galactic synchrotron emission: relativistic electrons spiral in the Galactic magnetic field and emit a broad nonthermal spectrum. In antenna-temperature units its approximate spectrum is $T_A\propto {\nu }^{-{\beta }_s}$ with ${\beta }_s$ around3, varying with the electron population and sky direction. It is a major, often dominant contamination at frequencies below roughly20–40GHz; radio point sources and bremsstrahlung can contribute in the same low-frequency region.

A high-frequency example is Galactic thermal dust emission. Grains heated by starlight have approximate modified-blackbody spectrum $I_{\nu }\propto {\nu }^{{\beta }_d}{B}_{\nu }(T_d)$, with grain temperatures of order tens of kelvin. Their emissivity-weighted emission rises rapidly through the microwave/submillimeter range and commonly dominates anisotropy contamination above roughly100–200GHz, especially at higher frequencies. Dusty extragalactic galaxies provide a related high-frequency foreground.

Synchrotron is the low-frequency contaminant and thermal dust the high-frequency contaminant. There is no universal crossover frequency at which either exceeds CMB anisotropy everywhere: sky masking, angular scale, polarization and source amplitude matter. Cleaner cosmological windows lie between these regimes, and multi-frequency observations distinguish the foreground spectra from a thermodynamic CMB temperature perturbation. The separation into low-frequency emission and high-frequency dust is also used in the Planck astrophysical-component products.