A measure of the magnetic field strength and electron density along the line of sight, causing polarization rotation.Rotation measure is a quantity in radio astronomy that quantifies how much the polarization angle of a radio wave rotates as it travels through a magnetized plasma. It depends on the integral of the electron density times the magnetic field component along the line of sight. This measurement is crucial for mapping magnetic fields in the Milky Way, in other galaxies, and in the intergalactic medium.
The concept was developed in the mid-20th century as radio astronomy matured, with key contributions from astronomers like Hanbury Brown and others who recognized the importance of Faraday rotation in interpreting polarized radio sources.
When linearly polarized radio waves pass through a magnetized plasma, the plane of polarization rotates due to the Faraday effect. The rotation angle is proportional to the square of the wavelength, and the proportionality constant is the rotation measure. By observing a source at multiple wavelengths, astronomers can measure the rotation measure and infer the magnetic field strength and electron density along the line of sight.
Rotation measure is used to map galactic magnetic fields, study the intergalactic medium, and understand the magnetospheres of pulsars and active galactic nuclei. It also helps calibrate polarization measurements in cosmic microwave background experiments.
The rotation measure of a distant quasar can be used to detect magnetic fields in the otherwise invisible intergalactic medium, revealing the cosmic web's magnetic structure.
| Δθ | variable | Rotation angle of polarization plane — polarization rotation angle radian |
| λ | variable | Wavelength of light — wavelength metre |
| RM | constant | Rotation measure, proportional to integrated electron density times magnetic field along the line of sight — rotation measure = varies (e.g., 0.812 rad m^-2 for typical radian per metre squared |
| RM | variable | Rotation measure — rotation measure radian per metre squared |
| n_e | variable | Electron number density — number density per metre cubed |
| B_parallel | variable | Magnetic field component along line of sight — magnetic field tesla |
| s | variable | Path length along line of sight — length metre |
| L | variable | Total path length through plasma — length metre |
| e | constant | Charge of a single electron — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | Rest mass of an electron — electron mass = 9.1093837015e-31 kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | Integration along the line of sight — integral operator |





















