Effect of plasma composition on the interpretation of Faraday rotation

Faraday rotation (FR) is widely used to infer the orientation and strength of magnetic fields in astrophysical plasmas. We first derive exact expressions of FR that are more general than the previous work in allowing for a plasma of arbitrary composition, arbitrary net charge and arbitrary radiation frequency. The latter includes low-frequency regimes where resonances occur and FR changes sign. We then show how the expressions can be used to constrain degeneracies between plasma density, composition and inferred magnetic field strength in astrophysically relevant ion-electron-positron plasmas of unknown positron to electron number density ratio. Electron-positron pairs may be prevalent in the plasma magnetospheres of pulsars, black holes and active galactic nuclei (AGN) jets, but the fraction of positive charge carriers that are protons or positrons has been difficult to determine. FR is sensitive to the plasma composition which may be helpful. A pure neutral electron-positron plasma has negligible FR, and the greater the fraction of positrons the higher the magnetic field strength required to account for the same FR. We consider parameters relevant to AGN jets and clusters to show the degeneracies in field strengths and plasma composition for a given FR measured value as a function of the plasma composition. We point out that these results can be used to constrain the plasma composition if an independent measurement of the magnetic field strength can be combined with the FR measure.