The Zeeman effect in astrophysical water masers and the observation of strong magnetic fields in regions of star formation

The present study solves the transfer equations for the polarized radiation of astrophysical 22-GHz water masers in the presence of a magnetic field which causes a Zeeman splitting that is much smaller than the spectral line breadth. The emphasis is placed on the relationship between the recently detected circular polarization in this maser radiation and the strength of the magnetic field. When the observed spectral line breadth is smaller than about 0.8 km/s (FWHM), it is calculated that the uncertainty is less than a factor of about 2. The accuracy is improved significantly when the angle between the line of sight and the direction of the magnetic field does not exceed about 45 deg. Uncertainty in the strength of the magnetic field due to lack of knowledge about which hyperfine transition is the source of the 22-GHz masers is removed. The 22-GHz maser feature is found to be the result of a merger of the three strongest hyperfine components.