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tokens: Stokes V spectrum profile characteristic of circular polarization generated by the Zeeman effect, but it can arise from scattering of a cloud outside the velocity range of the maser. Non-anti-symmetric Stokes V spectra were observed by Herpin et al. (2006) , but they can also be explained by a velocity gradient along the propagation path of the maser, or the lack of spatial resolution from the single-dish observations. 5.2. H<sub>2</sub>O masers 5.2.1. Simulations The relevant characteristic maser luminosities are given in Table 4 . We list the relevant luminosities for individual hyperfine transitions as well as the blended line. Compared to the SiO maser, radiative interactions remain relatively weak with respect to magnetic interactions up to high maser luminosities. This is due to the much smaller line strength of this maser transition, which means that the Zeeman effect will be the dominating polarizing mechanism up to high maser luminosities, and will thus follow Eq. ( 38 ) up to high maser brightness. Linear polarization will also remain rather low because the isotropic decay will be a dominant de-polarizing entity up to ( T b ΔΩ) sat (Ksr) at about ∼10 10 Ksr. Strong linear polarization is thus only seen for the strongest masers. Table 4. Characteristic maser luminosities for the 22 GHz water maser. For the regime T b ΔΩ ≪ ( T b ΔΩ) mag. sat , the maser circular polarization can be described by Eq. ( 38 ). A LTE analysis of the constant A F F ′ , gives for the individual hyperfine transitions, A 76 = 13.3, A 65 = 8.3, and A 54 = 1.0. A LTE analysis of a completely blended water maser line gives A blend = 8.2. Figure 15 shows the results of our full radiative transfer analysis of the circular polarization constants. Apart from the standard maser line profile, water masers are further broadened by their hyperfine structure. This leads to an overestimation of Δ v L . The dominant Zeeman effect though, comes from a single hyperfine transition. This produces higher Zeeman A F F ′ coefficients with respect to a LTE analysis. We observe that this effect is most pronounced for masers pumped at v th = 0.6 km s −1 , where the hyperfine transitions are minimally mixed. At v th = 2.0 km s −1 , the hyperfine broadening is negligible and the LTE value for the A F F ′ coefficient of the F = 7−6 hyperfine transition is returned for the weakest masers. Fig. 15. The A F F ′ coefficients of an isotropically pumped water maser at B = 20 G as a function of the magnetic field-propagation direction angle cos θ . The panels show different thermal widths v th = (a) 0.6 km s −1 , (b) 1.0 km s −1 , and (c) 2.0 km s −1 . Plots are given for different log( R / g Ω). The LTE solutions (constant over cos θ ) of the different hyperfine sub-transitions are indicated by a dotted line. Paradoxically, the preferred pumping of the hyperfine component with the strongest Zeeman effect has a consequence that the linear polarization deteriorates in the relevant intensity