3 Data analysis

In the presence of a magnetic field, B, the magnetic sublevels of a given molecular level J($\neq$0) lose their energy degeneracy. The emission which stem from this splitting have left- and right-circularly polarized components. If the magnetic field is small, but sufficient enough to cause splitting between the components greater than the width of the line itself (as is often the case for maser sources), then the total magnetic field strength may be deduced. If, however, the splitting is less than the width of the line, which is invariably the case for thermally excited gas in H$\,$ II and star forming regions, then only the line-of-sight component of the magnetic field, $B_{\scriptsize {\parallel}}$, can be determined. It can be shown that

$${ T_V(\nu) = -C\;\frac{{\rm d}T_I(\nu)}{\rm d\nu}\; B_{\scriptsize {\parallel}} {\scriptsize {[G]}},}$$ (1)

where T_V is the temperature of the Stokes-V spectrum (the difference between the left- and right-circularly polarized spectra), T_I is the temperature of the Stokes-I spectrum (approximated as the sum of the left- and right-circularly polarized spectra) and $\nu$ is the frequency. The term C gives the left-right line frequency split with magnetic field strength ( $\Delta\nu_{\rm g}$/B) and is a constant for a given molecular transition; it has, for example, a value of 1.93 Hz/$\mu$G for the SO $J_{\rm N}=1_2-1_1$ transition (see Table 1 and Appendix A).

All processing of the spectral line data, including the production of the Stokes-V and I spectra, was done in the software environment CLASS. The line-of-sight B field ( $B_{\scriptsize {\parallel}}$) was determined by scaling the I-derivative to the V spectrum (Eq. (1)), by method of least-squares-fit.

Long-period waviness, attributable to receiver effects and the bandpass, was present in the baselines of all the V-spectra; it was removed by either of two methods. The baselines of some spectra were directly fitted with an $n{\rm th}$order polynomial and then removed by subtracting the polynomial model. This procedure proved satisfactory for the narrow line sources (e.g. NGC2071A, S140IR, the dark cloud cores), since their spectra contained ample baseline and since any potential Zeeman response within the confines of the narrow line would be distinct from the long-period waviness in the baseline. A different procedure, however, was needed for the spectra of the broad-line sources (e.g. ORI-KL, SgrB2N and G5.89), since in those cases the baselines are more limited in extent, thus making difficult their characterization and placing at risk the accidental subtraction of a real Zeeman response from the V-spectrum. Instead, separate observations of line-free or ``sky'' positions were used to model the baselines. The longest integrations of such were performed daily, during antenna servicing periods, with the antenna positioned toward the zenith. Additionally, measurements of nearby sky positions were periodically taken while observing some of the Zeeman line splitting candidates. The baselines of the sky-spectra were characterized with $n{\rm th}$ order polynomial fits. The source V-spectra were significantly flattened (typically to better than 2${\rm nd}$ order curvature) upon subtraction of the sky spectra baseline model.