We performed a statistical analysis of the errors in the Stokes parameter measurements and derived from that the errors in the inferred magnetic fields. From analysis of the polarization images themselves, we estimate the following rms noise in the polarization measurements: Stokes V/I : ± 0.0023, Stokes Q/I : ± 0.0018; Stokes U/I : ± 0.0018. For Stokes Q and U the rms noise values are slightly smaller, because we applied a weighted running average to the Stokes images. This increases the signal-to-noise ratio in the weak linear polarization signals, although it reduces a little the spatial resolution.

From the errors in the Stokes measurements, we estimate the error in longitudinal field at 70 G with 60 G rms noise and a threshold of 55 G, and the error in the transverse field at 85 G with 60 G rms noise and a threshold of 180 G. Here, the rms noise is defined as the error when measuring the same quantity multiple times, without including systematic errors due to uncertainty in estimating the calibration constants. The threshold is the smallest value that can be measured above the zero level noise.

The error in measuring the vector field direction is highly dependent upon the strength of the magnetic field for each particular field vector. The stronger the field, the more accurate the direction estimate. From our calculations, it appears that there is a maximum error that can be reached given a specific field strength, but the average error is always between 0° and the maximum value. The following table shows the change in average and maximum errors for the zenith angles and the azimuth angles as a function of field strength:

where |B| is the absolute value of the field strength, and B_trans is just the field vector component transversal to the LOS. From the statistical distribution of the field strength, we estimate that the typical field strength observed was about 1000 G. Therefore, we can say that the typical average error in estimating the zenith angle is about 3° and maximum error is about 6°. For the transversal filed strength the typical value is probably 400 G. Therefore, for the azimuth angle we have typically a 5° error in average and 8° maximum error.

These are just the statistical errors derived only from known measurement errors. It is impossible to evaluate the errors in the vector direction that are related to the specific type of observation we made, i.e. measuring the polarization at a single wavelength position with a single and rather broad bandpass. We do not consider magneto-optical effects and we cannot distinguish between weak field and strong field approximation. In addition we cannot evaluate the effects due to Doppler shift of the spectral line and other effects that may change the profile of the spectral line.

We estimate the errors in the Doppler velocities of ± 0.17 Km/s with an rms noise of 0.11 Km/s. Here too, we want to emphasize that the so derived Doppler velocity maps are just a rough estimation of the effective Doppler velocities. Only measurements at multiple wavelength points across the spectral line can provide accurate velocity values.