2006A&A...453..699M

We assess the validity of the method of determination of the mean quadratic field modulus and we explore its limits. We analyse high spectral resolution, high signal-to-noise spectra of a few Ap stars, and of a superficially normal main-sequence A star, recorded over a broad wavelength range with EMMI at the NTT. We introduce a revised form of the regression equation describing the dependence of the second-order moment of the line profiles about their centre, in natural light, on various parameters of the corresponding transitions. We show that interpretation of the observed dependences allows one to determine the mean quadratic magnetic field modulus of the studied stars, and their vsin i. We explain why the contributions to the quadratic field of the mean square magnetic field modulus and of the mean square longitudinal field cannot in general be disentangled. For those stars of the sample that have resolved magnetically split lines, we show that the derived values of the quadratic field are mostly consistent with the values of the mean longitudinal magnetic field and of the mean magnetic field modulus at the observed phase. However there are some hints that they may occasionally slightly underestimate the actual field. This suggests that the method is unlikely to yield spurious field detections. In addition, we illustrate the importance for this type of analyses of using, as far as possible, samples of lines of a single ion, and to specify in the presentation of the results which ion was used. The results presented in this paper lend strong support to the validity of the quadratic field diagnostic method to obtain a realistic quantitative characterisation of the magnetic fields Ap and related stars.