Usually, H values obtained from lines of different elements are statistically combined with the aim to improve the precision of the effective field measurement. However, because of the non-homogeneous distribution of the elements, such an operation is not a priori expected to lead to any improvement and moreover its validity has yet to be proved.
In this framework, Leone and Catanzaro (()) have decided to quantify the importance of the non-homogeneous distribution of elements in measuring H, and have to this purpose carried out high resolution spectropolarimetric observations of the CP star HD24712 at three rotational phases. The spectra have been obtained at the Telescopio Nazionale Galileo equipped with the SARG spectrograph and the polarimetric module, the resolution was R=115000.
In this study the authors have established the dependence of measurements of H on the atomic weight of 24 elements (from carbon to erbium) at different ionisation states. At all 3 rotational phases considered, H values derived from different elements can differ by up to 800 G. They found an overall increase in H with atomic number and a maximum near Z=60. The behavior of sodium is quite singular as it always exhibits a negative value of the field, peaking at -0.39 kG when the rare earths give H= 1.2 kG (see Fig. 1.17). Under the assumption of a dipolar field, the authors concluded that the elements giving the largest values of H are concentrated near the positive polar region and that the other elements are more homogeneously distribuited over the stellar surface or concentrated in belts around the magnetic equator. Sodium seems to be localised in the negative magnetic hemisphere only.
This picture is corroborated by the equivalent width variability of the lines: up to iron, equivalent widths changes out-of-phase with respect to the H variability; elements heavier than iron present equivalent widths that are variable in-phase. No relation between the respective amplitudes of the equivalent width variations and the atomic number has been found.
As a general conclusion, the authors stated that measurements originating from different elements cannot in general be combined to improve the precision of H measurements. Indeed, any modelling attempt based on the periodic variations in H is subject to the risk that the sampling of the magnetic field over the stellar surface by the lines of a given chemical element is uneven or incomplete.