3 The magnetic field surface structure and the distribution of chemical elements

3.1 Helium

A schematic view of the helium distribution over the star surface is shown in Fig. 3.

Figure 3: The schematic view of the helium distribution over the CU Vir surface. The bold line indicates regions with helium overabundance, the dashed line does the ones with helium underabundance. The thin line shows the place where the magnetic field changes its sign.

The data have been taken from the paper of Kuschnig et al. (1999). Helium is concentrated weaker in the region of the negative compact maximum than in the region of the wide positive maximum. The thin line marks the region where the change of the magnetic field polarity takes place. It is seen from Fig. 4 that a helium spot of small size is located near the negative field maximum. The helium distribution is consistent with the assumption that it is concentrated in the regions with vertical magnetic field lines of force. However, it is not clear why helium has a weaker concentration in the region with the higher field intensity.

The data presented by Vauclair et al. (1979) suggest that the helium anomaly formation is strongly dependent on the helium diffusion flow $\nu_{\rm f}\rho$ (denotation see Vauclair). If this flow is larger than a certain critical range of the flow value $\triangle_{\rm c}$, then a normal helium abundance is observed; if the flux is smaller, then the abundance is decreased. The faint helium spot at the negative pole implies that the flow value is either at the upper or at the lower boundary of the range $\triangle_{\rm c}$. Taking into account that the mass loss at the negative strong pole is more likely to be greater than at the positive pole, it can be assumed that the helium diffusion flow is too strong there.

3.2 Silicon

Figure 4 presents schematically the regions of the Si concentration derived by different authors (A - Goncharskij et al. 1983; B - Kuschnig et al. 1999; C - Hatzes et al. 1997) and the region of maximum field strength (thin line).

At first sight, the Si distribution of different authors differs remarkably, however, one common property is noticeable: silicon is concentrated predominantly around the negative pole. In the region of the weaker positive field, the silicon abundance is lower than normal. Alecian & Vauclair (1981) and also Megessier (1984) discuss the importance of the horizontal field component for the diffusion of chemical elements in CP stars, silicon in particular. The calculation shows that in the case of the displaced dipole model, the horizontal magnetic field component has a maximum in a ring inside the marked circle. For this reason the conclusion of Hatzes (1997), that silicon in CU Vir is concentrated in the region, where the lines of force are mainly horizontal, is correct in first approximation. This inference, however, is contradicting to the absence of any silicon overabundance near the pole, where the lines of force are vertical.

It is seen in the diagrams that the existing techniques are capable of providing the distribution of chemical elements only on the visible area of the surface. From considerations of symmetry the derived map is more likely to describe the invisible hemisphere. When assuming that the chemical elements are, indeed, related to the magnetic field, one can imagine that the regions occupied by silicon (after Hatzes) should be transferred in the diagrams to the lower hemisphere symmetrically to the dipole plane (the plane, in which the CU Vir dipole is located, is practically coincident with the equatorial plane).
Thus the silicon regions will occupy all the space inside the area (bound by the thin line in Fig. 1A).

It is very interesting that - after the papers of all other authors - the silicon spot is divided into two ones. The difficulty of the assumptions made is that one of the silicon spots is outside the supposed region with horizontal orientation of the lines of force. If silicon is actually concentrated in the regions with the horizontal lines of force, then the magnetic "spot" can be assumed to have a complex structure. Modelling cannot reveal such a complex structure because of the insufficient number of measurements of $B_{\rm e}$.

Figure 4: The schematic view of the silicon distribution over the CU Vir surface (designation the same as in Fig. 3) A) data from Hatzes (1997), B) data from Kuschnig et al. (1997), C) data from Goncharskij et al. (1983).