## 3. Variability of the mean longitudinal magnetic fieldThe analysis of the Ap stellar spectra is usually complicated, due to the overabundances of some chemical elements, which are probably connected with the magnetic field structure. As it has been noted above, HD 83368 was very carefully studied by photometry (Kurtz, 1990; Kurtz et al., 1997) and also a large number of magnetic field measurements were carried out. Mathys (1995) has determined the values of the quadratic magnetic field, which is a function of the effective field and of the surface one . One of the problems of this work is the necessity to take into account the Doppler shift effects due to the non-homogeneous stellar surface distribution of the chemical elements and the effects of the magnetic intensification of some spectral lines. Special attention was given to the lithium line 6708 Å, and also to the lines of other elements with high values of Landé factor. The magnetic field geometry in Ap stars is often characterized by the parameter , where (Hensberge et al., 1977). For most of the Ap stars, the variation of the mean longitudinal magnetic field observed throughout the rotation cycle appears nearly sinusoidal: where is the angle between the line of sight and the axis of the magnetic field. Spherical geometry gives for the following exspression: where and For HD 83368, supposing a pure dipolar configuration of the magnetic field, Mathys (1991) has performed a least-squares fit of the values of previously observed by Thompson (1983) through photopolarimetry, and measurements of , obtained by Mathys in 1985, 1987 and 1988, with the Eq. (1). The fitted parameters are and , which give us . In the case of an oblique rotating magnetic dipole, the relation of the mean longitudinal magnetic field to the polar field strength is proportional to (Hensberge et al., 1977) where where u is the same as in Eq. (4). The variation of with the phase is shown in Fig. 2. It must be emphasized, that the mean surface magnetic field modulus for HD 83368 determined in such a way does not correspond to the recent estimate of the mean quadratic magnetic field = 11 kG by Mathys (Mathys, 1995, Mathys & Hubrig, 1997). The mean quadratic magnetic field is diagnosed from the second-order moment of the unpolarized line profile (about the line centre), , where the integration was carried out over the whole width of the observed line. Here is the equivalent width and is the unpolarized line profile. This moment characterizes the unpolarized line width, that includes the constant part (natural width, rotational and thermal Doppler broadening, instrumental profile, etc.) and the part variable with , which is proportional to the mean quadratic magnetic field. But, if we suppose that some lines under analysis are generated in the "abundance spots" on the stellar surface, then the line broadening due to the stellar rotation also would vary with and will not be constant as supposed by Mathys (1995). Consequently this evaluation of the mean quadratic magnetic field could be significantly greater than our estimation of the mean surface magnetic field modulus. © European Southern Observatory (ESO) 2000 Online publication: June 5, 2000 |