Figure 1—The principles of Zeeman Doppler imaging. Due to the Doppler effect, the disk of a rotating star can be subdivided into zones of equal radial velocity, each associated with a given Doppler shift. Consider two magnetic spots of opposite polarities and different Dopp the stellar surface, whose spectral coordinates are denoted X1 and X2. The intensity associated with this two-spot group consists of two absorption profiles (one for each s er shifts on spectrum I pot) centred on X; and X2. Through the Zeeman effect (weak field approximation), each magnetic spot induces small opposite spectral shifts (proportional to the algebraic line-of-sight component of the field) of the corresponding absorption profile in the right- and left-hand circularly polarised spectra I + V and I — V respectively (V denotes the circular polarisation Stokes parameter). signatures of both spots in the Stokes V parameter (obtained by subtracting the right- n The Zeeman handed from the left-handed circular polarisation spectra) no longer cancel each other as they would do in a non-rotating star (for which we have X; = X2). Moreover, the shape of the Stokes V profile informs us about the location of the parent magnetic spots on the visible stellar disk. Figure 2—Intensity and polarisation profiles for the RS CVn star system HR1099. The three panels show the system in 1992 December and at two different orbital phases during the 1993 observations. In each panel, the absorption line intensity and polarisation rate profiles are derived by summing 25 different lines observed simultaneously with the AAT échelle spectrograph. The 1993 observations reveal the details of a polarisation profile whose full relative amplitude is only about 0-3. The brighter component of the HR 1099 system, a K1 subgiant star, displays clear evidence of complex magnetic fields on its surface (three magnetic spots?), from the shape of the polarisation rate spectrum.
