The distribution of chromium on three AP stars: evidence for depleted chromium at the magnetic equator

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Abstract
Doppler images of the chromium distribution on the magnetic Ap stars ε Ursae Majoris, 45 Herculis, and ω Herculis are presented. All images are characterized by the presence of a depleted band and at least one depleted spot. ε Ursae Majoris and ω Herculis also show several spots of enhanced chromium lying in a ring of radius 40°–50° and surrounding a depleted spot. 45 Herculis shows such a ring-like feature as well, although there is no depleted spot at its centre. The shape and location of the depleted bands and spots strongly suggest that the band marks the location of the magnetic equator and the depleted spots mark the magnetic poles. Recent magnetic field measurements for ε Ursae Majoris confirm this hypothesis. If these stars have a simple magnetic field (dipole + quadrupole) then their Doppler images can be used to directly determine the obliquity angle of the magnetic axis as well as the decentring parameter of the dipole. Obliquity angles of 75°–85° and decentring parameters of 0.03–0.16 stellar radii are derived for the dipole of these stars. This decentring of the dipole is along the magnetic axis; however, 45 Herculis may also show evidence for decentring of the dipole perpendicular to the magnetic axis. If selective diffusion of elements in the presence of a magnetic field is responsible for the abundance inhomogeneities in Ap stars then two interpretations arise for the appearance of a depleted band at the magnetic equator and depleted spots at the magnetic poles. If chromium is depleted in regions where the field lines are vertical then the distributions for these stars show evidence for the presence of a strong quadrupole component to the magnetic field. On the other hand, if these stars are evolved, then the depleted band may result from the horizontal as well as vertical diffusion of chromium in the presence of an almost pure dipole field. The Doppler images, at the present time, tend to favour the horizontal diffusion interpretation.

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