Magnetic models of slowly rotating magnetic Ap stars: aligned magnetic and rotation axes

As a result of major surveys carried out during the past decade by Mathys and collaborators, we now have measurements with full phase coverage of several magnetic field moments, including the mean longitudinal field BE, the mean field modulus B-s, and in most cases the mean quadratic field B-mq and mean crossover field B-xover, for a sample of 24 chemically peculiar magnetic (Ap) stars. This represents an increase of a factor of order five in the stellar sample with data of this quality, compared to the situation a decade ago. We exploit this dataset to derive general and statistical properties of the stars in the sample, as follows. First, we fit the available field moment observations assuming a simple, axisymmetric multipole magnetic field expansion (with dipole, quadrupole, and octupole components) over each stellar surface. We show that this representation, though not exact, gives an adequate description of the available data for all the stars in this sample, although the fit parameters an in many cases not unique. We find that many of the stars require an important quadrupole and/or octupole field component to satisfy the observations, and that some (usually small) deviations from our assumed axisymmetric field distributions are certainly present. We examine the inclination i (0 less than or equal to i less than or equal to 90 degrees) of the rotation axis to the line of sight and the obliquity beta (0 less than or equal to beta less than or equal to 90 degrees) of the magnetic field with respect to the rotation axis, and show that the stars with periods of the ol der of a month or longer have systematically small values of beta: slowly rotating magnetic stars generally have their magnetic and rotation axes aligned to within about 20 degrees, unlike the short period magnetic Ap stars, in which beta is usually large. This is a qualitatively new result, and one which is very important for efforts to understand the evolution of magnetic fields and angular momentum in the magnetic Ap stars.