  AR Aur is the only eclipsing binary known to contain a HgMn star, making it
an ideal case for a detailed study of the HgMn phenomenon. HgMn stars are a
poorly understood class of chemically peculiar stars, which have traditionally
been thought not to possess significant magnetic fields. However, the recent
discovery of line profile variability in some HgMn stars, apparently
attributable to surface abundance patches, has brought this belief into
question. In this paper we investigate the chemical abundances, line profile
variability, and magnetic field of the primary and secondary of the AR Aur
system, using a series of high resolution spectropolarimetric observations. We
find the primary is indeed a HgMn star, and present the most precise abundances
yet determined for this star. We find the secondary is a weak Am star, and is
possibly still on the pre-main sequence. Line profile variability was observed
in a range of lines in the primary, and is attributed to inhomogeneous surface
distributions of some elements. No magnetic field was detected in any
observation of either stars, with an upper limit on the longitudinal magnetic
field in both stars of 100 G. Modeling of the phase-resolve longitudinal field
measurements leads to a 3 sigma upper limit on any dipole surface magnetic
field of about 400 G.
