A search for magnetic fields in the variable HgMn star $\alpha$ Andromedae

With this work, we have conducted an extensive search for magnetic fields in the photosphere of $\alpha$~And. We have acquired new circular polarisation spectra with the MuSiCoS and ESPaDOnS sp ectropolarimeters. We have also obtained FORS1 circular polarisation spectra fro m the ESO Archive, and considered all previously published magnetic data. This e xtensive dataset has been used to systematically test for the presence of magnet ic fields in the photosphere of $\alpha$~And. We have also examined the high-res olution spectra for line profile variability. The polarimetric and magnetic data provide no convincing evidence for photospheric magnetic fields. The highest-S/N phase- and velocity-resolved Stokes $V$ profiles, obtained with ESPaDOnS, allow us to place a $3\sigma$ upper limit of abou t 100~G on the possible presence of any undetected pure dipolar, quadrupolar or octupolar surface magnet ic fields (and just 50~G for fields with significant obliquity). We also conside r and dismiss the possible existence of more complex fossil and dynamo-generated fields, and discuss the implications of these results for explaining the non-un iform surface distribution of Hg. The very high-quality ESPaDOnS spectra have al lowed us to confidently detect variability of Hg~{\sc ii} $\lambda 6149$, $\lamb da 5425$ and $\lambda 5677$. The profile variability of the Hg~{\sc ii} lines is strong, and similar to that of the Hg~{\sc ii} $\lambda 3984$ line. On the ot her hand, variability of other lines (e.g. Mn, Fe) is much weaker, and appears to be attributable to orbital modulation, continuum normalisation differences and weak, variable fringing.