A search for weak or complex magnetic fields in the the B3V star iota Herculis

We obtained 128 high signal-to-noise ratio Stokes $V$ spectra of the B3V star $\iota$~Her on 5 consecutive nights in 2012 with the ESPaDOnS spectropolarimeter at the Canada-France-Hawaii Telescope, with the aim of searching for the presence of weak and/or complex magnetic fields. Least-Squares Deconvolution mean profiles were computed from individual spectra, averaged over individual nights and over the entire run. No Zeeman signatures are detected in any of the profiles. The longitudinal magnetic field in the grand average profile was measured to be $-0.24 \pm 0.32 $ G, as compared to $-0.22 \pm 0.32$ G in the null profile. Our observations therefore provide no evidence for the presence of Zeeman signatures analogous to those observed in the A0V star Vega by Lignieres et al. (2009). We interpret these observations in three ways. First, we compare the LSD profiles with synthetic Stokes $V$ profiles corresponding to organised (dipolar) magnetic fields, for which we find an upper limit of about 8~G on the polar strength of any surface dipole present. Secondly, we compare the grand average profile with calculations corresponding to the random magnetic spot topologies of Kochukhov & Sudnik (2013), inferring that spots, if present, of 2 degrees radius with strengths of 2-4 G and a filling factor of 50% should have been detected in our data. Finally, we compare the observations with synthetic $V$ profiles corresponding to the surface magnetic maps of Vega (Petit et al. 2010) computed for the spectral characteristics of $\iota$ Her. We conclude that while it is unlikely we would have detected a magnetic field identical to Vega's, we would have likely detected one with a peak strength of about 30 G, i.e. approximately four times as strong as that of Vega.