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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 ESPaDOnSspectropolarimeter at the Canada-France-Hawaii Telescope, with the aim ofsearching for the presence of weak and/or complex magnetic fields.Least-Squares Deconvolution mean profiles were computed from individualspectra, averaged over individual nights and over the entire run. No Zeemansignatures are detected in any of the profiles. The longitudinal magnetic fieldin the grand average profile was measured to be $-0.24 \pm 0.32 $ G, ascompared to $-0.22 \pm 0.32$ G in the null profile. Our observations thereforeprovide no evidence for the presence of Zeeman signatures analogous to thoseobserved in the A0V star Vega by Lignieres et al. (2009). We interpret theseobservations in three ways. First, we compare the LSD profiles with syntheticStokes $V$ profiles corresponding to organised (dipolar) magnetic fields, forwhich we find an upper limit of about 8~G on the polar strength of any surfacedipole present. Secondly, we compare the grand average profile withcalculations corresponding to the random magnetic spot topologies of Kochukhov& Sudnik (2013), inferring that spots, if present, of 2 degrees radius withstrengths of 2-4 G and a filling factor of 50% should have been detected in ourdata. Finally, we compare the observations with synthetic $V$ profilescorresponding to the surface magnetic maps of Vega (Petit et al. 2010) computedfor the spectral characteristics of $\iota$ Her. We conclude that while it isunlikely we would have detected a magnetic field identical to Vega's, we wouldhave likely detected one with a peak strength of about 30 G, i.e. approximatelyfour times as strong as that of Vega.

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