Weak magnetic fields in Ap/Bp stars: evidence for a dipole field lower limit and a tentative interpretation of the magnetic dichotomy

Aims. We investigated a sample of 28 well-known spectroscopically-identified magnetic Ap/Bp stars, with weak, poorly-determined or previously undetected magnetic fields. The aim of this study is to explore the weak part of the magnetic field distribution of Ap/Bp stars. Methods. Using the MuSiCoS and NARVAL spectropolarimeters at Télescope Bernard Lyot (Observatoire du Pic du Midi, France) and the cross-correlation technique Least Squares Deconvolution (LSD), we obtained 282 LSD Stokes V signatures of our 28 sample stars, in order to detect the magnetic field and to infer its longitudinal component with high precision (median σ = 40 G). Results. For the 28 studied stars, we obtained 27 detections of Stokes V Zeeman signatures from the MuSiCoS observations. Detection of the Stokes V signature of the 28th star (HD 32650) was obtained during science demonstration time of the new NARVAL spectropolarimeter at Pic du Midi. This result clearly shows that when observed with sufficient precision, all firmly classified Ap/Bp stars show detectable surface magnetic fields. Furthermore, all detected magnetic fields correspond to longitudinal fields which are significantly greater than some tens of G. To better characterise the surface magnetic field intensities and geometries of the sample, we phased the longitudinal field measurements of each star using new and previously-published rotational periods, and modeled them to infer the dipolar field intensity (Bd, measured at the magnetic pole) and the magnetic obliquity (β). The distribution of derived dipole strengths for these stars exhibits a plateau at about 1 kG, falling off to larger and smaller field strengths. Remarkably, in this sample of stars selected for their presumably weak magnetic fields, we find only 2 stars for which the derived dipole strength is weaker than 300 G.We interpret this "magnetic threshold" as a critical value necessary for the stability of large-scale magnetic fields, and develop a simple quantitative model that is able to approximately reproduce the observed threshold characteristics. This scenario leads to a natural explanation of the small fraction of intermediate-mass magnetic stars. It may also explain the near-absence of magnetic fields in more massive B and O-type stars