Context :

Aims : We have 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 have 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 \sigma = 40 G ) .

Results : For the 28 studied stars , we have obtained 27 detections of Stokes V Zeeman signatures from the MuSiCoS observations .
Detection of the Stokes V signature of the 28 ^ { th } star ( HD 32650 ) was obtained during science demonstration time of the new NARVAL spectropolarimeter at Pic du Midi .
This result shows clearly 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 have phased the longitudinal field measurements of each star using new and previously-published rotational periods , and modeled them to infer the dipolar field intensity and the magnetic obliquity .
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 .

Conclusions :