On the incidence of weak magnetic fields in DA white dwarfs

Context: About 10% of white dwarfs have magnetic fields with strength in the range between about 10^5 and 3x10^8 G. It is not known whether the remaining white dwarfs are not magnetic, or if they have a magnetic field too weak to be detected with the techniques adopted in the large surveys. Aims. We describe the results of the first survey specifically devised to clarify the detection frequency of kG-level magnetic fields in cool DA white dwarfs. Methods: Using the FORS1 instrument of the ESO VLT, we have obtained Balmer line circular spectropolarimetric measurements of a small sample of cool (DA6 - DA8) white dwarfs. Using FORS and UVES archive data, we have also revised numerous white dwarf field measurements previously published in the literature. Results: We have discovered an apparently constant longitudinal magnetic field of \sim9.5 kG in the DA6 white dwarf WD2105-820. This star is the first weak-field white dwarf that has been observed sufficiently to roughly determine the characteristics of its field. The available data are consistent with a simple dipolar morphology with magnetic axis nearly parallel to the rotation axis, and a polar strength of \simeq 56 kG. Our re-evaluation of the FORS archive data for white dwarfs indicates that longitudinal magnetic fields weaker than 10 kG had previously been correctly identified in at least three white dwarfs. Conclusions: We find that the probability of detecting a field of kG strength in a DA white dwarf is of the order of 10% for each of the cool and hot DA stars. If there is a lower cutoff to field strength in white dwarfs, or a field below which all white dwarfs are magnetic, the current precision of measurements is not yet sufficient to reveal it.