  The interpretation of high proper motion white dwarfs detected by Oppenheimer
et al (2001) was the start of a lively controversy. While the discoverers
identify a large fraction of their findings as dark halo members, others
interpret the same sample as essentially made of disc and/or thick disc stars.
We use the comprehensive description of Galactic stellar populations provided
by the "Besancon" model to produce a realistic simulation of Oppenheimer et al.
data, including all observational selections and calibration biases. The
conclusion is unambiguous: Thick disc white dwarfs resulting from ordinary
hypotheses on the local density and kinematics are sufficient to explain the
observed objects, there is no need for halo white dwarfs. This conclusion is
robust to reasonable changes in model ingredients. The main cause of the
misinterpretation seems to be that the velocity distribution of a proper motion
selected star sample is severely biased in favour of high velocities. This has
been neglected in previous analyses. Obviously this does not prove that no such
objects like halo white dwarfs can exist, but Oppenheimer et al. observations
drive their possible contribution in the dark matter halo down to an extremely
low fraction.
