Search for nearby counterparts to the moving objects in the Hubble Deep Field

Ibata et al. have recently discovered very faint, moving objects in the Hubble Deep Field (HDF). The number, apparent magnitudes and proper motions of these objects are consistent with old white dwarfs making up part of the Galactic dark halo. We review a number of ground-based proper motion surveys in which nearby dark-halo white dwarfs might be present, if they have the colours and absolute magnitudes proposed. No such objects have been found, whereas we argue here that several times more would be expected than in the HDF. We conclude that it is unlikely that hydrogen-atmosphere white dwarfs make up a significant fraction of the Galactic dark matter. No limits can be placed as yet on helium-atmosphere dwarfs from optical searches.