We present radial velocity observations of four binary white dwarf candidates identified through their over-luminosity .
We identify two new double-lined spectroscopic binary systems , WD 0311 - 649 and WD 1606+422 , and constrain their orbital parameters .
WD 0311 - 649 is a 17.7 h period system with a mass ratio of 1.44 \pm 0.06 and WD 1606+422 is a 20.1 h period system with a mass ratio of 1.33 \pm 0.03 .
An additional object , WD 1447 - 190 , is a 43 h period single-lined white dwarf binary , whereas WD 1418 - 088 does not show any significant velocity variations over timescales ranging from minutes to decades .
We present an overview of the 14 over-luminous white dwarfs that were identified by Bédard et al. , and find the fraction of double- and single-lined systems to be both 31 % .
However , an additional 31 % of these over-luminous white dwarfs do not show any significant radial velocity variations .
We demonstrate that these must be in long-period binaries that may be resolved by Gaia astrometry .
We also discuss the over-abundance of single low-mass white dwarfs identified in the SPY survey , and suggest that some of those systems are also likely long period binary systems of more massive white dwarfs .