We present the results of a radial velocity survey of 20 white dwarf plus M dwarf binaries selected as a follow up to a Hubble Space Telescope study that aimed to spatially resolve suspected binaries .
Our candidates are taken from the list of targets that were spatially unresolved with Hubble .
We have determined the orbital periods for 16 of these compact binary candidates .
The period distribution ranges from 0.14 to 9.16 d and peaks near 0.6 d. The original sample therefore contains two sets of binaries , wide orbits ( \approx 100 - 1000 au ) and close orbits ( \lesssim 1 - 10 au ) , with no systems found in the \approx 10 - 100 au range .
This observational evidence confirms the bimodal distribution predicted by population models and is also similar to results obtained in previous studies .
We find no binary periods in the months to years range , supporting the post common envelope evolution scenario .
One of our targets , WD 1504+546 , was discovered to be an eclipsing binary with a period of 0.93 d .