White dwarf-red dwarf binaries in the Sloan Digital Sky Survey

Context. A significant fraction of binary stars consisting of a white dwarf and a low-mass main-sequence star (red dwarf) are expected to be close binaries that are the end products of common-envelope (CE) evolution. Aims. To gain a better understanding of CE evolution, we want to study white dwarf-red dwarf binaries. For this it is fundamental to establish a well-defined sample. Methods. To reduce contamination by more distant sources, such as quasars, we have selected candidate white dwarf-red dwarf binaries from the catalogue of proper motion stars drawn from the intersection of the Sloan Digital Sky Survey (SDSS) and the USNO-B1.0 catalogue. To separate single from binary sources and to cut spurious sources out, we define selection criteria based on a combination of the $(u-g)$, $(g-r)$, and $(r-i)$ colours. Results. We evaluate and discuss the selection criteria on the basis of both the publicly available SDSS spectra and the predicted colours of white dwarf-red dwarf binaries. We define a sample of 651 binary candidates. However, we find that for r magnitudes brighter than ~16.5 the proper motion catalogue is heavily contaminated with sources that have incorrect colours due to the r magnitudes being relatively too faint, most likely due to saturation effects. Conclusions. We show that the level of contamination can be reduced by either excluding sources brighter than $r = 16.5$ mag or by excluding sources bluer than $(u-g) = -0.5$ or $(g-r) = -0.6$ and brighter than $r = 16.0$ mag. We expect ~85% of the remaining sources to be genuine white dwarf-red dwarf binaries. We estimate that we exclude ~5-10% of the white dwarf-red dwarf binaries in the proper motion catalogue