Abstract
We determine the orbits of four double-degenerate systems (DDs), composed of two white dwarfs and two white-dwarf-M-dwarf binaries. The four DDs, WD1022+050, WD1428+373, WD1824+040 and WD2032+188, show orbital periods of 1.157155(5), 1.15674(2), 6.26602(6) and 5.0846(3) d, respectively. These periods combined with estimates for the masses of the brighter component, based on their effective temperatures, allow us to constrain the masses of the unseen companions. We estimate that the upper limit for the contribution of the unseen companions to the total luminosity in the four DDs ranges between 10 and 20 per cent. In the case of the two white-dwarf-M-dwarf binaries, WD1042-690 and WD2009+622, we calculate the orbital parameters by fitting simultaneously the absorption line from the white dwarf and the emission core from the M dwarf. Their orbital periods are 0.337083(1) and 0.741226(2) d, respectively. We find signatures of irradiation on the inner face of the companion to WD2009+622. We calculate the masses of both components from the gravitational redshift and the mass-radius relationship for white dwarfs and find masses of 0.75-0.78 and 0.61-0.64M<SUB>solar</SUB> for WD1042-690 and WD2009+622, respectively. This indicates that the stars probably reached the asymptotic giant branch in their evolution before entering a common envelope phase. These two white-dwarf-M-dwarf binaries will become cataclysmic variables, although not within a Hubble time, with orbital periods below the period gap.
