Abstract
Context: Close white dwarf-red dwarf binaries must have gone through a common-envelope phase during their evolution. <ASTROBJ>DE CVn</ASTROBJ> is a detached white dwarf-red dwarf binary with a relatively short (~8.7 h) orbital period. Its brightness and the presence of eclipses makes this system ideal for a more detailed study. Aims: From a study of photometric and spectroscopic observations of <ASTROBJ>DE CVn</ASTROBJ> we derive the system parameters that we discuss in the framework of common-envelope evolution. Methods: Photometric observations of the eclipses are used to determine an accurate ephemeris. From a model fit to an average low-resolution spectrum of <ASTROBJ>DE CVn</ASTROBJ>, we constrain the temperature of the white dwarf and the spectral type of the red dwarf. The eclipse light curve is analysed and combined with the radial velocity curve of the red dwarf determined from time-resolved spectroscopy to derive constraints on the inclination and the masses of the components in the system. Results: The derived ephemeris is HJDmin = 2 452 784.5533(1) + 0.3641394(2) × E. The red dwarf in <ASTROBJ>DE CVn</ASTROBJ> has a spectral type of M3V and the white dwarf has an effective temperature of 8 000 K. The inclination of the system is 86<SUP>+3°</SUP><SUB>-2</SUB> and the mass and radius of the red dwarf are 0.41± 0.06 M<SUB>o</SUB> and 0.37<SUP>+0.06</SUP><SUB>-0.007</SUB> R<SUB>o</SUB>, respectively, and the mass and radius of the white dwarf are 0.51<SUP>+0.06</SUP><SUB>-0.02</SUB> M<SUB>o</SUB> and 0.0136<SUP>+0.0008</SUP><SUB>-0.0002</SUB> R<SUB>o</SUB>, respectively. Conclusions: We found that the white dwarf has a hydrogen-rich atmosphere (DA-type). Given that <ASTROBJ>DE CVn</ASTROBJ> has experienced a common-envelope phase, we can reconstruct its evolution and we find that the progenitor of the white dwarf was a relatively low-mass star (M<= 1.6~M<SUB>o</SUB>). The current age of this system is 3.3-7.3× 10<SUP>9</SUP> years, while it will take longer than the Hubble time for <ASTROBJ>DE CVn</ASTROBJ> to evolve into a semi-detached system.
