The mass and radius of the M dwarf companion to GD 448

We present spectroscopy and photometry of GD 448, a detached white dwarf – M dwarf binary with a period of 2.47 h. We find that the Na  I  8200-Å feature is composed of narrow emission lines, owing to irradiation of the M dwarf by the white dwarf, within broad absorption lines that are essentially unaffected by heating. Combined with an improved spectroscopic orbit and gravitational redshift measurement from spectra of the Hα line, we are able to derive masses for the white dwarf and M dwarf directly (0.41 ± 0.01 and 0.096 ± 0.004 M_⊙, respectively). We use a simple model of the Ca II emission lines to establish the radius of the M dwarf assuming the emission from its surface to be proportional to the incident flux per unit area from the white dwarf. The radius derived is 0.125 ± 0.020 R_⊙. The M dwarf appears to be a normal main-sequence star in terms of its mass and radius, and is less than half the size of its Roche lobe. The thermal time-scale of the M dwarf is much longer than the cooling age of the white dwarf, so we conclude that the M dwarf was unaffected by the common-envelope phase. The anomalous width of the Hα emission from the M dwarf remains to be explained, but the strength of the line may be due to X-ray heating of the M dwarf owing to accretion on to the white dwarf from the M dwarf wind.