The mass and radius of the M-dwarf in the short-period eclipsing binary RR Caeli

We present new photometry and spectroscopy of the eclipsing white dwarf-M-dwarf binary star RR Cae. We use timings of the primary eclipse from white-light photo-electric photometry to derive a new ephemeris for the eclipses. We find no evidence for any period change greater than vertical bar((over dot P)vertical bar/P approximate to 5 x 10(-12) over a time-scale of 10 yr. We have measured the effective temperature of the white dwarf, T-WD, from an analysis of two high resolution spectra of RR Cae and find T-WD = 7540 K +/- 175 K. We estimate a spectral type of M4 for the companion from the same spectra. We have measured the radial velocity of the white dwarf from the Balmer absorption lines and find that the semi-amplitude of the spectroscopic orbit is K-WD = 79.3 +/- 3.0 km s(-1). We have combined our radial velocity measurements of the M-dwarf with published radial velocities to determine a new spectroscopic orbit for the M-dwarf with a semi-amplitude of K-M = 190.2 +/- 3.5 km s(-1). We have combined this information with an analysis of the primary eclipse to derive relations between the inclination of the binary and the radii of the two stars. We use cooling models for helium white dwarfs with a wide range of hydrogen layer masses to determine the likely range of the white dwarf radius and, thus, the inclination of the binary and the mass and radius of the M-dwarf. The mass of the M-dwarf is (0.182-0.183) +/- 0.013 M-circle dot and the radius is (0.203-0.215) +/- 0.013 R-circle dot where the ranges quoted for these values reflect the range of white dwarf models used. In contrast to previous studies, which lacked a measurement of K-WD, we find that the mass and radius of the M-dwarf are normal for an M4 dwarf. The mass of the white dwarf is 0.440 +/- 0.022 M-circle dot. With these revised masses and radii we find that RR Cae will become a cataclysmic variable star when the orbital period is reduced from its current value of 7.3 h to 121 min by magnetic braking in 9-20 Gyr. We note that there is night-to-night variability of a few seconds in the timing of primary eclipse caused by changes to the shape of the primary eclipse. We speculate as to the possible causes of this phenomenon.