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 | \dot { P } | / P \approx 5 \times 10 ^ { -12 } over a timescale of 10 years .
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 } \pm 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 \pm 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 \pm 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 ) \pm 0.013 M _ { \odot } and the radius is ( 0.203 – 0.215 ) \pm 0.013 R _ { \odot } , 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 \pm 0.022 M _ { \odot } .
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 hours to 121 minutes 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 .