We present high precision, model independent, mass and radius measurements for 16 white dwarfs in detached eclipsing binaries and combine these with previously published data to test the theoretical white dwarf mass-radius relationship. We reach a mean precision of 2.4 per cent in mass and 2.7 per cent in radius, with our best measurements reaching a precision of 0.3 per cent in mass and 0.5 per cent in radius. We find excellent agreement between the measured and predicted radii across a wide range of masses and temperatures. We also find the radii of all white dwarfs with masses less than 0.48 M ⊙ to be fully consistent with helium core models, but they are on average 9 per cent larger than those of carbon-oxygen core models. In contrast, white dwarfs with masses larger than 0.52 M ⊙ all have radii consistent with carbonoxygen core models. Moreover, we find that all but one of the white dwarfs in our sample have radii consistent with possessing thick surface hydrogen envelopes (10 −5 ≥ M H /M WD ≥ 10 −4 ), implying that the surface hydrogen layers of these white dwarfs are not obviously affected by common envelope evolution.

We present high time resolution SDSS-g and SDSS-z light curves of the primary eclipse in SDSS J141126.20+200911.1, together with time-resolved X-Shooter spectroscopy and near-infrared JHK s photometry. Our observations confirm the substellar nature of the companion, making SDSS J141126.20+200911.1 the first eclipsing white dwarf/brown dwarf binary known. We measure a (white dwarf model dependent) mass and radius for the brown dwarf companion of M 2 = 0.050 ± 0.002 M and R 2 = 0.072 ± 0.004 M , respectively. The lack of a robust detection of the companion light in the z -band eclipse constrains the spectral type of the companion to be later than L5. Comparing the NIR photometry to the expected white dwarf flux reveals a clear K s -band excess, suggesting a spectral type in the range L7-T1.The radius measurement is consistent with the predictions of evolutionary models, and suggests a system age in excess of three Gyr. The low companion mass is inconsistent with the inferred spectral type of L7-T1, instead predicting a spectral type nearer T5. This indicates that irradiation of the companion in SDSS J1411 could be causing a significant temperature increase, at least on one hemisphere.

We present measurements of the component masses in 15 Cataclysmic Variables (CVs) -6 new estimates and 9 improved estimates. We provide new calibrations of the relationship between superhump period excess and mass ratio, and use this relation to estimate donor star masses for 225 superhumping CVs. With an increased sample of donor masses we revisit the implications for CV evolution. We confirm the high mass of white dwarfs in CVs, but find no trend in white dwarf mass with orbital period. We argue for a revision in the location of the orbital period minimum of CVs to 79.6 ± 0.2 min, significantly shorter than previous estimates. We find that CV donors below the gap have an intrinsic scatter of only 0.005 R around a common evolutionary track, implying a correspondingly small variation in angular momentum loss rates. In contrast to prior studies, we find that standard CV evolutionary tracks -without additional angular momentum loss -are a reasonable fit to the donor masses just below the period gap, but that they do not reproduce the observed period minimum, or fit the donor radii below 0.1 M .

We present a long-term programme for timing the eclipses of white dwarfs in close binaries to measure apparent and/or real variations in their orbital periods. Our programme includes 67 close binaries, both detached and semi-detached and with M-dwarfs, K-dwarfs, brown dwarfs or white dwarfs secondaries. In total, we have observed more than 650 white dwarf eclipses. We use this sample to search for orbital period variations and aim to identify the underlying cause of these variations. We find that the probability of observing orbital period variations increases significantly with the observational baseline. In particular, all binaries with baselines exceeding 10 yrs, with secondaries of spectral type K2 -M5.5, show variations in the eclipse arrival times that in most cases amount to several minutes. In addition, among those with baselines shorter than 10 yrs, binaries with late spectral type (>M6), brown dwarf or white dwarf secondaries appear to show no orbital period variations. This is in agreement with the so-called Applegate mechanism, which proposes that magnetic cycles in the secondary stars can drive variability in the binary orbits. We also present new eclipse times of NN Ser, which are still compatible with the previously published circumbinary planetary system model, although only with the addition of a quadratic term to the ephemeris. Finally, we conclude that we are limited by the relatively short observational baseline for many of the binaries in the eclipse timing programme, and therefore cannot yet draw robust conclusions about the cause of orbital period variations in evolved, white dwarf binaries.

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