We present ULTRACAM photometry and X-Shooter spectroscopy of the eclipsing double white dwarf binary CSS 41177 , the only such system that is also a double-lined spectroscopic binary .
Combined modelling of the light curves and radial velocities yield masses and radii for both white dwarfs without the need to assume mass-radius relations .
We find that the primary white dwarf has a mass of M _ { 1 } = 0.38 \pm 0.02 M _ { \odot } and a radius of R _ { 1 } = 0.0222 \pm 0.0004 R _ { \odot } .
The secondary white dwarf ’ s mass and radius are M _ { 2 } = 0.32 \pm 0.01 M _ { \odot } and R _ { 2 } = 0.0207 \pm 0.0004 R _ { \odot } , and its temperature and surface gravity ( T _ { 2 } = 11678 \pm 313 K , log ( g _ { 2 } ) = 7.32 \pm 0.02 ) put it close to the white dwarf instability strip .
However , we find no evidence for pulsations to roughly 0.5 % relative amplitude .
Both masses and radii are consistent with helium white dwarf models with thin hydrogen envelopes of \leq 10 ^ { -4 } M _ { * } .
The two stars will merge in 1.14 \pm 0.07 Gyr due to angular momentum loss via gravitational wave emission .