AM CVn-type systems are ultra-compact , hydrogen-deficient accreting binaries with degenerate or semi-degenerate donors .
The evolutionary history of these systems can be explored by constraining the properties of their donor stars .
We present high-speed photometry of Gaia14aae , an AM CVn with a binary period of 49.7 minutes and the first AM CVn in which the central white dwarf is fully eclipsed by the donor star .
Modelling of the lightcurves of this system allows for the most precise measurement to date of the donor mass of an AM CVn , and relies only on geometric and well-tested physical assumptions .
We find a mass ratio q = M _ { 2 } / M _ { 1 } = 0.0287 \pm 0.0020 and masses M _ { 1 } = 0.87 \pm 0.02 M _ { \odot } and M _ { 2 } = 0.0250 \pm 0.0013 M _ { \odot } .
We compare these properties to the three proposed channels for AM CVn formation .
Our measured donor mass and radius do not fit with the contraction that is predicted for AM CVn donors descended from white dwarfs or helium stars at long orbital periods .
The donor properties we measure fall in a region of parameter space in which systems evolved from hydrogen-dominated cataclysmic variables are expected , but such systems should show spectroscopic hydrogen , which is not seen in Gaia14aae .
The evolutionary history of this system is therefore not clear .
We consider a helium-burning star or an evolved cataclysmic variable to be the most likely progenitors , but both models require additional processes and/or fine-tuning to fit the data .
Additionally , we calculate an updated ephemeris which corrects for an anomalous time measurement in the previously published ephemeris .