We present a study of the hypothesis that white dwarfs undergo a spectral change from hydrogen- to helium-dominated atmospheres using a volume-limited photometric sample drawn from the Gaia-DR2 catalogue, the Sloan Digital Sky Survey (SDSS), and the Galaxy Evolution Explorer (GALEX). We exploit the strength of the Balmer jump in hydrogenatmosphere DA white dwarfs to separate them from helium-dominated objects in SDSS colour space. Across the effective temperature range from 20 000 to 9000 K, we find that 22 per cent of white dwarfs will undergo a spectral change, with no spectral evolution being ruled out at 5σ. The most likely explanation is that the increase in He-rich objects is caused by the convective mixing of DA stars with thin hydrogen layers, in which helium is dredged up from deeper layers by a surface hydrogen convection zone. The rate of change in the fraction of He-rich objects as a function of temperature, coupled with a recent grid of 3D radiation-hydrodynamic simulations of convective DA white dwarfs-which include the full overshoot region-lead to a discussion on the distribution of total hydrogen mass in white dwarfs.We find that 60 per cent of white dwarfs must have a hydrogen mass larger than MH/MWD = 10-10, another 25 per cent have masses in the range MH/MWD = 10-14-10-10, and 15 per cent have less hydrogen than MH/MWD = 10-14. These results have implications for white dwarf asteroseismology, stellar evolution through the asymptotic giant branch and accretion of planetesimals on to white dwarfs.
