From Hydrogen to Helium: The Spectral Evolution of White Dwarfs as Evidence for Convective Mixing

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 hydrogen-atmosphere DA white dwarfs to separate them from helium-dominated objects in SDSS colour space. Across the effective temperature range from 20000K to 9000K we find that 22% of white dwarfs will undergo a spectral change, with no spectral evolution being ruled out at 5$\sigma$. 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% of white dwarfs must have a hydrogen mass larger than $M_{\rm H}/M_{\rm WD} = 10^{-10}$, another 25% have masses in the range $M_{\rm H}/M_{\rm WD} = 10^{-14}-10^{-10}$, and 15% have less hydrogen than $M_{\rm H}/M_{\rm WD} = 10^{-14}$. These results have implications for white dwarf asteroseismology, stellar evolution through the asymptotic giant branch (AGB) and accretion of planetesimals onto white dwarfs.