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We present a detailed spectroscopic and photometric analysis of DA and DBwhite dwarfs drawn from the Sloan Digital Sky Survey with trigonometricparallax measurements available from the Gaia mission. The temperature and massscales obtained from fits to $ugriz$ photometry appear reasonable for both DAand DB stars, with almost identical mean masses of $\langle M \rangle =0.617~M_\odot$ and $0.620~M_\odot$, respectively. The comparison with similarresults obtained from spectroscopy reveals several problems with our modelspectra for both pure hydrogen and pure helium compositions. In particular, wefind that the spectroscopic temperatures of DA stars exceed the photometricvalues by $\sim$10% above $T_{\rm eff}\sim14,000$~K, while for DB white dwarfs,we observe large differences between photometric and spectroscopic masses below$T_{\rm eff}\sim16,000$~K. We attribute these discrepancies to the inaccuratetreatment of Stark and van der Waals broadening in our model spectra,respectively. Despite these problems, the mean masses derived from spectroscopy--- $\langle M \rangle = 0.615~M_\odot$ and $0.625~M_\odot$ for the DA and DBstars, respectively --- agree extremely well with those obtained fromphotometry. Our analysis also reveals the presence of several unresolved doubledegenerate binaries, including DA+DA, DB+DB, DA+DB, and even DA+DC systems. Wefinally take advantage of the Gaia parallaxes to test the theoreticalmass-radius relation for white dwarfs. We find that 65% of the white dwarfs areconsistent within the 1$\sigma$ confidence level with the predictions of themass-radius relation, thus providing strong support to the theory of stellardegeneracy.

A comprehensive spectroscopic and photometric analysis of DA and DB white dwarfs from SDSS and Gaia