The kinematics of the white dwarf population from the SDSS DR12
  We use the Sloan Digital Sky Survey Data Release 12, which is the largest
available white dwarf catalog to date, to study the evolution of the
kinematical properties of the population of white dwarfs in the Galactic disc.
We derive masses, ages, photometric distances and radial velocities for all
white dwarfs with hydrogen-rich atmospheres. For those stars for which proper
motions from the USNO-B1 catalog are available the true three-dimensional
components of the stellar space velocity are obtained. This subset of the
original sample comprises 20,247 objects, making it the largest sample of white
dwarfs with measured three-dimensional velocities. Furthermore, the volume
probed by our sample is large, allowing us to obtain relevant kinematical
information. In particular, our sample extends from a Galactocentric radial
distance $R_{\rm G}=7.8$~kpc to 9.3~kpc, and vertical distances from the
Galactic plane ranging from $Z=-0.5$~kpc to 0.5~kpc. We examine the mean
components of the stellar three-dimensional velocities, as well as their
dispersions with respect to the Galactocentric and vertical distances. We
confirm the existence of a mean Galactocentric radial velocity gradient,
$\partial\langle V_{\rm R}\rangle/\partial R_{\rm
G}=-3\pm5$~km~s$^{-1}$~kpc$^{-1}$. We also confirm North-South differences in
$\langle V_{\rm z}\rangle$. Specifically, we find that white dwarfs with $Z>0$
(in the North Galactic hemisphere) have $\langle V_{\rm z}\rangle<0$, while the
reverse is true for white dwarfs with $Z<0$. The age-velocity dispersion
relation derived from the present sample indicates that the Galactic population
of white dwarfs may have experienced an additional source of heating, which
adds to the secular evolution of the Galactic disc.
