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 _ { 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 _ { R } \rangle / \partial R _ { G } = -3 \pm 5 km s ^ { -1 } kpc ^ { -1 } .
We also confirm North-South differences in \langle V _ { z } \rangle .
Specifically , we find that white dwarfs with Z > 0 ( in the North Galactic hemisphere ) have \langle V _ { 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 .