We present optical spectroscopy and near-infrared photometry of 57 faint ( g = 19 - 22 ) high proper motion white dwarfs identified through repeat imaging of \approx 3100 square degrees of the Sloan Digital Sky Survey footprint by Munn et al .
( 31 ) .
We use ugriz and JH photometry to perform a model atmosphere analysis , and identify ten ultracool white dwarfs with T _ { eff } < 4000 K , including the coolest pure H atmosphere white dwarf currently known , J1657+2638 , with T _ { eff } = 3550 \pm 100 K. The majority of the objects with cooling ages larger than 9 Gyr display thick disc kinematics and constrain the age of the thick disc to \geq 11 Gyr .
There are four white dwarfs in our sample with large tangential velocities ( v _ { tan } > 120 km s ^ { -1 } ) and UVW velocities that are more consistent with the halo than the Galactic disc .
For typical 0.6 M _ { \odot } white dwarfs , the cooling ages for these halo candidates range from 2.3 to 8.5 Gyr .
However , the total main-sequence + white dwarf cooling ages of these stars would be consistent with the Galactic halo if they are slightly undermassive .
Given the magnitude limits of the current large scale surveys , many of the coolest and oldest white dwarfs remain undiscovered in the solar neighborhood , but upcoming surveys such as GAIA and the Large Synoptic Survey Telescope ( LSST ) should find many of these elusive thick disc and halo white dwarfs .