A deep WISE search for very late type objects and the discovery of two
  halo/thick-disk T dwarfs: WISE 0013+0634 and WISE 0833+0052
  A method is defined for identifying late T and Y dwarfs in WISE down to low
values of signal-to-noise. This requires a WISE detection only in the W2-band
and uses the statistical properties of the WISE multi-frame measurements and
profile fit photometry to reject contamination resulting from non-point-like
objects, variables and moving sources. To trace our desired parameter space we
use a control sample of isolated non-moving non-variable point sources from the
SDSS, and identify a sample of 158 WISE W2-only candidates down to a
signal-to-noise limit of 8. For signal-to-noise ranges >10 and 8-10
respectively, ~45% and ~90% of our sample fall outside the selection criteria
published by the WISE team (Kirkpatrick et al. 2012), due mainly to the type of
constraints placed on the number of individual W2 detections. We present
follow-up of eight candidates and identify WISE 0013+0634 and WISE 0833+0052,
T8 and T9 dwarfs with high proper motion (~1.3 and ~1.8 arcsec/yr). Both
objects show a mid-infrared/near-infrared excess of ~1-1.5 magnitudes, and are
K-band suppressed. Distance estimates lead to space motion constraints that
suggest halo (or at least thick disk) kinematics. We then assess the reduced
proper motion diagram of WISE ultracool dwarfs, which suggests that late T and
Y dwarfs may have a higher thick-disk/halo population fraction than earlier
objects.
