  The location of the red edge of the ZZ Ceti instability strip is defined
observationally as being the lowest temperature for which a white dwarf with a
H-rich atmosphere (DA) is known to exhibit periodic brightness variations.
Whether this cut-off in flux variations is actually due to a cessation of
pulsation or merely due to the attenuation of any variations by the convection
zone, rendering them invisible, is not clear. The latter is a theoretical
possibility because with decreasing effective temperature, the emergent flux
variations become an ever smaller fraction of the amplitude of the flux
variations in the interior. In contrast to the flux variations, the visibility
of the velocity variations associated with the pulsations is not thought to be
similarly affected. Thus, models imply that were it still pulsating, a white
dwarf just below the observed red edge should show velocity variations. In
order to test this possibility, we used time-resolved spectra of three DA white
dwarfs that do not show photometric variability, but which have derived
temperatures only slightly lower than the coolest ZZ Ceti variables. We find
that none of our three targets show significant periodic velocity variations,
and set 95% confidence limits on amplitudes of 3.0, 5.2, and 8.8km/s. Thus, for
two out of our three objects, we can rule out velocity variations as large as
5.4km/s observed for the strongest mode in the cool white dwarf pulsator ZZ
Psc. In order to verify our procedures, we also examined similar data of a
known ZZ Ceti, HL Tau 76. Applying external information from the light curve,
we detect significant velocity variations for this object with amplitudes of up
to 4km/s, making it only the third DAV for which velocity variations have been
measured. (abridged)
