  We present HAWK-I J-band light curves of five late-type T dwarfs (T6.5-T7.5)
with a typical duration of four hours, and investigate the evidence for
quasi-periodic photometric variability on intra-night timescales. Our
photometry reaches precisions in the range 7-20 mmag, after removing
instrumental systematics that correlate with sky background, seeing and
airmass. Based upon a Lomb-Scargle periodogram analysis, the latest object in
the sample - ULAS J2321 (T7.5) - appears to show quasi-periodic variability
with a period of 1.64 hours and an amplitude of 3 mmag.
  Given the low amplitude of variability and presence of systematics in our
lightcurves, we discuss a Bayesian approach to robustly determine if
quasi-periodic variability is present in a lightcurve affected by red noise.
Using this approach, we conclude that the evidence for quasi-periodic
variability in ULAS J2321 is not significant. As a result, we suggest that
studies which identify quasi-periodic variables using the false alarm
probability from a Lomb-Scargle periodogram are likely to over-estimate the
number of variable objects, even if field stars are used to set a higher false
alarm probability threshold. Instead we argue that a hybrid approach combining
a false alarm probability cut, followed by Bayesian model selection, is
necessary for robust identification of quasi-periodic variability in
lightcurves with red noise.
