  We present multi-colour photometry of the M8.5V ultracool dwarf "pulsar" TVLM
513-46546 (hereafter TVLM 513) obtained with the triple-beam photometer
ULTRACAM. Data were obtained simultaneously in the Sloan-g' and Sloan-i' bands.
The previously reported sinusoidal variability, with a period of 2-hrs, is
recovered here. However, the Sloan-g' and Sloan-i' lightcurves are
anti-correlated, a fact which is incompatible with the currently proposed
starspot explanation for the optical variability. The anti-correlated nature
and relative amplitudes of the optical lightcurves are consistent with the
effects of persistent dust clouds rotating on the surface of the star. In the
absence of other plausible explanations for the optical variability of TVLM
513, it seems likely that dust cloud coverage combined with the rapid rotation
of TVLM 513 is responsible for the optical variability in this object. However,
crude modelling of a photosphere with partial dust cloud coverage shows that
the anti-correlation can only be reproduced using cooler models than the
literature temperature of TVLM 513. We suggest this discrepancy can be removed
if more dust is present within the photosphere of TVLM 513 than theoretical
model atmospheres predict, though a definitive statement on this matter will
require the development of self-consistent models of partially dusty
atmospheres.
