  We present new observations of CO J=2-1 emission from the protoplanetary disk
around TW Hya. Emission is detected out to 240 au (4") and found to exhibit
azimuthal variations up to 20% beyond 180 au (3"), with the west side of the
disk brighter than the east. This asymmetry is interpreted as tracing the
shadow previously seen in scattered light. A reanalysis of the multi-epoch
observations of the dust shadow in scattered light from Debes et al. (2017)
suggests that an oscillatory motion would provide a better model of the
temporal evolution of the dust shadow rather than orbital motion. Both models
predict an angular offset between the dust shadow and the gas shadow of up to
~100 deg. We attribute this offset to the finite rate at which dust grains and
gas molecules can exchange heat, dominated by the collisional rate between gas
molecules and dust grains, $t_{\rm coll}$. The angular offsets derived are
equivalent to collisional timescales that range from the near instantaneous up
to $t_{\rm coll}$ ~ 10 years, depending on whether a straight or a curved dust
shadow, as suggested by HST observations reported by Debes et al. (2017), is
adopted. The inferred range of $t_{\rm coll}$ are consistent with those
predictions based on representative gas densities, temperatures, gas-to-dust
ratios and grain sizes. These results represent the first time empirical
constraints can be placed on $t_{\rm coll}$.
