  The recent emergence of detections of the kinetic Sunyaev-Zel'dovich (kSZ)
effect through cross-correlation techniques is encouraging for the prospects of
future cosmic microwave background (CMB) experiments. Extracting information on
the large-scale velocity fields and constraining cosmological parameters from
such kSZ measurements requires an understanding of the optical depth to CMB
photons through halos. Using cosmological hydrodynamic simulations we find that
there exists a low-scatter relation between the optical depth and thermal
Sunyaev-Zel'dovich (tSZ) signal of halos within a physical aperture. We propose
that such a relation can be used to break the degeneracy between optical depth
and line-of-sight velocity in kSZ measurements. The limiting factors in our
proposal are systematic uncertainties associated with the sub-grid physics
models in the simulations, which we calculate to be less than 10 percent. We
discuss future observational measurements that could potentially be used to
mitigate the systematic uncertainties in this scaling relation.
