We describe the first spectroscopic tomographic (spectrotomographic) weak-lensing measurement for a galaxy cluster based only on background galaxies with spectroscopically determined redshifts. We use the massive cluster A2029 to demonstrate the power of combining spectroscopy and lensing to obtain accurate masses and to overcome biases from contamination and photometric redshift errors. We detect the shear signal from the cluster at > 3.9s significance. The shear signal scales with source redshift in a way that is consistent with the angular diameter distance ratio variation in a ?CDM universe. Furthermore, the amplitude of the measured signal is consistent with the X-ray mass. Upcoming spectroscopic instruments such as the Prime Focus Spectrograph on Subaru will permit spectrotomographic weak-lensing measurements with a signal-to-noise ratio comparable with current photometric-redshift-based weak-lensing measurements for hundreds of galaxy clusters. Thus, spectrotomography may enable sensitive cosmological constraints that complement and are independent of other measurement techniques.
