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A tangential distortion of background source galaxies around foreground lensgalaxies in the Hubble Deep Field is detected at the 99.3% confidence level. Animportant element of our analysis is the use of photometric redshifts todetermine distances of lens and source galaxies and rest-frame B-bandluminosities of the lens galaxies. The lens galaxy halos obey a Tully-Fisherrelation between halo circular velocity and luminosity; the typical lensgalaxy, at a redshift z = 0.6, has a circular velocity of 210 +/-40 km/s at M_B= -18.5, if q_0 = 0.5. Control tests, in which lens and source positions andsource ellipticities are randomized, confirm the significance level of thedetection quoted above. Furthermore, a marginal signal is also detected from anindependent, fainter sample of source galaxies without photometric redshifts.Potential systematic effects, such as contamination by aligned satellitegalaxies, the distortion of source shapes by the light of the foregroundgalaxies, PSF anisotropies, and contributions from mass distributed on thescale of galaxy groups are shown to be negligible. A comparison of our resultwith the local Tully-Fisher relation indicates that intermediate-redshiftgalaxies are fainter than local spirals by 1.0 +/- 0.6 B mag at a fixedcircular velocity. This is consistent with some spectroscopic studies of therotation curves of intermediate-redshift galaxies. This result suggests thatthe strong increase in the global luminosity density with redshift is dominatedby evolution in the galaxy number density.Comment: Revised version with minor changes. 13 pages, 7 figures, LaTeX2e,  uses emulateapj and multicol styles (included). Accepted by Ap

Galaxy‐Galaxy Lensing in the Hubble Deep Field: The Halo Tully‐Fisher Relation at Intermediate Redshift