A tangential distortion of background source galaxies around foreground lens galaxies in the Hubble Deep Field is detected at the 99.3 % confidence level .
An important element of our analysis is the use of photometric redshifts to determine distances of lens and source galaxies and rest-frame B -band luminosities of the lens galaxies .
The lens galaxy halos obey a Tully–Fisher relation between halo circular velocity and luminosity ; the typical lens galaxy , at a redshift z = 0.6 , has a circular velocity of 210 \pm 40 \ > \mbox { km~ { } s \mbox { $ { } ^ { -1 } $ } } at M _ { B } = -18.5 , if q _ { 0 } = 0.5 .

Control tests , in which lens and source positions and source ellipticities are randomized , confirm the significance level of the detection quoted above .
Furthermore , a marginal signal is also detected from an independent , fainter sample of source galaxies without photometric redshifts .
Potential systematic effects , such as contamination by aligned satellite galaxies , the distortion of source shapes by the light of the foreground galaxies , PSF anisotropies , and contributions from mass distributed on the scale of galaxy groups are shown to be negligible .

A comparison of our result with the local Tully–Fisher relation indicates that intermediate-redshift galaxies are fainter than local spirals by 1.0 \pm 0.6 B mag .
at a fixed circular velocity .
This is consistent with some spectroscopic studies of the rotation curves of intermediate-redshift galaxies .
This result suggests that the strong increase in the global luminosity density with redshift is dominated by evolution in the galaxy number density .