  Weak gravitational lensing shear could be measured far more precisely if
information about unlensed attributes of source galaxies were available. Disk
galaxy velocity fields supply such information, at least in principle, with
idealized models predicting orders of magnitude more Fisher information when
velocity field observations are used to complement images. To test the level at
which realistic features of disk galaxies (warps, bars, spiral arms, and other
substructure) inject noise or bias into such shear measurements, we fit an
idealized disk model, including shear, to unsheared galaxies in the Illustris
TNG100 simulation. The inferred shear thus indicates the extent to which
unmodeled galaxy features inject noise and bias. We find that $\gamma_+$, the
component of shear parallel to the galaxy's first principal axis, is highly
biased and noisy because disks violate the assumption of face-on circularity,
displaying a range of intrinsic axis ratios ($0.85\pm0.11$). The other shear
component, $\gamma_\times$, shows little bias and is well-described by a double
Gaussian distribution with central core scatter $\sigma_{\text{core}} \approx$
0.03, with low-amplitude, broad wings. This is the first measurement of the
natural noise floor in the proposed velocity-field lensing technique. We
conclude that the technique will achieve impressive precision gains for
measurements of $\gamma_\times$, but little gain for measurements of
$\gamma_+$.

Instrumentation and Methods for Astrophysics;Cosmology and Nongalactic Astrophysics