  The distribution of mass in galaxy-scale strong gravitational lenses is often
modelled as an elliptical power law plus 'external shear', which notionally
accounts for neighbouring galaxies and cosmic shear. We show that it does not.
Except in a handful of rare systems, the best-fit values of external shear do
not correlate with independent measurements of shear: from weak lensing in 45
Hubble Space Telescope images, or in 50 mock images of lenses with complex
distributions of mass. Instead, the best-fit shear is aligned with the major or
minor axis of 88% of lens galaxies; and the amplitude of the external shear
increases if that galaxy is disky. We conclude that 'external shear' attached
to a power law model is not physically meaningful, but a fudge to compensate
for lack of model complexity. Since it biases other model parameters that are
interpreted as physically meaningful in several science analyses (e.g.
measuring galaxy evolution, dark matter physics or cosmological parameters), we
recommend that future studies of galaxy-scale strong lensing should employ more
flexible mass models.
