  The flux anomalies in four-image gravitational lenses can be interpreted as
evidence for the dark matter substructure predicted by cold dark matter (CDM)
halo models. In principle, these flux anomalies could arise from alternate
sources such as absorption, scattering or scintillation by the interstellar
medium (ISM) of the lens galaxy, problems in the ellipsoidal macro models used
to fit lens systems, or stellar microlensing. We apply several tests to the
data that appear to rule out these alternate explanations. First, the radio
flux anomalies show no significant dependence on wavelength, as would be
expected for almost any propagation effect in the ISM or microlensing by the
stars. Second, the flux anomaly distributions show the characteristic
demagnifications of the brightest saddle point relative to the other images
expected for low optical depth substructure, which cannot be mimicked by either
the ISM or problems in the macro models. Microlensing by stars also cannot
reproduce the suppression of the bright saddle points if the radio source sizes
are consistent with the Compton limit for their angular sizes. Third, while it
is possible to change the smooth lens models to fit the flux anomalies in some
systems, we can rule out the necessary changes in all systems where we have
additional lens constraints to check the models. Moreover, the parameters of
these models are inconsistent with our present observations and expectations
for the structure of galaxies. We conclude that low-mass halos remain the best
explanation of the phenomenon.
