  The non-detection of dark matter (DM) particles in increasingly stringent
laboratory searches has encouraged alternative gravity theories where gravity
is sourced only from visible matter. Here, we consider whether such theories
can pass a two-dimensional test posed by gravitational lensing -- to reproduce
a particularly detailed Einstein ring in the core of the galaxy cluster Abell
3827. We find that when we require the lensing mass distribution to strictly
follow the shape (ellipticity and position angle) of the light distribution of
cluster member galaxies, intracluster stars, and the X-ray emitting
intracluster medium, we cannot reproduce the Einstein ring, despite allowing
the mass-to-light ratios of these visible components to freely vary with radius
to mimic alternative gravity theories. Alternatively, we show that the detailed
features of the Einstein ring are accurately reproduced by allowing a smooth,
freely oriented DM halo in the lens model, with relatively small contributions
from the visible components at a level consistent with their observed
brightnesses. This dominant DM component is constrained to have the same
orientation as the light from the intracluster stars, indicating that the
intracluster stars trace the gravitational potential of this component. The
Einstein ring of Abell 3827 therefore presents a new challenge for alternative
gravity theories: not only must such theories find agreement between the total
lensing mass and visible mass, but they must also find agreement between the
projected sky distribution of the lensing mass and that of the visible matter,
a more stringent test than has hitherto been posed by lensing data.
