Testing the Nature of Dark Matter with Extremely Large Telescopes
  For nearly 40 years, dark matter has been widely assumed to be cold and
collisionless. Cold dark matter models make fundamental predictions for the
behavior of dark matter on small (<10 kpc) scales. These predictions include
cuspy density profiles at the centers of dark matter halos and a halo mass
function that increases as dN/dM ~ M^-1.9 down to very small masses. We suggest
two observational programs relying on extremely large telescopes to critically
test these predictions, and thus shed new light on the nature of dark matter.
(1) Combining adaptive optics-enabled imaging with deep spectroscopy to measure
the three-dimensional motions of stars within a sample of Local Group dwarf
galaxies that are the cleanest dark matter laboratories known in the nearby
universe. From these observations the inner slope of the dark matter density
profile can be determined with an accuracy of 0.20 dex, enabling a central cusp
to be distinguished from a core at 5 sigma significance. (2)
Diffraction-limited AO imaging and integral field spectroscopy of
gravitationally lensed galaxies and quasars to quantify the abundance of dark
substructures in the halos of the lens galaxies and along the line of sight.
Observations of 50 lensed arcs and 50 multiply-imaged quasars will be
sufficient to measure the halo mass function over the range 10^7 < M < 10^10
Msun at cosmological scales, independent of the baryonic and stellar
composition of those structures. These two observational probes provide
complementary information about the small scale structure, with a joint
self-consistent analysis mitigating limitations of either probe. This program
will produce the strongest existing constraints on the properties of dark
matter on small scales, allowing conclusive tests of alternative warm, fuzzy,
and self-interacting dark matter models.
