The core-cusp problem: a matter of perspective
  The existence of two kinematically and chemically distinct stellar
subpopulations in the Sculptor and Fornax dwarf galaxies offers the opportunity
to constrain the density profile of their matter haloes by measuring the mass
contained within the well-separated half-light radii of the two metallicity
subpopulations. Walker and Penarrubia have used this approach to argue that
data for these galaxies are consistent with constant-density `cores' in their
inner regions and rule out `cuspy' Navarro-Frenk-White (NFW) profiles with high
statistical significance, particularly in the case of Sculptor. We test the
validity of these claims using dwarf galaxies in the APOSTLE (A Project Of
Simulating The Local Environment) Lambda cold dark matter cosmological
hydrodynamics simulations of analogues of the Local Group. These galaxies all
have NFW dark matter density profiles and a subset of them develop two distinct
metallicity subpopulations reminiscent of Sculptor and Fornax. We apply a
method analogous to that of Walker and Penarrubia to a sample of 53 simulated
dwarfs and find that this procedure often leads to a statistically significant
detection of a core in the profile when in reality there is a cusp. Although
multiple factors contribute to these failures, the main cause is a violation of
the assumption of spherical symmetry upon which the mass estimators are based.
The stellar populations of the simulated dwarfs tend to be significantly
elongated and, in several cases, the two metallicity populations have different
asphericity and are misaligned. As a result, a wide range of slopes of the
density profile are inferred depending on the angle from which the galaxy is
viewed.
