The dependence of dark matter profiles on the stellar to halo mass
  ratio: a prediction for cusps vs cores
  We use 31 simulated galaxies from the MaGICC project to investigate the
effects of baryonic feedback on the density profiles of dark matter (DM)
haloes. The sample covers a wide mass range: 9.4e9<Mhalo/Msun<7.8e11, hosting
galaxies with stellar masses: 5.0e5<M*/Msun<8.3e10, i.e. from dwarf to L*. The
galaxies are simulated with several baryonic prescriptions, including a range
of stellar feedbacks. The main result is a clear dependence of the inner slope
of the DM density profile, \alpha\ in \rho r^\alpha, on the ratio between
stellar-to-halo mass (M*/Mhalo). This relation is independent of the stellar
feedback scheme, allowing a prediction for cusp vs core formation. When
M*/Mhalo is low, ~0.01%, energy from stellar feedback is insufficient to
significantly alter the inner DM density and the galaxy retains a cuspy
profile. At higher M*/Mhalo, feedback drives the expansion of the DM and
generates cored profiles. The flattest profiles form where M*/Mhalo~0.5%. Above
this ratio, stars formed in the central regions deepen the gravitational
potential enough to oppose this supernova-driven expansion process, resulting
in smaller cores and cuspier profiles. Combining the dependence of \alpha\ on
M*/Mhalo with the abundance matching relation between M* and Mhalo provides a
prediction for how \alpha\ varies with M*. Further, using the Tully-Fisher
relation allows a prediction for the dependence of the DM inner slope on the
observed rotation velocity of galaxies. The most cored galaxies are expected to
have Vrot~50km/s, with \alpha\ decreasing for more massive disc galaxies:
spirals with Vrot~150km/s have central slopes \alpha<-0.8, approaching the NFW
profile. This novel prediction for the dependence of \alpha\ on disc galaxy
mass can be tested using current observational data sets, and can be applied to
theoretical modeling of mass profiles and populations of disc galaxies.
