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.