The dependence of dark matter profiles on the stellar-to-halo mass ratio: a prediction for cusps versus cores

We use a suite of 31 simulated galaxies drawn from the MaGICC project to investigate the effects of baryonic feedback on the density profiles of dark matter haloes. The sample covers a wide mass range: 9.4 × 109 < M halo/ M < 7.8 × 1011, hosting galaxies with stellar masses in the range 5.0 × 105 < M */ M < 8.3 × 1010, i.e. from dwarf to L*. The galaxies are simulated with blastwave supernova feedback and, for some of them, an additional source of energy from massive stars is included. Within this feedback scheme we vary several parameters, such as the initial mass function, the density threshold for star formation, and energy from supernovae and massive stars. The main result is a clear dependence of the inner slope of the dark matter density profile, α in ρ ∝ r α, on the stellar-to-halo mass ratio, M */M halo. This relation is independent of the particular choice of parameters within our stellar feedback scheme, allowing a prediction for cusp versus core formation. When M */M halo is low, 0.01 per cent, energy from stellar feedback is insufficient to significantly alter the inner dark matter density, and the galaxy retains a cuspy profile. At higher stellar-to-halo mass ratios, feedback drives the expansion of the dark matter and generates cored profiles. The flattest profiles form where M */M halo ∼ 0.5 per cent. Above this ratio, stars formed in the central regions deepen the gravitational potential enough to oppose the supernova-driven expansion process, resulting in cuspier profiles. Combining the dependence of α on M */M halo with the empirical abundance matching relation between M * and M halo provides a prediction for how α varies as a function of stellar mass. Further, using the Tully-Fisher relation allows a prediction for the dependence of the dark matter inner slope on the observed rotation velocity of galaxies. The most cored galaxies are expected to have V rot ∼ 50 km s−1, with α decreasing for more massive disc galaxies: spirals with V rot ∼ 150 km s−1 have central slopes α ≤ −0.8, approaching again the Navarro-Frenk-White profile. This novel prediction for the dependence of α on disc galaxy mass can be tested using observational data sets and can be applied to theoretical modelling of mass profiles and populations of disc galaxies.