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 x 10(9) < M-halo/M-circle dot < 7.8 x 10(11), hosting galaxies with stellar masses in the range 5.0 x 10(5) < M-*/M-circle dot < 8.3 x 10(10), 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, alpha in rho alpha r(alpha), 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, less than or similar to 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 similar to 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 alpha on M-*/M-halo with the empirical abundance matching relation between M-* and M-halo provides a prediction for how alpha 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 similar to 50 km s(-1), with alpha decreasing for more massive disc galaxies: spirals with V-rot similar to 150 km s(-1) have central slopes alpha <= -0.8, approaching again the Navarro-Frenk-White profile. This novel prediction for the dependence of alpha 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.