Abstract
We use high resolution simulations of isolated dwarf galaxies to study the physics of dark matter cusp-core transformations at the edge of galaxy formation: M200 = 107 109M .We work at a resolution ( 4 pc minimum cell size; 250M per particle) at which the impact from individual supernovae explosions can be resolved, becoming insensitive to even large changes in our numerical `sub-grid' parameters. We nd that our dwarf galaxies give a remarkable match to the stellar light pro le; star formation history; metallicity distribution function; and star/gas kinematics of isolated dwarf irregular galaxies. Our key result is that dark matter cores of size comparable to the stellar half mass radius r1=2 always form if star formation proceeds for long enough. Cores fully form in less than 4 Gyrs for the M200 = 108M and 14 Gyrs for the 109M dwarf. We provide a convenient two parameter `coreNFW' tting function that captures this dark matter core growth as a function of star formation time and the projected stellar half mass radius. Our results have several implications: (i) we make a strong prediction that if CDM is correct, then `pristine' dark matter cusps will be found either in systems that have truncated star formation and/or at radii r > r1=2; (ii) complete core formation lowers the projected velocity dispersion at r1=2 by a factor 2, which is su cient to fully explain the `too big to fail problem'; and (iii) cored dwarfs will be much more susceptible to tides, leading to a dramatic scouring of the subhalo mass function inside galaxies and groups.