Dark matter cores all the way down

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 = 10^7 - 10^9 Msun. We work at a resolution (~4 pc minimum cell size; ~250 Msun 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 find that our dwarf galaxies give a remarkable match to the stellar light profile; 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 (r_1/2) always form if star formation proceeds for long enough. Cores fully form in less than 4 Gyrs for the M200 = 10^8 Msun and 14 Gyrs for the 10^9 Msun dwarf. We provide a convenient two parameter 'coreNFW' fitting 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 LCDM is correct, then 'pristine' dark matter cusps will be found either in systems that have truncated star formation and/or at radii r > r_1/2; (ii) complete core formation lowers the projected velocity dispersion at r_1/2 by a factor ~2, which is sufficient 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.