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: M-200 = 10(7)-10(9) M-circle dot. We work at a resolution (similar to 4 pc minimum cell size; similar to 250 M-circle dot 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 Gyr for the M-200 = 10(8) M-circle dot and similar to 14 Gyr for the 10(9) M-circle dot 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 Lambda cold dark matter 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 r1/2 by a factor of similar to 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 sub-halo mass function inside galaxies and groups.