  Simulations of the clustering of cold dark matter yield dark-matter halos
that have central density cusps, but observations of totally dark-matter
dominated dwarf spheroidal galaxies imply that they do not have cuspy central
density profiles. We use analytic calculations and numerical modelling to argue
that whenever stars form, central density cusps are likely to be erased. Gas
that accumulates in the potential well of an initially cuspy dark-matter halo
settles into a disc. Eventually the surface density of the gas exceeds the
threshold for fragmentation into self-gravitating clouds. The clouds are
massive enough to transfer energy to the dark-matter particles via dynamical
friction on a short time-scale. The halo's central cusp is heated to form a
core with central logarithmic density slope gamma=0 before stellar feedback
makes its impact. Since star formation is an inefficient process, the clouds
are disrupted by feedback when only a small fraction of their mass has been
converted to stars, and the dark matter dominates the final mass distribution.
