The Energetics of Cusp Destruction
  We present a new analytic estimate for the energy required to create a
constant density core within a dark matter halo. Our new estimate, based on
more realistic assumptions, leads to a required energy that is orders of
magnitude lower than is claimed in earlier work. We define a core size based on
the logarithmic slope of the dark matter density profile so that it is
insensitive to the functional form used to fit observed data. The energy
required to form a core depends sensitively on the radial scale over which dark
matter within the cusp is redistributed within the halo. Simulations indicate
that within a region of comparable size to the active star forming regions of
the central galaxy that inhabits the halo, dark matter particles have their
orbits radially increased by a factor of 2--3 during core formation. Thus the
inner properties of the dark matter halo, such as halo concentration, and final
core size, set the energy requirements. As a result, the energy cost increases
slowly with halo mass as M$_{\rm{h}}^{0.3-0.7}$ for core sizes $\lesssim1$ kpc.
We use the expected star formation history for a given dark matter halo mass to
predict dwarf galaxy core sizes. We find that supernovae alone would create
well over 4 kpc cores in $10^{10}$ M$_{\odot}$ dwarf galaxies \emph{if} 100% of
the energy were transferred to dark matter particle orbits. We can directly
constrain the efficiency factor by studying galaxies with known stellar content
and core size, such as Fornax. We find that the efficiency of coupling between
stellar feedback and dark matter orbital energy need only be at the 1% level or
less to explain Fornax's 1 kpc core.
