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 that, based on more realistic assumptions, leads to demands that are orders of magnitude lower than claimed in earlier works. We define a core size based on the logarithmic slope of the dark matter density profile as it is insensitive to the functional form used to fit observed data. The energy required to form a core sensitively depends on the radial scale over which dark matter within the cusp is redistributed within the halo. Simulations indicate that within a region in size comparable to the active star forming regions of the central galaxy inhabiting a 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 set the energy requirements. The energy cost increases slowly with halo mass as for core sizes ≲1 kpc. We use the expected star formation history for a given halo mass to predict dwarf galaxy core sizes. We find that supernovae alone would create well over 4 kpc cores in 1010 M galaxies 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. We find that the efficiency of coupling between stellar feedback and dark matter orbital energy need only be ≲1% to explain Fornax’s 1 kpc core.