1.3. Dynamics of Cusps
Another potential problem is whether cold dark matter predictions of cusps in the cores of galaxies are compatible with observations . The cold dark matter density in a generic spheroidal galactic halo may be parameterized by
where r0 is some scale factor. Early isothermal models of galactic haloes were nonsingular, with = 0, = = 2. These were superseded by Navarro-Frenk-White profiles  with central singularities: = 1, = 1, = 3, and more recently by even more singular profiles: = 1.5, = 1.5, = 3 . Observations do not support such singular cusps, and various attempts have been made to understand whether and how they might be weakened.
One suggestion has been that the annihilations of dark-matter particles in the cusps might generate particles and radiation pressure that would disperse the cusps. However, it seems questionable whether the annihilation rates found in plausible models are large enough, and the annihilations are so constrained by upper limits on synchrotron radiation that this mechanism seems unlikely to work .
Another suggestion made at this meeting, that seems more promising, is that black holes at the centers of galaxies  may disrupt the cusps via the gravitational slingshot effect acting on individual dark-matter particles , as seen in Fig. 4. This effect could be important during mergers, and simulations indicate that a further suppression of the core density would occur if there is a hierarchy of mergers. It does not seem at the moment that the apparent absence of cusps in generic galaxies is necessarily a big problem for cold dark matter.
Figure 4. The gravitational slingshot effect may suppress the density in a galactice core: the curves illustrate the reductions in the photon flux from relic annihilation, integrated over the indicated angular range, as found in different scenarios .
A more specialized question concerns the center of the Milky Way. As discussed in more detail below, this is known to contain a central massive object weighing ~ 3 × 106 solar masses, that is normally presumed to be a black hole . Like any other galaxy, one would expect the history of our own to have included a number of mergers, that are likely to have suppressed the central density spike. For this reason, the density of cold dark matter at the center of the Milky Way, and hence the rate of their annihilations, has a considerable uncertainty that must be borne in mind when assessing dark-matter detection strategies, as discussed later.