Cusps were perhaps the first potential discrepancy pointed out between the dark matter halos predicted by CDM and the observations of small galaxies that appeared to be dominated by dark matter nearly to their centers Flores and Primack (1994), Moore (1994). Pure dark matter simulations predicted that the central density of dark matter halos behaves roughly as ρ ∼ r−1. As mentioned above, dark matter halos have a density distribution that can be roughly approximated as ρNFW = 4ρs x−1(1 + x)−2, where x ≡ r / rs Navarro et al. (1996). But this predicted r−1 central cusp in the dark matter distribution seemed inconsistent with published observations of the rotation velocity of neutral hydrogen as a function of radius.
In small galaxies with significant stellar populations, simulations show that central starbursts can naturally produce relatively flat density profiles Governato et al. (2010), Governato et al. (2012), Pontzen and Governato (2012), Teyssier et al. (2013), Brooks (2014), Brooks and Zolotov (2014), Madau et al. (2014), Oñorbe et al. (2015), Nipoti and Binney (2015). Gas cools into the galaxy center and becomes gravitationally dominant, adiabatically pulling in some of the dark matter Blumenthal et al. (1986), Gnedin et al. (2011). But then the gas is driven out very rapidly by supernovae and the entire central region expands, with the density correspondingly dropping. Several such episodes can occur, producing a more or less constant central density consistent with observations, as shown in Fig. 6. The figure shows that galaxies in the THINGS sample are consistent with ΛCDM hydrodynamic simulations. But simulated galaxies with stellar mass less than about 3 × 106 M⊙ may have cusps, although Oñorbe et al. (2015) found that stellar effects can soften the cusp in even lower-mass galaxies if the star formation is extended in time. The observational situation is unclear. In Sculptor and Fornax, the brightest dwarf spheroidal satellite galaxies of the Milky Way, stellar motions may imply a flatter central dark matter radial profile than ρ ∼ r−1 Walker and Peñarrubia (2011), Amorisco and Evans (2012), Jardel and Gebhardt (2012). However, other papers have questioned this Jardel and Gebhardt (2013), Breddels and Helmi (2013), Breddels and Helmi (2014), Richardson and Fairbairn (2014).
Figure 6. Dark matter cores are generated by baryonic effects in galaxies with sufficient stellar mass. The slope α of the dark matter central density profile rα is plotted vs. stellar mass measured at 500 parsecs from simulations described in Pontzen and Governato (2012). The solid NFW curve assumes the halo concentrations given by Macciò et al. (2007). Large crosses: halos with > 5 × 105 dark matter particles; small crosses: > 5 ×104 particles. Squares represent galaxies observed by The HI Nearby Galaxy Survey (THINGS). (Fig. 3 in Pontzen and Governato 2014.)
Will baryonic effects explain the radial density distributions in larger low surface brightness (LSB) galaxies? These are among the most common galaxies. They have a range of masses but many have fairly large rotation velocities indicating fairly deep potential wells, and many of them may not have enough stars for the scenario just described to explain the observed rotation curves Kuzio de Naray and Spekkens (2011). Can we understand the observed distribution of the Δ1/2 measure of central density Alam et al. (2002) and the observed diversity of rotation curves Macciò et al. (2012b), Oman et al. (2015) ? This is a challenge for galaxy simulators.
Some authors have proposed that warm dark matter (WDM), with initial velocities large enough to prevent formation of small dark matter halos, could solve some of these problems. However, that does not appear to work: the systematics of galactic radial density profiles predicted by WDM do not at all match the observed ones Kuzio de Naray et al. (2010), Macciò et al. (2012a), Macciò et al. (2013). WDM that's warm enough to affect galaxy centers may not permit early enough galaxy formation to reionize the universe Governato et al. (2015). Yet another constraint on WDM is the evidence for a great deal of dark matter substructure in galaxy halos Zentner and Bullock (2003), discussed further below.