Central halo profiles
Have we really converged on the unique central structure of CDM halos? This is a hard numerical calculation to perform since we are always relaxation dominated on small scales. In a hierarchical universe the first halos to collapse will contain just a few particles and have relaxation times much shorter than a Hubble time.
Figure 7 shows the final density profile of one of the high resolution Local Group CDM halos. We also plot the final density profile of those particles that were located within highly non-linear regions at redshifts z = 10 and z = 20. The central 5 kpc of the halo is dominated by those particles that were in virialised halos at z = 10. Most of these halos contained just a few particles and their internal structure is completely dominated by resolution effects. Until we can adequately resolve objects collapsing at z = 10, we cannot claim to have converged upon the slope of the density profile at 1-2% of the virial radius.
Figure 7. The solid curve shows the density profile of the high resolution halo shown in Figure 5. The dotted and dashed curves show the density profiles of those particles that lie in regions of overdensity larger than 50 at z = 20 and z = 10 respectively. The long-dashed curve shows the difference between the solid and short-dashed curves. The radial density profile of the marked particles at z = 0 has a gradient of -3 which is similar to that of the Galactic spheroid.
Rotation curves of dwarf galaxies first highlighted potential problems with the structure of CDM halos (Moore 1994, Flores etal 1994, Burkert 1995). The quality of these data were recently questioned by several authors including van den Bosch & Swaters (2000) used rotation curves from 19 dwarf galaxies to claim that CDM halos are consistent with the data. However, to make this statement these authors had to throw away half of the galaxies and adopt unphysical (zero) mass to light ratios. Furthermore, seven of the remaining nine galaxies require concentration parameters in the range c=3-5 which cannot be obtained in any reasonable CDM model. One could rephrase the conclusions of these authors by stating that only 2 galaxies from a sample of 19 are consistent with CDM!
Finally, I show the H and HI rotation curves of the nearby dwarf NGC3109 (Blais-Oullette etal 2001). These data clearly show that beam smearing is not an issue for the nearby dwarf galaxies. Furthermore, only a constant density core can fit these data. CDM profiles with central cusps < - 1 are ruled out for any value of the concentration parameter. If CDM is correct then we are forced to conclude that galaxies such as NGC3109, NGC5585, IC2574, etc, are somehow strange and that their disk kinematics are somehow not measuring the mass distribution.
Acknowledgments I would like to thank Carlton Baugh for constructing Figure 3 and Figure 4. BM is supported by the Royal Society.