Dynamical Probes of The Halo Mass Function

We explore the relationship between the mass function of CDM halos and dynamical probes of the mass function such as the distribution of gravitational lens separations and the local velocity function. The compression of galactic halos by the cooling baryons, a standard component of modern models, leads to a feature in the distribution of lens separations near 3 arcsec or in the velocity function near 400 km/s. The two probes of the mass function, lens separations and the local velocity function, are mutually consistent. Producing the observed velocity function of galaxies or the separation distribution using standard adiabatic compression models requires more cold baryons, an equivalent cosmological density of Omega_b=0.02 compared to a total cosmological Omega_b=0.04, than are observed in standard accountings of the baryonic content of galaxies, Omega_b=0.006$, or our Galaxy, Omega_b<0.015. The requirement for a higher cold baryon density than is usually assigned to galaxies appears to be generic to models which use the standard adiabatic compression models for the transformation of the CDM halo by the cooling baryons. If real, this dynamical baryon discrepancy suggests either that we are neglecting half of the cold baryonic mass in standard galactic models (e.g. a MACHO, cold molecular or warm gas component), or that there is a problem with standard adiabatic compression models.