The expected mass function for low-mass galaxies in a cold dark matter cosmology: Is there a problem?

It is well known that the mass function for halos in cold dark matter (CDM) cosmology is a relatively steep power law [n(M) proportional to M-2] for low masses, possibly too steep to be consistent with observations. But how steep is the galaxy mass function ? We have analyzed the stellar and gas mass functions of the first luminous objects formed in a Lambda CDM universe, as calculated in the numerical simulation described by Gnedin in 2000. We have found that suppression of the low-mass end of the galaxy mass function emerges naturally, implying that perhaps no "new physics" beyond the standard model is needed. Although previous pure semianalytic and combined N-body/semianalytic treatments of the galaxy formation problem have suggested this result, the calculation found here is derived from the first fully hydrodynamic simulation with (1) sufficient mass and spatial resolution to individually resolve low-mass galaxies, (2) a physically plausible star formation and UV photon generation algorithm, and (3) allowance for inhomogeneity in radiation emission and absorption. In particular, we find that the stellar mass function is consistently flat at the low-mass end. Moreover, while the gas mass function follows the dark matter mass function until reionization at z similar to7, between z = 7 and z = 4 the gas mass function also flattens considerably at the low-mass end. At z = 4, the gas and stellar mass functions are fitted by a Schechter function with alpha approximate to -1.2 +/- 0.1, significantly shallower than the dark matter halo mass function and consistent with some recent observations. In addition, the low-mass objects found in the simulation are consistent with the observed relationship between luminosity and velocity dispersion for dwarf spheroidals. The flattening of the mass function is a result of two factors : (1) the dark matter halo mass (differential) function is consistent with the Press-Schechter formulation at low masses n(M) proportional to M-2 and (2) heating/cooling and ionization processes seem to cause baryons to collect in halos with the relationship M-b proportional to M-d(4) at low masses. Combining these two factors yields n(M-b) proportional to M-b(-5/4), comparable to the simulation results. Finally, although the simulation ends at z = 4, processes such as mergers and additional gas ejection can only further suppress the mass function at low masses from z = 4 to the present epoch. If these processes are significant, the fact that the simulation at z = 4 produces a "turnover" in the gas mass function corresponding approximately to that observed in dwarf galaxies today suggests that Lambda CDM could end up underproducing low-mass galaxies!