It is well known that the mass function for halos in CDM cosmology is a relatively steep power law ( n ( M ) \propto 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 massive luminous objects formed in a \Lambda CDM universe , as calculated in the numerical simulation described in Gnedin ( 2000ab ) .
Our analysis indicates that , as suspected , the relationship between luminous or gaseous matter and total ( primarily dark matter ) mass is not a linear scaling relation — i.e. , light does not trace mass .
While the dark matter mass function is steep , the stellar and gas mass functions are flatter for low mass objects .
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 \sim 7 , 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 fit by a Schechter function with \alpha \approx - 1.2 \pm 0.1 , significantly shallower than the dark matter halo mass function and consistent with some recent observations .
The baryonic mass functions are shallower because ( a ) the dark matter halo mass ( differential ) function is consistent with the Press-Schechter formulation at low masses n ( M ) \propto M ^ { -2 } and ( b ) heating/cooling and ionization processes appear to cause baryons to collect in halos with the relationship M _ { b } \propto M _ { d } ^ { 4 } at low masses .
Combining ( a ) and ( b ) gives n ( M _ { b } ) \propto M _ { b } ^ { -5 / 4 } , comparable to the simulation results .
Thus , the well known observational fact that low mass galaxies are underabundant as compared to expectations from numerical dark matter simulations or Press-Schechter modeling of CDM universes emerges naturally from these results , implying that perhaps no “ new physics ” beyond the standard model is needed .