The mass function of galaxy halos in a cold dark matter universe

Using large-scale N-body simulations we have determined the mass function of dark galaxy halos as a function of environment in a cold dark matter universe. The halo mass range covered in a single simulation is 10^10^ M_sun_ <~M_halo_<~10^15^M_sun_. Over the mass range 10^10^ M_sun_ <~M_halo_ <~ 10^13^ M_sun_ the mass function is well-fit by a power law of slope -1.0+/-0.1. The slope of the mass function in this mass range is independent of environment. The amplitude depends on the background density such that in low-density regions, galaxy number underdensity equals mass underdensity. The formation of massive galaxy halos is strongly biased towards high-density regions. Thus voids such as Bootes will be filled with low-mass galaxy halos, while massive galaxy halos will occur almost exclusively in high-density regions. We expect the mass density in the Bootes void to be ~1/4 the average mass density of the universe. The Press-Schecter prediction for the mass function does not agree well with the numerical prediction. For 10^10^ M_sun_ <~M_halo_ < 10^13^ M_sun_ the Press-Schecter mass function is well-fit by a power law of index -0.8 and for M_halo_>~ 10^13^ M_sun_ it deviates from a power law more strongly than the numerical mass function. In addition, the Press-Schecter prediction shows more evolution than the numerical mass function.