The linear bias in the Zeldovich approximation and a relation between the number density and the linear bias of dark halos

The linear bias of the dark halos from a model under the Zeldovich approxim ation is derived and compared with the fitting formula of simulation result s. While qualitatively similar to the Press-Schechter formula, this model g ives a better description for the linear bias around the turnaround point. This advantage, however, may be compromised by the large uncertainty of the actual behavior of the linear bias near the turnaround point. For a broad class of structure formation models in the cold dark matter framework, a ge neral relation exists between the number density and the linear bias of dar k halos. This relation can be readily tested by numerical simulations. Thus , instead of laboriously checking these models one by one, numerical simula tion studies can falsify a whole category of models. The general validity o f this relation is important in identifying key physical processes responsi ble for the large-scale structure formation in the universe.