Nonlinear stochastic biasing from the formation epoch distribution of darkhalos

We propose a physical model for nonlinear stochastic biasing of one-point s tatistics resulting from the formation epoch distribution of dark halos. In contrast to previous works based on extensive numerical simulations, our m odel provides for the first time an analytic expression for the joint proba bility function. Specifically, we derive the joint probability function of halo and mass density contrasts from the extended Press-Schechter theory. S ince this function is derived in the framework of the standard gravitationa l instability theory assuming the random Gaussianity of the primordial dens ity field alone, we expect that the basic features of the nonlinear and sto chastic biasing predicted from our model are fairly generic. As representat ive examples, we compute the various biasing parameters in cold dark matter models as a function of a redshift and a smoothing length. Our major findi ngs are that (1) the biasing of the variance evolves strongly as redshift, while its scale dependence is generally weak, and a simple linear biasing m odel provides a reasonable approximation at roughly R greater than or simil ar to 2(1 + z) h(-1) Mpc; and (2) the stochasticity exhibits moderate scale dependence, especially on R less than or similar to 20 h(-1) Mpc, but is a lmost independent of z. Comparison with the previous numerical simulations shows good agreement with the above behavior, indicating that the nonlinear and stochastic nature of the halo biasing can be essentially understood by taking into account the distribution of the halo mass and the formation ep och.