Measuring the nonlinear biasing function from a galaxy redshift survey

We present a simple method for evaluating the nonlinear biasing function of galaxies from a redshift survey. The nonlinear biasing is characterized by the conditional mean of the galaxy density fluctuation given the underlying mass density fluctuation 〈δ_g\δ〉, or by the associated parameters of mean biasing, b̂, and nonlinearity, b̃. Using the distribution of galaxies in cosmological simulations, at a smoothing of a few Mpc, we find that 〈δ_g|δ〉 can be recovered to a good accuracy from the cumulative distribution functions of galaxies and mass, C_g(δ_g) and C(δ), despite the biasing scatter. Then, using a suite of simulations of different cosmological models, we demonstrate that C(δ) can be approximated in the mildly non-linear regime by a cumulative lognormal distribution of 1 + δ with a single parameter σ, with deviations that are small compared to the difference between C_g and C. Finally, we show how the nonlinear biasing function can be obtained with adequate accuracy directly from the observed C_g in redshift space. Thus, the biasing function can be obtained from counts in cells once the rms mass fluctuation at the appropriate scale is assumed a priori. The relative biasing function between different galaxy types is measurable in a similar way. The main source of error is sparse sampling, which requires that the mean galaxy separation be smaller than the smoothing scale. Once applied to redshift surveys such as the Point Source Catalog Redshift Survey (PSCz), the Two-Degree Field (2dF), Sloan Digital Sky Survey (SDSS), or the Deep Extragalactic Evolutionary Probe (DEEP), the biasing function can provide valuable constraints on galaxy formation and structure evolution.