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 underlyin g mass density fluctuation <delta(g) \ delta >, or by the associated parame ters of mean biasing, (b) over cap, and nonlinearity, (b) over tilde. Using the distribution of galaxies in cosmological simulations, at a smoothing o f a few Mpc, we find that <delta(g) \ delta > can be recovered to a good ac curacy from the cumulative distribution functions of galaxies and mass, C-g (delta(g)) and C(delta), despite the biasing scatter. Then, using a suite o f simulations of different cosmological models, we demonstrate that C(delta ) can be approximated in the mildly nonlinear regime by a cumulative lognor mal distribution of 1 + delta with a single parameter sigma, with deviation s 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 accur acy directly from the observed C-g in redshift space. Thus, the biasing fun ction can be obtained from counts in cells once the rms mass fluctuation at the appropriate scale is assumed a priori. The relative biasing function b etween different galaxy types is measurable in a similar way. The main sour ce of error is sparse sampling, which requires that the mean galaxy separat ion be smaller than the smoothing scale. Once applied to redshift surveys s uch as the Point Source Catalog Redshift Survey (PSCz), the Two-Degree Fiel d (2dF), Sloan Digital Sky Survey (SDSS), or the Deep Extragalactic Evoluti onary Probe (DEEP), the biasing function can provide valuable constraints o n galaxy formation and structure evolution.