Determining Bias with Cumulant Correlators

The first non-trivial cumulant correlator of the galaxy density fieldQ21 is examined from the point of view of biasing. It is shown that to leading order it depends on two biasing parameters b, and b2, and on q21, the underlying cumulant correlator of the mass. As the skewness Q3 has analogous properties, the slope of the correlation function −γ, Q3, and Q21 uniquely determine the bias parameter on a particular scale to be b = γ/6(Q21−Q3), when working in the context of gravitational instability with Gaussian initial conditions. Thus on large scales, easily accessible with the future Sloan Digital Sky Survey and the 2 Degree Field Survey, it will be possible to extract b, and b2 from simple counts in cells measurements. Moreover, the higher order cumulants, QN , successively determine the higher order biasing parameters. From these it is possible to predict higher order cumulant correlators as well. Comparing the predictions with the measurements will provide internal consistency checks on the validity of the assumptions in the theory, most notably perturbation theory of the growth of fluctuations by gravity and Gaussian initial conditions. Since the method is insensitive to Ω, it can be successfully combined with results from velocity fields, which determine Ω/b, to measure the total density parameter in the universe.