What is Beta?

Measurements of the cosmological density parameter (Omega) using techniques that exploit the gravity-induced motions of galaxies yield, in linear perturbation theory, the degenerate parameter combination beta=Omega^{0.6}/b, where the linear bias parameter b is the ratio of the fluctuation amplitudes of the galaxy and mass distributions. However, the relation between the mass and the galaxy density fields depends on the complex physics of galaxy formation, and it can in general be non-linear, non-local, and stochastic. There is a growing consensus that the one-parameter model for bias is oversimplified. This leaves us with the following question: What is the quantity that is actually being measured by the different techniques? In order to address this question, we present estimates of beta from galaxy distributions constructed by applying a variety of biased galaxy formation models to cosmological N-body simulations. We compare the values of beta estimated using two different techniques: the anisotropy of the redshift-space power spectrum and an idealized version of the POTENT method. In most cases, we find that the bias factor b=Omega^{0.6}/beta derived from redshift-space anisotropy or POTENT is similar to the large-scale value of b_{sigma}(R) defined by the ratio of rms fluctuation amplitudes of the galaxy and mass distributions. However, non-linearity of bias and residual effects of non-linear gravitational evolution both influence beta estimates at the 10-20% level.