Biased Galaxy Formation and Measurements of β

Measurements of the cosmological density parameter Omega using techniquesthat exploit the gravity-induced motions of galaxies constrain, in linearperturbation theory, the degenerate parameter combination beta = Omega^{0.6}/b,where the linear bias parameter b is the ratio of the fluctuation amplitudes ofthe galaxy and mass distributions. However, the relation between the galaxy andmass density fields depends on the complex physics of galaxy formation, and itcan in general be non-linear, stochastic, and perhaps non-local. Theone-parameter linear bias model is almost certainly oversimplified, which leadsto the obvious question: What is the quantity beta that is actually measured bydifferent techniques? To address this question, we estimate beta from galaxydistributions that are constructed by applying a variety of locally biasedgalaxy formation models to cosmological N-body simulations. We compare thevalues of beta estimated using three different techniques: a density-densitycomparison similar to the POTENT analysis, a velocity-velocity comparisonsimilar to the VELMOD analysis, and an anisotropy analysis of theredshift-space power spectrum. In most cases, we find that beta estimated usingall three methods is similar to the asymptotic value ofOmega^{0.6}/b_{sigma}(R) at large R, where b_{sigma}(R) is the ratio of rmsgalaxy fluctuations to rms mass fluctuations on scale R. Thus, something closeto the conventional interpretation of beta continues to hold even for complexbias models. Moreover, we find that beta estimates made using these threemethods should, in principle, agree with each other. It is thus unlikely thatnon-linear or scale-dependent bias is responsible for the discrepancies thatexist among current measurements of beta from different techniques.Comment: 26 pages including 9 eps figures. Submitted to Ap