The 2dF Galaxy Redshift Survey: the amplitudes of fluctuations in the 2dFGRS and the CMB, and implications for galaxy biasing

Abstract

We compare the amplitudes of fluctuations probed by the 2dF Galaxy Redshift Survey (2dFGRS) and by the latest measurements of the cosmic microwave background (CMB) anisotropies. By combining the 2dFGRS and CMB data, we find the linear-theory rms mass fluctuations in 8 <it>h</it>−1 Mpc spheres to be <it>σ</it><inf>8m</inf>=0.73±0.05 (after marginalization over the matter density parameter Ω<inf>m</inf> and three other free parameters). This normalization is lower than the <it>COBE</it> normalization and previous estimates from cluster abundance, but it is in agreement with some revised cluster abundance determinations. We also estimate the scale-independent bias parameter of present-epoch <it>L</it><inf>s</inf>=1.9<it>L</it>∗ APM-selected galaxies to be <it>b</it>(<it>L</it><inf>s</inf>,<it>z</it>=0)=1.10±0.08 on comoving scales of 0.02<<it>k</it><0.15 <it>h</it> Mpc-1. If luminosity segregation operates on these scales, <it>L</it>∗ galaxies would be almost unbiased, <it>b</it> (<it>L</it><inf>*</inf>, <it>z</it>=0)≈0.96. These results are derived by assuming a flat ΛCDM Universe, and by marginalizing over other free parameters and fixing the spectral index <it>n</it>=1 and the optical depth due to reionization <it>τ</it>=0. We also study the best-fitting pair (Ω<inf>m</inf>, <it>b</it>), and the robustness of the results to varying <it>n</it> and <it>τ</it>. Various modelling corrections can each change the resulting <it>b</it> by 5–15 per cent. The results are compared with other independent measurements from the 2dFGRS itself, and from the Sloan Digital Sky Survey (SDSS), cluster abundance and cosmic shear.