Galaxy groups in the 2dFGRS: the number density of groups

The abundance of galaxy clusters as a function of mass is determined using the 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue. This is used to estimate the amplitude of the matter fluctuation spectrum, parametrised by the linear theory rms density fluctuations in spheres of 8h Mpc, σ8. The best-fitting value for this parameter is highly correlated with the mean matter density in the Universe, Ωm, and is found to satisfy σ8 = 0.25 Ω −0.92−4.5(Ωm−0.22) 2 m ± 10% (statistical) ±20% (systematic) for 0.18 ≤ Ωm ≤ 0.50, assuming that Ωm +ΩΛ = 1. This gives σ8 = 0.89 when Ωm = 0.25. A ∼ 20 per cent correction has been applied to undo the systematic bias inherent in the measurement procedure. Mock catalogues, constructed from large cosmological N-body simulations, are used to help understand and model these systematic errors. The abundance of galaxy groups as a function of group bJ band luminosity is also determined. This is used in conjunction with the halo mass function, determined from simulations, to infer the variation of halo mass-to-light ratio over four orders of magnitude in halo mass. The mass-to-light ratio shows a minimum value of 100hM⊙/L⊙ in the bJ band at a total group luminosity of LbJ ≈ 5 × 10 9 h −2 L⊙. Together with the observed Tully-Fisher relation, this implies that the observed rotation speed of Tully-Fisher galaxies is within ∼ 10 per cent of the typical circular speed of haloes hosting brightest galaxies of the same luminosity.