Galaxy groups in the 2dF Galaxy Redshift Survey: the number density of groups

The abundance of galaxy clusters as a function of mass is determined from the 2dF Galaxy Redshift Survey (2dFGRS) Percolation-Inferred Galaxy Group (2PIGG) catalogue. This is used to estimate the amplitude of the matter fluctuation spectrum, parametrized by the linear theory rms density fluctuations in spheres of radius 8h−1 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(Ω m−0.22) 2m± 10 per cent (statistical) ±20 per cent (systematic) for 0.18 ≤Ωm≤ 0.50, assuming that Ωm+ΩΛ= 1. This gives σ8= 0.89 when evaluated at 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 100 h M⊙/L⊙ in the bJ band at a total group luminosity of L b J≈ 5×109h−2 L⊙. Together with the observed Tully–Fisher (TF) relation, this implies that the observed rotation speed of TF galaxies with L b J≤ 1010h−2 L⊙ is within ∼10 per cent of the typical circular speed of the haloes that host them.