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, sigma(8). The best-fitting value for this parameter is highly correlated with the mean matter density in the Universe, Omega(m), and is found to satisfy sigma(8) = 0.25 Omega(-0.92-4.5(Omega m-0.22)2) +/- 10 per cent (statistical) +/- 20 per cent (systematic) for 0.18 <= Omega(m) <= 0.50, assuming that Omega(m) + Omega(Lambda) = 1. This gives sigma(8) = 0.89when evaluated at Omega(m) = 0.25. A similar to 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 b(J)-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-circle dot/L(circle dot)in the b(J) band at a total group luminosity of L-bJ approximate to 5x10(9) h(-2) L-circle dot. Together with the observed Tully-Fisher (TF) relation, this implies that the observed rotation speed of TF galaxies with L-bJ epsilon 10(10) h(-2) L-circle dot is within similar to 10 per cent of the typical circular speed of the haloes that host them.