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 8 { \it h } ^ { -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 _ { m } ^ { -0.92 - 4.5 ( \Omega _ { m } -0.22 ) ^ { 2 } } \pm 10 \% ( statistical ) \pm 20 \% ( systematic ) for 0.18 \leq \Omega _ { m } \leq 0.50 , assuming that \Omega _ { m } + \Omega _ { \Lambda } = 1 .
This gives \sigma _ { 8 } = 0.89 when \Omega _ { m } = 0.25 .
A \sim 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 hM _ { \odot } / L _ { \odot } in the b _ { J } band at a total group luminosity of L _ { b _ { J } } \approx 5 \times 10 ^ { 9 } { \it h } ^ { -2 } { L _ { \odot } } .
Together with the observed Tully-Fisher relation , this implies that the observed rotation speed of Tully-Fisher galaxies is within \sim 10 per cent of the typical circular speed of haloes hosting brightest galaxies of the same luminosity .