On determining the cluster abundance normalization

Different determinations currently suggest scattered values for the power spectrum normalization on the scale of galaxy clusters, σ8. Here we concentrate on the constraints coming from the X-ray temperature and luminosity functions (XTF and XLF), and investigate several possible sources of discrepancies in the results. We conclude that the main source of error in both methods is the mass scaling relation involved, in particular the way its intrinsic scatter and systematic normalization are treated. For temperature-derived constraints, we use a sample adapted from the Highest X-ray Flux Galaxy Cluster Sample (HIFLUGCS), and test for several sources of systematic error. We parametrize the mass–temperature relation with an overall factor T*, which varies between approximately 1.5 and 1.9 in the literature, with simulations typically giving lower results than empirically derived estimates. After marginalizing over this range of T*, we obtain a 68 per cent confidence range of σ8= 0.77+0.05−0.04 for a standard Λ-cold dark matter (ΛCDM) model. Most other determinations have chosen a single value for T*, and hence have neglected an important source of uncertainty. For luminosity-derived constraints we use the XLF from the REFLEX survey and explore how sensitive the final results are to the details of the mass–luminosity, M–L, conversion. Assuming a uniform systematic uncertainty of ±20 per cent in the amplitude of the mass–luminosity relation by Reiprich & Böhringer, we derive σ8= 0.79+0.06−0.07 for the same standard ΛCDM model. Although the XTF- and XLF-derived constraints agree very well with each other, we emphasize that such results can change by approximately 10–15 per cent, depending on how uncertainties in the L–T–M conversions are interpreted and included in the analysis. We point out that in order to achieve precision cosmology on σ8 using cluster abundance, it is first important to separate the uncertainty in the scaling relation into its intrinsic and overall normalization parts. Careful consideration of all sources of scatter is also important, as is the use of the most accurate formulae and full consideration of dependence on cosmology. A significant improvement will require the simultaneous determination of mass using a variety of distinct methods, such as X-ray observations, weak lensing, Sunyaev–Zel'dovich measurements and velocity dispersions of member galaxies, for a moderately large sample of clusters.

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