S-Z anisotropy and cluster counts: Consistent selection of σ₈ and the temperature-mass relation

The strong dependence of the mass variance parameter, σ₈, on the adopted cluster mass-temperature relation is explored. A recently compiled X-ray cluster catalog and various mass-temperature relations are used to derive the corresponding values of σ₈. Calculations of the power spectrum of the CMB anisotropy induced by the Sunyaev-Zeldovich effect and cluster number counts are carried out in order to assess the need for a consistent choice of the mass-temperature scaling and the parameter σ₈. We find that the consequences of inconsistent choice of the mass-temperature relation and σ₈ could be quite substantial, including a considerable mis-estimation of the magnitude of the power spectrum and cluster number counts. Our results can partly explain the large scatter between published estimates of the power spectrum and number counts. We also show that the range of values of the power-law index in the scaling C _ℓ∼σ₈^6-7 deduced in previous studies is likely overestimated; we obtain a more moderate dependence, C _ℓ∼σ₈⁴.