The main uncertainty in current determinations of the power spectrum normalization , \sigma _ { 8 } , from abundances of X-ray luminous galaxy clusters arises from the calibration of the mass–temperature relation .
We use our weak lensing mass determinations of 30 clusters from the hitherto largest sample of clusters with lensing masses , combined with X-ray temperature data from the literature , to calibrate the normalization of this relation at a temperature of 8 keV , M _ { 500 c, 8 keV } = ( 8.7 \pm 1.6 ) h ^ { -1 } 10 ^ { 14 } M _ { \sun } .
This normalization is consistent with previous lensing-based results based on smaller cluster samples , and with some predictions from numerical simulations , but higher than most normalizations based on X-ray derived cluster masses .
Assuming the theoretically expected slope \alpha = 3 / 2 of the mass–temperature relation , we derive \sigma _ { 8 } = 0.88 \pm 0.09 for a spatially-flat \Lambda CDM universe with \Omega _ { m } = 0.3 .
The main systematic errors on the lensing masses result from extrapolating the cluster masses beyond the field-of-view used for the gravitational lensing measurements , and from the separation of cluster/background galaxies , contributing each with a scatter of 20 % .
Taking this into account , there is still significant intrinsic scatter in the mass–temperature relation indicating that this relation may not be very tight , at least at the high mass end .
Furthermore , we find that dynamically relaxed clusters are 75 \pm 40 \% hotter than non-relaxed clusters .