We present a measurement of the one-point probability distribution function ( PDF ) of the thermal Sunyaev-Zel ’ dovich ( tSZ ) decrement in the pixel temperature histogram of filtered 148 GHz sky maps from the Atacama Cosmology Telescope ( ACT ) .
The PDF includes the signal from all galaxy clusters in the map , including objects below the signal-to-noise threshold for individual detection , making it a particularly sensitive probe of the amplitude of matter density perturbations , \sigma _ { 8 } .
We use a combination of analytic halo model calculations and numerical simulations to compute the theoretical tSZ PDF and its covariance matrix , accounting for all noise sources and including relativistic corrections .
From the measured ACT 148 GHz PDF alone , we find \sigma _ { 8 } = 0.793 \pm 0.018 , with additional systematic errors of \pm 0.017 due to uncertainty in intracluster medium gas physics and \pm 0.006 due to uncertainty in infrared point source contamination .
Using effectively the same data set , the statistical error here is a factor of two lower than that found in ACT ’ s previous \sigma _ { 8 } determination based solely on the skewness of the tSZ signal .
In future temperature maps with higher sensitivity , the tSZ PDF will break the degeneracy between intracluster medium gas physics and cosmological parameters .