We present a measurement of the one-point probability distribution function (PDF) of the thermal Sunyaev-Zeldovich (tSZ) decrement in the pixel temperature histogram of filtered 148 GHz sky maps from the Atacama Cosmology Telescope (ACT). The PDF inc
ludes 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 ACTs 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.
We present a detection of the unnormalized skewness <T^3> induced by the thermal Sunyaev-Zeldovich (tSZ) effect in filtered Atacama Cosmology Telescope (ACT) 148 GHz cosmic microwave background temperature maps. Contamination due to infrared and radi
o sources is minimized by template subtraction of resolved sources and by constructing a mask using outlying values in the 218 GHz (tSZ-null) ACT maps. We measure <T^3>= -31 +- 6 mu K^3 (measurement error only) or +- 14 mu K^3 (including cosmic variance error) in the filtered ACT data, a 5-sigma detection. We show that the skewness is a sensitive probe of sigma_8, and use analytic calculations and tSZ simulations to obtain cosmological constraints from this measurement. From this signal alone we infer a value of sigma_8= 0.79 +0.03 -0.03 (68 % C.L.) +0.06 -0.06 (95 % C.L.). Our results demonstrate that measurements of non-Gaussianity can be a useful method for characterizing the tSZ effect and extracting the underlying cosmological information.
