The Atacama Cosmology Telescope: A Measurement of the Thermal
  Sunyaev-Zel'dovich One-Point PDF
  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.
