On the Cluster Physics of Sunyaev-Zel'dovich and X-ray Surveys III:
  Measurement Biases and Cosmological Evolution of Gas and Stellar Mass
  Fractions
  Gas masses tightly correlate with the virial masses of galaxy clusters,
allowing for a precise determination of cosmological parameters by means of
large-scale X-ray surveys. However, according to recent Suzaku X-ray
measurements, gas mass fractions, f_gas, appear to be considerably larger than
the cosmic mean at the virial radius, R_200, questioning the accuracy of the
cosmological parameter estimations. Here, we use a large suite of cosmological
hydrodynamical simulations to study measurement biases of f_gas. We employ
different variants of simulated physics, including radiative gas physics, star
formation, and thermal feedback by active galactic nuclei. Computing the mass
profiles in 48 angular cones, whose footprints partition the sphere, we find
anisotropic gas and total mass distributions that imply an angular variance of
f_gas at the level of 30%. This anisotropic distribution originates from the
recent formation epoch of clusters and from the strong internal
baryon-to-dark-matter density bias. In the most extreme cones, f_gas can be
biased high by a factor of two at R_200 in massive clusters, thereby providing
a potential explanation for high f_gas measurements by Suzaku. While projection
lowers this factor, there are other measurement biases that may (partially)
compensate. We find that at R_200, f_gas is biased high by 20% when assuming
hydrostatic equilibrium masses, i.e., neglecting the kinetic pressure, and by
another ~10-20% due to the presence of density clumping. At larger radii, both
measurement biases increase dramatically. While the cluster sample variance of
the true f_gas decreases to a level of 5% at R_200, the sample variance that
includes both measurement biases remains fairly constant at the level of
10-20%. The constant redshift evolution of f_gas within R_500 for massive
clusters is encouraging for using gas masses to derive cosmological parameters.
