  The uniformity of the helium-to-hydrogen abundance ratio in X-ray emitting
intracluster medium (ICM) is one of the commonly adopted assumptions in X-ray
analyses of galaxy clusters and cosmological constraints derived from these
measurements. In this work, we investigate the effect of He sedimentation on
X-ray measurements of galaxy clusters in order to assess this assumption and
associated systematic uncertainties. By solving a set of flow equations for a
H-He plasma, we show that the helium-to-hydrogen mass ratio is significantly
enhanced in the inner regions of clusters. The effect of He sedimentation, if
not accounted for, introduces systematic biases in observable properties of
clusters derived using X-ray observations. We show that these biases also
introduce an apparent evolution in the observed gas mass fractions of X-ray
luminous, dynamically relaxed clusters and hence biases in observational
constraints on the dark energy equation of state parameter, w, derived from the
cluster distance-redshift relation. The Hubble parameter derived from the
combination of X-ray and Sunyaev-Zel'dovich effect (SZE) measurements is
affected by the He sedimentation process as well. Future measurements aiming to
constrain w or H_0 to better than 10% may need to take into account the effect
of He sedimentation. We propose that the evolution of gas mass fraction in the
inner regions of clusters should provide unique observational diagnostics of
the He sedimentation process.
