Impact of thermal diffusion and other abundance anomalies on
  cosmological uses of galaxy clusters
  Depending on the topology of the magnetic field and characteristics of
turbulent motions, diffusion can significantly affect the distribution of
elements, in particular helium, in the intracluster medium (ICM). As has been
noted previously, an incorrect assumption about the helium abundance will lead
to an error in the iron abundance determined from X-ray spectroscopy. The
corresponding effect on the temperature measurement is negligibly small. An
incorrectly assumed helium abundance will also lead to a systematic error in
angular distance measurements based on X-ray and Sunyaev-Zeldovich (SZ)
observations of clusters of galaxies. Its magnitude is further amplified by the
associated error in the metal abundance determination, the impact being larger
at lower ICM temperatures. Overall, a factor of 2-5 error in the helium
abundance will lead to an ~ 10-25 % error in the angular distance.
  We solve the full set of Burgers equations for a multi-component intracluster
plasma to determine the maximal effect of diffusion on the interpretation of
X-ray and microwave observations of clusters of galaxies. For an isothermal
cluster, gravitational sedimentation can lead to up to a factor of ~ 5-10
enhancements of helium and metal abundances in the cluster center on a ~ 3-7
Gyr timescale. In cool-core clusters on the contrary, thermal diffusion can
counteract gravitational sedimentation and effectively remove helium and metals
from the cluster inner core. In either case, a significant, up to ~ 40 %, error
in the metal abundances determined by means of X-ray spectroscopy is possible.
The angular distance determined from X-ray and SZ data can be underestimated by
up to ~ 10-25 %.
