Constraining galaxy cluster temperatures and redshifts with eROSITA
  survey data
  The nature of dark energy is imprinted in the large-scale structure of the
Universe and thus in the mass and redshift distribution of galaxy clusters. The
upcoming eROSITA mission will exploit this method of probing dark energy by
detecting roughly 100,000 clusters of galaxies in X-rays. For a precise
cosmological analysis the various galaxy cluster properties need to be measured
with high precision and accuracy. To predict these characteristics of eROSITA
galaxy clusters and to optimise optical follow-up observations, we estimate the
precision and the accuracy with which eROSITA will be able to determine galaxy
cluster temperatures and redshifts from X-ray spectra. Additionally, we present
the total number of clusters for which these two properties will be available
from the eROSITA survey directly. During its four years of all-sky surveys,
eROSITA will determine cluster temperatures with relative uncertainties of
Delta(T)/T<10% at the 68%-confidence level for clusters up to redshifts of
z~0.16 which corresponds to ~1,670 new clusters with precise properties.
Redshift information itself will become available with a precision of
Delta(z)/(1+z)<10% for clusters up to z~0.45. Additionally, we estimate how the
number of clusters with precise properties increases with a deepening of the
exposure. Furthermore, the biases in the best-fit temperatures as well as in
the estimated uncertainties are quantified and shown to be negligible in the
relevant parameter range in general. For the remaining parameter sets, we
provide correction functions and factors. The eROSITA survey will increase the
number of galaxy clusters with precise temperature measurements by a factor of
5-10. Thus the instrument presents itself as a powerful tool for the
determination of tight constraints on the cosmological parameters.
