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 instrument will exploit this method of probing dark energy by detecting ~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.

We simulate the spectra of galaxy clusters for a variety of different cluster masses and redshifts while taking into account the X-ray background as well as the instrumental response. An emission model is then fit to these spectra to recover the cluster temperature and redshift. The number of clusters with precise properties is then based on the convolution of the above fit results with the galaxy cluster mass function and an assumed eROSITA selection function.

During its four years of all-sky surveys, eROSITA will determine cluster temperatures with relative uncertainties of ΔT/T ≲ 10% at the 68%-confidence level for clusters up to redshifts of z ~ 0.16 which corresponds to ~1670 new clusters with precise properties. Redshift information itself will become available with a precision of Δz/ (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. For the above clusters, the fraction of catastrophic failures in the fit is below 20% and in most cases it is even much smaller. 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. In particular, the standard way of estimating parameter uncertainties significantly underestimates the true uncertainty, if the redshift information is not available.

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. At the same time, this sample of clusters will extend our understanding of cluster physics, e.g. through precise L_X − T scaling relations.