Synthetic simulations of the extragalactic sky seen by eROSITA: I. Pre-launch selection functions from Monte-Carlo simulations

Context. Studies of galaxy clusters provide stringent constraints on models of structure formation. Provided that selection effects are under control, large X-ray surveys are well suited to derive cosmological parameters, in particular those governing the dark energy equation of state. Aims. We forecast the capabilities of the all-sky eROSITA (extended ROentgen Survey with an Imaging Telescope Array) survey to be achieved by the early 2020s. We bring special attention to modelling the entire chain from photon emission to source detection and cataloguing. Methods. The selection function of galaxy clusters for the upcoming eROSITA mission is investigated by means of extensive and dedicated Monte-Carlo simulations. Employing a combination of accurate instrument characterisation and a state-of-the-art source detection technique, we determine a cluster detection efficiency based on the cluster fluxes and sizes. Results. Using this eROSITA cluster selection function, we find that eROSITA will detect a total of approximately 10(5) clusters in the extra-galactic sky. This number of clusters will allow eROSITA to put stringent constraints on cosmological models. We show that incomplete assumptions on selection effects, such as neglecting the distribution of cluster sizes, induce a bias in the derived value of cosmological parameters. Conclusions. Synthetic simulations of the eROSITA sky capture the essential characteristics impacting the next-generation galaxy cluster surveys and they highlight parameters requiring tight monitoring in order to avoid biases in cosmological analyses.