The XMM Cluster Survey: forecasting cosmological and cluster scaling-relation parameter constraints

We forecast the constraints on the values of Sigma(8), (m) and cluster scaling-relation parameters which we expect to obtain from the XMM Cluster Survey (XCS). We assume a flat Lambda cold dark matter Universe and perform a Monte Carlo Markov Chain analysis of the evolution of the number density of galaxy clusters that takes into account a detailed simulated selection function. Comparing our current observed number of clusters shows good agreement with predictions. We determine the expected degradation of the constraints as a result of self-calibrating the luminosity-temperature relation (with scatter), including temperature measurement errors, and relying on photometric methods for the estimation of galaxy cluster redshifts. We examine the effects of systematic errors in scaling relation and measurement error assumptions. Using only (T, z) self-calibration, we expect to measure (m) to +/- 0.03 (and (Lambda) to the same accuracy assuming flatness), and Sigma(8) to +/- 0.05, also constraining the normalization and slope of the luminosity-temperature relation to +/- 6 and +/- 13 per cent (at 1 Sigma), respectively, in the process. Self-calibration fails to jointly constrain the scatter and redshift evolution of the luminosity-temperature relation significantly. Additional archival and/or follow-up data will improve on this. We do not expect measurement errors or imperfect knowledge of their distribution to degrade constraints significantly. Scaling-relation systematics can easily lead to cosmological constraints 2 Sigma or more away from the fiducial model. Our treatment is the first exact treatment to this level of detail, and introduces a new 'smoothed ML' (Maximum Likelihood) estimate of expected constraints.