The cosmological analysis of X-ray cluster surveys: IV. Testing ASpiX with template-based cosmological simulations.

Following extensive tests on analytical toy-catalogues (paper III), we present the results of a more realistic study over a 711 deg2 template-based cosmological simulation. Dark matter halos from the Aardvark simulation have been ascribed luminosities, temperatures and core-radii, using local scaling relations and assuming self-similar evolution. Predicted X-ray sky-maps are converted into XMM event lists using an instrumental simulator. The XXL pipeline run on the resulting sky images, produces an 'observed' cluster catalogue over which the tests have been performed. This allowed us to investigate the relative power of various combinations of count-rate, hardness-ratio, apparent-size and redshift information. Two fitting methods were used : a traditional MCMC approach and a simple minimisation procedure (Amoeba) whose mean uncertainties are a posteriori evaluated by means of synthetic catalogues. Results were analysed and compared to the predictions from a Fisher analysis (FA). For this particular catalogue realisation, assuming perfectly known scaling relations, the CR-HR combination gives $\sigma_8$ and $\Omega_m$ at the 10% level, while CR-HR-r$_c$-z improves this to $\leq$ 3%. Adding a second hardness ratio improves results from the CR-HR1-r$_c$ combination, but to a lesser extent than adding redshift information. When all coefficients of the M-T relation (including scatter) are also fitted, cosmological parameters are constrained to within 5-10%, and larger for the M-T coefficients (up to a factor of two for the scatter). Errors returned by the MCMC, by Amoeba, and by FA predictions, are in most cases in excellent agreement and always within a factor of two. We also study the impact of the scatter of the M-Rc relation on the number of detected clusters: for the cluster typical sizes usually assumed, the larger the scatter, the lower the number of detected objects.