Studying X-ray instruments with galaxy clusters

Aims. Our aim is to apply a scientific approach to the problem of the effective area cross-calibration of the XMM-Newton EPIC instruments. Using a sample of galaxy clusters observed with XMM-Newton EPIC, we aim to quantify the effective area cross-calibration bias between the EPIC instruments as implemented in the public calibration database in November 2021 in the 0.5-6.1 keV energy band. Methods. We tested two methods for evaluating the effective area cross-calibration bias for CCD-type X-ray instruments. Namely, we compared the evaluation of the cross-calibration bias by modelling it before the convolution of the spectral models with the redistribution matrix or by analysing the convolved products. We applied the methods to a sample of galaxy clusters observed with XMM-Newton/EPIC instruments. We invested significant efforts in controlling and keeping the systematic uncertainties of the cross-calibration bias below 1%. The statistical uncertainties are similar, and thus we can reliably measure effects at the 1% level.XMM. Results. On average, the two methods differ very little; the only difference in the cross-calibration bias is at the highest energies, and by maximum of 3%. The effective area cross-calibration in the 0.5-6.1 keV band between MOS and pn is biased at a substantial level. The MOS/pn bias is systematic, suggesting that the MOS (pn) effective area may be calibrated too low (high), by similar to 3-27% on average depending on the instrument and energy band. The excellent agreement between the energy dependences (i.e. shapes) of the effective area of MOS2 and pn suggest that they are correctly calibrated, within in the 0.5-4.5 keV band. Comparison with an independent dataset of point sources (3XMM) confirms this. The cluster sample indicates that the MOS1/pn effective area shape cross-calibration has an approximately linear bias amounting to a maximum of similar to 10% in the 0.5-1.5 keV band. Conclusions. The effective area cross-calibration of XMM-Newton/EPIC instruments in November 2021 in the 0.5-1.5 keV band was relatively successful. However, the cluster-to-cluster rms scatter of the bias is substantial compared to the median bias itself. Thus, a statistically robust implementation of the cross-calibration uncertainties to a scientific analysis of XMM-Newton/EPIC data should include the propagation of the scatter to the best-fit parameters, instead of a simple average bias correction of the effective area.