confidence for both ACIS-I and ACIS-S detectors after the stacking. The measured flux can be converted into a mixing angle using the average sample properties of Tab. \[tab:mix\]. The resulting mixing angles in the simulations are $\rm{4.1^{+3.2}_{-2.3}}$ (ACIS-I, CI:68) and $\rm{14.8^{+3.9}_{-5.2}}$ (ACIS-S, CI:68). These simulations show the detection efficiency of our stacking method. There is some hint that the limits of ACIS-S are biased high which is in agreement with the limits obtained from real data (see Fig. \[fig:literature\] the best constraints).

There are small fluctuations in the residuals of less than 2 per cent. To asses the uncertainties introduced by our de-redshifting technique of the RMF response files we tested many different combinations of smoothing and number of iterations. The best results were obtained calculating the average of 100 iterations and smoothing them using a Gaussian filter ($\rm{\sigma = 1~pixel}$). This procedure proved most effective in recovering the simulated flux (see Fig. \[fig:fakelinemerge\]). The residual structures seen in the merged spectra are partially caused by the averaging over many cluster spectra of different temperatures which are not perfectly modelled by the two temperature component `apec` model. More complex models however made the fit less stable and did not improve 