an `apec` model without lines [compare e.g. @2014ApJ...789...13B]. This procedure provided a goodness of fit comparable to the fitting process used in this study. We concluded that the modelling with two temperature collisionally ionised plasma emission (`XSPEC` `apec` model) is appropriate for the spectra in this study.

There are some remaining residuals between the model and data in the merged spectra. A large fraction of these residuals are likely caused by the systematic effects of averaging and de-redshifting the responses and spectra (see simulated spectra in Fig. \[fig:fakelinemerge\]). As these features are narrower than the response, they cannot and should not be fitted by Gaussian lines. Modelling the emission lines separately [e.g. as @2014ApJ...789...13B] does not significantly improve the fit, except for the two strongest features at 3.85 and 4.7keV (perhaps due to incomplete modelling of the temperature structure, as discussed in Appendix \[sec:residuals\]). If these two features are included in our model, there is no significant change to our limits. We conclude that the two temperature plasma model is appropriate for this study. There are no strong emission lines expected over the range in temperature in the region of the 3.55keV line, which could explain the strength of previous 