\[fig:lineall\] shows the upper limits on the flux derived from observations of A1795 (deepest observation in the sample), where we obtained a $\rm{3\sigma}$ upper limit of $\rm{3.22\times10^{-6}~cm^{-2}~s^{-1}}$ from merged ACIS-I observations ($\rm{\sim613~ks}$) and $\rm{4.73\times10^{-6}~cm^{-2}~s^{-1}}$ from ACIS-S ($\rm{\sim241~ks}$).

Using equation (\[eqn:sin\]) this translates to one of the deepest upper limits on the mixing-angle for individual clusters $\rm{sin^2(2\Theta) \leq 4.4\times10^{-10}}$ (ACIS-I data). The limits on the additional flux that we could derive in the individual systems depend on the exposure time and on how well the cluster emission is modelled by a two component collisionally-ionised plasma model. For a detailed list of constraints see Tab. \[tab:indi\_limits\].

Limits in merged spectra {#sec:merge_lim}
------------------------

The fits to the merged data provide deeper upper limits on the flux by about a factor of three for ACIS-I compared to the individual spectra (see Fig. \[fig:linemerge\] and Tab. \[tab:mix\]). To turn this flux into a limit on the expected mixing-angle in the 7.1keV sterile neutrino scenario we estimated the average mass and luminosity distance of the cluster sample. We weighted the contributions to the average with their expected contribution $\rm{\omega_{i,DM}}$ to the DM line flux with the formula used by @2014ApJ...789...13B,

$$\rm{\omega_{i,DM} = \frac{M_{i,DM}(1+z_i)}{4\pi~D^2_{i,L}}\times\frac{exp_i}{exp_{tot}}}
\label{eqn:weights}$$

where i 