the case of sterile neutrino decay the measured additional flux at $\rm{\sim3.55~keV}$ would be related to two defining properties of the particles: The particle mass $\rm{m_s}$ and the mixing-angle $\rm{sin^2(2\Theta)}$, which describes interaction of the sterile neutrinos with its active neutrino counter-parts and thus the likelihood of decay in the $\rm{\gamma/\nu}$ channel. They are related through [as used by @2014ApJ...789...13B]

$$\rm{sin^2(2\Theta) = \frac{F_{DM}~10^{14}~M_{\odot}}{\frac{12.76}{cm^2~s}~M^{FOV}_{DM}~(1+z)}}~\left(\frac{D_L}{100~Mpc}\right)^2\left(\frac{1~keV}{m_s}\right)^4
\label{eqn:sin}$$

where $\rm{F_{DM}}$ is the observed flux of the DM decay line, $\rm{M^{FOV}_{DM}}$ is the expected DM mass within the field of view (FOV) of the observation, $\rm{D_L}$ is the luminosity distance of the cluster, and z its redshift.

The paper is structured as follows: Sect. 2 describes the sample of clusters and the data reduction, Sect. 3 describes the fitting of individual cluster spectra, in Sect. 4 the procedure for fitting merged spectra is introduced, Sect. 5 explains how DM masses in the FOV were estimated, in Sect. 6 the upper limits for an additional 3.55keV line emission are presented, in Sect. 7 the results are discussed comparing to other studies, and in Sect. 8 our findings are summarized.

For all our analysis we used a standard $\rm{\Lambda CDM}$ cosmology with $\rm{H_0=71~km~s^{-1}~Mpc^{-1}}$, $\rm{\Omega_M=0.27}$ and $\rm{\Omega_{\Lambda}=0.73}$ and 