The $\nu$ MSM does not explain the unconfirmed results of the LSND experiment (Aguilar et al. 2001). There are other models that try to account for it by introducing a sterile neutrino with the mass around 1 eV. There are also models that explain not all, but only some of these phenomena (e.g. LSND and DM, but not the baryon asymmetry as e.g. in de Gouvea 2005) We do not give any review here. We would like to stress that, although our work is motivated by the recent results on the $\nu$ MSM, our method and results do not rely on any particular model.

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Namely, if luminosity distance D_L is much greater than the characteristic scale of the DM distribution $\rho_{\textsc{dm}}(r)$ .

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...

According to Klypin et al. (2002), the choice of e.g. the Moore profile Ghigna et al. (2000) or a generalization thereof, as compared to the NFW profile, would change the results by $\la$ $1\%$ for $r< 3~{\rm kpc}$ . As we are using observations away from the center, this difference is completely negligible, so we choose to use the NFW profile.

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... paper

When quoting results of Klypin et al. (2002), we do not take the effects of baryon compression on DM into account. While these effects make DM distribution in the core of the MW denser, they are hard to compute precisely. Thus the values we adopt give us a conservative lower bound on the estimated DM signal.

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...%)

Abazajian & Koushiappas (2006) claim that the MW results of Boyarsky et al. (2006c); Riemer-Sørensen et al. (2006a) are uncertain by about a factor of 3. This conclusion was based on the range of virial masses of the MW DM halo $M_{{\rm vir}}= (0.7{-}2.0)$ $\times$ $10^{12}~M_\odot$ in Klypin et al. (2002). However, as just demonstrated, the authors of Boyarsky et al. (2006c) have chosen parameters of DM halo conservatively. The flux they used, corresponded to the favored models A₁ or B₁ in Klypin et al. (2002), with $M_{{\rm vir}}\sim 1.0$ $\times$ $10^{12}~M_\odot$ . These models provide the lowest bound on the derived flux of DM decay (if one does not take into account the highly implausible "maximum disk'' (A₂ or B₂) models of Klypin et al. 2002). Even in the latter case, the DM flux will be $30{-}50\%$ lower than the one used in work Boyarsky et al. (2006c). Therefore, parameters of the MW DM halo from Boyarsky et al. (2006c) provide the conservative estimate so we use them in our work as well.

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... exposures)

We processed the blank sky data with newer SAS distribution, xmmsas_20050815_1803-6.5.0, and obtained slightly different exposure times than those in the public data.

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... August-September 2005)

We are very grateful to Prof. T. Maccarone for sharing this data with us before it became publicly available through the XMM data archive.

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... 2006)

As discussed in Sect. 3.1, the estimates for DM flux do not vary significantly if one uses NFW instead of the isothermal DM density profile. In the case of UMi, the cored (isothermal) profile will clearly produce a more conservative estimate than will the cuspy NFW profile. Indeed, taking NFW parameters for UMi from the recent paper Wu (2007) gives a $\sim$ 20% higher estimate for the DM mass within the FoV.

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...Wilkinson et al. 2006)

For the detailed studies of mass distribution in dwarf spheroidals, see Gilmore et al. (2007). We are grateful to Prof. G. Gilmore for sharing the numbers with us before their paper became available. The statistical uncertainty in determining these numbers is below 10%. The systematic uncertainties are much harder to estimate. One of the major sources of the systematic errors comes from violation of the main assumptions of the method: deviation from equilibrium and from the spherical distribution of matter in a galaxy. In other known examples it provides a factor of 2 uncertainty, which should be a conservative estimate in the case of UMi, as it is rather spherical. Another typical uncertainty - determination of the mass of the stars - is not important for UMi, as it has a very high mass-to-light ratio.

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... channel

For earlier works, discussing cosmological and astrophysical effects of decaying DM, see e.g. Berezhiani & Khlopov (1990); Doroshkevich et al. (1989); de Rujula & Glashow (1980); Berezhiani et al. (1987,1990). The extensive review of the results can also be found in the book Khlopov (1997).

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