ρ$_{NFW}$ ( r ) = M$_{vir}$ 4 πα 1 r ( r$_{s}$ + r ) $_{2}$, (3) r$_{γα}$ = E$_{γ}$ ( T ) N$_{FeXXVI}$ + R$_{γ}$ ( T ) N$_{FeXXVII}$ E$_{α}$ ( T ) N$_{FeXXVI}$ + R$_{α}$ ( T ) N$_{FeXXVII}$ (1) F$_{s}$ = ∫$_{Ω}$ ρ$_{NFW}$ ( ⃗ r ) 4 π ( ⃗ r$_{0}$ − ⃗ r ) 2 Γ c 2 2 d $^{3}$⃗ r , (4) Γ = 1 . 38 × 10 − $^{22}$sin$^{2}$(2 θ ) ( m$_{s}$ 1keV ) 5 s − $^{1}$. (5) N$_{FeXXVII}$ N$_{FeXXVI}$ = E$_{γ}$ ( T ) − r$_{γα}$E$_{α}$ ( T ) r$_{γα}$R$_{α}$ ( T ) − R$_{γ}$ ( T ) (2) sin$^{2}$(2 θ ) = (4 . 1 ± 2 . 2) × 10 − $^{12}$. (6) Γ = (9 . 0 ± 4 . 8) × 10 − $^{28}$s − $^{1}$. (7) III. RADIATIVE DECAYS OF STERILE NEUTRINOS 2 15 keV is from the theoretical model (see, [7]). Therefore the expected value of the intensity in the FeXXVI Ly γ line is 0 . 038 × I$_{Ly}$$_{α}$ = 6 . 3 + 0 . 4 − 0 . 4 × 10 − 6 ph / (cm 2 s) and is much smaller than the measured intensity by Suzaku. Therefore, the excess of the intensity in the 8.7 keV line equals ≈ (1 . 1 ± 0 . 6) × 10 − 5 ph / (cm 2 s). Decays of sterile neutrinos in the dark matter halo of the Milky Way are a promising way to explain the excess in the 8.7 keV line. The amount dark matter within the field of view of the Suzaku observation (see Fig. 1 of [4]) is only a minute fraction of the total mass of the dark matter halo of the Milky Way. We consider the model of the Milky Way dark halo presented in [9] and used to derive constraints on the sterile neutrino parameters by [10]. The Milky Way halo density is described by the Navarro-Frenk-White (NFW) profile To demonstrate that this excess cannot be explained by ion- ization and recombination processes, we calculate the ratio of the fully stripped (FeXXVII) ionic fraction to the hydrogen- like iron ionic fraction using the ratio of the intensities of the FeXXVI Ly γ to Ly α lines as a function of temperature T . The ratio r$_{γα}$ of the FeXXVI Ly γ to FeXXVI Ly α iron line intensities is given by where the dark matter halo parameters of preferred models obtained in [9] correspond to M$_{vir}$ = 10$^{12}$M$_{⊙}$, r$_{s}$ = 21 . 5 kpc and numerical constant α ≃ 1 . 64 (see [10]). A mass within the field of view of M$_{fov}$ ≃ 2 . 5 × 10$^{6}$M$_{⊙}$ is derived from this model. The decay flux into a solid angle Ω (within the field of view) is given by (see, e. g. [11]) where E$_{γ}$ and E$_{α}$ are the impact excitation rate coe ffi cients, and R$_{γ}$ and R$_{α}$ are the rate coe ffi cients for the contribution from recombination to the Ly γ and Ly α spectral lines, re- spectively. Excitation and recombination rate coe ffi cients are taken from [8]. From Eq. (1) the ratio of the fully stripped (FeXXVII) ionic fraction to the hydrogen-like iron ionic fraction is where | ⃗ r$_{0}$ | = 8 . 5 kpc is the distance to the Galactic center. The decay rate Γ is given by (e.g. [11] and references therein) Note that we do not use the assumption of collisional ioniza- tion equilibrium. To estimate the value of the mixing angle, we use the inferred value of m$_{s}$ = 17 . 4keV and the value of the energy flux excess. Then, from Eqs. (4), (5) the value of the mixing angle is given by For the best fit value of the intensity ratio of the Ly γ to Ly α iron lines (1 . 77 × 10 − $^{5}$/ (1 . 66 × 10 − $^{4}$) ≈ 0 . 107) found by [4], we find that the ratio of the fully stripped (FeXXVII) ion fraction to the hydrogen-like iron ion fraction lies in the range ( − 40 , − 20) when the electron temperature is in the range (5 keV, 15 keV). Since the ratio of the fully stripped (FeXXVII) to hydrogen-like (FeXXVI) ion fractions should not be nega- tive, we conclude that the excess cannot be explained by ion- ization and recombination processes. A more physically ac- ceptable explanation of the excess is that of sterile neutrino decays, under the assumption that sterile neutrinos constitute a significant fraction of dark matter. In the next section, we calculate the mixing angle using our inferred value of the in- tensity excess in the 8.7 keV line. Using Eq. (5) we derive the following constraint on the decay rate: Note that the derived values of the mixing angle of sin$^{2}$(2 θ ) = (4 . 1 ± 2 . 2) × 10 − 12 and decay rate of Γ = (9 . 0 ± 4 . 8) × 10 − $^{28}$s − 1 lie in the allowed region for a dark matter sterile neu- trino with a mass of 17-18 keV (see [12]). Such a neutrino is capable of accounting for a substantial fraction, if not all, of the dark matter. The sterile neutrino possesses a radiative decay channel de- caying to an active neutrino and a photon with energy E = m$_{s}$c $^{2}$/ 2. Since the excess in the 8.7 keV line corresponds to a sterile neutrino mass of 17 . 4 keV, in this section we estimate the mixing angle sin$^{2}$(2 θ ) and decay rate for such a sterile neu- trino. Using the excess in the 8.7 keV line intensity equal to I$_{excess}$ ≈ (1 . 1 ± 0 . 6) × 10 − $^{5}$ph / (cm$^{2}$s) and the definition of the energy flux F$_{s}$ = I$_{excess}$ × E , we find that the value of the energy flux excess in the 8.7 keV line equals (9 . 6 ± 5 . 2) × 10 − $^{5}$keV / (cm$^{2}$s). An additional contribution of comparable strength comes in a point-like source if a cusp of dark matter develops around the centar black hole. The dark matter cusp mass is constrained observationally by stellar orbit measurements and is taken to be 3 × 10$^{6}$M$_{⊙}$ within the central 0.001 pc. This is comparable to the mass of the central black hole. Such a cusp is natu- rally produced via adiabatic contraction of dark matter around the black hole within its sphere of influence, about 3 pc for the Milky Way black hole [13], [14]. Typically about as much mass is captured in the spike as is in the central black hole and with a density profile of ρ ∝ r − 9 / 4 or even steeper. Dynami- cal histories of merging complicate this picture. In particular,