neutrino

value ρ(R o )=0.3 GeV/cm 3 [44]. Using these definitions,
we can write r = √ Ro 2 + l 2 − 2R o l cos θ and the upper
limit for Event the l integral Rates √
in Dependence Eq. (A3) can on be θ max
obtained as
l max = R o cos θ + Rs 2 − Ro 2 sin 2 θ for a given θ.
For the NFW profile, some values for 〈J 2 〉 Ω ∆Ω and
〈J 1 〉 Ω ∆Ω are summarized in Table VII.
0.1 ◦ 1 ◦ 5 ◦ 25 ◦ 50 ◦ 70 ◦ 90 ◦
〈J 2 〉 Ω ∆Ω 0.14 1.35 5.94 19.68 27.75 31.73 33.42
〈J 1 〉 Ω ∆Ω 0.00027 0.018 0.30 3.69 8.79 12.24 14.90
TABLE VII: The values of J factors for NFW profile for
θ max =0.1 ◦ , 1 ◦ , 5 ◦ , 25 ◦ , 50 ◦ , 70 ◦ , 90 ◦ .
In Fig. 20 we show 〈J n 〉 Ω ∆Ω factors as a function of
θ max for DM annihilation (n =2)andDMdecay(n =1)
evaluated for a cone wedge between θ max − 1 ◦ and θ max