FIG. 3: PAMELA data fitting for positron fraction in Model I and Model II. where T = E − m$_{p}$ is the proton kinetic energy. We can use K$_{0}$ , δ , V$_{c}$ and L to classify the astrophysical models that are compatible with the B/C ratio into three types [8], where K$_{0}$ and δ appear in the diffusion coefficient K . And each type is characterized by the flux of anti-protons. To suppress the anti-proton flux, we choose the parameters which can produce the minimal anti-protons: δ = 0 . 85, K$_{0}$ = 0 . 0016 kpc $^{2}$Myr − $^{1}$, L =1 kpc, and V$_{c}$ = 13 . 5 km s − $^{1}$. Similarly, the anti-proton flux at the heliosphere boundary is formally solved to be where For details, please see Appendix B. 15 dN S ¯ p dx = Γ$_{eff}$ Γ$_{total}$ ∑ I,F ( C 2 $_{I,F}$R$_{I,F}$ ) × 1 R$_{I,F}$ d ˜ N dx$_{I,F}$ ⊗ dN dx I,F p . (31) Φ ¯ p $_{⊙}$( E ) = 1 Γ$_{total}$ × β$_{¯}$ p 4 π × dN S ¯ p dE × H ¯ $_{p}$( E ) , (30) σ ann p ¯ p = { 661(1 + 0 . 0115 T − 0 . 774 − 0 . 984 T 0 . $^{0151}$)mbarn , for T < 15 . 5 GeV 36 T − 0 . $^{5}$mbarn , for T ≥ 15 . 5GeV , (29) annihilation rate is given by Γ$_{ann}$ = ( n$_{H}$ + 4 2 / $^{3}$n$_{He}$ ) σ ann p ¯ p v$_{¯}$ p with [41] 0.01 0.03 0.1 0.3 10 100 500 FERMI+PAEMALA fit ATIC+PAMELA fit PAMELA08 Background