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Gamma ray emissivity caused by nuclear interactions of FEP protons with solar wind matter will be determined according to Stecker (M1971), Dermer (1986a,b). by

Fyph (, r, 9, t) = 2 ]dE/ (El, - mlc4) ' Ffa ( r, 9, t), (1.13.17)

where Enm;nEy) = Ey + m^c4j4Ey . Let us introduce Eq. 1.13.1 in Eq. 1.13.16 and Eq. 1.13.17 by taking into account Eq. 1.13.14:

dE, n where x 7 ( )Nop(EkX^n(Ek)(Vt1)-3/2exp(-3r2t^2r12t]dEk , (LmS)

B(r,9,t) = 33/227/2n1/2r12n1 (0,t)u1 (0,t)/r2u (r,0,t) (1.13.19)

is the time in which the density of FEP at a distance of 1 AU reaches the maximum value. The space distribution of gamma ray emissivity for different t/t1 will be determined mainly by function f (t, t1) = r "2 (i/t1 )-3/2 exp(- 3r 2tJ 2n2t), (1.13.21)

where t1, determined by Eq. 1.13.20, corresponds to some effective value of Ek in dependence of EY, according to Eq. 1.13.16 and Eq. 1.13.17. The biggest gamma ray emission is expected in the inner region r < r{ = r1 (2t/3t1 )1/2, (1.13.22)

where the level of emission «r~2 (t/t1 )-3//2. Outside this region gamma ray emissivity decreases very quickly with r as « r- exp(-(r/rj) ). For an event with total energy 1032 ergs at t = t1 = 103sec, rt = 1013cm, n1(0,t) = 5 cm-3, Kp (Ek ) = 4 x 1022 cm2/sec, we obtain for emissivity of gamma rays with energy > 100 MeV:

FY (ey> 0.1 GeV, r) 108 r "2 photon.cm -3sec-1. (1.13.23)

Let us note that at the distance of 5 solar radius it gives 10 15 photon.cm 3sec 1). Eq. 1.13.18 describes the space-time variations of gamma ray emissivity distribution from interaction of solar energetic protons with solar wind matter (see Fig. 1.13.1).

Fig. 1.13.1. Expected for the event with energy 1032 ergs space-time emissivity distribution of gamma rays with energy > 100 MeV for different time t after FEP generation in units of time maximum t1 on 1 AU, determined by Eq. (1.13.20). The curves are from t/t1 = 0.001 up to t/t1 = 100. From Dorman (2001a).

Fig. 1.13.1. Expected for the event with energy 1032 ergs space-time emissivity distribution of gamma rays with energy > 100 MeV for different time t after FEP generation in units of time maximum t1 on 1 AU, determined by Eq. (1.13.20). The curves are from t/t1 = 0.001 up to t/t1 = 100. From Dorman (2001a).

1.13.5. Expected angle distribution and time variations of gamma ray fluxes for observations inside the Heliosphere during FEP events

Let us assume that the observer is inside the Heliosphere at the distance robs < ro from the Sun and helio-latitude 6>obs (here ro is the radius of Heliosphere). The sight line of observation we can determine by the angle 0sl, computed from the equatorial plane from direction to the Sun to the North. In this case the expected angle distribution and time variations of gamma ray fluxes will be

\Ey, robs ,6>si, t) = J FYh ((y , L(robs, 3sl A t)dL ■

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