Af Ek Af W r t

Ek E2

To determine the parameters E1, E2, E3 we use observations of solar CR events as well as observations of galactic CR modulation in interplanetary space. The time dependences of galactic CR primary fluxes for effective rigidities R =2, 5, 10 and 25 GV were found in Belov et al. (1990) on the basis of ground measurements of muon and neutron components as well as measurements in stratosphere on balloons and in space on satellites and spacecrafts. The residual modulation (relative to the flux out of the Heliosphere) for R ~ 10 GV in the minimum and maximum of solar activity was determined as 6 and 24 % (what is in good agreement with results on CR-SA hysteresis effects according to Dorman and Dorman, 1967a,b, 1968; Dorman, M1975b; Dorman et al., 1997a,b). According to convection-diffusion model of CR solar cycle modulation (Parker, M1963; Dorman, 1959, M1975b), the slope of the residual spectrum AD(R)/ D0 (RR-5

reflects the dependence A(R(AD(r)/D0(R))-1 ~ R5. In Belov et al. (1990) the spectral index 5 was determined as ¡~ 0.4 at 2 - 5 GV, ¡~ 1.1 at 5-10 GV, and ¡~ 1.6 at 10-25 GV. Eq. 1.13.12 will be in agreement with these results and with data on FEP events in smaller energy region if we choose E1 = 0.05 GeV/nucleon, E2 = 2 GeV/nucleon, and E3 = 5 GeV/nucleon.

The dependence of the transport path from the level of solar activity is characterized by A, (W). This parameter can be determined from investigations of galactic CR modulation in the interplanetary space on the basis of observations by neutron monitors and muon telescopes for several solar cycles. According to Dorman and Dorman (1967a,b, 1968), Dorman (M1975b), Dorman et al. (1997a,b),

A, (W W_1/3 for the period of high solar activity and A, (WW_1 for the period of low solar activity. According to Dorman et al. (1997a,b), the hysteresis phenomenon in the connection of long term CR intensity variation with solar activity cycle can be explained well by the analytical approximation of this dependence, taking into account the time lag of processes in the interplanetary space relative to caused processes on the Sun:

f f W ^ ~~~~ |i-w (1 --1 /Wmax I Ai (W, r, t) = Ai (Wmax )xfW(t - uj/Wmax ) 3 3 ^ ^ "^ ) , (1.13.13)

where Wmax is the sunspot number in maximum of solar activity and A i (Wmax ) 1012cm.

1.13.3. The 2nd factor: space time distribution of solar wind matter

The detail information on the 2-nd factor for distances smaller than 5 AU from the Sun was obtained by the mission of Ulysses. Important information for bigger distances (up to about 100 AU) was obtained from missions Pioneer 10, 11, Voyager 3, 4, but only not far from the ecliptic plane. If we assume for the first approximation the model of Parker (M1963) of radial solar wind expanding into the interplanetary space which is in good accord with all available data of direct measurements in the Heliosphere, then the behavior of the matter density of solar wind will be described by the relation n(r,0) = n1 (e)u1 (o)r\ /(r2u(r,0]), (1.13.14)

where n1(0) and u1(0) are the matter density and solar wind speed at the helio-latitude 0 on the distance r = r1 from the Sun (r1 = 1AU). The dependence u(r,0) is determined by the interaction of solar wind with galactic CR and anomaly component of CR, with interstellar matter and interstellar magnetic field, by interaction with neutral atoms penetrating from interstellar space inside the Heliosphere, by the nonlinear processes caused by these interactions (Dorman, 1995a,b; Le Roux and Fichtner, 1997; see also below, Chapter 3). According to calculations of Le Roux and Fichtner (1997) the change of solar wind velocity can be described approximately as u(r) = u1(1 - b(rlro ^

where the distance to the terminal shock wave r° ~ 74 AU and parameter b ~ 0.13 ■0.45 in dependence of subshock compression ratio (from 3.5 to 1.5) and from injection efficiency of pickup protons (from 0 to 0.9). From our investigations of CR-SA hysteresis phenomenon (Dorman and Dorman, 1967a,b, 1968; Dorman, M1975b; Dorman et al., 1997a,b), we estimate ro = 100 AU .

1.13.4. The 3rd factor: gamma ray generation by FEP in the Heliosphere

Let us consider in the first generation of neutral pions. According to Stecker (M1971), Dermer (1986a,b), the neutral pion generation caused by nuclear interactions of energetic protons with hydrogen atoms through reaction p + p ^ n° + anything will be determined by

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