Y

photons/(cm3.sec.GeV),

about 10 times smaller than expected from bremsstrahlung gamma ray emissivity. Obtained in Cesarsky et al. (1978) gamma ray spectrum is too hard and contradicts to measurements by COMPTEL (Strong et al., 1994) and to theoretical models of Skibo and Ramaty (1993), Pohl (1993, 1994). On the basis of investigation of the CR hysteresis effect relative to solar activity (Dorman and Dorman 1967a,b), is possible to determine the modulation of CR in the interplanetary space in the minimum of solar activity and to restore the demodulated spectrum of galactic CR out of the Heliosphere (Dorman M1975a,b; Zusmanovich, M1986; Belov et al., 1990). For galactic CR electrons the demodulated differential spectrum Ne (Ee)

according to Webber (1987) can be described by power law « E-Y with graduelly increasing y with increasing of Ee from y = 2.3 for Ee ~ l-2 GeV to y = 3.2 for Ee = 30-100 GeV:

for Ee < 3 GeV, for 3 GeV < Ee < 10 GeV, (1.12.15) for 10 GeV < Ee < 400 GeV, where Ne (Ee) is in units of electron/(cm2.sec.sr.GeV). The demodulated differential energy spectrum of CR electrons described by Eq. 1.12.15 will give the expected gamma ray emissivity in accordance with measurements by COMPTEL (Strong et al. 1994) and with theoretical models Skibo and Ramaty (1993); Pohl (1993, 1994).

1.13. Gamma ray generation in space plasma by interactions of flare energetic particles with solar and stellar winds

1.13.1. The matter of problem and the main three factors

The generation of gamma rays by interaction of flare energetic particles (FEP) with solar and stellar wind matter shortly was considered in Dorman (1996, 1997). In Dorman (2001a) was given a development of this research with much more details. As an example we consider the first the situation with gamma ray generation in the interplanetary space by solar FEP in periods of great events, determined mainly by three factors:

The 1st factor - by the space-time distribution of solar FEP in the Heliosphere, their energetic spectrum and chemical composition (see review in Dorman, M1957, M1963a,b, M1978; Dorman and Miroshnichenko, M1968; Dorman and Venkatesan, 1993; Stoker, 1995; Miroshnichenko, M2001). For this distribution can be important nonlinear collective effects (especially for great events) of FEP pressure and kinetic stream instability (Berezinsky et al., M1990; Dorman, Ptuskin, and Zirakashvili, 1990, Zirakashvili et al., 1991; see in more details below, Chapter 3).

The 2nd factor - by the solar wind matter distribution in space and its change during solar activity cycle; nonlinear effects will also be important for this distribution: pressure and kinetic stream instability of galactic CR as well as of solar FEP (especially in periods of very great events) - see references above and in more details below, in Chapter 3.

The 3rd factor - by properties of solar FEP interaction with the solar corona and solar wind matter accompanied with gamma ray generation through decay of neutral pions (Stecker, M1971; Dermer, 1986a,b; see above Section 1.12.2).

After consideration of these 3 factors we calculate the expected space-time distribution of gamma ray emissivity, and expected fluxes of gamma rays for measurements on the Earth's orbit of a dependence upon time after the moment of FEP generation, for different directions of gamma ray observations. We calculate expected fluxes also for different distances from the Sun inside and outside the Heliosphere. We expect that the same 3 factors will be important for gamma ray generation by stellar FEP in stellar winds, but for some types of stars the total energy in FEP is several orders higher than in solar flares and the speed of lost matter is several orders higher than from the Sun (Gershberg and Shakhovskaya, 1983; Korotin and Krasnobaev, 1985; Gershberg et al., 1987; Kurochka, 1987).

According to Dorman (2001a), observations of gamma rays generated in interactions of solar FEP with solar wind matter can give during the periods of great events valuable information about the 3D-distribution of solar wind matter as well as about properties of solar FEP and its propagation parameters. Especially important will be observations of gamma rays generated in interactions of stellar FEP with stellar wind matter. In this case information can be obtained about total energy and energetic spectrum in stellar FEP, about the mode of FEP propagation, as well as information about stellar wind matter distribution. 1.13.2. The 1st factor: solar FEP space-time distribution

The problem of solar FEP generation and propagation through the solar corona and in the interplanetary space as well as its energetic spectrum and chemical and isotopic composition was reviewed in Dorman (M1957, M1963a,b, M1978), Dorman and Miroshnichenko (M1968), Dorman and Venkatesan (1993), Stoker (1995), Miroshnichenko (M2001). In the first approximation, according to numeral data from observations of many events for about 5 solar cycles the time change of solar FEP and energy spectrum change can be described by the solution of isotropic diffusion (characterized by the diffusion coefficient k- (Ek)) from some pointing instantaneous source Qi (Ek,r, t) = Noi8(r>(t) of solar FEP of type i (protons, a - particles and heavier particles, electrons) by

Ni (Ek,r,t) = Noi(Ek )[( ()t)3/2 ]1 xexp(- r2/(4k (Ek )t)> (1.13.1)

where N0i (Ek) is the energetic spectrum of total number of solar FEP in the source. At the distance r = r the maximum of solar FEP density

Ni max Ek )>Noi (Ek ) = 21/233/2n"1/2exp(- 3/2 j-3 = 0.925 r- (1.13.2) will be reached according to Eq. 1.13.1 at the moment tmax(Ek j= iV6^ > (113 3)

and the space distribution of solar FEP density at this moment will be

Ni (Ek, W > = (5^n)>2 r1-3 exp(- 3r2 / 2^2 )= 4.146r1-3 exp(- 3r2/2r12) .(1.13.4)

According to numerical experimental data the energetic spectrum of generated solar energetic particles in the source can be described approximately as (see the review in Dorman and Venkatesan, 1993):

where y increases with increasing of energy from about 0^1 at Ek < 1 GeV/nucleon to about 6^7 at Ek ~ 10 ^ 15 GeV/nucleon. Parameters Noi and y are changing sufficiently from one event to other: for example, for the greatest observed event of February 23, 1956 Noi = 1034 1035 , in the event of November 15, 1960

Noi = 3 x 1032, in the event of July 18, 1961 Noi = 4 x 1031, in the event of May 23,

1967 Noi ~ 1031. For the greatest observed event of February 23, 1956 parameter y had values ~ 1.2 at Ek ~ 0.3 GeV/nucleon, y ~ 2.2 at Ek ~ 1 GeV/nucleon , y ~ 4 at Ek ~ 5 ■ 7 GeV/nucleon, and y ~ 6^7 at Ek ~ 10 ■ 15 GeV/nucleon. This change of y is typical for many great solar energetic particle events: see in Dorman (M1957,

M1963a,b) about event of February 23, 1956, and review about many events in Dorman (M1963a,b, M1978), Dorman and Miroshnichenko (M1968), Dorman and Venkatesan (1993), Stoker (1995), Miroshnichenko (M2001). Approximately the behavior of value y in Eq. 1.13.5 can be described as

where parameters yo and Eko are different for individual events , but typically they are in intervals 2 <yo < 5 and 2 < Eko < 10 GeV/nucleon. The position of maximum in Eq. 1.13.5 taking into account Eq. 1.13.6 is determined by

Ek max = Eko exp(- Yo ) , Noi {Ek max ) = Noi . (1.13.7)

The total energy contained in FEP will be according to Eq. 1.13.5-1.13.7:

Etot = Noi IEk(EklEkmax) d(Ek/Ekmax) = bNoiEkmax , (1.13.8)

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