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sinp exp

2 1 1 photon.cm" .sr" .sec" . (1.13.31)

Expected fluxes of gamma rays with energy Ey > 0.1 GeV during a large FEP

event with total energy 1032 ergs for different directions of observation characterized by an angle 9 from 2° up to 179° as a dependence upon t/t1 are shown in Fig. 1.13.2-1.13.5.

Fig. 1.13.2. Expected fluxes of gamma rays with energy more than 100 MeV during FEP event with total energy 1032 ergs for directions from 9 = 2° to 9 = 10° from the Sun as a dependence on t/t1 , where t1 was determined by Eq. (1.13.20).

Fig. 1.13.3. The same as in Fig. 1.13.2, but for 9 = 12° to 9 = 26°.

Relative 1

Fig. 1.13.3. The same as in Fig. 1.13.2, but for 9 = 12° to 9 = 26°.

Fig. 1.13.4. The same as in Fig. 1.13.2, but for 9 = 28° to 9 = 70°.

Fig. 1.13.5. The same as in Fig. 1.13.2, but for 9 = 75° to 9 = 179°

Relative time after FEP ejection

Fig. 1.13.5. The same as in Fig. 1.13.2, but for 9 = 75° to 9 = 179°

1.13.6. Gamma rays from interaction of FEP with stellar wind matter

Let us suppose that some observer is at the distance robs >> ro, where ro is radius of a stellar-sphere. In this case

2 ro

OYpH (( robs, t )= 2nro-b2s J cos OdO J r2drFYpH ((, r,9, t), (1.13.32)

where F^h ((y,r,O, t) was determined by Eq. (1.13.18). For spherical symmetrical modes of FEP propagation and stellar wind matter distribution, we obtain

Kh ((robs,t)= 4nr0~b2FY rb¿1 ) )-1 rf^(hi) 1 ph.cm-2sec-1, (1.13.33)

v rl where O(x) is the probability function. For a flare star with total energy in an FEP event of 1036 ergs and n1(o,t) = 500 cm- the expected emissivity at t = t1 = 103sec will be

FYp(( > 0.1GeV,r) 1014r"2 photon.cm-3.sec-1. (1.13.34) For this case Eq. (1.13.33) gives

(( > 0.1GeV,robs,t)= 2x 1028ro-b2s(t/t1 )-1 (t^t)2] ph.cm-2sec-1. (1.13.35)

v rl

According to Eq. 1.13.35 for t1 = 103sec at t =10 sec and 100 sec the value

—(3^/1))2 >> 1 and o(x) = 1, then at the distance robs = 1019cm(about 3 pc) the r1

expected gamma ray flux OrpH ( > 0.1 GeV,robs, t) will be 2x10-8 and 2x10-9

ph.cm-2sec-1, respectively. Eq. 1.13.35 shows that the total flux of gamma rays from stellar wind generated by FEP interaction with wind matter must fall inverse proportional with time and does not depend upon the details of the event. It is important for the separation of gamma ray generation in stellar wind from the direct generation in stellar flare.

1.13.7. Expected gamma ray fluxes from great FEP events

Estimates according to Eq. 1.13.31 show that in periods of great solar FEP events with total energy = 1032 ergs the expected flux of gamma rays with energy >

100 MeV in the direction 2° from the Sun at t/t1 =1/3 reaches = 10-3photon.cm-2.sr-1.sec-1. It means that according to Fig. 1.13.2 the expected flux in the same direction at t/t1 = 1/30 reaches = 2 x 10-2photon.cm-2.sr-1.sec-1. In the direction 30° from the Sun (see Fig. 1.13.4) expected gamma ray fluxes are much smaller: the maximum will be at t/t1 = 1/3 and reaches value only

= 10-5 photon.cm-2.sr-1.sec-1. Expected gamma ray fluxes are characterized by great specific time variations, which depend from direction of observations relative to the Sun, total FEP flux from the source, parameters of FEP propagation (summarized in value of t1), and properties of solar wind (see Fig. 1.13.1 for expected space time distribution of gamma ray emissivity and Fig. 1.13.2-1.13.5 for expected gamma ray fluxes).

1.13.8. On the possibility of monitoring gamma rays generated by FEP interactions with solar wind matter; using for forecasting of great radiation hazard

At energies above about 30 MeV pair production is the dominant photon interaction in most materials. In gamma ray Pair Telescopes this process is used to detect the arrival of a gamma ray photon through the electron-positron pair created in the detector. The space-telescopes COS-B and EGRET are well known (collection area of the latter about 1600 cm2 ), which gave well energy and spatial resolution (see review in Weekes, 2000). These telescopes can detect objects with gamma ray fluxes of an energy bigger than 100 MeV at the detection limit of present day gamma ray telescopes of order 10-6-10-7 photon.cm-2.sec-1; these fluxes are several orders lower than expected from FEP interactions with solar wind matter (see Fig. 1.13.2-1.13.5). According to Gehrels and Michelson (1999) a further advance in the energy and spatial resolution is expected from the Gamma ray Large Area Space Telescope (GLAST). In this telescope solid state detectors will be use as the tracking material instead of a gas filled chamber. It is planned to be launched in 2006. This telescope will allow for improved energy resolution (10% resolution) and spatial location (0.5-5.0 arc minutes). Figures 1.13.2-1.13.5 show that present gamma ray telescopes might measure expected gamma ray fluxes in periods of great FEP events. These observations of gamma rays generated in interactions of FEP with solar wind matter can give important information about 3D-distribution of the solar wind as well as about properties of solar FEP generation and propagation parameters. Let us note that the model of isotropic diffusion may be used only after about 15-30 minutes after an FEP event starting on the Earth, when the expected gamma ray fluxes are not so big, but measurable with present gamma ray telescopes and those available/planned in the near future. To obtain more exact information about solar wind properties as well as about the mode of FEP generation and propagation during the beginning stage, in the first several minutes after an FEP event starting on the Earth and starting even before this (when it is expected the biggest fluxes of gamma rays in directions of a few degrees from the Sun), - it is necessary to recalculate the expected space-time distribution of gamma ray emissivity and gamma ray fluxes in the frame of more real and more complicated model of solar CR propagation based on the theory of anisotropic diffusion and kinetic equation. Let us note that these observations can be used for forecasting of great radiation hazard in the Earth's environment (Dorman, 2001f).

1.14. Gamma ray generation in space plasma by interactions of galactic CR with solar and stellar winds

1.14.1. The matter of problem and the main three factors

The generation of gamma rays by the interaction of galactic CR with solar and stellar winds matter was considered in Dorman (1996, 1997b, 2001b). These was considered the situation with gamma ray generation in the interplanetary space by galactic CR and expected time variations of gamma ray fluxes dependent on the direction of the observations and in connection with solar activity (SA) cycle (about 11 years from minimum to minimum of SA) and with the solar magnetic cycle (with a period of about 22 years including odd and even SA cycles, and periods of reversal general solar magnetic field near both maximums of SA). By data obtained from investigations of the hysteresis phenomenon in dependence of galactic CR intensity from solar activity level it was determined the change of CR density distribution in the Heliosphere during solar cycle as a dependence on particle energy. On the basis of observational data and investigations of CR nonlinear processes in the Heliosphere we also determined the space-time distribution of solar wind matter. Then we calculate the generation of gamma rays by the decay of neutral pions generated in the nuclear interactions of modulated galactic CR with solar wind matter and determine the expected space-time distribution of gamma-ray emissivity. on the basis of these results we calculate the expected time variation of the angle distribution and spectra of gamma ray fluxes generated by interaction of modulated galactic CR with solar wind matter for local (inside the Heliosphere) and distant observers (for stellar winds).

The space-time distribution of gamma ray emissivity will be determined mainly by 3 factors:

The 1st factor - space-time distribution of galactic CR in the Heliosphere, their energetic spectrum and chemical composition; for this distribution nonlinear collective effects of galactic CR pressure and kinetic stream instability can be important (Berezinsky et al., M1990; Dorman, Ptuskin, and Zirakashvili, 1990; Zirakashvili et al., 1991; Dorman, 1995b; Le Roux and Fichtner, 1997; see also below, Chapter 3).

The 2nd factor - the solar wind matter distribution in space and its change during the solar activity cycle; for this distribution pressure and kinetic stream instability of galactic CR also be important will (Dorman, 1995b; Le Roux and Fichtner, 1997; see also below, Chapter 3).

The 3rd factor - properties of galactic CR interaction with solar wind matter accompanied with gamma ray generation through the 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 the expected fluxes of gamma rays for measurements on the Earth's orbit as a dependence on the level of solar activity for different directions of gamma ray observations. We also calculate the expected gamma ray fluxes for different distances from the Sun inside the Heliosphere (local observations) and outside (distant observations). We expect that the same 3 factors will play an important role for gamma ray generation by galactic CR in stellar winds, but for some types of stars the speed of lost matter is several orders higher than from the Sun.

Observations of gamma rays generated in interactions of galactic CR with solar wind matter can give valuable information about the 3D-distribution of solar wind matter as well as on properties of galactic CR global modulation and its propagation parameters. Especially important will be observations of gamma rays generated in interactions of galactic CR with stellar wind matter. It will be shown that in this case important information on galactic CR modulation in the stellar-sphere can be obtained as well as information about stellar activity and stellar wind.

1.14.2. The 1st factor: galactic CR space-time distribution in the Heliosphere

The problem of galactic CR propagation through interplanetary space as well as modulation of its intensity and energetic spectrum in the Heliosphere (the 1st factor) was reviewed in Dorman (M1957, M1963a,b, M1975b), and taking into account CR nonlinear processes in Dorman (1995b). According to this research the convection-diffusion modulation of energy spectra of proton component of galactic CR can be described in the quasy-stationary approximation of the spherical symmetrical geometry (Parker, 1958, M1963; Dorman, 1959) as

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