Info

For a-particles the differential energy spectrum will be the same, but the coefficient will be 0.7 instead of 2.2 and E will denote the energy/nucleon. According to Dermer (1986a,b) the inclusion of additional channels of nuclear interactions p-He, a-H, and a-He gives an increase in gamma ray emissivity of 28%, 9%, and about 2% relative top-H channel considered above.

Fig. 1.12.1. The inclusive cross-section <7n(Ek) for reactions p + p + anything as a dependence upon the kinetic energy of protons Ek . Calculated according to Eq. 1.12.4.

Therefore for rough estimations we can consider only the channel p-H and then multiply the result by a factor 1.39; if we also take into account heavier nuclei this factor will be 1.45. For the demodulated differential energy CR proton spectrum (Eq. 1.12.5) with factor 1.45, the expected gamma ray emissivity per l atom H in cm3 was found by Dermer (1986a,b) as Qpn(Ey) in units photons/(cm3 sec GeV), which can be approximated in the energy interval from 10-3 GeV up to 103 GeV by lg(Qpn-21.4 - y[1 + (lg(Er/Er,max)) J1/2 , (1.12.6)

where y = 2.75 and Ey max denotes the position where Qpn (ey) attains the maximum:

1.12.3. Gamma ray generation by CR electrons in space plasma (bremsstrahlung and inverse Compton effect)

By using results of Cesarsky et al. (1978) on the bremsstrahlung gamma ray generation by electrons of galactic CR in the interstellar medium, we obtain for the expected bremsstrahlung gamma ray flux from some volume of space plasma at some distance robs from this volume the following formula:

Fy,bs Vobs, Er)= robs 1 cos Odd \ dr \ \ dE\Ee, Ey)Ne (Ee, rO^r,0,^,(1.12.8)

-n/2 0 0 Ey where the definitions are the same as for Eq. 1.12.1, but Ee is the energy of electrons and Ne(Ee,r,O,$) is the space distribution of the differential intensity of the electron component of CR. In Eq. 1.12.8 obs(Ee,Er) is the cross-section of bremsstrahlung gamma ray generation with energy Ey by electrons with energy Ee, which according to Cesarsky et al. (1978) can be approximated by the following equation:

obs(E,Er) = ar? {(2Ee2 - 2EeEy + E2y E-V - ( - Ey )-XV2 }, (1.12.9)

where a ~ 1/137 is the fine structure constant, re is the classical electron radius, (px and p2 are functions from variable

x(z = 1)= 34.259, x(( = 2)= 20.302. The functions p1 and p2 are tabulated in Blumental and Gould (1970). According to Pohl (1994) for the standard He-to-H ratio of 0.1 for space plasma matter roughly p1 ~ p2 ~ 58 and obs(Ee,Ey ) 0.42re2 ((4/3)- (/Ee)- (e^Ee )2), (1.12.11)

For the demodulated differential energy spectrum of electrons in the interstellar space Ne(Ee) by Cesarsky et al. (1978) was used spectrum of CR electrons measured on r = r1 = 1AU from the Sun in the minimum of solar activity:

Ne (Ee ) = Ne (Ee, r1 ) = 10-2 E-18 electron/(cm3.sec.GeV). (1.12.12)

The expected bremsstrahlung gamma ray emissivity per l atom H in cm3 for this spectrum was found by Cesarsky et al. (1978) in the form

Qbs(eJ = 10-264EYl* photons/(cm3.sec.GeV). (1.12.13)

For the total inverse Compton gamma ray emissivity (for starlight and 2.7 °K photons) was found

Was this article helpful?

0 0

Post a comment