4sid ^ E^ . This corresponds to an increase of 4sid approximately an order (from ~ 0.02% to ~ 0.2%) as energy increases from 1011 eV to 3 x 1015eV. Such regularity in the variations of Asid agrees with the mode of variations of the content of the daughter nuclei depending on the particle energies in the 109 ^10n eV (see below, Section 1.2.6). The time of the maximum is shifted with increasing the particle energies to 13h of sidereal time, which corresponds to the appearance of the drift flux of CR with energies > 3 x1015eV from the Galaxy across the magnetic force lines. In this case the anisotropy amplitude increases rather rapidly with energy and reaches several tens of percent at 1019-102° eV. The results on the anisotropy discussed may be approximated by the expression
0.2 x((/3 x1015eV)°'2%, if 1011eV < Ek < 3 x1015eV,
0.2x(k/3x1015eV)'6%, if 3x1015eV<Ek < 1020eV, which gives ^sid = 0.03% at Ek = 3 x1011 eV ; Asid = 0.2% at Ek = 3 x1015 eV and Asid = 35% at Ek = 2 x1019 eV .
1.2.6. Relationships between the observed CR spectrum, the anisotropy, the relative content of the daughter nuclei, and the transport scattering path
It can be easily shown (see in Ginzburg and Syrovatsky, M1963; Dorman, 1969) that any diffusion model of CR propagation in the Galaxy involves a certain relationship between the observed CR spectrum D(Ek) and the total spectrum of generation in all sources F(Ek),the mean penetrable amount of the interstellar matter X (Ek) (determining the relative content of the daughter nuclei of the type of Li, Be, B and some secondary isotopes which are explicitly absent from the sources), the anisotropy amplitude Add (Ek), and the transport scattering path in the
where AG (Ek) is the transport path averaged over the entire region of particle propagation; A Gloc (Ek) is the local transport path in the region of the measurements of the anisotropy. It follows from the comparison between Eq. 1.2.1 and Eq. 1.2.4, that
It should be expected that, although A G (Ek) and A Gloc (Ek) may be qualitatively different, the mode of their dependence on Ek is most probably the same. Then it follows from Eq. 1.2.2) that if the total spectrum of CR generation F (Ek )<* Ek-25 the observed spectrum D(Ek )<* E-2'7 in the interval 1011eV < Ek < 3 x1015eV, and D(Ek)oc E-31 in the interval 3x1015eV < Ek < 1020eV. Thus the data presented above on the anisotropy are in agreement with the assumption of the unified spectrum of CR generation in the Galaxy of the form F (Ek) E-2'5 (the solid curve in Fig. l.2.2) in the entire energy range of 1011eV < Ek < 1020eV. This result is definitely indicative of the galactic origin of CR up to ~ 1020 eV. In this case, according to the estimates of Hillas and Ouldridge (1975), if the CR of such high energies are protons or not too heavy nuclei, it is necessary for them to be retained and that the galactic magnetic field HG of ~ 2 x10-6 Gs intensity would extend to the distances of at least 1 kps on either side of the galactic plane (this conclusion agrees with the measurements by Davies et al. (1974) of the Faraday rotation of the pulsar radiation, according to which HG = (2.2 ± 0.4)x 10-6 Gs on the average in the said region). It should be noted that if A G (Ek) is described by the dependence of the type Eq. 1.2.5, the following important conclusion may be drawn from Eq. 1.2.3: the penetrable amount of interstellar medium X(Ek) at Ek ~ 3x1015eV should be an order smaller than that at Ek ~ 1011eV. Such mode of variations in X(Ek) depending on Ek is confirmed by the data of the direct measurements of the chemical composition of the CR in the energy range Ek < 3 x1011 eV (where it was found that X«E-02). Of course, it would be extremely important to verify whether such trend also takes place at higher energies (the available data on the chemical composition in the high- and super-high energy ranges are not reliable yet). Thus if Eq. 1.2.5 is valid this means that the relative portion of the daughter nuclei and secondary isotopes should rapidly decrease with increasing energy and already between intervals 1 and 2 the observed CR composition should be close to the composition of the accelerated particles in the sources.
1.2.7. Chemical composition in the 109 eV/nucleon < Ek < 3 x 1011 eV/nucleon range and the expected dependence of A g (Ek) and (Ek)
According to numerous experimental data on the chemical composition of CR, the relative content of the daughter nuclei in the range 109 < Ek < 3 x 1011 eV/nucleon decreases with increasing energy as E-02. Therefore the penetrable amount of interstellar matter XG will also similarly decrease with increasing Ek. Since, according to Eq. 1.2.3, XG then AG « E°'2in the above mentioned energy range. At the same time it follows from Eq. 1.2.4 that the sidereal anisotropy amplitude ^sid is (if other conditions being equal) « AG, whence ^sid « E0'2 , as the particle energy decreases, ^sid should also decrease and reach ~ 0.01%, which agrees with the measurement data (Jacklin, 1965; Dorman et al., 1967, 1969). Let us note that in the above mentioned energy range the ground based measurements of the sidereal anisotropy are difficult owing to the additional scattering of particles and distortion of their trajectories in the Heliosphere which give rise to the problem of correct interpretation of the observation results. Therefore, the available data on the sidereal anisotropy in the low energy range should be treated as rough estimates.
1.2.8. Chemical composition in the energy range 3 x 107 eV/nucleon < Ek < 109 eV/nucleon and the nature of the scattering elements in the Galaxy
Since, the content of the daughter nuclei and secondary isotopes is practically invariants, as the particle energy decreases further down to the lower boundary of interval 3, it should be expected that Xg ~ const in the range
3 x 10 eV/nucleon < Ek < 10 eV/nucleon and hence, according to Eq. 1.2.4
A G = const too. Therefore, from the analysis of Fig. 1.9.4-1.9.8 in Section 1.9.7, when the particle scattering in the Galaxy is determined by the inhomogeneities with field structure of various complexities, the smallest scale of the inhomogeneities should be at least smaller than R,1ini /300Ho . Since
Ek min = 3 x107 eV/nucleon corresponds to Rmin = 2 x108V, this gives
A1 < 3 x 1011 cm at Ho = 2 x10-6Gs (otherwise, as follows from Fig. 1.9.4-1.9.8 in Section 1.9.7 AG should abruptly increase with decreasing Ekmin, which would result in a pronounced decrease of the relative content of the daughter nuclei at very low energies).
If, however, the particles are scattered in the Galaxy by the magnetic clouds X1 may be many orders larger, since according to Fig. 1.9.1 from Section 1.9.3 in this case AG = const with decreasing Ek (even though Ek << Ekmin). Of course, the real situation may be more complex, namely, the variations in X may be accompanied not only by the variations in the parameters a and P characterizing the spectrum of the scattering elements, but also by a change of the relative importance of the scattering of particles of various energies by the magnetic clouds and the inhomogeneities of the form j = l, 2, 5 (see below in Section 1.9).
1.2.9. The nature of the energy boundary between intervals 3 and 2
According to the analysis of Bishara and Dorman (1973a,b,c, 1974a,b, 1975) carried out on the basis of many years underground measurements of the CR muon component, the energy boundary between intervals 3 and 2 (the upper energy boundary of CR modulation in the interplanetary space) is 150-300 GeV (this boundary varies markedly throughout the 11-year solar activity cycle). Let us note that the CR modulation in the Heliosphere is very significant in the energy range studied (the particle flux is modulated by a factor of from ~ 2—5 to several thousands). In accordance with the numerous theoretical and experimental data, however, the amplitude of the spectral modulation is determined only by the rigidity R and velocity v of the particles. Therefore the modulation amplitude for all particles with the same ratios A/Z and the same energy/nucleon (the same R and v) is also the same, i.e. CR relative chemical composition inside the Heliosphere will be the same as that in the interstellar space.
At higher energies the modulation spectrum falls with increasing particle rigidity R as R_2or even more rapidly, whereas at lower energies the spectrum modulation depth SD(R)/Do (RR_(0-8^10). The upper energy boundary of the CR heliospheric modulation is owed to the magnetic inhomogeneities spectrum in interplanetary space being limited at the side of X by certain X2, the largest scale of the inhomogeneities. According to Bishara and Dorman (1974b) the elements of the sector structure are most probably such largest scale of inhomogeneities. Therefore at a velocity of the solar wind ~ 400 km/sec, the complete revolution of a force line of the regular component of the interplanetary magnetic field (in the form of the Archimedes spiral) is in each about 6 A.U., for four sectors X2 = 1.5 A.U. whence the upper boundary Ek min = 270 GeV at H = 4 x10—5 Gs. When moving away from the Sun (at distances more than 6 A.U. from the Sun), X is almost invariant, but H decreases (approximately inversely to the distance r from the Sun) and, therefore, Ek max (r) = 270(r/re)—1 GeV, the size of the effective modulation region decreases with increasing the particle energy. According to Fig. 1.9.4—1.9.8 at j = l in Section 1.9.7 and Fig. 1.9.1 in Section 1.9.3, at Ek > Ekmax the transport path in interplanetary space A ^ Ej2, and since the modulation depth «A 1 at the ultrarelativistic energies it will be « E-2, which explains the results of Bishara and Dorman (1973a,b,c, 1974a,b, 1975).
At Ej < Ej max the dependence of A on Ek is determined by the parameters A1IA2 , a and P, and (as can be seen from Fig. 1.9.4-1.9.8 at j = l in Section 1.9.7
and Fig. 1.9.1 in Section 1.9.3) the appropriate selection of these parameters may
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