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corresponding to the background gamma rays from about 3 x 10 cm of interstellar medium, which is much bigger than the gamma ray background in all directions from the galactic disc; this variable gamma ray flux can be measured by present day gamma ray telescopes (described in Gehrels and Michelson, 1999; Weekes, 2000).

1.15. On the interaction of extra high energy gamma rays with the magnetic fields of the Sun and the planets

1.15.1. The matter of the problem

In the last 10-15 years several CR events with energies above the predicted Greisen-Zatsepin-Kuzmin cutoff at ~ 4 x 1019 eV have been detected (Efimov et al., 1991, Bird et al., 1994, Hayashida et al. 1994). It is not excluded that some of these events are initiated by extra high energy (EHE) photons which content in CR above ~ 1019 eV (McBreen and Lambert, 1981; Aharonian et al., 1991; Karakula et al., 1994; Karakula and Tubek, 1995; Karakula and Bednarek, 1995; Karakula, 1996; Stanev and Vankov, 1996; Kasahara, 1997; Bednarek, 1999); they also may be owed to the interaction of CR hadrons with the microwave background radiation (Wdowczyk and Wolfendale, 1990; Halzen et al., 1990), or by the decay of massive particles, such as Higgs and Gauge bosons predicted by some more exotic theories (Bhattacharjee et al., 1998). Gamma rays with energies above 1019 eV may develop magnetic e± pair cascades in the dipole magnetic field of compact objects in the Solar system: the Earth, the Sun, Jupiter, and others. The cascades initiated by EHE photons in the Earth's dipole magnetic field have been considered by McBreen and Lambert (1981) and Aharonian et al. (1991). The EHE CR events with energies > 1020 eV were analyzed under the hypothesis of their photonic origin by Karakula et al. (1994), Karakula and Tubek (1995), Karakula and Bednarek (1995), Karakula (1996), Stanev and Vankov (1996), Kasahara (1997), Bednarek (1999). In Bednarek (1999) there are discussed the observational consequences of the cascading of EHE gamma rays in the magnetic field of the Sun. The magnetic field of the Sun is about an order of magnitude stronger than that of the Earth, for which photons have to have energies above ~ 5x1019 eV in order to cascade efficiently. Therefore detection of secondary photons from cascades initiated in the magnetic field of the Sun may allow investigation of the photon content in the EHE CR spectrum at energies about an order of magnitude lower, provided that a large enough detector of CR showers is available. According to Bednarek (1999) the content of EHE gamma rays in the highest energy CR can be investigated by observations of high energy CR showers from the direction of the Sun. If photons are numerous at the highest energies then a deficit of showers with energies > 1019 eV, and multiple synchronous showers at lower energies might be detected from the certain circle around the Sun. Bednarek (1999) investigates these processes by performing Monte Carlo simulations of cascades initiated by EHE photons in the magnetic field of the Sun. Based on simulations he predict that the Auger array (see the short description in Section 4.5 in Dorman, M2004) may detect multiple, synchronous showers initiated by photons with energies above ~ 1016 eV at a rate about one per year if photons are common above 1019 eV in CR.

1.15.2. Magnetic e± pair cascades in the magnetosphere of the Sun

According to Erber (1966), an EHE photon with energy E can convert into e" pair in the magnetic field B if the dimensionless parameter

and mc2 is the electron's rest energy. The secondary e" pairs can then produce synchrotron photons in the magnetic field, which energies are high enough to produce the next generation of e" pairs. Bednarek (1999) simulates the development of such a type of cascade by using the Monte Carlo method and applying the rates of e" pair production by a gamma ray photon and synchrotron emission by secondary e" pairs are given by Baring (1988). Bednarek (1999) notes that except Kasahara (1997), all previous simulations of such a type of cascade based on the approximate rates of pair production and synchrotron emission given by Erber (1966). The magnetic field of the Sun during the minimum of solar activity can be well approximated as a dipole with a magnetic moment

In Bednarek (1999) the influence of the active regions on the Sun with strong magnetic fields was neglected, since they dominate only in the solar phosphere and chromosphere. CR EHE photons may initiate cascades in the dipole magnetic field of the Sun if their energies are

EY > EYmin = XY,thmc2Bcir'3l\mst] 1 + 3cos2 p j MeV, (1.15.4)

where XY,th ~ 0.05 . Taking into account Eq. 1.15.1-1.15.3, the threshold for which photons have chance of cascading efficiently, will be

EY> EYmm = 1.13X1012/\Bs surJ 1 + 3cos2 p j MeV. (1.15.5)

In Eq. 1.15.5 Bs sur is the magnetic field at the surface of the Sun, and p is the zenith angle of the photon at the moment of its closest approach to the Sun.

It is assumed that photons are injected randomly within the circle with radius rc around the Sun. The number of secondary photons from cascades initiated by primary photons with energy 1019 and 1020 eV, within a circle rc = 1.5; 2 and 3 rs around the Sun (where rs is the radius of the Sun) are shown in Fig. 1.15.1.

Fig. 1.15.1. The average number of secondary gamma rays (within AlogEy = 0.1) from cascades initiated by one hundred primary EHE photons with energies 1019 eV (panel a)

and ten photons with energy 1020 eV (panel b) which are injected within the circle rc = 1.5 rs (the thickest full curve), 2 rs, and 3 rs (the thinnest two full curves) around the Sun. According to Bednarek (1999).

In Fig. 1.15.1 the secondary photons are grouped into bins A(log Ey)=0.1, and the results are averaged over 100 simulations in the case of 1019 eV primary photons, and 10 simulations in the case of 1020 eV photons. Note that all primary photons with energy 1019 eV injected within the circle rc = 1.5 rs from the Sun cascade, but only part of such photons interact if injected within a larger circle (61% for rc = 2 rs, and 33% for rc = 3 rs). All primary photons with energy 1020

eV cascade if injected within the range considered of parameter rc .

1.15.3. The possibility that extra high energy CR spectrum at > 1019 eV contains significant proportion of photons

Next, in Bednarek (1999) the possibility was considered that the extra high energy CR spectrum at > 1019 eV contains significant proportion of photons. He computes the spectra of secondary cascade gamma rays assuming that the primary photons, which enter the magnetosphere of the Sun at certain circle rc, have a power law spectrum with the spectral index -2.7 and a cutoff at different energies. In Fig. 1.15.2 (panel a) are shown the spectra of secondary photons (multiplied by the photon energy square) from cascades initiated by primary extra high energy photons injected within rc = 1.5, 2, and 3 rs . The primary photon spectrum extends up to Emax = 3 x 1020 eV and is normalized to the observed CR spectrum at 10 eV.

Fig. 1.15.2. Panel a: the spectra of secondary gamma rays (multiplied by the square of the photon energy) from the cascades initiated by the primary photons with the power law spectrum and spectral index -2.7 above 1018 eV and the cutoff at 3x1020 eV (marked by the dotted curve); the spectra emerging from the Sun's magnetosphere are shown for primary photons injected within the circle rc = 1.5 rs around the Sun (the thickest full curve), 2 rs, and 3 rs (the thinnest curves). Panel b: as in panel a but for the primary gamma ray spectrum injected within rc = 2 rs and extending up to 3x1020 eV (thin curve) and 3x1021 eV (thick curve). The observed CR spectrum is schematically marked by the dashed curve. According to Bednarek (1999).

Fig. 1.15.2. Panel a: the spectra of secondary gamma rays (multiplied by the square of the photon energy) from the cascades initiated by the primary photons with the power law spectrum and spectral index -2.7 above 1018 eV and the cutoff at 3x1020 eV (marked by the dotted curve); the spectra emerging from the Sun's magnetosphere are shown for primary photons injected within the circle rc = 1.5 rs around the Sun (the thickest full curve), 2 rs, and 3 rs (the thinnest curves). Panel b: as in panel a but for the primary gamma ray spectrum injected within rc = 2 rs and extending up to 3x1020 eV (thin curve) and 3x1021 eV (thick curve). The observed CR spectrum is schematically marked by the dashed curve. According to Bednarek (1999).

The observed CR spectrum is indicated in Fig. 1.15.2 schematically by the dashed curve. The primary photon spectrum which extends above 1018 eV is shown by the dotted curve. In Fig. 1.15.2 (panel b) are shown that the spectrum of secondary gamma rays, produced by the primary gamma ray spectrum with a cut off at 3x1021 eV, is almost the same as in the case of its cut off at 3x1020 eV.

1.15.4. Summering of main results and discussion

Simulations of Bednarek (1999) show that a significant part of extra high energy photons with energies above 1019 eV should cascade if injected within the circle of rc = 2 rs around the Sun. However, the solid angle corresponding to such a circle on the sky is relatively small (~ 2.2x10-5 sr). The Auger experiment is expected to detect about 50-100 particles with energy > 1020 eV per year (Boratav, 1997; see also the short description of Auger experiment in Section 4.5 in Dorman, M2004) and about 2x104 particles with energy > 1019 eV per year. Some showers initiated by particles with energy > 1019 eV should be detected from the circle of 2 rs around the Sun within a few years of operation. Let us assume that all these particles with an energy above 1019 eV are photons. Bednarek's (1999) simulations show that these photons should cascade in the Sun's magnetic field, and as a result of cascading about 12 secondary photons with energy > 1017 eV and 50 secondary photons with energy > 1016 eV should arrive at the Earth's surface synchronously with a rate corresponding to the number of events with energy > 1019 eV expected from the direction of the Sun. Bednarek (1999) estimates the energy weighted perpendicular spread of secondary photons (its half thickness) based on the simulations described above. It is found that secondary photons from a cascade initiated by a primary photon with energy 1019 eV should fall on the Earth's surface within the circle with average radius ~ 19 km (an estimate based on ten simulations). If the primary photons have an energy 1020 eV, then the secondary photons should be contained within the circle with radius ~ 51 km.

If such synchronous multiple showers initiated by photons with energies above 1017 eV can be observed by the Auger experiment, then a bunch containing half of the number of these secondary photons should fall on the Auger array with a frequency of about one per year. Note that for such photon bunches the effective detection area of the Auger array becomes larger by a factor close to two for geometrical reasons. Observation of such multiple showers from the direction of the Sun should make possible the estimate of the content of the photons in CR with energy above 1019 eV at a level of 10 percent during several years of operation.

The spectra of secondary photons produced within the circle rc around the Sun by primary photons with the spectrum observed in CR with energy above 1019 eV (and with normalization to the observed CR spectrum) are shown in Fig. 1.15.2 (panels a and b). Based on these computations Bednarek (1999) estimated the ratio of CR photons to CR particles at lower energies (see Table 1.15.1).

Table 1.15.1. The ratios of CR photons to CR particles at energy E from the direction of the Sun at primary CR energy 3x1020 eV. According to Bednarek (1999).

E, eV

rdrs

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