Interactions with Photon Fields (Cosmic Gamma Radiation) Part 2

Interactions of hadrons with radiation fields

In astrophysical environments the radiation density often exceeds the density of gas component. In these conditions the interactions of high energy hadrons with radiation can dominate over interactions with matter, albeit the relevant cross-sections are relatively small. The main processes of hadron-photon interactions include (i) inverse Compton scattering:(ii) electron-positron pair production: (iii) photodisintegration of nuclei:(iv) photomeson production :In extremely dense radiation fields the secondary may effectively interact with photons before they decay.

Except for the inverse Compton scattering, all other processes take place only above certain kinematic thresholds:

(in the rest frame of projectile particles) for the pair production, photodis-integration, and pion production, respectively.

The process of inverse Compton scattering of protons is identical to the inverse Compton scattering of electrons, but the energy loss rate of protons is suppressed, for the fixed energy of both particles, by a factor ofGenerally, this process does not have noticeable astrophysical applications. At energies above the pair production threshold, the inverse Compton energy loss rate is significantly (by a factor ofslower compared to the losses caused by pair-production.

In certain conditions the pair-production may result in significant spectral distortions of highest energy protons propagating through dense photon fields. The cross-section of this process is quite large (the same Bethe-Heitler cross-section in the rest frame of proton), but in each interaction only a small fraction of the proton energy is transferred to the secondary electrons (Blumenthal, 1990). Therefore the energy loss rate of protons remains relatively slow. Moreover, the energy region where this process dominates is quite narrow. It is limited by the energy interval of protons

(o>0 is the average energy of target photons). When the proton energy exceeds the pion production threshold, the hadronic photomeson interactions well dominate over the pair production (see e.g. Berezinsky and Grigoreva, 1988; Geddes et al., 1996)

The photodisintegration of nuclei may have a strong impact on the formation of the chemical composition of very high energy cosmic rays in compact astrophysical objects (Karakula and Tkaczyk, 1993) as well as in the intergalactic medium (e.g. Stecker, 1969). However, this process does not lead to significant production of high energy Y-rays.

Photomeson production is the most important channel for transformation of the kinetic energy of protons into high energy Y-rays, electrons and neutrinos. Close to the energy threshold, the process proceeds through single-pion production,At higher energies, multi-pion production channels begin to dominate.

Cross-sections of these processes are basically well known from particle accelerator experiments. For astrophysical applications the data obtained with Y-ray beams at energies from 140 MeV to 10 GeV are quite sufficient, if one takes into account the fact that for typical broad-band target photon spectra the hadron-photon interactions are contributed mainly from the region not far from the energy threshold, i.e.

The photomeson processes in radiation fields have been studied by Miicke et al. (1999) using the Monte-Carlo code SOPHIA. Recently Atoyan and Dermer (2003) suggested a simple approach for approximation of the pion production cross-sections by the sum of two step-functions andfor the single-pion and multi-pion channels respectively, with forfor

The inelasticities in these two energy intervals are approximated byand 0.6, respectively. Finally, applying the ^-function approximation to calculations of the spectra of secondary particles (assumingwith 2 photons perwith 1 electron and 3 neutrinos produced in every charged pion decay), this simple approach appears quite accurate for an adequate treatment of production rates and energy spectra of secondary products.

The cross-sections of interactions of secondary electrons and Y-rays with the ambient photons exceed by three orders of magnitude the photomeson cross-sections. Therefore the electrons and Y-rays cannot leave the active region of pion production, but rather initiate electromagnetic cascades in the surrounding photon and magnetic fields. The standard spectra of the low-energy cascade Y-rays that eventually escape the source are not sensitive to the initial spectral distributions, and thus contain information only about the total hadronic power of the source. On the other hand the secondary neutrinos freely escape the production region, and thus carry direct information about the energy spectra of accelerated protons.

Another interesting feature of the mixed hadronic/electromagnetic cascades in radiation dominated environments is the effective transport of primary nonthermal energy released in accelerated protons further away from a central engine through production and escape of secondary neutrons. This important channel of energy transport, pointed out first by Eichler and Wiita (1978), has been explored by many authors (Kirk and Mastichiadis, 1989; Sikora et al., 1989; Giovanoni and Kazanas, 1990, Atoyan and Dermer, 2003, etc.). The presence of dense photon fields in the compact particle accelerators may have an even more fundamental impact. It has been recently recognised (Derishev et al., 2003) that in relativistic flows, e.g. in GRBs or AGN jets, the multiple conversions of relativistic particle from charged to neutral statemay allow a strong (up to the bulk Lorenz factor squared) energy gain in each cycle, whereas in the standard relativistic shock acceleration scenario the energy gainoccurs only in the first circle (Achterberg et al., 2001) . This novel acceleration mechanism, which is capable of boosting protons in GRBs and AGN jets to maximum available energies (limited by the condition of confinement in the magnetic field), could be a key to the solution of the problem of the highest energy,particles observed in cosmic rays.