Relativistic electrons - directly accelerated, or secondary products of various hadronic processes – may result in copious Y-ray production caused by interactions with ambient targets in forms of gas (plasma), radiation and magnetic fields. In different astrophysical environments Y-ray production may proceed with high efficiency through bremsstrahlung, inverse Compton scattering and synchrotron (and/or curvature) radiation, respectively.
Generally, Y-ray production in a given process is effective when the relevant radiative cooling time does not significantly exceed (i) the source age, (ii) the time of non-radiative losses caused by adiabatic expansion or by particle escape, and (iii) the cooling time of competing radiation mechanisms resulting in low-energy photons outside the Y-ray domain. As long as the charged particles are effectively confined to the Y-ray production region, in some circumstances these conditions could be fulfilled even in environments with relatively low gas and photon densities or a weak magnetic field. More specifically, the Y-ray production efficiency could be close to 1 even when
(R is the characteristic linear size of the production region, c is the speed of light). In such cases the secondary Y-rays escape the source without significant internal absorption.
Each of the above mentioned gamma-ray production mechanisms has its major "counterpart" – a gamma-ray absorption mechanism of the same electromagnetic origin – resulting in electron-positron pair production in matter (the counterpart of bremsstrahlung), in photon gas (the counterpart of inverse Compton scattering), and in a magnetic field (the counterpart of synchrotron radiation). As discussed above, the Y-ray production mechanisms and their absorption counterparts have similar cross-sections, therefore the condition for radiation
generally implies small optical depths for the corresponding Y-ray absorption process,
But in many astrophysical scenarios, in particular in compact galactic and extragalactic objects with favourable conditions for particle acceleration, the radiation processes proceed so fast that
At these conditions the internal Y-ray absorption becomes unavoidable. If the Y-ray production and absorption processes occur in relativistic regimes, namely when
in hydrogen gas,
in photon gas (Klein-Nishina regime), or
in the magnetic field (quantum regime), the problem cannot be reduced to a simple absorption effect. In this regime, the secondary electrons produce a new generation of high energy Y-rays, and these photons again produce electron-positron pairs, so an electromagnetic cascade develops.
The characteristics of electromagnetic cascades in matter have been comprehensively studied in the context of interactions of cosmic rays with the Earth’s atmosphere (see e.g. Rossi and Greisen, 1941; Nishimura, 1967; Ivanenko, 1968), as well as for calculations of the performance of detectors of high energy particles (e.g. Nelson et al., 1985). The theory of electromagnetic cascades in matter can be applied to some sources of high energy cosmic radiation, in particular to the "hidden source" scenarios like massive black holes in centers of AGN or young pulsars inside the dense shells of recent supernovae explosions (see e.g. Berezinsky et al., 1990). Also, within the so-called "beam dump" models (see e.g. Halzen and Hooper, 2002) applied to X-ray binaries, protons accelerated by the compact object (a neutron star or a black hole), hit the atmosphere of the normal companion star (Berezinsky, 1976; Eichler and Vestrand, 1984) or the accretion disk (Cheng and Ruderman, 1989; Anchordoqui et al., 2003) and thus result in the production of high energy neutrinos and Y-rays. In such objects, the thickness of the surrounding gas can significantly exceed 100 g/cm2, thus the protons produced in the central source would initiate (through the production of high energy Y-rays and electrons) electromagnetic showers. These sources perhaps represent the "best hope" of neutrino astronomy, but they are generally considered as less attractive targets for gamma-ray astronomy. However, the Y-ray emission in these objects is not fully suppressed. The recycled radiation with spectral features determined by the thickness ("grammage") of the gas shell, should be seen in Y-rays in any case, unless the synchrotron radiation of secondary electrons dominates over the bremsstrahlung losses and channels the main fraction of the nonthermal energy into the sub-gamma-ray domain.
The development of electromagnetic cascades in photon gas and magnetic fields is a more common phenomenon in astrophysics. In photon fields such cascades can be created on almost all astronomical scales, from compact objects like accreting black holes, fireballs in gamma-ray bursts, and sub-pc jets of blazars, to large-scale (up to > 100 kpc) AGN jets and > 1 Mpc clusters of galaxies. Very high energy Y-rays emitted by astronomical objects and interacting with diffuse extragalactic photon fields initiate electromagnetic cascades in the entire Universe.The superposition of contributions of Y-rays from these cascades should constitute a significant fraction of the observed diffuse extragalactic background.
Bonometto and Rees (1971) were the first who realized the astrophysical importance of electron-photon cascades supported by y-Y pair-production and inverse Compton scattering in dense photon fields. When the so-called compactness parameter (Guilbert et al., 1983)
(L is the luminosity and R is the radius of the source) is less than 10, then the cascade develops in the linear regime, i.e. when the soft radiation produced by cascade electrons does not have a significant feedback effect on the cascade development. In many cases, including the cascade development in compact objects, this approximation works quite well.
The properties of linear cascades in photon fields have been quantitatively studied using the method of Monte Carlo simulations (Protheroe, 1986; Protheroe and Stanev, 1993; Mastichiadis et al., 1994, Miike et al., 1999) or by solving the cascade equations.Generally, the kinetic equations that describe the cascade development can be solved only numerically. However, with some simplifications it is possible to derive useful analytical approximations (Svensson, 1987; Zdziarski, 1988; Coppi and Blandford, 1990) which help to understand the features of the steady-state solutions for cascades in photon fields.
Cascade development in a magnetic field is a key element for understanding of the physics of pulsar magnetospheres (Sturrok, 1971; Baring and Harding, 2001). Therefore it is generally treated as a process associated with very strong magnetic fields. However, such cascades could be triggered in some other (at first glance unusual) sites like the Earth’s geomagnetic field, accretion disks of massive black holes (Bednarek, 1997), etc. In general, the pair cascades in magnetic fields are effective when the product of the particle (photon or electron) energy and the strength of the B-field becomes close to the "quantum threshold" of about
Gauss,unless we assume a specific, regular field configuration. An approximate method, similar to the so-called approximation A of cascade development in matter (e.g. Rossi and Greisen, 1941), has been applied by Akhiezer et al. (1994). Although this theory quite satisfactorily describes the basic features of photon-electron showers, it does not provide adequate accuracy for a quantitative description of the cascade characteristics (Anguelov and Vankov, 1999).
As long as we are interested in the one-dimensional cascade development (which seems to be quite sufficient for many astrophysical purposes), all 3 types of cascades can be described by the same integro-differential equations as the ones derived by Landau and Rumer (1938), but in each case specifying the cross-sections of the relevant interaction processes. The solution of these equations over a broad range of energies is, however, not a trivial task. Such a study based on the numerical solutions of the so-called adjoint cascade equations.The results of this investigation shows that the electron-photon cascade curves in photon gas and a magnetic field have features quite different from the cascade development in matter. The energy spectra of cascade particles are also considerably different from the conventional cascade spectra in matter. The spectra of cascade particles in the magnetic field have properties intermediate between those for cascade spectra in matter and in radiation fields. Although for certain astrophysical scenarios the development of cascades in "pure" environments can be considered as an appropriate and fair approximation, in some conditions the interference of the processes associated with interactions of cascade electrons and Y-rays with both the ambient photon gas and magnetic field (or matter) can significantly change the character of cascade development, and consequently the spectra of observed Y-rays. The impact of such interference is very complex and quite sensitive to the choice of the principal parameters. Therefore each practical case is a subject to independent studies.
