Astron. Astrophys. 331, L57-L60 (1998)

2. The high energy model for extragalactic sources

2.1. The "two-flow" model

The paradigm of the present work is the two flow model as proposed by Sol et al. (1989) to explain radio phenomena in active galactic nuclei. The jet structure is divided in two parts. The first component is a subrelativistic MHD () electron-proton jet carrying most of the kinetic energy, flowing out of the central regions of the nuclei, launched from a magnetized accretion disk (Ferreira & Pelletier 1995). This flow is responsible for large scale structures such as two-sided kpc-Mpc jets, extended lobes, and hot spots where the kinetic energy can be dissipated by a strong shock (Pelletier & Roland 1986). The second component is a relativistic electron-positron pair beam confined by the jet and responsible for the small scale structures ( pc) such as superluminal motions observed in VLBI.

This model was applied to high energy extragalactic sources (Henri & Pelletier 1991; Henri et al. 1993, and MHP). All these works deal with a relativistic pair plasma to produce high energy photons ( and X-ray) by Inverse Compton scattering (IC) of soft photon emitted by an accretion disk. The anisotropy of the incoming photons have different consequencies. First, the incident radiation power is converted into bulk motion by the anisotropic Compton emission of the pair plasma. This is the so called "Compton rocket" effect (O'Dell 1981). Without reheating, this effect is not efficient enough to explain the superluminal motions observed in VLBI (Phinney 1982). But, as the sub-relativistic jet can carry a large amount of energy without suffering strong IC losses, it can act as an energy reservoir for the beam. The pairs can be re-accelerated continuously, the rocket effect is extended on longer distances and final bulk Lorentz factors of order of 10 can be achieved (Henri & Pelletier 1991; Renaud & Henri 1998). Secondly, the X- and gamma-ray photons are beamed by Doppler boosting effect in the jet direction, and can explain the huge high energy emission by lowering the compactness of the high energy source. In this case, a gamma-ray photosphere may exist in the beam structure (MHP, under different hypothesis see also Blandford & Levinson 1995). The high energy spectrum is characterized by a spectral break associated to the lack of gamma-ray (or hard X-ray in the present case) photons absorbed in the pair production process. The non-thermal X-ray spectrum is produced internally by IC effect.

2.2. The high energy spectrum

In the present model, the high energy photons are produced by IC effect on soft photons. The seeds photons can be internally produced as synchrotron radiation (Ghisellini 1991; Marscher & Bloom 1996), or come externally from a disk emission. In this last case, they can be scattered by surrounding clouds (Sikora et al. 1994), or come directly like in Dermer & Schlickeiser (1993). As in MHP, we will only consider here the photons coming from a standard accretion disk (Shakura & Sunyaev 1973). The high energy spectrum is thus a pure Inverse Compton spectrum altered by the pair creation. We recall here the main results of MHP's model.

2.3. The pair model scenario

Thereafter, the photons energies are in units, the subscripts s and 1 are used respectively for the soft disk photons and for the high energy scattered photons. The pair density distribution is assumed to be a power-law with an index , taken between and . It is supposed to be isotropic in a frame moving with a relativistic speed . A small number of relativistic particles is supposed to be created near the black hole at the base of the jet by different effects such as Penrose process, or magnetic reconnection. Then, some soft photons (with a density ) are IC scattered to produce X and gamma-ray photons. In the moving frame the opacity to pair production varies as

where is the pair density at a distance z above the black hole.

The huge number of soft photons leads to creation of new pairs along the jet. As the pair cascade becomes saturated, the particle population increases by pair production. When it becomes optically thick, the soft photon population decreases by IC absorption. Then pair production ceases and the pair density decreases, being governed by annihilation that takes place on a longer timescale. The evolution of the particle and photon populations is described by two continuity equations (see MHP, Eq. (57)). The boundary conditions were chosen in MHP at a distance where the soft photons are strongly (exponentially) absorbed by the pairs over a length as short as the width of the jet (). The plasma becomes there optically thick for both pair production and Thomson scattering, namely

then denotes approximately the localization of the 0.511 MeV photosphere. The opacity parameter prevents the solutions from an unphysical strong absorption. is to be found by integrating the system backwards, down to small z, where the soft photon density matches emitted by the disk. For the high energy photons are still absorbed by the pair production effect (see Eq. (1)). Only the absorption of by IC effect and by annihilation can explain the drop of , and the formation of an energy dependant gamma-ray photosphere. This differential absorption explains the spectral break observed above MeV energies in the laboratory frame.

© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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