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Astron. Astrophys. 326, 51-58 (1997)

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4. Discussion

4.1. The deficit at low energies

We have seen in the previous section that in case of FSRQ the [FORMULA] -ray spectra deviate from power-law below 70 MeV. This is most significant with 3.0 [FORMULA] when the emission of variable sources at flare state is considered. In the time-averaged spectrum the effect is less pronounced which indicates that if there is a deficit in the average spectra, it will be weaker since we have better statistics there.

The extrapolation of X-ray data or the OSSE spectra for many sources imply a spectral break at a few MeV energies. These breaks have to be extended features regardless of their origin, even if an annihilation feature is superimposed. This is because the standard radiation processes like inverse Compton scattering are not monochromatic, when the target photon distribution is neither beamed or monochromatic. So even if there were a sharp break in the electron spectrum, the corresponding break in the [FORMULA] -ray spectrum would be smeared out. It is, however, questionable whether this is sufficient to account for the observed deficit below 70 MeV, which is a factor 10 higher in energy than the typical break energy. EGRET's statistics are limited in this energy range, and hence it needs some effort to produce such a strong signal at 50-70 MeV. We would then also expect a signal at 70-100 MeV where the statistics are much better.

We therefore prefer to interprete our result in the sense that the [FORMULA] -ray emission of FSRQ between a few hundred keV and a few GeV is not a one-component spectrum, but rather the superposition of different emission processes.

If the jet material consists of pair plasma we may expect annihilation and lepton-lepton bremsstrahlung to dominate the spectrum up to a few tens of MeV while inverse-Compton scattering is more efficient at higher energies (Böttcher and Schlickeiser 1995). The comptonisation part of the spectrum is related to the electron spectrum at high particle energies where the physical reaction timescales are shortest. This may explain why at flare state we see a deficit below 70 MeV.

In case the jet is made of ordinary matter we have to consider bremsstrahlung and Coulomb interactions besides the inverse Compton scattering.

Generally the observed behaviour can also be caused by a low-energy cut-off in the electron injection spectrum (Böttcher and Schlickeiser 1996).

4.2. The cut-off at high energies

BL Lacs are defined as having only weak, if any, optical lines. That translates to them having only little backscattering material in the vicinity of the central machine. Hence we can expect different environmental conditions in BL Lacs and quasars, as far as opacity is concerned. The main source of opacity - photon-photon pair production - requires a sufficient number of target photons of the energy


where µ is the collision angle cosine in the observers frame, and [FORMULA] is the energy of the [FORMULA] -ray to be absorpted.

Standard calculations show that the interaction of [FORMULA] -rays with themselves is reduced due to the equivalent of the Klein-Nishina effect, which applies when the target photon energy is very much larger than the limit given by Eq.2 (Pohl et al. 1995, Dermer and Gehrels 1995). Interactions of [FORMULA] -rays with the X-ray continuum may affect the total [FORMULA] -ray spectrum. What we observe, a cut-off only at highest energies, looks more like an additional target photon source coming into play. This could be an accretion disk, accretion disk emission backscattered by thermal clouds, or synchrotron photons produced in the jet itself.

For [FORMULA] -rays with dimensionless energy [FORMULA] the optical depth for pair production by collisions with ambient photons of energy [FORMULA] is






For the original accretion disk photon the collision angle is unfavorable ([FORMULA]) so that the UV photons can only interact with [FORMULA] -rays of 100 GeV energy or more (Böttcher and Dermer 1995). In the direct comptonization of the accretion disk photons the Klein-Nishina cut-off may lead to spectral turn-overs at around 10 GeV (Böttcher et al. in prep.): that is a basic characteristic of the emission process and can not account for cut-offs which occur only at flare state.

In case of the backscattered accretion disk photons


a target photon energy [FORMULA] eV is sufficient to produce a cut-off at a few GeV observed [FORMULA] -ray energy. Here the delta-function is a simple approximation of the accretion disk spectrum with luminosity L and [FORMULA] is the assumed re-scattering rate with scattering optical depth [FORMULA]. Then



with z in units of 0.01 pc and [FORMULA] in units of [FORMULA]. If [FORMULA] is larger than unity, [FORMULA] increases sharply beyond unity and produces a cut-off in the [FORMULA] -ray spectrum at around 6 GeV (before redshift). However, correlations between optical depth and [FORMULA] -ray flux above 100 MeV can only occur when the [FORMULA] -ray outburst is due to an increased level of target photons, for instance an accretion disk flare. Any variation in the spectrum of radiating electrons in the jet will have no impact on the optical depth.

If electrons with Lorentz factors of [FORMULA] do exist in the jets (as is required for the TeV emission of BL Lacs), then these will produce a synchrotron continuum up to X-ray energies, which provides a large number of target photons for pair production. The optical depth for this process is


where [FORMULA] is the Doppler factor of the jet in units of ten, [FORMULA] is the effective jet radius in light days ([FORMULA] cm) in the jet frame, and [FORMULA] is the [FORMULA] synchrotron luminosity at energy [FORMULA] in units of [FORMULA] ergs/sec. So if a [FORMULA] -ray outburst is caused by the injection of a large number of high-energy electrons, the [FORMULA] -ray emission above a few GeV may be self-damped. However, detailed simulations of cooling pair plasma including first order and second order Fokker-Planck coefficients for all interaction processes (Böttcher, Pohl, and Schlickeiser, in prep.) show that the high end of the synchrotron spectrum is likely to be swamped by synchrotron-self-Compton emission, which may have a hard spectrum in the relevant energy range so that [FORMULA] in Eq.7 increases with [FORMULA], i.e. decreases with [FORMULA]. In that case the cut-off would be very smooth and the energy at which it occurs would vary strongly for different X-ray luminosities and Doppler factor. Thus there would be no good argument why the bulk of FSRQ considered here should show the cut-off at roughly the same energy.

To summarize: though opacity can in principle account for cut-offs at a few GeV photon energy, and seems to be required to explain the correlation with the [FORMULA] -ray flux level, there is no clear answer as to the source of the target photons for the photon-photon pair production. However, our findings will further constrain models and simulations for the evolution of pair jets.

4.3. The relation to the diffuse [FORMULA] -ray background

We have seen that the time and source averaged [FORMULA] -ray spectrum of AGN is softer than that of the extragalactic [FORMULA] -ray background. The spectrum of the average AGN is dominated by that of FSRQ, partly since we have three times more objects of this class than BL Lacs, partly since individual FSRQ are on average brighter. It is interesting to see that the average BL Lac has a spectrum which is compatible with that of the [FORMULA] -ray background and harder than that of FSRQ. If unresolved AGN would indeed be responsible for the bulk of the [FORMULA] -ray background, the BL Lacs may have to play a stronger rôle than previously thought. Here we outline a scenario which would account for this.

The BL Lacs have on average a much smaller redshift with values between 0.031 and 0.94, while more than 50 % of the objects in the FSRQ class have redshifts in excess of 1.0. This indicates that in case of FSRQ we observe a fair range of the luminosity function directly, in contrast to the BL Lac case where we see only the tip of the iceberg. In other words, we expect the [FORMULA] -ray [FORMULA] distribution of BL Lacs to peak at lower [FORMULA] -ray fluxes than that of FSRQ. As a result the contribution of BL Lacs to the diffuse extragalactic [FORMULA] -ray background may be strong despite the small number of directly observed objects, and hence it may be that BL Lacs provide the bulk of the [FORMULA] -ray background. This would of course require that FSRQ and BL Lacs do not have drastically different evolution properties. The reader should note that at least for radio selected BL Lacs co-adding of undetected sources has resulted in a excess of around 3 [FORMULA] significance (Lin et al. 1997), which provides further evidence that this class of sources does emit [FORMULA] -rays at lower flux levels.

There is yet another effect by which BL Lacs can contribute to the extragalatic [FORMULA] -ray background. Distant BL Lacs may emit [FORMULA] -rays at energies higher than 100 GeV like the close-by objects seen by Whipple. These [FORMULA] -rays will pair produce on the low-energy extragalactic background before reaching us. Since the pairs will immediately comptonize the microwave background, the energy of the TeV [FORMULA] -rays will go into an electromagnetic cascade and finally reappear in the form of [FORMULA] -rays at only a few GeV energy (Coppi and Aharonian 1997). Depending on the luminosity distribution between GeV and TeV emission of the average BL Lac, this process may dominate over the direct contribution to the GeV background for particular redshifts z. This effect would results in a hardening of the background spectrum in the EGRET energy range.

We should however not completely exclude the possibility that the spectrum of the extragalactic [FORMULA] -ray background is ill-determined. The separation of background and galactic emission due to cosmic ray interactions with thermal gas is relatively easy to do by correlation between intensity and the gas column density. In contrast the expected spectrum of the inverse Compton emission is similar to that of the extragalactic background and the intensity varies little with position at high latitudes, so that we we cannot exclude the possibility that part of the background intensity at higher [FORMULA] -ray energies is misidentified inverse Compton emission.

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© European Southern Observatory (ESO) 1997

Online publication: April 20, 1998