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When an emitting plasma has a bulk relativistic motion relative to a fixed observer, its emission is beamed in the forward direction (in the fixed frame), a direct consequence of the transformation of angles in special relativity. An observer located in or near the path of such a plasma sees much more intense emission than if the same plasma were at rest. Time scales for variability are also shorter, and this can cause the emission region to appear to move superluminally in the transverse direction (Appendix A). Strong relativistic beaming is thought to explain the rapid variations, high polarization, and high luminosities that characterize blazars (Blandford and Rees 1978), and if present in blazars, it must also be present in other radio-loud AGN. The consequences of the anisotropic beamed radiation pattern are considerable (Appendices B and C), introducing significant selection effects in almost any flux-limited sample.

4.1 Evidence for Relativistically Beamed Gamma-Rays

More than forty blazars have now been detected with the EGRET high energy experiment on the Compton Gamma-Ray Observatory (von Montigny et al. 1995). Without exception, all EGRET-detected extragalactic objects are radio-loud blazars, either FSRQ or BL Lac objects (primarily the former). Not only are blazars bright at E geq 100 MeV, in many cases their observed gamma-ray luminosity dominates the luminosity in other wavebands by a factor between 1 and 1000. Multiwavelength spectra of the superluminal quasar 3C 279 (Fig. 4) show that the ratio of gamma-ray to bolometric luminosity increases with overall luminosity (Maraschi et al. 1994a).

Figure 4. Multiwavelength spectra of the gamma-ray-bright superluminal quasar 3C 279 (Maraschi et al. 1994a) at two epochs, a high state in June 1991 and a low state in January 1993. In the high state, the gamma-ray luminosity is ten times the luminosity in the synchrotron component seen at lower energies, while in the low state the two are comparable. (Copyright American Astronomical Society, reproduced with permission.

In several blazars, the observed high-energy gamma-rays are highly variable, on time scales of a few days. (6) For example, the intensity of 3C 279 (z = 0.538) declined by a factor of 4-5 in less than 3 days (Fig. 5; Kniffen et al. 1993), and the blazar PKS 0528+134 (z = 2.06) more than doubled its intensity in 5 days (Hunter et al. 1993).

Figure 5. Gamma-ray light curve of the superluminal quasar 3C 279 during the bright outburst in June 1991 (Kniffen et al. 1993). The combination of rapid variability and high gamma-ray luminosity strongly suggests the emission is relativistically beamed. (Copyright American Astronomical Society, reproduced with permission.)

This rapid variability leads to a largely model-independent argument that the gamma-rays, at least, must be relativistically beamed (Maraschi et al. 1992). This argument does not depend on which physical mechanism gives rise to the gamma-ray emission, simply on the observed luminosity and variability time scales at high energies. Specifically, in order for gamma-rays to escape the source, the optical depth to pair production, taugammagamma , must be of order unity or less, which is equivalent to saying the compactness, a convenient dimensionless parameter that represents source luminosity divided by dimension, must be less than about 40 at the threshold for pair-production. That is, taugammagamma ~ curlyl / 40 << 1, where curlyl = (L/r) (sigmaT / mec3) is the compactness, L and r are the source luminosity and dimension, respectively, and me and c are the usual constants (electron mass and speed of light). The Thomson cross section, sigmaT, is appropriate because most pairs will be produced by X-gamma interactions.

For 3C 279 and PKS 0528+134, the inferred values for the compactness are 5000 to 15,000, well in excess of the optical depth limit. In order that we observe gamma-rays from these blazars, the true gamma-ray luminosity, curlyL, must be much smaller than observed and the true dimension much larger. Relativistic beaming has the effect that Lobs = delta4 curlyL [Eq. (B5)], where delta is the Doppler beaming factor (Appendix A). If r is estimated from the variability time scale (r ~ deltac Deltat), then

Equation 1 (1)

The limit curlyl ltapprox 40 then translates to delta gtapprox 6 for 3C 279 and delta gtapprox 7 for PKS 0528+134, where Lobs has been evaluated at X-ray energies under reasonable spectral assumptions (Maraschi et al. 1992); similar limits are obtained for all the gamma-ray blazars (Dondi and Ghisellini 1995). For comparison, the values derived in an entirely independent way from a synchrotron self-Compton calculation using radio and X-ray data (see Sec. 4.4) are gtapprox 18 for 3C 279 and 3 for PKS 0528+134 (Ghisellini et al. 1993).

Note that no radio-quiet AGN have been detected so far with EGRET. One cannot rule out that, since gamma-ray power appears to correlate with radio power (Padovani et al. 1993), radio-quiet AGN might still have blazar-like spectra with high-energy (> 50 MeV) emission well below the sensitivity of EGRET. This is unlikely, however, because OSSE observations of Seyfert 1 galaxies show steep cutoffs above ~ 50 keV, in sharp contrast to the hard spectra of radio-loud objects (Kurfess et al. 1994). The difference in gamma-ray properties may then be related to radio-loudness, which in turn must be closely associated with relativistic beaming.

6 The variability time scale can be defined in several ways, including the doubling time [td = < F > (dF/dt)-1] or the e-folding time [te = (dln F / dt)-1]. Either is fine for the rough estimates here as long as it is derived from a substantial change in flux (gtapprox 30%). Back.

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