Variability and Beaming of GeV Gamma-Ray-Loud Blazars

Abstract

Abstract Considering the Klein–Nishina effects for high-energy $\gamma$-ray emissions, we derived a corrected form of the basic Elliot–Shapiro formula. Two new lower limits to the time scales of the variability expected from an accreting Schwarzschild black hole and Kerr black hole were derived, respectively. For a sample of 25 GeV $\gamma$-ray-loud blazars known to have the shortest time scales of flux variability, $t_\mathrm{min}$, we studied the corrected Elliot–Shapiro relations between $t_\mathrm{min}$ and the GeV $\gamma$-ray luminosities in both the high and low states, respectively. We observe that: (1) No sources have been observed to have GeV $\gamma$-ray luminosities in the low state above the corrected Eddington limit being produced by a Kerr black hole and a Schwarzschild black hole. (2) Only one source has been observed to have a luminosity in the high state above the corrected Eddington limit being produced by a Kerr black hole and a Schwarzschild black hole, which is a new argument for not invoking relativistic beaming models for the present EGRET observational data alone. Our conclusion is that if one considers the Klein–Nishina effect, the evidence for beamed emission from the present gamma-ray data alone is weak. Obviously, our conclusion is consistent with that of Dermer and Gehrels (1995, ApJ, 447, 103), but it is a new independent evidence.