Fermi-LAT analyses show that the gamma-ray photon spectral indices Gamma(gamma) of a large sample of blazars correlate with the vF(v) peak synchrotron frequency ns according to the relation Gamma(gamma) =d-k log v(s). The same function, with different constants d and k, also describes the relationship between Gamma(gamma) and peak Compton frequency nC. This behavior is derived analytically using an equipartition blazar model with a log-parabola description of the electron energy distribution (EED). In the Thomson regime, k=k(EC)=3b/4 for external Compton (EC) processes and k=k(SSC)=9b/16for synchrotron self-Compton (SSC) processes, where b is the log-parabola width parameter of the EED. The BL Lac object Mrk 501 is fit with a synchrotron/SSC model given by the log-parabola EED, and is best fit away from equipartition. Corrections are made to the spectral-index diagrams for a low-energy power-law EED and departures from equipartition, as constrained by absolute jet power. Analytic expressions are compared with numerical values derived from self-Compton and EC scattered gamma-ray spectra from Lya broad-line region and IR target photons. The Gamma(gamma) versus ns behavior in the model depends strongly on b, with progressively and predictably weaker dependences on gamma-ray detection range, variability time, and isotropic gamma-ray luminosity. Implications for blazar unification and blazars as ultra-high energy cosmic-ray sources are discussed. Arguments by Ghisellini et al. that the jet power exceeds the accretion luminosity depend on the doubtful assumption that we are viewing at the Doppler angle.
Dermer, CD,Yan DH,Yan, DH,et al. NEAR-EQUIPARTITION JETS WITH LOG-PARABOLA ELECTRON ENERGY DISTRIBUTION AND THE BLAZAR SPECTRAL-INDEX DIAGRAMS[J]. ASTROPHYSICAL JOURNAL,2015,809(2):174.
Dermer, CD,闫大海,Yan, DH,Zhang, L,Finke, JD,&Lott, B.(2015).NEAR-EQUIPARTITION JETS WITH LOG-PARABOLA ELECTRON ENERGY DISTRIBUTION AND THE BLAZAR SPECTRAL-INDEX DIAGRAMS.ASTROPHYSICAL JOURNAL,809(2),174.
Dermer, CD,et al."NEAR-EQUIPARTITION JETS WITH LOG-PARABOLA ELECTRON ENERGY DISTRIBUTION AND THE BLAZAR SPECTRAL-INDEX DIAGRAMS".ASTROPHYSICAL JOURNAL 809.2(2015):174.