Spectral Index Changes with Brightness for γ-Ray Loud Blazars

Based on Fermi 1FGL and 2FGL data, a sample of 572 γ-ray loud blazars are selected, in which each sources has both γ-ray flux and spectral index in 1FGL and 2FGL, respectively. Theoretic relation of spectral index changes depending on γ-ray brightness is obtained. The correlations between the ratio of γ-ray flux densities and the differences of the γ-ray spectral indices are discussed for the three subclasses of HBL, LBL and FSRQs. Results show that the ratio is related with the differences for the three subclasses. It is consistent with the theoretical result and it indicates that the spectrum becomes flat as the source brightens in the γ-ray band.