The Relationship between the Inverse Compton Peak Frequency and the γ-ray Photon Spectral Index for Blazars

The relationship between the inverse Compton peak frequency ($\lg {\nu }_p^{\text{IC}}$) and $\gamma$-ray photon spectral index ({\rm $\Gamma$}) for different subclasses of blazars was studied using Fermi/LAT (Large Area Telescope) 4FGL-DR3 (The 4th Fermi Gamma-ray LAT-Data Release 3) blazars as a sample. The results show that: there is a strong negative correlation between $\lg {\nu }_p^{\text{IC}}$ and $\Gamma$ for all subclass samples of blazars, indicating that the $\gamma$-ray photon spectral index has a strong dominant effect on the inverse Compton spectrum of blazars, and the inverse Compton peak frequency can be quickly estimated using the relationship between them. The spectrum energy distributions (SEDs) of the inverse Compton emission for different subclass sample of blazars may have different spectral structure functions. Therefore, for different samples, different functions should be used to fit their SEDs.