Broadband Spectral Index Distribution of Blazar and its Taxonomic Function

There are two obvious peaks in the spectral energy distribution (SED) of the blazar, of which the low energy peak is the synchrotron radiation peak. There is an inverse correlation between the peak power of the synchrotron radiation peak of the blazar and the peak frequency, so the spectral index plane constructed by the multi-band composite spectral index related to the SED peak can be used as a classifier for the two subclasses of the blazar (flat-spectrum radio quasar (FSRQ) and BL-Lac object). In this paper, the cross matching of multi-wavelength data for the blazars in the Fermi four Catalogue (4FGL-DR3) is carried out through the database of Strasbourg Observatory, and multi-wavelength data set is obtained. Basing on this data set, we find that the distributions of the 8 broad band spectral indices, (α_rw1, α_rw2, α_rw3, α_ro, α_rγ, α_w1w2, α_w1w3) and α_w3x, have obvious bimodal structure, and clearly distinguish the two subclasses of blazed variants (FSRQ and BL Lac). Through the support vector machine model in machine learning technology, we further analyze the classification effect of spectral index plane on subclasses of blazar, and find that most of the accuracy rates are above 80%.