The spectral index study for Fermi blazars

In this work, we compiled a sample of 1172 4FGL blazars with available spectral information and broadband intensities to the study the spectral indices. Based on this sample, we studied the correlations of spectral indices, and further studied BCU classification by using multi-band spectral indices. Among these sources, there are 196 BCUs, we manage to classify these sources into either FSRQs or BL Lacs through three methods: 1) for the $\alpha _{\mathrm{ro}}$ – $\alpha _{\mathrm{ox}}$ plane, we classified 135 sources into BL Lac candidates; 2) for the $\alpha _{\mathrm{ro}}$ – $\alpha _{\upgamma}$ plane, we classified them into 40 FSRQ candidates and 156 BL Lac candidates; and 3) for the $\alpha _{\upgamma}$ – ${\mathrm{log}} F$ plane, we classified them into 45 FSRQ candidates and 151 BL Lac candidates. From those above results, we see that 36 BCUs were consistently classified as FSRQ candidates by the latter two methods and that 128 BCUs were consistently classified as BL Lac candidates by all the three methods. The completeness is 92.9%, 88.1% and 88.1% for the corresponding result from three methods through comparing with the 4FGL updated catalogue. The correlations of spectral indices were investigated individually for FSRQs and BL Lacs. FSRQs showed very weak anti-correlations for $\alpha _{\mathrm{ro}}$ vs $\alpha _{\upgamma}$ and $\alpha _{\mathrm{ox}}$ vs $\alpha _{\upgamma}$ , positive correlation for $\alpha _{\mathrm{x}\upgamma}$ vs $\alpha _{\upgamma}$ . On the contrary, BL Lacs showed positive correlations for $\alpha _{\mathrm{ro}}$ vs $\alpha _{\upgamma}$ and $\alpha _{\mathrm{ox}}$ vs $\alpha _{\upgamma}$ , anti-correlation for $\alpha _{\mathrm{x}\upgamma}$ vs $\alpha _{\upgamma}$ .