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 α ro $\alpha _{\mathrm{ro}}$ – α ox $\alpha _{\mathrm{ox}}$ plane, we classified 135 sources into BL Lac candidates; 2) for the α ro $\alpha _{\mathrm{ro}}$ – α γ $\alpha _{\upgamma}$ plane, we classified them into 40 FSRQ candidates and 156 BL Lac candidates; and 3) for the α γ $\alpha _{\upgamma}$ – log F ${\mathrm{log}} F$ 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 α ro $\alpha _{\mathrm{ro}}$ vs α γ $\alpha _{\upgamma}$ and α ox $\alpha _{\mathrm{ox}}$ vs α γ $\alpha _{\upgamma}$ , positive correlation for α x γ $\alpha _{\mathrm{x}\upgamma}$ vs α γ $\alpha _{\upgamma}$ . On the contrary, BL Lacs showed positive correlations for α ro $\alpha _{\mathrm{ro}}$ vs α γ $\alpha _{\upgamma}$ and α ox $\alpha _{\mathrm{ox}}$ vs α γ $\alpha _{\upgamma}$ , anti-correlation for α x γ $\alpha _{\mathrm{x}\upgamma}$ vs α γ $\alpha _{\upgamma}$ .

中文翻译：

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费米耀变体的光谱指数研究

在这项工作中，我们汇编了 1172 个 4FGL 耀变体的样本，这些样本具有可用的光谱信息和宽带强度，以研究光谱指数。在此样本的基础上，我们研究了频谱指标的相关性，并利用多波段频谱指标进一步研究了 BCU 分类。在这些来源中，有 196 个 BCU，我们设法通过三种方法将这些来源分类为 FSRQ 或 BL Lac：1) 对于 α ro $\alpha _{\mathrm{ro}}$ – α ox $\alpha _ {\mathrm{ox}}$ 平面，我们将 135 个源分类为 BL Lac 候选；2）对于α ro $\alpha _{\mathrm{ro}}$ – α γ $\alpha _{\upgamma}$ 平面，我们将它们分为40个FSRQ候选和156个BL Lac候选；和 3) 对于 α γ $\alpha _{\upgamma}$ – log F ${\mathrm{log}} F$ 平面，我们将它们分为 45 个 FSRQ 候选和 151 个 BL Lac 候选。从上述结果中，我们看到 36 个 BCU 被后两种方法一致归类为 FSRQ 候选者，128 个 BCU 被所有三种方法一致归类为 BL Lac 候选者。通过与4FGL更新目录的比较，三种方法对应结果的完整性分别为92.9%、88.1%和88.1%。分别研究了 FSRQ 和 BL Lac 的光谱指数的相关性。FSRQ 对 α ro $\alpha _{\mathrm{ro}}$ vs α γ $\alpha _{\upgamma}$ 和 α ox $\alpha _{\mathrm{ox}}$ vs 显示出非常弱的反相关性α γ $\alpha _{\upgamma}$ ， α x γ $\alpha _{\mathrm{x}\upgamma}$ 与 α γ $\alpha _{\upgamma}$ 的正相关。相反，