Relations between the flux densities (F) and spectral indices () can help us analyze the emission process. In this paper, we choose 8 blazars (0235+164, 0430+052, 1156+295, 3C345, 1308+326, 1413+135, 3C454.3, and 1749+096) from the University of Michigan Radio Observatory (UMRAO) database to study the relations between the spectral indices () and flux densities at 14.5GHz (). The main results are the following. (1) There are strong anticorrelations between and , with the correlation coefficient r in the range from to . (2) The distributions show elliptic appearance, which have been fitted by elliptic curves. (3) For most of the sources, the time intervals of elliptic circle () are consistent with the quasi-periodicities calculated by the averaged light curves and spectral variances ().

中文翻译：

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八种Blazar的光谱指数与通量密度之间的关系

通量密度（F）和光谱指数（）之间的关系可以帮助我们分析发射过程。在本文中，我们从密歇根大学无线电天文台（UMRAO）中选择了8种blazar（0235 + 164、0430 + 052、1156 + 295、3C345、1308 + 326、1413 + 135、3C454.3和1749 + 096）数据库以研究光谱指数（）与14.5 GHz（）处的通量密度之间的关系。主要结果如下。（1）和之间有很强的反相关性，相关系数r在从到的范围内。（2）分布显示椭圆外观，已通过椭圆曲线拟合。（3）对于大多数来源，时间间隔为椭圆圆（）与通过平均光曲线和光谱方差（）计算出的准周期一致。