A Study of the Periodicity of Spectral Index in a Broad Radio Band of the BL Lac Object AO 0235+164

We have collected from many references flux-density data of the BL Lac object AO 0235+164 in the radio bands near 4.8GHz and 14.5GHz within about 20 years. We construct long-term light curves for the object. The light curves show that the AO 0235+164 is very active. We use the Jurkevich method and the Discrete Correlation Function (DCF) to analyze the period of the spectral index across the broad radio band 4.8GHz to 14.5GHz. The DCF was introduced by Edelson & Krolik (1988). The Jurkevich method and the DCF method are good in the sense that all data are used and there is no need to interpolate to set artificial datapoints. In addition, the DCF method also gives a reasonable error estimate.We also study possible correlations between flux density and the broad-band spectral index using the linear-regression method. Our results lead to the conclusions as follows. (i) The broad-band spectral index has a period of variation of about 5.30 years. Such a conclusion is consistent with the period of 5.59±0.47 years for the flux densities in radio bands found by previous studies (F.K.LIU.). The result also agrees with the near-equility of variation periods for optical flux densities and spectral indices found by Zheng et al. (2008). (ii) There is a strong correlation between the broad-band spectral index and the flux density at 4.8GHz, but there is an anti-correlation between the broad-band spectral index and the flux density at 14.5GHz. This is consistent with the analysis results of correlations between the broad-band spectral index and the flux densities at the 22GHz and 37GHz bands of the BL Lac object Mkn 421 (Li et al. 2011).