A correlation-delay analysis of AO 0235 + 164 and its spectral evolution

In this paper, the method of discrete correlation function proposed by Edelson and Krolik is introduced in some details. This method is suitable for correlation analysis of flux density data in various wavebands that are distributed unevenly in time due to irregularity of the observations. We have tested the method in the two extreme cases of perfect and zero correlation. The testing results prove that the DCF method is feasible. With this method, we have made correlation analysis of the flux densities at four wavebands of the AO 0235 + 164. The results show that the variations of flux density at 5 GHz, 8 GHz, 14.5 GHz and the optical B band are apparently correlated, and that the variation comes earlier in the higher frequency band than in the lower. This may imply that either the radiations at these bands (from radio to optical) originate from the same mechanism, or that the radiations are correlated. In addition, we have also found the spectral index in the radio band to vary in time, mainly in the form of spectrum inversion. Various lines of evidence indicate that the radio outbursts of AO 0235 + 164 are associated with the forming of shock waves in relativistic jets, and the spectral analysis of multiple wavebands and the study of spectral evolution may be an effective way to reveal the underlying relationship.