Variable Radio Echoes from a Jet in QSO 0957 + 561. II. Statistical Significance of the Result

Abstract

At the previous publication (Oknyanskij, 1997) we considered and used a new algorithm for time-delay investigations in case when the time delay was a linear function of time and the echo response intensity was a power-low function of the delay. We applied this method to investigate optical-to-radio delay in the double quasar 0957 + 561 (generally accepted to be a case of gravitational lensing). It was found in this way that the radio variations (5 MHz) followed the optical ones, but the time delay was a linear function of time with the mean value being about 2370 day and with the rate of increase V≈ 110 days/year. Here we use Monte-Carlo simulations to estimate the significance of the results. We estimate (with the 95% confidence level) that the probability of getting the same result by chance (if real V value was equal to 0 days/year) is less then 5%. We also show that the method can determinate the actual rate of increase Va of the time delay in the artificial light curves, which have the same data spacing, power spectrum and noise level as real ones. We briefly consider some other possible fields for using the method.