Could the inter-band lag of active galactic nucleus vary randomly?

The inter-band lags among the optical broad-band continua of active galactic nuclei (AGNs) have been intensively explored over the past decade. However, the nature of the lags remains under debate. Here utilizing two distinct scenarios for AGN variability, i.e., the thermal fluctuation of accretion disk and the reprocessing of both the accretion disk and clouds in the broad line region, we show that, owing to the random nature of AGN variability, the inter-band lags of an individual AGN would vary from one campaign with a finite baseline to another. Specifically, the thermal fluctuation scenario implies larger variations in the lags than the reprocessing scenario. Moreover, the former predicts a positive correlation between the lag and variation amplitude, while the latter does not result in such a correlation. For both scenarios, averaging the lags of an individual AGN measured with repeated and non-overlapping campaigns would give rise to a stable lag, which is larger for a longer baseline and gets saturation for a sufficiently long baseline. However, obtaining the stable lag for an individual AGN is very time-consuming. Alternatively, it can be equivalently inferred by averaging the lags of a sample of AGNs with similar physical properties, thus can be properly compared with predictions of AGN models. In addition, discussed are several new observational tests suggested by our simulations as well as the role of the deep high-cadence surveys of the Wide Field Survey Telescope in enriching our knowledge of the lags.