Multi-band optical micro-variability observations of BL Lacertae

We have observed BL Lacertae in the B, R and I bands for 2 nights in July, 1999, and 3 nights in July, 2001. The observations resulted in almost evenly sampled light curves, with an average sampling interval of ${\sim} 5$ min. Because of the dense sampling and the availability of light curves in three bands we are able to study the intra-night flux and spectral variability of the source in detail. The source is significantly variable in all bands, showing variations on different time scales. On average, the variability amplitude increases from ${\sim} 5\%$ in the I band, to ${\sim} 5.5\%$ in the R and ${\sim} 6.5\%$ in the B band light curves.The rising and decaying time scales are comparable within each band, but they increase from the B, to R and I band light curves. The optical power spectrum shows a red noise component with a slope of ${\sim} {-}2$. Cross-correlation analysis shows that in most cases the delay between the variations in the B and I band light curves is less than ${\sim} {\pm} 0.4$ hrs. However, the cross-correlation functions are asymmetric, implying complex delays of the I band variations with respect to the B band variations. Furthermore, in one case we find that the I band variations are significantly delayed (by ${\sim} 0.2$ hrs) with respect to the B band variations. We also detect significant spectral variations. We find that the spectrum hardens, (i.e. it gets flatter) as the flux increases, and the flattest spectral index corresponds to the maximum B band flux. The rate of the spectral variations does not remain the same during the observations. Our results imply that the fast, intra-night variations of the source correspond to perturbations of different regions in the jet which cause localized injections of relativistic particles on time scales much shorter that the average sampling interval of the light curves. The variations are controlled by the cooling and light crossing time scales, which are probably comparable.