The long-term optical spectral variability of BL Lacertae

Context.We present the results from a study of the long-term optical spectral variations of BL Lacertae, using the long and well-sampled B and R-band light curves of the Whole Earth Blazar Telescope (WEBT) collaboration, binned in time intervals of 1 day. Aims.We study the relation between the long-term spectral variations and the respective flux variations of the source. Methods.Using cross-correlation techniques to investigate whether there are any delays between the flux variations in different energy bands and between the flux and spectral variations. Results.The relation between spectral slope and flux (the spectrum gets bluer as the source flux increases) is well described by a power-law model, although there is significant scatter around the best-fitting model line. To some extent, this is due to the spectral evolution of the source (along well-defined loop-like structures) during low-amplitude events, which are superimposed on the major optical flares, and evolve on time scales of a few days. The B and R-band variations are well correlated, with no significant, measurable delays larger than a few days. On the other hand, we find that the spectral variations lead those in the flux light curves by ~4 days. During at least the largest amplitude flares, the B-band variations appear to evolve faster than those in the R band. Conclusions.We confirm the “bluer-when-brighter” mild chromatism of the long-term variations, and we show that it can be explained if the flux increases/decreases faster in the B than in the R band. We also report the discovery of the lag between spectral and flux changes. These two features can be explained in terms of Doppler factor variations due to changes in the viewing angle of a curved and inhomogeneous emitting jet