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We present the results of our study of cross-correlations between long-term multiband observations of the radio variability of the blazar 3C 279. More than a decade (2008–2022) of radio data were collected at seven different frequencies ranging from 2 to 230 GHz. The multiband radio light curves show variations in flux, with the prominent flare features appearing first at higher-frequency and later in lower-frequency bands. This behaviour is quantified by cross-correlation analysis, which finds that the emission at lower-frequency bands lags that at higher-frequency bands. Lag versus frequency plots are well fit by straight lines with negative slope, typically ∼−30 day GHz−1. We discuss these flux variations in conjunction with the evolution of bright moving knots seen in multiepoch Very Long Baseline Array maps to suggest possible physical changes in the jet that can explain the observational results. Some of the variations are consistent with the predictions of shock models, while others are better explained by a changing Doppler beaming factor as the knot trajectory bends slightly, given a small viewing angle to the jet.

PG 1553 + 113 is one of the few blazars with a convincing quasi-periodic emission in the gamma-ray band. The source is also a very high energy (VHE; >100 GeV) gamma-ray emitter. To better understand its properties and identify the underlying physical processes driving its variability, the MAGIC Collaboration initiated a multiyear, multiwavelength monitoring campaign in 2015 involving the OVRO 40-m and Medicina radio telescopes, REM, KVA, and the MAGIC telescopes, Swift and Fermi satellites, and the WEBT network. The analysis presented in this paper uses data until 2017 and focuses on the characterization of the variability. The gamma-ray data show a (hint of a) periodic signal compatible with literature, but the X-ray and VHE gamma-ray data do not show statistical evidence for a periodic signal. In other bands, the data are compatible with the gamma-ray period, but with a relatively high p-value. The complex connection between the low- and high-energy emission and the non-monochromatic modulation and changes in flux suggests that a simple one-zone model is unable to explain all the variability. Instead, a model including a periodic component along with multiple emission zones is required.

In 2021 BL Lacertae underwent an extraordinary activity phase, which was intensively followed by the Whole Earth Blazar Telescope (WEBT) Collaboration. We present the WEBT optical data in the BVRI bands acquired at 36 observatories around the world. In mid-2021 the source showed its historical maximum, with R = 11.14. The light curves display many episodes of intraday variability, whose amplitude increases with source brightness, in agreement with a geometrical interpretation of the long-term flux behaviour. This is also supported by the long-term spectral variability, with an almost achromatic trend with brightness. In contrast, short-term variations are found to be strongly chromatic and are ascribed to energetic processes in the jet. We also analyse the optical polarimetric behaviour, finding evidence of a strong correlation between the intrinsic fast variations in flux density and those in polarization degree, with a time delay of about 13 h. This suggests a common physical origin. The overall behaviour of the source can be interpreted as the result of two mechanisms: variability on time-scales greater than several days is likely produced by orientation effects, while either shock waves propagating in the jet, or magnetic reconnection, possibly induced by kink instabilities in the jet, can explain variability on shorter time-scales. The latter scenario could also account for the appearance of quasi-periodic oscillations, with periods from a few days to a few hours, during outbursts, when the jet is more closely aligned with our line of sight and the time-scales are shortened by relativistic effects.