We have assembled the historical variability data of Mrk 421 at radio 15 GHz, X-ray, and γ-ray bands, spanning about 6.3, 10.3, and 7.5 yr, respectively. We analyzed the variability by using three methods. The results indicated that there is a period of 287.6 ± 4.4 days for 15 GHz, 309.5 ± 5.8 days for X-ray and 283.4 ± 4.7 days for γ-ray, respectively. This period can be reasonably explained by the nonballistic helical motion of the emitting material. The correlation analysis suggested that the variabilities of radio 15 GHz, X-ray, and γ-ray are remarkably correlated, and the emission of radio 15 GHz lags behind that of X-ray, and the X-ray flux lags behind the γ-ray. This suggests that the γ-ray is derived from inverse-Compton (IC) scattering of the synchrotron photons, supporting the synchrotron self-Compton (SSC) model. Moreover, the time delay between different wavebands could be explained by the shock-in-jet models, in which a moving emission region produces the radio to γ-ray activity, implying that the emission region of γ-ray is closer to the center than ones of X-ray and radio emission.

The typical blazar S5 0716+714 is very interesting due to its rapid and large-amplitude variability and high duty cycle of microvariability in the optical band. We analyze the observations in the I, R, and V bands obtained with the 1.0 m telescope at Weihai observatory of Shandong University from 2011 to 2018. The model of synchrotron radiation from turbulent cells in a jet has been proposed as a mechanism for explaining microvariability seen in blazar light curves. Parameters such as the sizes of turbulent cells, the enhanced particle densities, and the location of the turbulent cells in the jet can be studied using this model. The model predicts a time lag between variations, as observed in different frequency bands. An automatic model fitting method for microvariability is developed, and the fitting results of our multi-frequency microvariability observations support the model. The results show that both the amplitude and duration of flares decomposed from the microvariability light curves conform to the log-normal distribution. The turbulent cell size is within the range of about 5–55 au, and the time lags of the microvariability flares between the I–R and R–V bands should be several minutes. The time lags obtained from the turbulence model are consistent with the fitting statistical results, and the time lags of flares are correlated with the time lags of the whole light curve.

A comprehensive study of multifrequency correlations can shed light on the nature of variation for blazars. In this work, we collect the long-term radio, optical, and γ-ray light curves of PKS 1502+106. After performing the localized cross-correlation function analysis, we find that correlations between radio and γ-ray or V band are beyond the 3σ significance level. The lag of the γ-ray relative to 15 GHz is days, translating to a distance of parsec (pc) between them. Within uncertainties, the locations of the γ-ray and optical emitting regions are roughly the same, and are away from the jet base within 1.2 pc. The derived magnetic field in optical and γ-ray emitting regions is about 0.36 G. The logarithm of γ-ray flux is significantly linearly correlated with that of V-band fluxes, which can be explained by the synchrotron self-Compton process, the external Compton processes, or the combination of them. We find a significant linear correlation in the plot of (polarization degree) versus at V band, and use the empirical relation Π ∼ sin ⁿ θ′ (θ′ is the observing angle in the comoving frame blob) to explain it. The behaviors of color index (generally redder when brighter at the active state) and γ-ray spectral index (softer when brighter) could be well explained by the twisted jet model. These findings suggest that the curvature effect (mainly due to the change of the viewing angle) is dominant in the variation phenomena of fluxes, spectral indices, and polarization degrees for PKS 1502+106.

The variation mechanism of blazars is a long-standing open question. Observations of polarization can provide us with more information to constrain models. In this work, we collect long-term multiwavelength data on AO 0235+164, and analyse the correlations between them by using the local cross-correlation function. We find that both γ-ray and the optical V-band light curves are correlated with the radio light curve beyond the 3σ significance level. The regions emitting the γ-ray and optical radiation coincide within errors, and are located pc upstream of the core region of 15 GHz, which is beyond the broad-line region. The color index shows the redder-when-brighter trend in the low flux state, but turns to the bluer-when-brighter trend in the high flux state, while the γ-ray spectral index always shows the softer-when-brighter trend. We propose that such complex variation trends can be explained by the increasing jet component with two constant components. The optical polarization degree (PD) flares and optical flux flares are not synchronous. It seems that one flux peak is sandwiched by two PD peaks, which have inverse rotation trajectories in the qu plane. The helical jet model can schematically show these characteristics of polarization with fine-tuned parameters. The change in viewing angle is suggested to be the primary variable that leads to all these variations, although other possibilities such as the shock-in-jet model or the hadronic model are not excluded completely.

The BL Lacertae OJ 287 is a supermassive black hole binary system with complex physics of its irregular flares. During 2016 October–2017 April, a surprising outburst in the X-ray, UV, and optical bands was detected, while no variability was seen in the γ-ray light curve. During the outburst, the X-ray light curves were dominated by the soft X-rays, whose peak in luminosity was ∼10⁴⁶ erg s⁻¹—more than 10 times higher than the mean level before the outburst—and a “softer-when-brighter” phenomenon was exhibited. These above phenomena have been reported by some previous works. The hardness ratio showed negligible evolution with flare time and soft X-ray luminosity. Critically, the luminosity of the soft X-rays decayed following a power law of t ^−5/3, which occurs in most tidal disruption events (TDEs), and a similar trend can be seen in the UV and optical bands during the soft X-ray declining period. Helium and oxygen narrow emission lines are strengthened prominently in the optical spectra of postoutburst epochs, that could be attributed to the surrounding gas caused by TDE. We discuss three possible origins of the event, including the jet’s precession, the aftereffects of the black hole–disk impaction, and the TDE. Our results show that the TDE is the more likely scenario to explain the outburst.

Blazar PG 1553+113 is thought to be a host of supermassive black hole binary system. A 2.2 yr quasi-periodicity in the γ-ray light curve was detected, possibly a result of jet precession. Motivated by the previous studies based on the γ-ray data, we analyzed the X-ray light curve and spectra observed during 2012–2020. The 2.2 yr quasi-periodicity might be consistent with the main-flare recurrence in the X-ray light curve. When a weak rebrightening in the γ-ray was observed, a corresponding relatively strong brightening in the X-ray light curve can be identified. The harder-when-brighter tendency in both X-ray main and weak flares was shown, as well as a weak softer-when-brighter behavior for the quiescent state. We explore the possibility that the variability in the X-ray band can be interpreted with two-jet precession scenario. Using the relation between jets and accretion disks, we derive the primary black hole mass ≃3.47 × 10⁸ M _☉ and mass of the secondary one ≃1.40 × 10⁸ M _☉, and their mass ratio ∼0.41.