We present the most densely sampled multi-band optical photometric observations of the peculiar BL Lacertae object OJ 287 from 2015 to 2025 with a focus on its optical activity on diverse timescales. We present a total of 2296, 10927, 11484, and 2982 data points in B, V, R, and I bands, respectively. The densely sampled observations allow us to keep track of the source evolution that it has exhibited since the start of the predicted major optical flaring activity at the end of 2015. The study reveals clear and persistent bluer when brighter trends in both the long-term and short-term variations. Different bands were cross-correlated with discrete correlation functions, which peak at zero lag, implying co-spatial emission. Using eight optical spectra in the low flux states of OJ 287 taken from 2017 October 21 to 2017 November 22, from Steward Observatory, we estimate the central black hole mass to be at least 3.89 × 10^9 M_⊙ from the [O III] line width. The emission mechanism of the binary black hole blazar, and its possible implication in various aspects of multi-messenger astronomy are briefly discussed.

Context. The BL Lac object 3C 371 is one of the targets regularly monitored by the Whole-Earth Blazar Telescope (WEBT), a collaboration of observers studying blazar variability on both short and long timescales. Aims. We aim to evaluate the long-term multi-wavelength (MWL) behaviour of 3C 371, comparing it with results derived from its optical emission in our previous study. For this, we make use of the multi-band campaigns organised by the WEBT collaboration in optical and radio between January 2018 and December 2020, and of public data from Swift and Fermi satellites and the MOJAVE Very Large Interferometry programme. Methods. We evaluated the variability shown by the source in each band by quantifying the amplitude variability parameter, and also looked for a possible inter-band correlation using the z-discrete correlation function. We also present a deep analysis of the optical-UV, X-ray, and gamma-ray spectral variability. With the MOJAVE data, we performed a kinematics analysis, looking for components propagating along the jet and calculating its kinematics parameters. We then used this set of parameters to interpret the source MWL behaviour, modelling its broadband spectral energy distribution (SED) with theoretical blazar emission scenarios. Results. The MWL variability of the source in the UV, X-ray, and gamma-ray bands is comparable to that in optical, especially considering the lower coverage of the first two wavebands. On the other hand, the radio bands show variability of much lower magnitude. Moreover, this MWL emission shows a high degree of correlation, which is compatible with zero lag, again with the exception of the radio emission. The radio VLBI images reveal super-luminal motion of one of the identified components, which we used to set constraints on the jet kinematics and parameters, and to estimate a viewing angle of theta = (9.6 +/- 1.6)degrees, a Doppler factor of delta = 6.0 +/- 1.1, and a Lorentz factor of Gamma = 6.0 +/- 1.8. The polarised radio emission was found to be anti-correlated with the total flux, and to follow the same behaviour as the polarised optical radiation. The optical-UV spectral behaviour shows a mild harder-when-brighter trend on long timescales, and other trends such as redder-when-brighter on shorter timescales. We successfully modelled the broadband emission with a leptonic scenario, where we compared the low and high emission states during the period of complete MWL coverage. The difference between these two states can be ascribed mainly to a hardening of the distribution of particles. The derived features of the source confirm that 3C 371 is a BL Lac whose jet is not well aligned with the line of sight.

Due to its peculiar and highly variable nature, the blazar 3C 454.3 has been extensively monitored by the WEBT team. Here, we present for the first time these long-term optical flux and color variability results using data acquired in B, V, R, and I bands over a time span of about two decades. We include data from WEBT collaborators and public archives such as SMARTS, Steward Observatory, and Zwicky Transient Facility. The data are binned and segmented to study the source over this long term when more regular sampling was available. During our study, the long-term spectral variability reveals a redder-when-brighter trend, which, however, stabilizes at a particular brightness cutoff of similar to 14.5 mag in the I band, after which it saturates and evolves into a complex state. This trend indicates increasing dominance of jet emission over accretion disk (AD) emission until jet emission completely dominates. Plots of the variation in spectral index (following F nu proportional to nu -alpha ) reveal a bimodal distribution using a one-day binning. These correlate with two extreme phases of 3C 454.3, an outburst or high-flux state and a quiescent or low-flux state, which are respectively jet- and AD-dominated. We have also conducted intraday variability studies of nine light curves and found that six of them are variable. Discrete correlation function analysis between different pairs of optical wave bands peaks at zero lags, indicating cospatial emission in different optical bands.

The BL Lac 1ES 2344+514 is known for temporary extreme properties (e.g., a shift of the synchrotron SED peak energy $\nu_{synch,p}$ above 1keV). While those extreme states were so far observed only during high flux levels, additional multi-year observing campaigns are required to achieve a coherent picture. Here, we report the longest investigation of the source from radio to VHE performed so far, focusing on a systematic characterisation of the intermittent extreme states. While our results confirm that 1ES 2344+514 typically exhibits $\nu_{synch,p}>$1keV during elevated flux periods, we also find periods where the extreme state coincides with low flux activity. A strong spectral variability thus happens in the quiescent state, and is likely caused by an increase of the electron acceleration efficiency without a change in the electron injection luminosity. We also report a strong X-ray flare (among the brightest for 1ES 2344+514) without a significant shift of $\nu_{synch,p}$. During this particular flare, the X-ray spectrum is among the softest of the campaign. It unveils complexity in the spectral evolution, where the common harder-when-brighter trend observed in BL Lacs is violated. During a low and hard X-ray state, we find an excess of the UV flux with respect to an extrapolation of the X-ray spectrum to lower energies. This UV excess implies that at least two regions contribute significantly to the infrared/optical/ultraviolet/X-ray emission. Using the simultaneous MAGIC, XMM-Newton, NuSTAR, and AstroSat observations, we argue that a region possibly associated with the 10 GHz radio core may explain such an excess. Finally, we investigate a VHE flare, showing an absence of simultaneous variability in the 0.3-2keV band. Using a time-dependent leptonic modelling, we show that this behaviour, in contradiction to single-zone scenarios, can instead be explained by a two-component model.

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.

Context. Blazars are beamed active galactic nuclei (AGNs) known for their strong multi-wavelength variability on timescales ranging from years down to minutes. Many different models have been proposed to explain this variability. Aims. We aim to investigate the suitability of the twisting jet model presented in previous works to explain the multi-wavelength behaviour of BL Lacertae, the prototype of one of the blazar classes. According to this model, the jet is inhomogeneous, curved, and twisting, and the long-term variability is due to changes in the Doppler factor due to variations in the orientation of the jet-emitting regions. Methods. We analysed optical data of the source obtained during monitoring campaigns organised by the Whole Earth Blazar Telescope (WEBT) in 2019-2022, together with radio data from the WEBT and other teams, and gamma-ray data from the Fermi satellite. In this period, BL Lacertae underwent an extraordinary activity phase, reaching its historical optical and gamma-ray brightness maxima. Results. The application of the twisting jet model to the source light curves allows us to infer the wiggling motion of the optical, radio, and gamma-ray jet-emitting regions. The optical-radio correlation shows that the changes in the radio viewing angle follow those in the optical viewing angle by about 120 days, and it suggests that the jet is composed of plasma filaments, which is in agreement with some radio high-resolution observations of other sources. The gamma-ray emitting region is found to be co-spatial with the optical one, and the analysis of the gamma-optical correlation is consistent with both the geometric interpretation and a synchrotron self-Compton (SSC) origin of the high-energy photons. Conclusions. We propose a geometric scenario where the jet is made up of a pair of emitting plasma filaments in a sort of double-helix curved rotating structure, whose wiggling motion produces changes in the Doppler beaming and can thus explain the observed multi-wavelength long-term variability.

Context. The BL Lac object 3C 371 was observed by the Transiting Exoplanet Survey Satellite (TESS) for approximately a year, between July 2019 and July 2020, with an unmatched two-minute imaging cadence. In parallel, the Whole Earth Blazar Telescope (WEBT) Collaboration organized an extensive observing campaign, providing three years of continuous optical monitoring between 2018 and 2020. These datasets allow for a thorough investigation of the variability of the source. Aims. The goal of this study is to evaluate the optical variability of 3C 371. Taking advantage of the remarkable cadence of TESS data, we aim to characterize the intra-day variability (IDV) displayed by the source and identify its shortest variability timescale. With this estimate, constraints on the size of the emitting region and black hole mass can be calculated. Moreover, WEBT data are used to investigate long-term variability (LTV), including in terms of the spectral behavior of the source and the polarization variability. Based on the derived characteristics, we aim to extract information on the origin of the variability on different timescales. Methods. We evaluated the variability of 3C 371 by applying the variability amplitude tool, which quantifies variability of the emission. Moreover, we employed common tools, such as ANOVA (ANalysis Of VAariance) tests, wavelet and power spectral density (PSD) analyses to characterize the shortest variability timescales present in the emission and the underlying noise affecting the data. We evaluated the short- and long-term color behavior to understand its spectral behavior. The polarized emission was analyzed, studying its variability and possible rotation patterns of the electric vector position angle (EVPA). Flux distributions of the IDV and LTV were also studied with the aim being to link the flux variations to turbulent and/or accretion-disk-related processes. Results. Our ANOVA and wavelet analyses reveal several entangled variability timescales. We observe a clear increase in the variability amplitude with increasing width of the time intervals evaluated. We are also able to resolve significant variations on timescales of as little as ∼0.5 h. The PSD analysis reveals a red-noise spectrum with a break at IDV timescales. The spectral analysis shows a mild bluer-when-brighter (BWB) trend on long timescales. On short timescales, mixed BWB, achromatic and redder-when-brighter signatures can be observed. The polarized emission shows an interesting slow EVPA rotation during the flaring period, where a simple stochastic model can be excluded as the origin with a 3σ significance. The flux distributions show a preference for a Gaussian model for the IDV, and suggest it may be linked to turbulent processes, while the LTV is better represented by a log-normal distribution and may have a disk-related origin.

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 polarisation 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.

We study the broadband emission of Mrk 501 using multiwavelength observations from 2017 to 2020 performed with a multitude of instruments, involving, among others, MAGIC, Fermi's Large Area Telescope (LAT), NuSTAR, Swift, GASP-WEBT, and the Owens Valley Radio Observatory. Mrk 501 showed an extremely low broadband activity, which may help to unravel its baseline emission. Nonetheless, significant flux variations are detected at all wave bands, with the highest occurring at X-rays and very-high-energy (VHE) γ -rays. A significant correlation (>3 σ ) between X-rays and VHE γ -rays is measured, supporting leptonic scenarios to explain the variable parts of the emission, also during low activity. This is further supported when we extend our data from 2008 to 2020, and identify, for the first time, significant correlations between the Swift X-Ray Telescope and Fermi-LAT. We additionally find correlations between high-energy γ -rays and radio, with the radio lagging by more than 100 days, placing the γ -ray emission zone upstream of the radio-bright regions in the jet. Furthermore, Mrk 501 showed a historically low activity in X-rays and VHE γ -rays from mid-2017 to mid-2019 with a stable VHE flux (>0.2 TeV) of 5% the emission of the Crab Nebula. The broadband spectral energy distribution (SED) of this 2 yr long low state, the potential baseline emission of Mrk 501, can be characterized with one-zone leptonic models, and with (lepto)-hadronic models fulfilling neutrino flux constraints from IceCube. We explore the time evolution of the SED toward the low state, revealing that the stable baseline emission may be ascribed to a standing shock, and the variable emission to an additional expanding or traveling shock.

We report the flux and spectral variability of PG 1553+113 on intra-night (IDV) to short-term timescales using BVRI data collected over 91 nights from 28 February to 8 November 2019 employing ten optical telescopes: three in Bulgaria, two each in India and Serbia, and one each in Greece, Georgia, and Latvia. We monitored the blazar quasi-simultaneously for 16 nights in the V and R bands and 8 nights in the V, R, I bands and examined the light curves (LCs) for intra-day flux and colour variations using two powerful tests: the power-enhanced F-test and the nested ANOVA test. The source was found to be significantly (> 99%) variable in 4 nights out of 27 in R-band, 1 out of 16 in V-band, and 1 out of 6 nights in I-band. No temporal variations in the colours were observed on IDV timescale. During the course of these observations the total variation in R-band was 0.89 mag observed. We also investigated the spectral energy distribution (SED) using B, V, R, and I band data. We found optical spectral indices in the range of 0.878+-0.029 to 1.106+-0.065 by fitting a power law to these SEDs of PG 1553+113. We found that the source follows a bluer-when-brighter trend on IDV timescales. We discuss possible physical causes of the observed spectral variability.

Blazars are active galactic nuclei (AGN) with relativistic jets whose non-thermal radiation is extremely variable on various timescales1-3. This variability seems mostly random, although some quasi-periodic oscillations (QPOs), implying systematic processes, have been reported in blazars and other AGN. QPOs with timescales of days or hours are especially rare4 in AGN and their nature is highly debated, explained by emitting plasma moving helically inside the jet5, plasma instabilities6,7 or orbital motion in an accretion disc7,8. Here we report results of intense optical and γ-ray flux monitoring of BL Lacertae (BL Lac) during a dramatic outburst in 2020 (ref. 9). BL Lac, the prototype of a subclass of blazars10, is powered by a 1.7 × 108 MSun (ref. 11) black hole in an elliptical galaxy (distance = 313 megaparsecs (ref. 12)). Our observations show QPOs of optical flux and linear polarization, and γ-ray flux, with cycles as short as approximately 13 h during the highest state of the outburst. The QPO properties match the expectations of current-driven kink instabilities6 near a recollimation shock about 5 parsecs (pc) from the black hole in the wake of an apparent superluminal feature moving down the jet. Such a kink is apparent in a microwave Very Long Baseline Array (VLBA) image.

Variability is one of the main observational characteristics of blazars. Studying variability is an efficient method to reveal the nature of active galactic nuclei. In the present work, we report optical R-band photometry observations of a TeV blazar, 1ES 2344 + 514, carried out with a 70 cm telescope in the period of 1998 July–2017 November at Abastumani Observatory, Georgia. Based on the optical R-band observations, the optical variation behaviors on both short timescales and long timescales are investigated. Three methods (Jurkevich, discrete correlation function, and power spectrum analysis) are used to investigate periodicity in the light curve. In addition, combined with multiwavelength data, the jet physical properties are discussed. The following conclusions are drawn: (1) A variability of ΔR = 0.155 mag (15.356 − 15.201 mag) over a timescale of ΔT = 12.99 minutes is detected during our 628 days of monitoring. (2) According to the Kelvin–Helmholtz thermal instability, if the magnetic field intensity (B) for the source is greater than a critical value (B c ), it will reduce the incidence of intraday variations in the light curves. (3) The physical parameters of the dissipation region are obtained by fitting the spectral energy distribution with a one-zone synchrotron self-Compton model for the average and flare states. (4) The three methods show that there are periods of P = 2.72 ± 0.47 yr, P = 1.61 ± 0.18 yr, P = 1.31 ± 0.17 yr, and P = 1.05 ± 0.07 yr. When a binary black hole system is adopted with a period of P = 2.72 ± 0.41 yr, we obtain the orbital parameters for the binary black hole system as follows: M = 8.08 × 109 M ⊙, the sum of the semiaxes is r = 7.18 × 1016 cm, and the lifetime of the binary black hole is τ merge = 6.24 × 102 yr.

ABSTRACT Blazar S5 0716+714 is well-known for its short-term variability, down to intraday time-scales. We here present the 2-min cadence optical light curve obtained by the TESS space telescope in 2019 December–2020 January and analyse the object fast variability with unprecedented sampling. Supporting observations by the Whole Earth Blazar Telescope Collaboration in B, V, R, and I bands allow us to investigate the spectral variability during the TESS pointing. The spectral analysis is further extended in frequency to the UV and X-ray bands with data from the Neil Gehrels Swift Observatory. We develop a new method to unveil the shortest optical variability time-scales. This is based on progressive de-trending of the TESS light curve by means of cubic spline interpolations through the binned fluxes, with decreasing time bins. The de-trended light curves are then analysed with classical tools for time-series analysis (periodogram, autocorrelation, and structure functions). The results show that below 3 d there are significant characteristic variability time-scales of about 1.7, 0.5, and 0.2 d. Variability on time-scales $\lesssim 0.2$ d is strongly chromatic and must be ascribed to intrinsic energetic processes involving emitting regions, likely jet substructures, with dimension less than about 10−3 pc. In contrast, flux changes on time-scales $\gtrsim 0.5$ d are quasi-achromatic and are probably due to Doppler factor changes of geometric origin.

Among active galactic nuclei, blazars show extreme variability properties. We here investigate the case of the BL Lac object S4 0954+65 with data acquired in 2019-2020 by the Transiting Exoplanet Survey Satellite (TESS) and by the Whole Earth Blazar Telescope (WEBT) Collaboration. The 2-min cadence optical light curves provided by TESS during three observing sectors of nearly one month each, allow us to study the fast variability in great detail. We identify several characteristic short-term time-scales, ranging from a few hours to a few days. However, these are not persistent, as they differ in the various TESS sectors. The long-term photometric and polarimetric optical and radio monitoring undertaken by the WEBT brings significant additional information, revealing that i) in the optical, long-term flux changes are almost achromatic, while the short-term ones are strongly chromatic; ii) the radio flux variations at 37 GHz follow those in the optical with a delay of about three weeks; iii) the range of variation of the polarization degree and angle is much larger in the optical than in the radio band, but the mean polarization angles are similar; iv) the optical long-term variability is characterized by a quasi-periodicity of about one month. We explain the source behaviour in terms of a rotating inhomogeneous helical jet, whose pitch angle can change in time.

Aims. We present a detailed characterisation and theoretical interpretation of the broadband emission of the paradigmatic TeV blazar Mrk 421, with a special focus on the multi-band flux correlations. Methods. The dataset has been collected through an extensive multi-wavelength campaign organised between 2016 December and 2017 June. The instruments involved are MAGIC, FACT, Fermi -LAT, Swift , GASP-WEBT, OVRO, Medicina, and Metsähovi. Additionally, four deep exposures (several hours long) with simultaneous MAGIC and NuSTAR observations allowed a precise measurement of the falling segments of the two spectral components. Results. The very-high-energy (VHE; E > 100 GeV) gamma rays and X-rays are positively correlated at zero time lag, but the strength and characteristics of the correlation change substantially across the various energy bands probed. The VHE versus X-ray fluxes follow different patterns, partly due to substantial changes in the Compton dominance for a few days without a simultaneous increase in the X-ray flux (i.e., orphan gamma-ray activity). Studying the broadband spectral energy distribution (SED) during the days including NuSTAR observations, we show that these changes can be explained within a one-zone leptonic model with a blob that increases its size over time. The peak frequency of the synchrotron bump varies by two orders of magnitude throughout the campaign. Our multi-band correlation study also hints at an anti-correlation between UV-optical and X-ray at a significance higher than 3 σ . A VHE flare observed on MJD 57788 (2017 February 4) shows gamma-ray variability on multi-hour timescales, with a factor ten increase in the TeV flux but only a moderate increase in the keV flux. The related broadband SED is better described by a two-zone leptonic scenario rather than by a one-zone scenario. We find that the flare can be produced by the appearance of a compact second blob populated by high energetic electrons spanning a narrow range of Lorentz factors, from γ ′ min =2×10 4 to γ ′ max =6×10 5 .

In this work, we present 8523 pairs of R -band optical photometry observations for the quasar 3C 454.3 made during the period of 2006 October–2018 February on the 70 cm meniscus telescope at Abastumani Observatory, Georgia, to study its intraday variabilities (IDVs) and long-term variations, and we have come to the following results. (1) We detected 10 outbursts, a Δ R = 3.825 mag variation, and some IDVs. The IDV timescales are from 4.1 to 285 minutes, with the corresponding variability amplitude being A = 2.9%–43.67%. The amplitude increases with IDV timescale. (2) The largest variation over a 1 day timescale is Δ R = 1.38 mag. (3) The IDV timescales suggest that the emission sizes are from 8.9 × 10 13 cm to 6.20 × 10 15 cm, and the magnetic field strengths are B = 0.18–0.79 G. (4) Period analysis results show three possible long-term periods, p = 3.04 ± 0.02 yr, p = 1.66 ± 0.06 yr, and p = 1.20 ± 0.03 yr in the optical light curve. We adopted the accretion disk models and the lighthouse models to period p = 3.04 ± 0.02 yr: in the accretion disk models, the binary black holes have masses M = 1.17 × 10 9 M ⊙ ; in the lighthouse models, we used two boosted jet flux densities to fit the observational light curve. (5) WWZ analysis gives some short-period (high-frequency) signals associated with strong bursts (JD 2,454,302 and JD 2,454,521) with variable frequencies and lasting for the entire observation time span (11.3 yr).