arXiv subjects

M. Villata

Publications and source records attributed to M. Villata.

At least 19 recordsLinked to original sources

arXiv2026

Detection of optical quasi-periodic oscillation in the blazar 3C 454.3

We analyzed 19 years of $R$-band data of the blazar 3C 454.3 from the Whole Earth Blazar Telescope (WEBT) archive, along with new data from its members and from public archives such as those provided by the Small and Moderate Aperture Research Telescope System (SMARTS) and the Steward Observatory projects to search for quasi-periodic oscillations (QPOs). We detected a QPO of $\sim$ 433 days using Lomb-Scargle periodogram, which lasted from MJD 54980--58450 as detected by the weighted wavelet Z-transform technique, making it one of the most persistent QPOs ever detected in the optical regime. The phase dispersion minimization technique was also performed to further validate this QPO claim. We detected this signal at a global significance of $2.53\sigma$ across all methodologies. To explain the observed QPO, we have considered both models focused on the accretion disk around the super-massive black hole (SMBH), and those based purely on jet emissions. Plausible jet-based models involve a shock moving down the jet in a helical magnetic field, whereas the SMBH models could involve Lense-Thirring effect-induced jet precession or dual jets in a binary SMBH system. We introduce a novel approach to distinguish genuine QPOs from spurious signals arising from annual seasonal gaps, a common limitation of ground-based observations.

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arXiv2025

Multiband optical variability on diverse timescales of the blazar Ton 599 from 2011 to 2023

(Shortened)Context: We analyze the optical variability of the FSRQ Ton 599 using BVRI photometry from the WEBT collaboration (2011-2023), complemented by photometric and spectroscopic data from the Steward Observatory.\\ Aims: To characterize short- and long-term optical variability -- including flux distributions, intranight changes, color evolution, and spectra -- to constrain physical parameters and processes in the central engine.\\ Methods: We tested flux distributions in each filter against normal and log-normal, explored the RMS-flux relation and derived PSDs. We quantified intranight variability using a $\chi^2$ test and fractional variability. From variability timescales, we estimated the emitting region size and magnetic field. Long-term variability was studied by segmenting the light curve into 12 intervals and analyzing flux statistics. For multi-filter flares, we computed spectral slopes, redshift-corrected fluxes, monochromatic luminosities and generated Color-magnitude and color-time diagrams. From low-flux spectra, we measured Mg II line and estimated the black hole mass.\\ Results: Ton 599 showed strong optical variability. Log-normal distributions fit the fluxes better, and all bands show a positive RMS-flux relation with red-noise PSDs.Intranight variability is detected, and used in constraining the emission region and magnetic field.The R band reaches a peak flux of 23.5 mJy, corresponding to a monochromatic luminosity of $log({\nu}L{\nu})= 48.48 [erg/s]$. We found a redder-when-brighter trend at low fluxes (thermal), achromatic behavior at intermediate levels (possibly due to jet orientation changes), and a bluer-when-brighter trend at high fluxes (synchrotron). Long-term color changes are modest, short-term are significant, with a negative correlation between the amplitude of color changes and the average flux. The estimated SMBH mass is order of $10^8 M_\odot$.

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arXiv2025

Twenty years of blazar monitoring with the INAF radio telescopes

The extreme variability of blazars, in both timescale and amplitude, is generally explained as the effect of a relativistic jet closely aligned to the observer's line-of-sight. Due to causality arguments, variability characteristics translate into spatial information about the emitting region of blazars. Since radiation at different wavelengths is emitted in different parts of the jet, multi-frequency observations provide us with a virtual view of the structure of the jet on different scales. Radio--gamma-ray correlations, moreover, are essential to reveal where and how the high-energy radiation is produced. We present here the observations collected within the blazar radio monitoring program that we are running at the Medicina and Noto telescopes. It aims at investigating how the variability characteristics and spectral energy distribution of blazars evolve in time. Since 2004, observation have been performed at 5, 8, 24, and 43 GHz on 47 targets, with monthly cadence; the monitoring program is still active at frequencies of 8 and 24 GHz. The database we built in more than twenty years of activity comprises to date about 21000 flux density measurements. Some basic analysis tools have been applied to the data to characterise the detected variability and offer a first glance at the wealth of information that such a program can provide about blazars.

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arXiv2024

Multiband Optical Variability of the Blazar 3C 454.3 on Diverse Timescales

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 $\sim$ 2 decades. We include data from WEBT collaborators and public archives such as SMARTS, Steward Observatory, and ZTF. 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 (RWB) trend, which, however, stabilizes at a particular brightness cutoff $\sim$ 14.5 mag in the I-band, after which it saturates and evolves into a complex state. This trend indicates increasing jet emission dominance over accretion disk emission until jet emission completely dominates. Plots of the spectral index variation (following $F_{\nu} \propto \nu^{-\alpha}$) 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 quiescent or low flux state, which are respectively jet and accretion disk dominated. We have also conducted intra-day variability studies of nine light curves and found that six of them are variable. Discrete Correlation Function (DCF) analysis between different optical waveband pairs peak at zero lags, indicating co-spatial emission in different optical bands.

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arXiv2024

Multi-wavelength picture of the misaligned BL Lac object 3C 371

The BL Lac object 3C 371 is one of the targets that are regularly monitored by the Whole Earth Blazar Telescope (WEBT) Collaboration to study blazar variability on both short and long timescales. We aim to evaluate the long-term multiwavelength (MWL) behaviour of 3C 371, comparing it with the results derived for its optical emission in our previous study. For this, we make use of the multi-band campaigns organized 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. We evaluate the variability shown by the source in each band with the amplitude variability quantification, as well as possible interband 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 perform a kinematics analysis, looking for components propagating along the jet, calculating its kinematics parameters. This set of parameters is later used for the interpretation of the source MWL behaviour, modelling the broadband spectral energy distribution (SED) of the source with theoretical blazar emission scenarios.

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arXiv2024

A wiggling filamentary jet at the origin of the blazar multi-wavelength behaviour

Blazars are beamed active galactic nuclei known for their strong multi-wavelength variability on timescales from years down to minutes. 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. 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. 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. 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.

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arXiv2024

Optical variability of the blazar 3C 371: from minute to year timescales

The BL Lac object 3C 371 has been observed by the Transiting Exoplanet Survey Satellite (\textit{TESS}) for approximately a year, between July 2019 and July 2020, with an unmatched 2-minute observing 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. The goal of this study is evaluating the optical variability of 3C 371. Taking advantage of the remarkable cadence of \textit{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 is used to investigate long-term variability (LTV), including understanding spectral behaviour of the source and the polarization variability. Based on the derived characteristics, information on the origin of the variability on different timescales is extracted. We evaluated the variability applying the variability amplitude tool that quantifies how variable the emission is. Moreover, we employed common tools like 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. Short- and long-term colour behaviours have been evaluated to understand the spectral behaviour of the source. The polarized emission was analyzed, studying its variability and possible rotation patterns of the electric vector position angle (EVPA). Flux distributions of IDV and LTV were also studied with the aim of linking the flux variations to turbulent and/or accretion disc related processes.

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arXiv2023

Extreme photometric and polarimetric variability of blazar S4 0954+65 at its maximum optical and $\gamma$-ray brightness levels

In 2022 the BL Lac object S4 0954+65 underwent a major variability phase, reaching its historical maximum brightness in the optical and $\gamma$-ray bands. We present optical photometric and polarimetric data acquired by the Whole Earth Blazar Telescope (WEBT) Collaboration from 2022 April 6 to July 6. Many episodes of unprecedented fast variability were detected, implying an upper limit to the size of the emitting region as low as $10^{-4}$ parsec. The WEBT data show rapid variability in both the degree and angle of polarization. We analyse different models to explain the polarization behaviour in the framework of a twisting jet model, which assumes that the long-term trend of the flux is produced by variations in the emitting region viewing angle. All the models can reproduce the average trend of the polarization degree, and can account for its general anticorrelation with the flux, but the dispersion of the data requires the presence of intrinsic mechanisms, such as turbulence, shocks, or magnetic reconnection. The WEBT optical data are compared to $\gamma$-ray data from the Fermi satellite. These are analysed with both fixed and adaptive binning procedures. We show that the strong correlation between optical and $\gamma$-ray data without measurable delay assumes different slopes in faint and high brightness states, and this is compatible with a scenario where in faint states we mainly see the imprint of the geometrical effects, while in bright states the synchrotron self-Compton process dominates.

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arXiv2023

The optical behaviour of BL Lacertae at its maximum brightness levels: a blend of geometry and energetics

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.

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arXiv2022

Multiwavelength periodicity search in a sample of $γ$-ray bright blazars

We present the results of a long-term periodicity search in a sample of $γ$-ray blazars within a multiwavelength context. These blazars have been selected from the Steward Observatory sample as part of its optical monitoring program between 2008 and 2018. We study 15 sources with a temporal coverage in their optical total and polarized emission sufficiently large ($>9$ years) to perform a reliable long-term periodicity analysis. We collect data from several observatories to extend the coverage, enabling the search of longer periods. In addition, data are also gathered in the high-energy ($E>100$ MeV) $γ$-ray band from the $\textit{Fermi}$ Large Area Telescope; and in the 15-GHz radio band from the Owens Valley Radio Observatory. We identify 5 promising candidates to host quasi-periodic emission, AO 0235+164, PKS 1222+216, Mrk 501, BL Lacertae and 1ES 2344+514 with periods in one or more bands and statistical significances $\sim$3$σ$ after trial factor correction. AO 0235+164 shows a period of $\sim$8.2 years in the R band; PKS 1222+216 has a quasi-periodic modulation in its total and polarized optical emission of $\sim$1.6 years; Mrk 501 displays a $\sim$5-year quasi-periodicity in optical and radio wavelengths; BL Lacertae presents a period of $\sim$1.8 years in its polarized emission; and 1ES 2344+514 shows a hint of a $\sim$5.5-year period in its optical R band. We interpret these results in the framework of the most common models and scenarios, namely the presence of a binary supermassive black hole system; or geometrical effects like helical or precessing jets.

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arXiv2021

The complex variability of blazars: Time-scales and periodicity analysis in S4 0954+65

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.

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arXiv2020

The dual nature of blazar fast variability. Space and ground observations of S5 0716+714

Blazar S5 0716+714 is well-known for its short-term variability, down to intra-day 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, auto-correlation 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 < 0.2 d is strongly chromatic and must be ascribed to intrinsic energetic processes involving emitting regions, likely jet sub-structures, with dimension less than about milliparsec. In contrast, flux changes on time-scales > 0.5 d are quasi-achromatic and are probably due to Doppler factor changes of geometric origin.

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arXiv2020

Multi-Wavelength Variability of BL Lacertae Measured with High Time Resolution

In an effort to locate the sites of emission at different frequencies and physical processes causing variability in blazar jets, we have obtained high time-resolution observations of BL Lacertae over a wide wavelength range: with the \emph{Transiting Exoplanet Survey Satellite} (TESS) at 6,000-10,000 Å with 2-minute cadence; with the Neil Gehrels \emph{Swift} satellite at optical, UV, and X-ray bands; with the Nuclear Spectroscopic Telescope Array at hard X-ray bands; with the \emph{Fermi} Large Area Telescope at $γ$-ray energies; and with the Whole Earth Blazar Telescope for measurement of the optical flux density and polarization. All light curves are correlated, with similar structure on timescales from hours to days. The shortest timescale of variability at optical frequencies observed with TESS is $\sim 0.5$ hr. The most common timescale is $13\pm1$~hr, comparable with the minimum timescale of X-ray variability, 14.5 hr. The multi-wavelength variability properties cannot be explained by a change solely in the Doppler factor of the emitting plasma. The polarization behavior implies that there are both ordered and turbulent components to the magnetic field in the jet. Correlation analysis indicates that the X-ray variations lag behind the $γ$-ray and optical light curves by up to $\sim 0.4$ days. The timescales of variability, cross-frequency lags, and polarization properties can be explained by turbulent plasma that is energized by a shock in the jet and subsequently loses energy to synchrotron and inverse Compton radiation in a magnetic field of strength $\sim3$ G

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arXiv2020

A New Multi-Wavelength Census of Blazars

Context:Blazars are the rarest and most powerful active galactic nuclei, playing a crucial and growing role in today multi-frequency and multi-messenger astrophysics. Current blazar catalogs, however, are incomplete and particularly depleted at low Galactic latitudes. Aims: We aim at augmenting the current blazar census to build a catalog of blazar candidates with homogeneous sky coverage that can provide candidate counterparts to unassociated gamma-ray sources, sources of high-energy neutrino emission, and ultra-high energy cosmic rays. Methods: Starting from the ALMA Calibrator Catalog we built a catalog of 1580 blazar candidates (ALMA Blazar Candidates, ABC) for which we collect multi-wavelength information. We also compared ABC sources with existing blazar catalogs. Results: The ABC catalogue fills the lack of low Galactic latitude sources in current blazar catalogues. ABC sources are significantly dimmer than known blazars in Gaia g band, and they appear bluer in SDSS and WISE colors. The majority of ABC sources (~ 90%) have optical spectra that classify them as QSO, while the remaining sources resulted galactic objects. ABC sources are similar in X-rays to known blazar, while in gamma-rays they are on average dimmer and softer, indicating a significant contribution of FSRQ sources. Making use of WISE colours, we classified 715 ABC sources as candidate gamma-ray blazar of different classes. Conclusions: We built a new catalogue of 1580 candidate blazars with a rich multi-wavelength data-set, filling the lack of low Galactic latitude sources in current blazar catalogues. This will be particularly important to identify the source population of high energy neutrinos or ultra-high energy cosmic rays. The data collected by the upcoming LSST surveys will provide a key tool to investigate the possible blazar nature of these sources.

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arXiv2020

Unveiling the monster heart: unbeamed properties of blazar 4C 71.07

4C 71.07 is a high-redshift blazar whose optical radiation is dominated by quasar-like nuclear emission. We here present the results of a spectroscopic monitoring of the source to study its unbeamed properties. We obtained 24 optical spectra at the Nordic Optical Telescope (NOT) and William Herschel Telescope (WHT) and 3 near-infrared spectra at the Telescopio Nazionale Galileo (TNG). They show no evidence of narrow emission lines. The estimate of the systemic redshift from the H$β$ and H$α$ broad emission lines leads to $z_{\rm sys}=2.2130 \pm 0.0004$. Notwithstanding the nearly face-on orientation of the accretion disc, the high-ionization emission lines present large broadening as well as noticeable blueshifts, which increase with the ionizing energy of the corresponding species. This is a clear indication of strong ionized outflows. Line broadening and blueshift appear correlated. We applied scaling relationships to estimate the mass of the supermassive black hole from the Balmer and C IV lines, taking into account the prescriptions to correct for outflow. They give $M_{\rm BH} \sim 2 \times 10^9 \, M_\odot$. We derived an Eddington luminosity $L_{\rm Edd} \sim 2.5 \times 10^{47} \rm \, erg \, s^{-1}$ $\sim L_{\rm disc}$, and a broad line region luminosity $L_{\rm BLR} \sim 1.5 \times 10^{46} \rm \, erg \, s^{-1}$. The line fluxes do not show significant variability in time. In particular, there is no line reaction to the jet flaring activity detected in 2015 October and November. This implies that the jet gives no contribution to the photoionization of the broad line region in the considered period.

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arXiv2020

Quasi-periodic behaviour in the optical and γ-ray light curves of blazars 3C 66A and B2 1633+38

We report on quasi-periodic variability found in two blazars included in the Steward Observatory Blazar Monitoring data sample: the BL Lac object 3C 66A and the Flat Spectrum Radio Quasar B2 1633+38. We collect optical photometric and polarimetric data in V and R bands of these sources from different observatories: St. Petersburg University, Crimean Astrophysical Observatory, WEBT-GASP, Catalina Real-Time Transient Survey, Steward Observatory, STELLA Robotic Observatory and Katzman Automatic Imaging Telescope. In addition, an analysis of the $γ$-ray light curves from $\textit{Fermi}$-LAT is included. Three methods are used to search for any periodic behaviour in the data: the Z-transform Discrete Correlation Function, the Lomb-Scargle periodogram and the Weighted Wavelet Z-transform. We find evidences of possible quasi-periodic variability in the optical photometric data of both sources with periods of $\sim$3 years for 3C 66A and $\sim$1.9 years for B2 1633+38, with significances between 3$σ$ and 5$σ$. Only B2 1633+38 shows evidence of this behaviour in the optical polarized data set at a confidence level of 2$σ$-4$σ$. This is the first reported evidence of quasi-periodic behaviour in the optical light curve of B2 1633+38. Also a hint of quasi-periodic behaviour is found in the $γ$-ray light curve of B2 1633+38 with a confidence level $\geqslant$2$σ$, while no periodicity is observed for 3C 66A in this energy range. We propose different jet emission models that could explain the quasi-periodic variability and the differences found between these two sources.

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arXiv2020

Multiwavelength behaviour of the blazar 3C279: decade-long study from $γ$-ray to radio

We report the results of decade-long (2008-2018) $γ$-ray to 1 GHz radio monitoring of the blazar 3C 279, including GASP/WEBT, $\it{Fermi}$ and $\it{Swift}$ data, as well as polarimetric and spectroscopic data. The X-ray and $γ$-ray light curves correlate well, with no delay > 3 hours, implying general co-spatiality of the emission regions. The $γ$-ray-optical flux-flux relation changes with activity state, ranging from a linear to a more complex dependence. The behaviour of the Stokes parameters at optical and radio wavelengths, including 43 GHz VLBA images, supports either a predominantly helical magnetic field or motion of the radiating plasma along a spiral path. Apparent speeds of emission knots range from 10 to 37c, with the highest values requiring bulk Lorentz factors close to those needed to explain $γ$-ray variability on very short time scales. The Mg II emission line flux in the `blue' and `red' wings correlates with the optical synchrotron continuum flux density, possibly providing a variable source of seed photons for inverse Compton scattering. In the radio bands we find progressive delays of the most prominent light curve maxima with decreasing frequency, as expected from the frequency dependence of the $τ=1$ surface of synchrotron self-absorption. The global maximum in the 86 GHz light curve becomes less prominent at lower frequencies, while a local maximum, appearing in 2014, strengthens toward decreasing frequencies, becoming pronounced at $\sim5$ GHz. These tendencies suggest different Doppler boosting of stratified radio-emitting zones in the jet.

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arXiv2019

Investigating the multiwavelength behaviour of the flat spectrum radio quasar CTA 102 during 2013-2017

We present a multiwavelength study of the flat-spectrum radio quasar CTA 102 during 2013-2017. We use radio-to-optical data obtained by the Whole Earth Blazar Telescope, 15 GHz data from the Owens Valley Radio Observatory, 91 and 103 GHz data from the Atacama Large Millimeter Array, near-infrared data from the Rapid Eye Monitor telescope, as well as data from the Swift (optical-UV and X-rays) and Fermi ($γ$ rays) satellites to study flux and spectral variability and the correlation between flux changes at different wavelengths. Unprecedented $γ$-ray flaring activity was observed during 2016 November-2017 February, with four major outbursts. A peak flux of (2158 $\pm$ 63)$\times$10$^{-8}$ ph cm$^{-2}$ s$^{-1}$, corresponding to a luminosity of (2.2 $\pm$ 0.1)$\times$10$^{50}$ erg s$^{-1}$, was reached on 2016 December 28. These four $γ$-ray outbursts have corresponding events in the near-infrared, optical, and UV bands, with the peaks observed at the same time. A general agreement between X-ray and $γ$-ray activity is found. The $γ$-ray flux variations show a general, strong correlation with the optical ones with no time lag between the two bands and a comparable variability amplitude. This $γ$-ray/optical relationship is in agreement with the geometrical model that has successfully explained the low-energy flux and spectral behaviour, suggesting that the long-term flux variations are mainly due to changes in the Doppler factor produced by variations of the viewing angle of the emitting regions. The difference in behaviour between radio and higher energy emission would be ascribed to different viewing angles of the jet regions producing their emission.

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