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Rapid quasi-periodic oscillations in the relativistic jet of BL Lacertae


Blazars are active galactic nuclei (AGN) with relativistic jets whose non-thermal radiation is extremely variable on various timescales1,2,3. 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.

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Fig. 1: Optical R-band light curves.
Fig. 2: Model-data comparison.
Fig. 3: Parsec-scale jet of BL Lac.
Fig. 4: Sketch of the development of the QPOs.

Data availability

The data taken and assembled by the WEBT collaboration are stored in the WEBT archive at the Osservatorio Astrofisico di Torino, INAF ( The published data are available on request to the WEBT President, Massimo Villata (

Code availability

The computer code used in this study is available in the Zenodo repository:; license:


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We dedicate this paper to Dr. Valeri M. Larionov, who was a prominent member of the WEBT collaboration. The research reported here is based on work supported in part by US National Science Foundation grants AST-2108622 and AST-2107806, and NASA Fermi GI grants 80NSSC20K1567, 80NSSC21K1917 and 80NSSC21K1951; by Shota Rustaveli National Science Foundation of Georgia under contract FR-19-6174; by the Bulgarian National Science Fund of the Ministry of Education and Science under grants DN 18-10/2017, DN 18-13/2017, KP-06-H28/3 (2018), KP-06-H38/4 (2019) and KP-06-KITAJ/2 (2020), and by National RI Roadmap Project D01-383/18.12.2020 of the Ministry of Education and Science of the Republic of Bulgaria; by JSPS KAKENHI grant #19K03930 of Japan; by the Ministry of Education, Science and Technological Development of the Republic of Serbia (contract 451-03-9/2021-14/200002) and observing grant support from the Institute of Astronomy and Rozhen NAO BAS through the bilateral joint research project ‘Gaia Celestial Reference Frame (CRF) and fast variable astronomical objects’; by the Agenzia Spaziale Italiana (ASI) through contracts I/037/08/0, I/058/10/0, 2014-025-R.0, 2014-025-R.1.2015 and 2018-24-HH.0 to the Italian Istituto Nazionale di Astrofisica (INAF). H.Z. is supported by the NASA Postdoctoral Program at Goddard Space Flight Center, administered by ORAU. M.V.P. is partially supported by the Russian Foundation for Basic Research grant 20-02-00490. G.B. acknowledges support from the State Agency for Research of the Spanish MCIU through the ‘Center of Excellence Severo Ochoa’ award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) and from the Spanish ‘Ministerio de Ciencia e Innovacíon’ (MICINN) through grant PID2019-107847RB-C44. M.D.J. thanks the Brigham Young University Department of Physics and Astronomy for continued support of the extragalactic monitoring programme under way at the West Mountain Observatory. R.C. thanks ISRO for support under the AstroSat archival data utilization programme and BRNS for support through a project grant (sanction no. 57/14/10/2019-BRNS). The measurements at the Hans Haffner Observatory, Hettstadt, Germany, were supported by Baader Planetarium, Mammendorf, Germany. This study was based (in part) on observations conducted using the 1.8-m Perkins Telescope Observatory (PTO) in Arizona, USA, which is owned and operated by Boston University. These results made use of the Lowell Discovery Telescope (LDT) at Lowell Observatory. Lowell Observatory is a private, non-profit institution dedicated to astrophysical research and public appreciation of astronomy, and operates the LDT in partnership with Boston University, the University of Maryland and the University of Toledo. This paper is partly based on observations made with the IAC-80 operated on the island of Tenerife by the Instituto de Astrofisica de Canarias in the Spanish Observatorio del Teide and on observations made with the LCOGT telescopes, one of whose nodes is located at the Observatorios de Canarias del IAC on the island of Tenerife in the Observatorio del Teide. This paper is partly based on observations made with the Nordic Optical Telescope, owned in collaboration by the University of Turku and Aarhus University, and operated jointly by Aarhus University, the University of Turku and the University of Oslo, representing Denmark, Finland and Norway, the University of Iceland and Stockholm University at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofisica de Canarias. The VLBA is an instrument of the NRAO, USA. The NRAO is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

Author information

Authors and Affiliations



S.G.J.: developing and writing the paper, optical and VLBA observations and data reduction, periodicity analysis, data modelling; A.P.M.: VLBA observations and analysis, theoretical modelling, writing the paper; C.M.R. and M.V.: WEBT coordinators, optical data assembling, REDFIT analysis, writing the paper; Z.R.W.: optical observations and transformations, correlation analysis and simulation of light curves, WWZ analysis, VLBA image modelling, writing the paper; H.Z.: kink instability model development and application, theoretical model writing; L.D.: kink instability model development and application; J.L.G.: VLBA data imaging; M.V.P.: CWT analysis; S.S.S.: optical observations, γ-ray data reduction and description; V.M.L.: optical data reduction and WEBT data assembling; R.C.: power spectral response method analysis; V.M.L., D.C., W.P.C., O.M.K., A.M., K.Matsumoto and F.M.: leaders of observational groups that contributed more than 1,000 measurements to the optical datasets; the rest of the authors are members of the WEBT collaboration and have contributed to the paper by providing results of optical observations.

Corresponding author

Correspondence to S. G. Jorstad.

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Extended data figures and tables

Extended Data Fig. 1 BL Lac R-band optical and γ-ray data in 2020.

a, R-band flux density light curve (n = 16,497). The solid magenta curve during the outburst plots a spline approximation of the long-term trend. b, Degree of polarization versus time (n = 1,285). c, Position angle of polarization versus time (n = 1,285). The red and blue dotted lines mark directions along and transverse to the jet axis, respectively. d, γ-Ray light curve (n = 1,398). The grey area denotes the 1σ uncertainty in the time of ejection of superluminal knot K (dotted grey line). Different symbols and colours indicate observations conducted by different telescopes, designations of which are given in Extended Data Table 1. The error bars are 1σ uncertainties (in plot a, they are smaller than the symbols).

Extended Data Fig. 2 Correlation analysis.

a, z-Transformed discrete correlation function correlations between the γ-ray and R-band light curves for the entire dataset (black), between the γ-ray flux and R-band flux density residuals (blue) and between the theoretical γ-ray and R-band light curves (red) during the highest outburst state shown in Fig. 2. b, z-Transformed discrete correlation function correlations between the R-band flux density and degree of polarization for similar periods as in plot a. The dotted red horizontal lines correspond to 3σ probability of chance occurrence.

Extended Data Fig. 3 VLBA total-intensity images of BL Lac at 43 GHz.

The global intensity peak is 3.148 Jy beam−1 and contour levels start at 0.4% of the peak, then increase by factors of √2. Images are convolved with a circular beam of radius 0.1 mas (bottom-left circle). The coloured circles represent the FWHM areas of Gaussian components used to model the intensity distribution at each epoch, with colours matching those in Fig. 3b.

Extended Data Fig. 4 REDFIT periodograms.

a, For optical flux densities. b, For γ-ray fluxes. c, For degree of polarization. The black curves show the corrected periodograms; the blue lines represent the theoretical red-noise spectra; the red lines mark the 99% (solid) and 95% (dashed) significance levels. The periods corresponding to the most significant peaks, touching or exceeding the 99% levels, are indicated.

Extended Data Fig. 5 CWT magnitude scalograms.

For the R-band light curve (a), the γ-ray light curve (b) and the fractional polarization curve (c). Black contours in a and b indicate periods significant at the 99% level; grey contours in c indicate periods significant at the 92% level. Dashed white curves represent a cone of influence (COI), in which the information outside is affected by edge artefacts; numbers near contours indicate some periods for clarity.

Extended Data Fig. 6 WWZ transforms.

For the R-band light curve (a), the γ-ray light curve (b) and the fractional polarization curve (c). Dashed black curves indicate periods significant at the 99% level; numbers near contours indicate some periods for clarity.

Extended Data Fig. 7 QPOs in optical R-band flux density.

a, Oscillations in optical R-band flux density during the outburst over the time interval 13 August 2020 to 18 September 2020 (n = 8,106), with the long-term trend subtracted. For comparison, the red curve represents a sinusoidal function with a period of 0.55 days and an amplitude of 20 mJy. b, Average profile of the optical flux density pulse (solid red curve). different colours indicate different pulses (2, 5, 7, 8, 9 and 12, as numbered in Fig. 1b). c, Average profile (solid black curve) of fractional polarization pulses (colour symbols), each normalized by its maximum, and normalized average profile of R-band flux density pulse (solid red curve). In all plots, error bars represent 1σ uncertainties.

Extended Data Fig. 8 MCMC model parameters.

a, Triangle plot of posterior distributions of model parameters, sampled from 64 walkers with 60,000 iterations through MCMC; dashed lines in the histogram represent 16%, 50% and 84% quantiles, respectively (from left to right), for each parameter (see Methods). be, Distributions of residuals between the data and the model presented in Fig. 2 for R-band flux density (b), degree (c) and position angle (d) of polarization, and γ-ray flux (e).

Extended Data Table 1 Optical telescopes

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Jorstad, S.G., Marscher, A.P., Raiteri, C.M. et al. Rapid quasi-periodic oscillations in the relativistic jet of BL Lacertae. Nature 609, 265–268 (2022).

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