Context. The TeV BL Lac object PG 1553+113 is one of the primary candidates for a binary supermassive black hole system. Aims. We study the flux and spectral variability of PG 1553+113 on intra-night to long-term timescales using (i) BVRI data collected over 76 nights from January 2016 to August 2019 involving nine optical telescopes and (ii) historical VR data (including ours) obtained for the period from 2005 to 2019. Methods. We analysed the light curves using various statistical tests, fitting and cross-correlation techniques, and methods for the search for periodicity. We examined the colour-magnitude diagrams before and after the corresponding light curves were corrected for the long-term variations. Results. Our intra-night monitoring, supplemented with literature data, result in a low duty cycle of ∼(10–18)%. In April 2019, we recorded a flare, which marks the brightest state of PG 1553+113 for the period from 2005 to 2019: R ≃ 13.2 mag. This flare is found to show a clockwise spectral hysteresis loop on its VR colour-magnitude diagram and a time lag in the sense that the V-band variations lead the R-band ones. We obtain estimates of the radius, the magnetic field strength, and the electron energy that characterize the emission region related to the flare. We find a median period of (2.21 ± 0.04) years using the historical light curves. In addition, we detect a secondary period of about 210 days using the historical light curves corrected for the long-term variations. We briefly discuss the possible origin of this period.

We present here the detection of a possible quasi-periodic oscillation (QPO) signal in the X-ray light curve of the active galactic nucleus 3C 120, a broad line radio galaxy at z = 0.033. The hint of a QPO at the 3σ level at 7.1 × 10−6 Hz (∼1.65 days) was detected based on the analysis of X-ray data acquired in the 3–79 keV band by the Nuclear Spectroscopic Telescope Array (NuSTAR). The data, when processed separately in the soft (3–10 keV), hard (10–79 keV) and the total (3–79 keV) bands using four different techniques, namely discrete correlation function, Lomb Scargle periodogram, structure–function, and power spectral density indicated the presence of a QPO. 3C 120 very well fits in the negative correlation in the frequency of the QPO versus the black hole mass (FQPO versus MBH) diagram known for stellar-mass and supermassive black hole sources. Considering the observed signs of QPO to represent the innermost stable orbit of the accretion disk, we found a black hole mass of 1.9×109 M⊙ for a Kerr black hole and 3.04×108 M⊙ for a Schwarzschild black hole. This deduced black hole mass from QPO measurement is a few times larger than the black hole mass obtained from reverberation mapping observations.

We present an analysis of the BVRI photometry of the blazar BL Lacertae on diverse timescales from 2020 mid-July to mid-September. We have used 11 different optical telescopes around the world and have collected data over 84 observational nights. The observations cover the onset of a new activity phase of BL Lacertae that started in 2020 August (termed as the 2020 August flare by us), and the analysis is focused on the intranight variability. On short-term timescales, (i) flux varied with ∼2.2 mag in the R band, (ii) the spectral index was found to be weakly dependent on the flux (i.e., the variations could be considered mildly chromatic), and (iii) no periodicity was detected. On intranight timescales, BL Lacertae was found to predominantly show bluer-when-brighter chromatism. We also found two cases of significant interband time lags of the order of a few minutes. The duty cycle of the blazar during the 2020 August flare was estimated to be quite high (∼90% or higher). We decomposed the intranight light curves into individual flares and determined their characteristics. On the basis of our analysis and assuming the turbulent jet model, we determined some characteristics of the emitting regions: Doppler factor, magnetic field strength, electron Lorentz factor, and radius. The radii determined were discussed in the framework of the Kolmogorov theory of turbulence. We also estimated the weighted mean structure function slope on intranight timescales, related it to the slope of the power spectral density, and discussed it with regard to the origin of intranight variability.

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