We present recent optical photometric observations of the blazar OJ 287 taken during 2015 September–2016 May. Our intense observations of the blazar started in 2015 November and continued until 2016 May and included detection of the large optical outburst in 2015 December that was predicted using the binary black hole model for OJ 287. For our observing campaign, we used a total of nine ground-based optical telescopes of which one is in Japan, one is in India, three are in Bulgaria, one is in Serbia, one is in Georgia, and two are in the USA. These observations were carried out in 102 nights with a total of ∼1000 image frames in BVRI bands, though the majority were in the R band. We detected a second comparably strong flare in 2016 March. In addition, we investigated multiband flux variations, colour variations, and spectral changes in the blazar on diverse time-scales as they are useful in understanding the emission mechanisms. We briefly discuss the possible physical mechanisms most likely responsible for the observed flux, colour, and spectral variability.

We analysed the multiband optical behaviour of the BL Lacertae object, S5 0716+714, during its outburst state from 2014 November to 2015 March. We took data on 23 nights at three observatories, one in India and two in Bulgaria, making quasi-simultaneous observations in B, V, R, and I bands. We measured multiband optical fluxes, colour, and spectral variations for this blazar on intraday and short time-scales. The source was in a flaring state during the period analysed and displayed intense variability in all wavelengths. R-band magnitude of 11.6 was attained by the target on 2015 January 18, which is the brightest value ever recorded for S5 0716+714. The discrete correlation function method yielded good correlation between the bands with no measurable time lags, implying that radiation in these bands originate from the same region and by the same mechanism. We also used the structure function technique to look for characteristic time-scales in the light curves. During the times of rapid variability, no evidence for the source to display spectral changes with magnitude was found on either of the time-scales. The amplitude of variations tends to increase with increasing frequency with a maximum of ∼22 per cent seen during flaring states in B band. A mild trend of larger variability amplitude as the source brightens was also found. We found the duty cycle of our source during the analysed period to be ∼90 per cent. We also investigated the optical spectral energy distribution of S5 0716+714 using B, V, R, and I data points for 21 nights. We briefly discuss physical mechanisms most likely responsible for its flux and spectral variations.

In this work, we report the presence of rapid intra-night optical variations in both flux and polarization of the blazar BL Lacertae during its unprecedented 2020–2021 high state of brightness. The object showed significant flux variability and some colour changes, but no firmly detectable time delays between the optical bands. The linear polarization was also highly variable in both polarization degree and angle (electric vector polarization angle). The object was observed from several observatories throughout the world, covering a total of almost 300 h during 66 nights. Based on our results, we suggest that the changing Doppler factor of an ensemble of independent emitting regions, travelling along a curved jet that at some point happens to be closely aligned with the line of sight, can successfully reproduce our observations during this outburst. This is one of the most extensive variability studies of the optical polarization of a blazar on intra-night time-scales.

We obtained and analysed more than 100 h of multicolour optical time series of the blazar CTA 102 during its 2012 and 2016 outbursts. The object reached almost 11th mag at the end of 2016, which is perhaps the brightest blazar state ever observed! During both outbursts, CTA 102 showed significant and rapid variability on intra-night time-scales, reaching up to 0.2 mag for 30 min on some occasions. The ‘rms-flux’ relation, built for all data sets, shows a large scatter and no apparent saturation on the magnitude scale. The ensemble structure function of the light curves can be fitted well with a straight line of a slope of ∼0.4. The time lags between the different optical bands appear to be consistent with zero, taking into account our time resolution. We discuss different variability scenarios and favour the changing Doppler factor of the emitting blobs as the most plausible one to account for the observed intra-night variability.

We report observations of the flickering variability of the symbiotic recurrent nova RS Oph at quiescence in five bands (UBVRI). We find evidence of a correlation between the peak-to-peak flickering amplitude (ΔF) and the average flux of the hot component (F_av). The correlation is highly significant, with a correlation coefficient of 0.85 and a p-value of ∼10⁻²⁰. Combining the data from all wavebands, we find a dependence of the type $$\Delta F \propto F_{{\rm av}}^k$$, with power-law index k = 1.02 ± 0.04 for the UBVRI flickering of RS Oph. Thus, the relationship between the amplitude of variability and the average flux of the hot component is consistent with linearity. The rms amplitude of flickering is on average 8 per cent (±2 per cent) of F_av. The detected correlation is similar to that found in accreting black holes/neutron stars and cataclysmic variables. The possible reasons are briefly discussed. The data are available upon request from the authors.