Optical Variability of Three Extreme TeV Blazars

We present the results of optical photometric observations of three extreme TeV blazars, 1ES 0229$+$200, 1ES 0414$+$009, and 1ES 2344$+$514, taken with two telescopes (1.3 m Devasthal Fast Optical Telescope, and 1.04 m Sampuranand Telescope) in India and two (1.4 m Milankovi\'{c} telescope and 60 cm Nedeljkovi\'{c} telescope) in Serbia during 2013--2019. We investigated their flux and spectral variability on diverse timescales. We examined a total of 36 intraday $R-$band light curves of these blazars for flux variations using the power-enhanced {\it F}-test and the nested ANOVA test. No significant intraday variation was detected on 35 nights, and during the one positive detection the amplitude of variability was only 2.26 per cent. On yearly timescales, all three blazars showed clear flux variations in all optical wavebands. The weighted mean optical spectral index ($\alpha_{BR}$), calculated using $B - R$ color indices, for 1ES 0229$+$200 was 2.09 $\pm$ 0.01. We also estimated the weighted mean optical spectral indices of 0.67 $\pm$ 0.01 and 1.37 $\pm$ 0.01 for 1ES 0414$+$009, and 1ES 2344$+$514, respectively, by fitting a single power-law ($F_{\nu} \propto \nu^{-\alpha}$) in their optical ({\it VRI}) spectral energy distributions. A bluer-when-brighter trend was only detected in the blazar 1ES 0414$+$009. We briefly discuss different possible physical mechanisms responsible for the observed flux and spectral changes in these blazars on diverse timescales.