Multi-band optical variability on diverse timescales of the TeV blazar TXS 0506+56, the first cosmic neutrino source

We report the first extensive optical flux and spectral variability study of the TeV blazar TXS 0506+056 on intra-night to long-term timescales using BVRI data collected over 220 nights between January 21, 2017 to April 9, 2022 using 8 optical ground-based telescopes. In our search for intraday variability (IDV), we have employed two statistical analysis techniques, the nested ANOVA test and the power enhanced F-test. We found the source was variable in 8 nights out of 35 in the R-band and in 2 of 14 in the V-band yielding Duty Cycles (DC) of 22.8% and 14.3%, respectively. Clear colour variation in V - R was seen in only 1 out of 14 observing nights, but no IDV was found in the more limited B, I, and B - I data. During our monitoring period the source showed a 1.18 mag variation in the R-band and similar variations are clearly seen at all optical wavelengths. We extracted the optical (BVRI) SEDs of the blazar for 44 nights when observations were carried out in all four of those wavebands. The mean spectral index (\alpha) was determined to be 0.897+-0.171