Raiteri, C.M.Villata, M.Larionov, V.M.Jorstad, S.G.Marscher, Alan P.Weaver, Z.R.Acosta-Pulido, J.A.Agudo, IvanAndreeva, T.S.Arkharov, A.A.Bachev, R.Benítez, E.Berton, M.Björklund, I.Borman, G.A.Bozhilov, V.Carnerero, M.I.Carosati, D.Casadio, CarolinaChen, W.P.Damljanovic, G.D’Ammando, F.Escudero, JuanFuentes, A.Giroletti, M.Grishina, T.S.Gupta, A.C.Hagen-Thorn, V.A.Hart, M.Hiriart, D.Hou, W.-J.Ivanov, D.Kim, J.-Y.Kimeridze, G.N.Konstantopoulou, C.Kopatskaya, E.N.Kurtanidze, O.M.Kurtanidze, S.O.Lähteenmäki, A.Larionova, E.G.Larionova, L.V.Marchili, N.Markovic, G.Minev, M.Morozova, D.A.Myserlis, I.Nakamura, M.Nikiforova, A.A.Nikolashvili, M.G.Otero-Santos, J.Ovcharov, E.Pursimo, T.Rahimov, I.Righini, S.Sakamoto, T.Savchenko, S.S.Semkov, E.H.Shakhovskoy, D.Sigua, L.A.Stojanovic, M.Strigachev, A.Thum, C.Tornikoski, M.Traianou, E.Troitskaya, Y.V.Troitskiy, I.S.Tsai, A.Valcheva, A.Vasilyev, A.A.Vince, O.Zaharieva, E.2022-04-282022-04-282021-05-21C.M. Raiteri, M. Villata, V.M. Larionov, S.G. Jorstad, A.P. Marscher, Z.R. Weaver, J.A. Acosta-Pulido, I. Agudo, T. Andreeva, A. Arkharov, R. Bachev, E. Benítez, M. Berton, I. Björklund, G.A. Borman, V. Bozhilov, M.I. Carnerero, D. Carosati, C. Casadio, W.P. Chen, G. Damljanovic, F. D’Ammando, J. Escudero, A. Fuentes, M. Giroletti, T.S. Grishina, A.C. Gupta, V.A. Hagen-Thorn, M. Hart, D. Hiriart, W.-.J. Hou, D. Ivanov, J.-.Y. Kim, G.N. Kimeridze, C. Konstantopoulou, E.N. Kopatskaya, O.M. Kurtanidze, S.O. Kurtanidze, A. Lähteenmäki, E.G. Larionova, L.V. Larionova, N. Marchili, G. Markovic, M. Minev, D.A. Morozova, I. Myserlis, M. Nakamura, A.A. Nikiforova, M.G. Nikolashvili, J. Otero-Santos, E. Ovcharov, T. Pursimo, I. Rahimov, S. Righini, T. Sakamoto, S.S. Savchenko, E.H. Semkov, D. Shakhovskoy, L.A. Sigua, M. Stojanovic, A. Strigachev, C. Thum, M. Tornikoski, E. Traianou, Y.V. Troitskaya, I.S. Troitskiy, A. Tsai, A. Valcheva, A.A. Vasilyev, O. Vince, E. Zaharieva. 2021. "The complex variability of blazars: time-scales and periodicity analysis in S4 0954+65." Monthly Notices of the Royal Astronomical Society, Volume 504, Issue 4, pp. 5629 - 5646. https://doi.org/10.1093/mnras/stab12680035-87111365-2966https://hdl.handle.net/2144/44309Among active galactic nuclei, blazars show extreme variability properties. We here investigate the case of the BL Lac object S4 0954+65 with data acquired in 2019–2020 by the Transiting Exoplanet Survey Satellite (TESS) and by the Whole Earth Blazar Telescope (WEBT) Collaboration. The 2-min cadence optical light curves provided by TESS during three observing sectors of nearly 1 month each allow us to study the fast variability in great detail. We identify several characteristic short-term time-scales, ranging from a few hours to a few days. However, these are not persistent, as they differ in the various TESS sectors. The long-term photometric and polarimetric optical and radio monitoring undertaken by the WEBT brings significant additional information, revealing that (i) in the optical, long-term flux changes are almost achromatic, while the short-term ones are strongly chromatic; (ii) the radio flux variations at 37 GHz follow those in the optical with a delay of about 3 weeks; (iii) the range of variation of the polarization degree and angle is much larger in the optical than in the radio band, but the mean polarization angles are similar; (iv) the optical long-term variability is characterized by a quasi-periodicity of about 1 month. We explain the source behaviour in terms of a rotating inhomogeneous helical jet, whose pitch angle can change in time.p. 5629 - 5646en-US© 2020 The Authors.Article10.1093/mnras/stab1268627668