Context. The BL Lac object 3C 371 has been observed by the Transiting Exoplanet Survey Satellite (TESS) for approximately a year, between
July 2019 and July 2020, with an unmatched 2-minute observing cadence. In parallel, the Whole Earth Blazar Telescope (WEBT) Collaboration
organized an extensive observing campaign, providing three years of continuous optical monitoring between 2018 and 2020. These datasets allow
for a thorough investigation of the variability of the source.
Aims. The goal of this study is evaluating the optical variability of 3C 371. Taking advantage of the remarkable cadence of TESS data, we aim to
characterize the intra-day variability (IDV) displayed by the source and identify its shortest variability timescale. With this estimate, constraints
on the size of the emitting region and black hole mass can be calculated. Moreover, WEBT data is used to investigate long-term variability (LTV),
including understanding spectral behaviour of the source and the polarization variability. Based on the derived characteristics, information on the
origin of the variability on different timescales is extracted.
Methods. We evaluated the variability applying the variability amplitude tool that quantifies how variable the emission is. Moreover, we employed
common tools like ANOVA (ANalysis Of VAariance) tests, wavelet and power spectral density (PSD) analyses to characterize the shortest vari-
ability timescales present in the emission and the underlying noise affecting the data. Short- and long-term colour behaviours have been evaluated
to understand the spectral behaviour of the source. The polarized emission was analyzed, studying its variability and possible rotation patterns
of the electric vector position angle (EVPA). Flux distributions of IDV and LTV were also studied with the aim of linking the flux variations to
turbulent and/or accretion disc related processes.
Results. We find several entangled variability timescales owing to the ANOVA and wavelet analyses. We observe a clear increase of the variability
amplitude with increasing width of time intervals evaluated. We are also able to resolve significant variations as fast as ∼0.5 hours. The PSD
analysis reveals a red noise spectrum with a break at IDV timescales. The spectral analysis shows a mild bluer-when-brighter (BWB) trend on long
timescales. On short timescales, mixed BWB, achromatic and redder-when-brighter (RWB) signatures can be observed. The polarized emission
shows an interesting slow EVPA rotation during the flaring period, with a 3σ significance of not being caused by a simple stochastic model. The
flux distributions show a preference for a Gaussian model for IDV, possible linked to turbulent processes, while LTV is better represented by a
log-normal distribution, that can possibly be linked to a disc-related origin.