(Note: this is a shortened version of the original A&A-style structured abstract). The physical nature of the strong photometric variability of T Tau Sa, the more massive member of the Southern infrared companion to T Tau, has long been debated. Intrinsic luminosity variations due to variable accretion were originally proposed but later challenged in favor of apparent fluctuations due to time-variable foreground extinction. In this paper we use the timescale of the variability as a diagnostic for the underlying physical mechanism. Because the IR emission emerging from Sa is dominantly thermal emission from circumstellar dust at <=1500K, we can derive a minimum size of the region responsible for the time-variable emission. In the context of the variable foreground extinction scenario, this region must be (un-) covered within the variability timescale, which implies a minimum velocity for the obscuring foreground material. If this velocity supercedes the local Kepler velocity we can reject foreground extinction as a valid variability mechanism. The variable accretion scenario allows for shorter variability timescales since the variations in luminosity occur on much smaller scales, essentially at the surface of the star, and the disk surface can react almost instantly on the changing irradiation with a higher or lower dust temperature and according brightness. We have detected substantial variations at long wavelengths in T Tau S: +26% within four days at 12.8 micron. We show that this short-term variability cannot be due to variable extinction and instead must be due to variable accretion. Using a radiative transfer model of the Sa disk we show that variable accretion can in principle also account for the much larger (several magnitude) variations observed on timescales of several years. For the long-term variability, however, also variable foreground extinction is a viable mechanism.
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